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GEOD. LIST
GOD. 66 (89) 1
S. 1–75
ZAGREB, OUJAK 2012.
SADRAJ
Pregledni znanstveni èlanci
Solariæ, N., Solariæ, M., Švehla: Nove revolucionarne moguænosti u geodeziji
koje pruaju otkriæa za koja su dobivene Nobelove nagrade za fiziku
2005. i 1997. godine...................................................................................................1
Medved, Ganiæ, Vuliæ: Analiza utjecaja pogrešaka pomoænih velièina
pri odreðivanju geometrijskih popravaka duljina .................................................21
Struèni èlanak
Kuburiæ, Æiroviæ: Primjena inteligentnih tehnika za masovnu procjenu
nekretnina .................................................................................................................39
Vijesti ..................................................................................................................................59
Pregled struènog tiska i softvera ..........................................................................................71
Predstojeæi dogaðaji .............................................................................................................75
CONTENTS
Reviews
Solariæ, N., Solariæ, M., Švehla: New Revolutionary Possibilities in Geodesy
Providing the Discoveries Awarded for Physics in 2005 and 1997......................1
Medved, Ganiæ, Vuliæ: An Analysis of the Impact of Errors Occurring
in the Auxiliary Parameters while Determining Geometric Corrections
of Distance ................................................................................................................21
Professional paper
Kuburiæ, Æiroviæ: The Application of Intelligent Techniques for Massreal
Estate Appraisal .......................................................................................................39
News ...................................................................................................................................59
Publications and Software review.........................................................................................71
Forthcoming events .............................................................................................................75
Naslovna stranica: Medalja koja se dodjeljuje za Nobelovu nagradu za fiziku i kemiju,
(izvor: http://www.nobelprize.org).
II
INHALT
Wissenschaftliche Übersichtsartikel
Solariæ, N., Solariæ, M., Švehla: Neue revolutionäre Möglichkeiten
in der Geodäsie, die Entdeckungen bieten, für die Nobelpreise für Physik
in 2005 und 1997 verliehen wurden........................................................................1
Medved, Ganiæ, Vuliæ: Analyse der Auswirkung von Fehlern der Hilfsgrößen
bei der Festlegung von geometrischen Längenkorrekturen ................................21
Fachartikel
Kuburiæ, Æiroviæ: Anwendung von intelligenten Techniken für massenweise
Beurteilung von Liegenschaften .............................................................................39
Nachrichten .........................................................................................................................59
Bücher- und Softwareschau ..................................................................................................71
Termine ...............................................................................................................................75
SOMMAIRE
Contributions sciéntifiques synoptiques
Solariæ, N., Solariæ, M., Švehla: Des possibilités nouvelles révolutionnaires
en géodésie qui donnent des découverts pour lesquels les Prix Nobel
pour la physique ont été obtenus en 2005 et 1997 ...............................................1
Medved, Ganiæ, Vuliæ: L’analyse de l’influence des erreurs de valeurs auxiliaires
lors de la détermination des corrections géométriques de longueurs ................21
Contribution professionnelle
Kuburiæ, Æiroviæ: L’application de techniques intelligentes pour l’évaluation
massive des biens immobiliers................................................................................39
Actualités .............................................................................................................................59
Revue de la littérature professionnelle et du software ..........................................................71
Evénements precedents ........................................................................................................75
[email protected]
Obzornwenau~nwestatxi
Solari~, N., Solari~, M., [vehla: Nowe revolÎcionnwe vozmo`nosti
v geodezii, pozvoliv{ie otkrwtij, za kotorwe bwli polu~enw Nobelevskie
premii za dosti`enij v fizike v 2005 i 1997 godah .............................................1
Me¶ve¶x, Gani~, Vuli~: Analiz vlijnij pogre{noste vspomogatelxnwh veli~in
pri opredelenii geometri~eskih ispravleni dlinw ...........................................21
Specialxnajstatxj
Kuburi~, ^irovi~: Primenenie intelligentnwh metodov dlj massovo ocenki
nedvi`imoste ..........................................................................................................39
Novosti................................................................................................................................59
Obzor specialxno pe~ati i programmnogo obespe~enij ........................................................71
Predstoj|ie sobwtij ...........................................................................................................75
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
1
UDK 528.08:06.068NOBEL:53:001.894
Pregledni znanstveni èlanak
Nove revolucionarne moguænosti u geodeziji
koje pruaju otkriæa za koja su dobivene
Nobelove nagrade za fiziku 2005. i 1997. godine
Nikola SOLARIÆ, Miljenko SOLARIÆ – Zagreb1,
Draen ŠVEHLA – Darmstadt2
SAETAK. Nobelovu nagradu za fiziku 2005. godine dobili su Roy J. Glauber, John L.
Hall i Theodor W. Hänsch za unapreðenja u podruèju optike. Nobelovu nagradu
za fiziku 1997. godine dobili su Steven Chu, Claude Cohen-Tannoudji i William D.
Phillips za otkriæe i razvoj metode hlaðenja i hvatanja u zamku atoma laserskom svjetlošæu. Unapreðenja koja su predloili Theodor W. Hänsch i John L. Hall uz podršku i
otkriæa Stevena Chua, Claudea Cohen-Tannoudjija i Williama Phillipsa pruaju nove
revolucionarne moguænosti znatnog unapreðenja toènosti mjerenja u geodeziji i u velikom broju drugih podruèja znanosti i primjena. Tako æe se s pomoæu optièkih satova
moæi izmjeriti vrijeme èak preciznije nego atomskim satovima, te æe se na taj naèin moæi
preciznije odrediti orbite navigacijskih satelita, a to znaèi i poloaji odreðivanih toèaka
na površini Zemlje. Osim toga, otvara se moguænost odreðivanja razlike gravitacijskih
potencijala izmeðu toèaka na površini Zemlje uz primjenu Einsteinove opæe teorije relativnosti. Na taj æe se naèin moæi izravnim mjerenjima povezati visine izmeðu kontinenata, a i poboljšati povezivanja nivelmanskih mrea izmeðu pojedinih drava unutar kontinenata. Osim toga bit æe omoguæeno i preciznije mjerenje duljina.
Kljuène rijeèi: femtolaser, frekvencijski èešalj, frekvencijski lineal, optièki sat, mjerenje razlika gravitacijskog potencijala.
1. Uvod
U posljednjih tridesetak godina došlo je do revolucionarnog razvoja u izradi
geodetskih instrumenata: elektronièkih tahimetara, digitalnih nivelira, total1
Prof. emeritus dr. sc. Nikola Solariæ, èlan emeritus Akademije tehnièkih znanosti Hrvatske, Geodetski fakultet
Sveuèilišta u Zagrebu, Kaèiæeva 26, HR-10000 Zagreb, e-mail: [email protected],
prof. dr. sc. Miljenko Solariæ, Geodetski fakultet Sveuèilišta u Zagrebu, Kaèiæeva 26, HR-10000 Zagreb,
e-mail: [email protected],
2
Dr.-Ing. Draen Švehla, dipl. ing. geod., European Space Agency, Navigation Office, Robert Bosch Str. 5,
D-64293 Darmstadt, Deutschland, e-mail: [email protected]
2
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
nih stanica, GPS3-a i skenera. Meðutim, zahvaljujuæi znanstvenom doprinosu fizièara koji su primili Nobelove nagrade za fiziku za 1997. i 2005. godinu stvorene su nove revolucionarne moguænosti još toènijeg mjerenja vremena, èak toènijeg od mjerenja s pomoæu najpreciznijih atomskih satova. Osim
toga to æe omoguæiti preciznu spektroskopiju, preciznije mjerenje duljina, provjeru Einsteinove teorije relativnosti, provjeru razlièitih konstanti u podruèju
atomistike, a nalazit æe i veliku primjenu u satelitskoj navigaciji, geodeziji i
industriji.
2. Nobelova nagrada za otkriæa iz fizike za 2005. godinu
Nobelovu nagradu za otkriæa na podruèju fizike za 2005. godinu dobili su Roy J.
Glauber, John L. Hall i Theodor W. Hänsch (slika 1).
Slika 1. Dobitnici Nobelove nagrade za fiziku 2005. godine (URL 1).
Roy J. Glauber dobio je pola nagrade jer je pokazao u teoriji kako kvantna teorija
moe biti primijenjena pri opisu optièkih pojava za detekcije svjetlosti (URL 13).
John L. Hall i Theodor W. Hänsch dobili su drugu polovinu nagrade za doprinose
u razvoju laserske spektroskopije na temelju preciznih mjerenja optièkim frekvencijskim èešljem. Njihova metoda omoguæuje da se preciznom spektroskopijom
utvrdi toènija kvantna struktura materije i postigne veæa toènost u provjeravaju
temeljnih teorija u fizici. Neki pokušavaju metodu mjerenja optièkim frekventnim
èešljem nazvati i metodom mjerenja optièkim frekvencijskim ravnalom (engl. ruler) ili linealom, jer se zupci èešlja vide kao crtice lineala izmeðu kojih se interpolacijom precizno mjeri frekvencija lasera, slièno kao duljina linealom (ravnalom)
na papiru.
3
GPS – Global Positioning System (globalni pozicijski sustav)
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
3
2.1. Optièki frekvencijski èešalj
Danas se ni najbrim elektronièkim brojaèima (frekvencmetrima) ne moe direktno mjeriti frekvencija optièkih valova, jer današnji najbri frekvencmetri mogu mjeriti frekvencije samo do frekvencije mikrovalova (» 1 · 1010 Hz). Meðutim,
frekvencija vidljive svjetlosti znatno je veæa 400–790 THz (4,0–7,9 · 1014 Hz).
Otkriæe Theodora Hänscha i Johna Halla omoguæilo je da se i današnjim elektronièkim frekvencmetrima mogu indirektno mjeriti frekvencije i optièkih valova.
Razvoj na tom podruèju poèeo je 1970-ih godina, kada je razvijen harmonijski
optièki frekvencijski niz. Tako je pokazano da postoji moguænost mjerenja optièkih frekvencija s pomoæu elektronièkih frekvencmetara. Polazeæi od mikrovalova
definiranih cezijevim atomskim satom generirane su više frekvencije uzastopnim
koracima s pomoæu nelinearnih diodnih mješaèa, kristala i drugih nelinearnih
ureðaja. Na poèetku èak kad je i pokrenut takav frekvencijski niz vrlo brzo je prekinut nakon nekoliko sekundi ili minuta. Do naglog poboljšanja došlo je 1999. godine u Münchenu, kad je prema Hänschovoj originalnoj ideji primijenjen femtosekundni ultrabrzi spregnuti laser4 koji u optièkom mediju generira seriju stabilnih frekvencijskih linija poèevši od frekvencije mikrovalova cezijeva atomskog sata ili H-masera5, pa dalje do vidljive svjetlosti (slika 2). Za razliku od vremenske domene6 generirani laserski femtosekundni impulsi u optièkom mediju u
frekventnoj domeni izgledaju kao stabilne frekventne linije, te na taj naèin definiraju optièki frekvencijski èešalj s razmakom izmeðu crtkanih linija definiranim
frekvencijom ponavljanja paketa svjetlosti fp. Hänschova ispitivanja pokazala su
Slika 2. Ultrastabilne optièke frekvencije u fotonskom kristalnom vlaknu koje nastaju
poèevši od neke frekvencije mikrovalova (URL 2).
4
Spregnuti femtosekundni laser (engl. mode locked laser) je femtosekundni laser iz kojeg izlazi niz vrlo kratkih
paketa svjetlosti, kod kojih paket koji izleti iz lasera uvijek ima oscilacije elektriènog polja u paketu u fazi kao na
primjer na slici 3 (URL 8), (URL 9)
5
U novije vrijeme pojavilo se rješenje definiranja frekvencije ponavljanja laserskih paketa svjetlosti korištenjem
GPS prijamnika.
6
Domena – (engl. domain – polje, podruèje)
4
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
visok stupanj stabilnosti i jednolikog razmaka izmeðu linija frekvencije, ali se dogaðao fazni pomak unutar paketa u optièkom sredstvu (slika 3). Zato je bio poznat samo precizni razmak izmeðu pojedinih frekvencija, a ne i njihova apsolutna
vrijednost frekvencije (detaljnije o tome u sljedeæem potpoglavlju).
2.2. Ultrabrzi spregnuti femtosekundni laser
Iz ultrabrzog femtosekundnog spregnutog lasera dobiju se vrlo kratki paketi svjetlosti od priblino 100 fs (10–13 s). Paketi su meðusobno razmaknuti za T = 12,5 ns
(ponavljanje paketa je 80 MHz) (slika 3). Kada paketi svjetlosti dolaze u optièko
sredstvo s nekim indeksom loma svjetlosti u kojem je grupna brzina svjetlosti
manja od fazne brzine, u paketu dolazi do pomaka u fazi impulsa (URL 3).
E(t)
T
Dj
fp
T
vfaze
vgrupe
– amplituda elektromagnetskog vala u ovisnosti o vremenu
– vrijeme
– pomak u fazi impulsa u paketu, jer je fazna brzina svjetlosti u optièkom
sredstvu veæa od grupne brzine svjetlosti
– frekvencija ponavljanja paketa svjetlosti
– vrijeme izmeðu paketa
– fazna brzina svjetlosti
– grupna brzina svjetlosti
Slika 3. Grafièki prikaz vrlo kratkih paketa svjetlosti iz femtosekundnog lasera u ovisnosti o vremenu, u optièkom sredstvu s nekim indeksom loma svjetlosti u kojem je grupna brzina svjetlosti manja od fazne brzine. Zato dolazi do pomaka u
fazi u paketu (URL 3).
Fotonski kristal u vlaknu ima periodiènu optièku nanostrukturu. To je posebni
optièki materijal koji pokazuje tok svjetlosti, a najèešæe je u obliku optièkog vlakna. Pusti li se vrlo brzi niz paketa impulsa iz femtosekundnog lasera s frekvencijom ponavljanja paketa svjetlosti fp kroz fotonsko kristalno vlakno, rezonantni
atomski medij u fotonskom kristalnom vlaknu nema dovoljno vremena da se potpuno relaksira izmeðu dva uzastopna paketa impulsa, jer je ponavljanje takvog
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
5
niza laserskih paketa svjetlosti vrlo brzo. Zato se nakon svakog paketa svjetlosti u
mediju dobiju sve više frekvencije, a razmak izmeðu crtkanih linija frekvencije je
frekvencija fp. Buduæi da je razmak izmeðu frekvencijskih linija konstantan, za
svaku liniju moe se izraèunati njezina frekvencija. Tako nastaje frekventni èešalj
(slika 4), gdje je f0 pomak u frekvenciji koji nastaje zbog faznog pomaka vala Dj u
Dj
optièkom sredstvu vlakna, f0 =
, gdje je T – vrijeme jednog perioda.
T
I(f)
F
f0
T
N
2n
X2
takt
–
–
–
–
–
–
–
–
intenzitet svjetlosti u ovisnosti o frekvenciji
frekvencija
pomak u frekvenciji (zbog pomaka u fazi Dj)
vrijeme jednog perioda
n-ti zubac u optièkom frekvencijskom èešlju
2n-ti zubac u optièkom frekvencijskom èešlju
nelinearni kristal za umnaanje frekvencije 2 puta
frekvencije koje moe izmjeriti frekvencmetar
Slika 4. Niz frekvencija svjetlosti koje nastaju u fotonskom kristalnom vlaknu poèevši
od frekvencije atomskog sata, frekvencijski èešalj i odreðivanje faznog pomaka
f0 (URL 1).
Doprinos J. Halla i Th. Hänscha je u tome što su predloili kako da se izmjeri f0,
da bi se odredila apsolutna vrijednost frekvencije pojedinih zubaca u frekvencijskom èešlju. Do tada je utvrðeno da je raspored zubaca u optièkom frekvencijskom èešlju vrlo precizno jednoliko rasporeðen, ali nije bila poznata toèna apsolutna frekvencija pojedinog zupca u èešlju. Frekvencija ponavljanja fp moe se
mjeriti pomoæu fotodetekcije izlaznog niza paketa svjetlosti iz lasera, te se moe
izraèunati frekvencija n-tog zupca (n·fp) na poèetku èešlja i frekvencija zupca pri
kraju èešlja 2·n·fp. Frekvencija signala s n-tog zupca (n·fp+f0) pomnoi se s 2 i
6
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
oduzme se frekvencija signala s 2n-tog zupca (2·n·fp+ f0). Na taj naèin dobije se
frekvencija f0 (takt), koja je manja od frekvencije mikrovalova i moe se mjeriti
frekvencmetrom:
2 (n·fp+f0) – (2·n·fp+ f0) = f0 takt.
Tako se svakom zupcu u frekvencijskom èešlju moe izraèunati toèna apsolutna
frekvencija.
3. Dobitnici Nobelove nagrade za fiziku 1997. godine
Nobelovu nagradu za otkriæa iz fizike za 1997. godinu za lasersko hlaðenje atoma
dobili su Steven Chu, Claude Cohen-Tannoudji i William D. Phillips (slika 5).
Slika 5. Dobitnici Nobelove nagrade za fiziku 1997. godine (URL 4).
3.1. Mjerenje frekvencije svjetlosti koja izlazi iz CW-lasera
Da bi se precizno izmjerila frekvencija svjetlosti iz CW-lasera7, koji kontinuirano
zraèi svjetlost, treba medij u laseru ohladiti na vrlo nisku temperaturu. To je potrebno da zbog gibanja atoma odnosno iona kod viših temperatura za zraèenja
svjetlosti ne bi došlo do Dopplerovskog efekta i pomicanja (promjene) frekvencije
zraèene svjetlosti. Da bi se umirili atomi, odnosno ioni, medij u laseru ohladi se s
pomoæu više lasera (slika 6) (Kozma i dr. 2007). To je moguæe prema otkriæu i razvoju metode hlaðenja i hvatanja u zamku atoma laserskom svjetlošæu. U zamci atomi se umire te se medij u laseru ohladi. Za to otkriæe dobili su Nobelovu nagradu za
fiziku 1997. godine Steven Chu, Claude Cohen-Tannoudji i William D. Phillips.
Da bi se izmjerila frekvencija CW-lasera, svjetlosni signal frekvencije fcw vodi se
na sklop za oduzimanje (slika 6), a na njega se vodi i signal sa susjednog zupca
7
CW-laser – (engl. Continues wave laser – kontinuirani valni laser, stalno zraèi svjetlost)
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
7
Slika 6. Mjerenje frekvencije svjetlosti ultrastabilnog CW-lasera s pomoæu frekvencijskog èešlja (Kozma i dr. 2007).
lineala m·fp + f0. Njihova razlika je nia frekvencija (mikroval) ftakt, koja se moe
izmjeriti frekvencmetrom. Frekvencija CW-lasera moe se izraèunati po formuli
fcw = m·fp + f0 + ftakt, jer se mjeri i fp, a i f0.
Frekvencijski èešalj omoguæit æe postizanje relativne preciznosti mjerenja frekvencije i vremena do 10–18, a do sada je veæ postignuto bolje od 10–17.
Vidljiva svjetlost ima 100 000 puta više frekvencije od mikrovalova. Kako je stabilnost sata proporcionalna radnoj frekvenciji sata, satovi koji rade s pomoæu optièkih prijelaza (u vidljivoj svjetlosti ili ekstremno ultraljubièastoj svjetlosti – XUV)
trebali bi pruati veæu stabilnost u odnosu na definirane mikrovalne prijelaze u
atomskim satovima. Ta èinjenica veæ je dugo poznata. Kad se optièki satovi dokau stabilnijima i toènijima nego mikrovalni standardi, to æe vjerojatno dovesti i
do nove definicije sekunde na osnovi optièkih frekvencijskih standarda, vjerojatno
ne prije 2019. godine (URL 12), a neki predviðaju i prije.
4. Optièki sat
Optièki sat je sat koji mjeri vrijeme s pomoæu optièkih frekvencijskih standarda i
optièkog frekvencijskog èešlja. Sastoji se od optièkog frekvencijskog standarda,
koji se osniva na zraèenju svjetlosti iz hlaðenih atoma ili iona u optièkoj zamci, da
bi se zbog Dopplerovskog efekta smanjilo pomicanje i širenje zraèenih frekvencija.
8
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
U optièkom satu signal iz cezijeva atomskog sata ili H-masera odlazi na elektroniku za upravljanje (slika 7), koja upravlja femtosekundnim laserom i optièkim
frekvencijskim èešljem. Zatim prema izmjerenim frekvencijama f0, fp, ftakt i fCW korigira frekvenciju i vrijeme atomskog sata u duim vremenskim periodima, pa se
dobije toènije vrijeme. Zbog toga optièki frekvencijski standardi mogu znatno poveæati preciznost i stabilnost najboljih atomskih cezijevih satova i H-masera. Pritom ako optièki frekvencijski standard pogriješi za jedan titraj, tada to manje djeluje na vrijeme, nego ako atomski sat pogriješi za jedan titraj.
Slika 7. Shematski prikaz optièkog sata i poveæanje preciznosti i stabilnosti atomskog
sata pomoæu optièkog frekvencijskog èešlja.
Danas se u više laboratorija u svijetu istrauje koji bi optièki frekvencijski standard bio najbolji. Obièno se ispituje koji je od dvaju optièkih frekvencijskih standarda bolji. Uz njih se ne stavljaju atomski satovi da ne bi kvarili rezultate optièkih frekvencijskih standarda.
Nakon otkriæa prvog atomskog sata 1955. godine taj je sat uvršten u nacionalne vremenske slube pojedinih drava, a na slici 8 vidi se kako se mijenjala njihova mjerna nesigurnost tijekom godina. Danas su mali atomski satovi ugraðeni i u GPS-satelite. Najbolji atomski satovi imaju relativnu mjernu nesigurnost 5 · 10–15, a danas veæ optièki satovi mogu biti toèniji od atomskih satova priblino više stotina puta, tj. mogu imati mjernu nesigurnost 8,6 · 10–18, nakon
uzimanja prosjeka za 3 sata mjerenja (Chou i dr. 2010). Osim toga iz slike se vidi
da se u posljednje vrijeme s optièkim satovima naglo smanjuje relativna nesigurnost, a postoje i perspektive daljnjega naglog poboljšanja. Laboratoriji diljem svijeta nastoje razviti optièke frekvencijske standarde bazirane na razlièitim idejnim rješenjima, s razlièitim atomima ili ionima. Za sada su se meðu naj-
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
9
Slika 8. Kako se mijenjala relativna mjerna nesigurnost atomskih satova tijekom godina i zatim optièkih satova (Švehla 2008a).
boljima pokazali ioni aluminija, ive i berilija. Danas se ne moe kazati koje æe od
idejnih rješenja biti najbolje za meðunarodni vremenski odnosno frekvencijski standard. Pokušava se i s kvantnim logièkim satovima, koji rade na principu kvantnih logièkih zakljuèivanja u kvantnim raèunalima (URL 7), te se na
taj naèin stabilizira laser. Oèekuje se da æe se optièki frekvencijski standardi
razviti toliko da bi nakon 2019. godine moglo doæi i do nove definicije sekunde
(URL 12).
5. Usporedbe frekvencije i vremena dvostrukim linijama
Pri opaanju satelita sve opaaèke stanice na Zemlji trebaju imati u istom
trenutku isto vrijeme TAI (time atomic international). Zato se moraju usporeðivati (komparirati, prenositi) frekvencije i vremena izmeðu pojedinih stanica.
Usporedbe frekvencije atomskih satova ispod relativne toènosti od 10–17 zahtijevaju vrlo toèna laserska mjerenja ili mjerenja u mikrovalnom podruèju. Za postizanje relativne toènosti od 10–17 kod vala nositelja frekvencije od 10 GHz (atomskih
satova), mora se mjeriti fazna razlika s vrlo visokom toènošæu od 10–7 [cycle8] ili
manje od 1 mrad. S druge strane, za mjerenja s optièkim frekvencijama od nekoliko stotina THz za postizanje relativne toènosti od 10–17 moralo bi se mjeriti s
toènošæu od samo 1 mHz, tj. znatno manje precizno. Relativna toènost koja se
moe postiæi u usporedbi frekvencije nakon razdoblja od jedne sekunde u rasponu
je od 10–13 do 10–15, dok se 10–17 moe postiæi nakon razdoblja od 10 000 sekundi
(Švehla 2008a, slide 34).
8
cycle – engleski krug odnosno 2p
10
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
Da bi se eliminirao utjecaj atmosfere i geometrije9 u prijenosu frekvencije izmeðu
dviju toèaka na Zemlji s pomoæu opaanja satelita u Zemljinoj orbiti, primjenjuje
se metoda s pomoæu dvostrukih linija, odnosno signal se istovremeno emitira i
prima u oba smjera. Za razliku od GPS-a gdje se mjerenja izvode samo u jednom
smjeru, dvostrukim linijama je moguæe direktno usporediti frekvenciju izmeðu toèke na Zemlji i u Zemljinoj orbiti. Ako se istovremeno mjeri s dvije toèke na površini Zemlje prema istom satelitu, moguæe je direktno izmjeriti razliku frekvencija
izmeðu atomskih satova na Zemlji i na taj naèin mjeriti razlike geopotencijala
(Švehla 2008b, Švehla 2008c, Schiller i dr. 2009). Slika 9 prikazuje takav sustav
usporedbe frekvencija s pomoæu satelita u LEO-orbiti (Low Earth Orbit) korištenjem Columbus modula na Meðunarodnoj svemirskoj postaji (Švehla 2008b). Slièan
je koncept predloen za Galileo i geostacionarnu orbitu (Švehla 2008c). Slika 10
prikazuje atomske satove i nacionalne metrološke laboratorije vremena u
IGS-mrei (Internacionational GNSS Service). Mrea IGS-stanica upotrebljava se
za odreðivanje orbita GNSS10-satelita (GPS, GLONASS, Galileo), ali i za usporedbu vremena i frekvencije izmeðu nacionalnih metroloških laboratorija koji definiraju realizaciju vremena UTC11 i TAI12.
Slika 9. Usporedbe (komparacije, prijenos) frekvencije i vremena dvostrukim linijama preko LEO13 ili GEO14 (Švehla 2008a).
Stanice za opaanje GNSS-satelita (slika 10) na taj naèin dvostrukim linijama
usporeðuju svoja vremena i frekvencije.
9
geometrije – udaljenosti izmeðu stanica, odnosno satelita
GNSS – Global Navigation Satellite Systems (Globalni navigacijski satelitski sustav)
11
UTC – Universal Time Coordinated (koordinirano svjetsko vrijeme)
12
TAI – Time Atomic International
13
LEO – Low Earth Orbit
14
GEO – Geostationary Earth Orbit
10
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–20
11
Slika 10. H-maseri, cezijevi atomski satovi, rubidijevi atomski satovi i laboratoriji
slube vremena u IGS15-mrei za odreðivanje orbita GNSS-satelita, izmeðu
kojih se metodom dvostrukih linija usporeðuju vrijeme i frekvencije za odreðivanje vremena TAI (Švehla 2008a).
6. Odreðivanje razlike gravitacijskih potencijala izmeðu dviju toèaka
na površini Zemlje
Razlika gravitacijskih potencijala izmeðu dviju toèaka na Zemlji moe se izmjeriti
na osnovi kvantne mehanike i Einsteinove opæe teorije relativnosti.
Fotoelektrièni efekt prvi je primijetio Alexandre Edmond Becquerel 1839. godine, tj.
uoèio je da svjetlost kada padne na neke metalne površine oslobaða iz njih kvante
svjetlosti (poslije nazvane fotoni). Einstein je 1905. godine objasnio tu pojavu fotoelektriènog efekta uvodeæi hipotezu kvanta svjetlosti (fotona), za što je dobio Nobelovu
nagradu 1921. godine (URL 5). Tako je Einstein svjetlosti dodao i korpuskularna
svojstva. Naime, svjetlost se moe prema Einsteinu pojasniti kao valna pojava, ali i
korpuskularno kao roj svjetlosnih zrnaca (èestica) elektromagnetske energije (fotona)
kad treba pojasniti neke optièke pojave, napose fotoefekt (Paar 2006, str. 4).
Odnos izmeðu energije fotona E i njegove frekvencije elektromagnetskih valova f
izraen je Planck–Einsteinovom jednadbom. Ona glasi:
E = hP × f ,
15
(1)
IGS – u IGS-mrei ima više od 200 stanica širom svijeta, koje suraðuju i usporeðuju svoje frekvencije i vremena
12
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
gdje je Planckova konstanta hP = 6,626 068 96 · 10–34 J · s16 (nazvana je u èast
njemaèkog fizièara Maxa Plancka) i f – frekvencija elektromagnetskih valova
(URL 5). Pritom je Planckova konstanta faktor proporcionalnosti izmeðu energije
i frekvencije, a to je najmanja konstanta u fizici. Svaki foton je nedjeljiv, ne moe
se dijeliti na dijelove. Ne postoji polovica ili treæina fotona. Foton je cijeli ili ga nema (Paar 2006, str. 4).
Ukupna energija tijela u relativistièkoj mehanici po Einsteinovoj opæoj teoriji relativnosti (Ivanoviæ 1962) definirana je Einsteinovom relacijom ekvivalentnosti
energije i mase:
E = m × c2,
(2)
gdje je m masa i c brzina svjetlosti u vakuumu (c = 2,999792458· 108 m · s–1).
Ovom jednadbom izraena je povezanost energije i mase, koja pokazuje da su
energija i masa linearno povezane, a faktor proporcionalnosti je kvadrat brzine
svjetlosti. Iz nje se vidi da masa sadri vrlo veliku energiju, jer se masa mnoi s
vrlo velikim kvadratom brzine svjetlosti, koja je inaèe velika. Tako kad bi se jedan
gram mase pretvorio u energiju, dobili bismo oko 1014 J energije (Kulišiæ 1989,
str. 143), a to je golema kolièina energije. Zbog toga i atomska bomba ima tako
strašno razornu snagu.
Kad se izjednaèe jednadbe (1) i (2), dobije se kao da foton ima masu:
m = hP × f × c-2 .
(3)
Iz klasiène mehanike poznato je da je gravitacijski potencijal V uistinu potencijalna energija gravitacijskih sila U za jediniènu masu (m=1). Tako se za potencijalnu energiju gravitacijskih sila U za tijelo s masom m moe napisati prema
(URL 6) da je:
U = m × V.
(4)
Za foton u gravitacijskom polju Zemlje u toèki A moe se napisati da je njegova
potencijalna energija jednaka UA = m·VA, gdje je m masa fotona i VA potencijal
gravitacijskog polja Zemlje u toèki A.
Za foton u toèki B na isti se naèin moe napisati da je UB = m·VB, gdje je VB potencijal gravitacijskog polja Zemlje u toèki B.
Pri prijelazu fotona u gravitacijskom polju Zemlje iz toèke A s gravitacijskim potencijalom VA u toèku B na površini Zemlje s potencijalom VB energija æe mu se
promijeniti za iznos:
DE = DU = U B - U A = ( VB - VA ) × hP × f × c-2 .
16
J (joule, dul) = N · m = kg · m2 · s–2
(5)
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
13
Istovremeno æe se fotonu promijeniti i frekvencija za Df = fB – fA, te se moe napisati da su omjer prirasta frekvencije fB – fA i frekvencije fA i omjer prirasta energije i energije jednaki, tj. da je:
fB - fA
DE
=
.
fA
E
(6)
Kad se jednadbe (1) i (5) uvrste u (6), dobije se da je:
fB - fA
= ( VB - VA ) × c-2 .
fA
(7)
Iz te jednadbe (7) dobije se da je razlika potencijala jednaka:
æf
ö
B
÷
VB - VA = c 2ç
ç f - 1÷.
è A
ø
(8)
Tako se vrlo toènim mjerenjem frekvencije nekog optièkog standarda u toèki A i
zatim u toèki B moe izraèunati razlika potencijala u toèkama A i B. Pritom se
brzina svjetlosti c moe uzeti kao poznata velièina.
Zatim se moe izraèunati i visinska razlika DH izmeðu ekvipotencijalnih ploha
koje prolaze kroz toèke A i B. Iz mehanike je poznato da je rad ili energija jednaka
produktu sile i duljine puta, kad sila i put lee na istom pravcu. Tako diferencijal
energije pri pomaku mase m za diferencijalni put dr iznosi:
dE = F · dr.
(9)
Zamislimo da je Zemlja homogeno tijelo s masom M koncentriranom u središtu
masa (teištu) Zemlje, tada primjenom Newtonova zakona o privlaèenju masa, sila privlaèenja Zemlje na tijelo mase m iznosi:
F=G×
M ×m
,
r2
(10)
gdje su:
G
– gravitacijska konstanta
M – masa Zemlje
m – masa tijela
r
– udaljenost izmeðu središta masa (teišta) Zemlje i materijalne toèke mase m.
Uvoðenjem jednadbe (10) u (9) dobije se da je:
dE = F × dr = G ×
M ×m
dr ,
r2
14
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
odnosno da je ukupna energija jednaka:
¥
E = òG ×
r
M ×m
M ×m
dr = G ×
,
r2
r
(11)
Buduæi da je energija jednaka produktu mase i potencijala bit æe:
M ×m
G×M
Energija G × r
=
= V.
Potencijal =
=
m
r
masa
(12)
Uvoðenjem jednadbe (12) u (8) slijedi da je:
æ
ö
ç
÷
G×M
G×M
G × Mç
1
1
÷
VB - VA =
=
»
HB ö æ
H A ö÷
R çæ
( R + H B) ( R + H A )
÷÷
÷ ç1 +
çç1 +
R ø è
R øø
èè
æ
ö
G×M
G×M
2ç fB
»- 1÷
÷,
2 (H B - H A ) = 2 × DH BA = c ç
R
R
è fA
ø
(13)
odnosno bit æe:
æf
ö R2
B
÷
DH BA = - c 2ç
1
çf
÷G × M .
è A
ø
Ubrzanje sile tee g jednako je: g =
nadba (14) moe napisati ovako:
(14)
G×M
(gdje je R radijus Zemlje), pa se jedR2
DH BA = -
ö
c2 æ
ç fB - 1÷.
ç
÷
g è fA
ø
(15)
Iz te jednadbe (15) moe se izraèunati i visinska razlika toèaka B i A, gdje se mogu uzeti kao vrlo toène poznate velièine brzina svjetlosti c i ubrzanje sile tee g.
Pritom æe se frekvencija fA i frekvencija fB morati izmjeriti s toènošæu 10–18, da bi
se postigla centimetarska toènost u odreðivanju razlike visina.
Prof. A. Bjerhammar iz Švedske prvi je obradio ideju o korištenju kvantne mehanike i opæe teorije relativnosti za odreðivanje geopotencijala odnosno visinske razlike 1974. godine (Vermeer 1983, Muminagiæ 1984). Meðutim, u to vrijeme nije se
mogla postiæi zadovoljavajuæa nesigurnost mjerenja frekvencije s tadašnjim atomskim satovima, pa je njegova ideja bila gotovo zaboravljena. Naime, ako bi se mjerila frekvencija s mjernom nesigurnosti od 10–16 tada bi se visinska razlika mogla
odrediti s mjernom nesigurnosti od 1 m. Ova je metoda oivjela kada su izraðeni
hidrogenski maserski satovi sa stabilnosti frekvencije od 10–13. Meðutim, ta se
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
15
stabilnost odrava u relativno kratkom vremenskom intervalu od 103 s (tj. 16 minuta i 40 sekundi), što je još dodatno ogranièilo korištenje Bjerhammarove metode. Zbog uporabe satova ta metoda za odreðivanje visina nazvana je i kronometrijski nivelman (chronometric levelling).
Danas se uz primjenu optièkog frekvencijskog èešlja otvara moguænost postizanja
relativne mjerne nesigurnosti optièke frekvencije od 10–17, a to znaèi da bi se veæ
danas mogle odreðivati visinske razlike na 1 decimetar. Meðutim, vjerojatno je da
æe se ta mjerna nesigurnost za nekoliko godina smanjiti – poboljšati, a to znaèi da
se u buduænosti otvara moguænost odreðivanja visinskih razlika kronometrijskim
nivelmanom s mjernom nesigurnosti od 1 cm.
Slika 11. Mjerenje razlike gravitacijskih potencijala izmeðu dviju toèaka na površini
Zemlje korištenjem misije ACES (Švehla 2008a).
Mjerenja razlika gravitacijskih potencijala na površini Zemlje jedan je od glavnih
znanstvenih ciljeva misije ACES17 na Meðunarodnoj svemirskoj postaji. Gravitacijski potencijal mjeren optièkim satovima odnosno frekvencmetrima i dvosmjernom vezom ACES pokazao je da je danas relativna toènost optièkih satova
8,6 · 10–18. Na taj naèin moguæe je odrediti razliku gravitacijskih potencijala s priblinom mjernom nesigurnosti od 10 cm po visini. Buduæi da se u Europi u pojedinim zemljama polazilo od mareografa iz njihovih zemalja, ima velikih razlika u visinama izmeðu pojedinih zemalja: od 0,3 m do 0,5 m. Zato se i dogodilo da je 2004.
godine pri gradnji mosta preko rijeke izmeðu Njemaèke i Švicarske došlo do velikih razlika u visini (od 36 cm), te je trebalo promijeniti projekt mosta, što je znatno poskupjelo projekt. Ako se nastavi poveæavati toènost optièkih satova, za 5 do
10 godina moe se oèekivati da æe se postiæi toènost mjerenja vremena i frekvencija takova da æe se moæi odreðivati razlike visina od 1 cm. Tada æe se vjerojatno
moæi i povezati nivelmanske mree pojedinih drava u Europi, a i u svijetu, s priblino centimetarskom toènošæu.
17
ACES – engl. Atomic Clock Ensemble in Space (atomski sat komplet u svemiru)
16
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
Gravitacijski potencijal na bilo kojoj toèki Zemljine površine mijenja se s vremenom
zbog utjecaja relativnog pomicanja Mjeseca i Sunca oko Zemlje, te regionalnih i lokalnih promjena uzrokovanih hidrološkim i klimatskim promjenama (topljenje leda
na polarnim kapama, promjene vodnog nivoa velikih slivova rijeka, npr. Amozone,
itd.). Te promjene potencijala nisu u isto vrijeme jednake na svim toèkama na površini Zemlje. Satelitske misije kao što su CHAMP18, GRACE19 i GOCE20 mjere statièko i vremenski promjenjivo gravitacijsko polje Zemlje do maksimalne rezolucije
od oko 100–500 km, za razliku od predloene metode, gdje se mjerenja gravitacjskog potencijala izvode izravno izmeðu bilo kojih udaljenih toèaka. Za razliku
od nivelmana, gdje su duljine veznih toèaka limitirane duinom vizure, predloena
mjerenja gravitacijskog potencijala mogu se izvoditi na udaljenostima do nekoliko
tisuæa kilometara, praktièno izmeðu bilo kojih dviju toèaka na površini Zemlje.
7. Precizna mjerenja duljina
Novi naèini mjerenja duljina na principu optièkog frekvencijskog èešlja razvijaju se,
a omoguæit æe višebojnu interferenciju i zbog pulsirajuæeg naèina rada istovremeno
i TOF (time-of-flight = vrijeme leta) informaciju. Metoda TOF je poznati princip
apsolutnog mjerenja duljina. Kratki optièki puls reflektira se od udaljenog predmeta do kojeg se mjeri duljina i mjeri se kašnjenje tog signala u odnosu na odaslani
signal. Slièno se mjerilo i duljine impulsnim naèinom (Benèiæ i Solariæ 2008). Duljina
se moe izraèunati iz vremena kašnjenja svjetlosnog signala, ako se to vrijeme pomnoi s brzinom svjetlosti i razdijeli s 2. Oèekuje se da æe kombinacija metode TOF
i višebojne interferencije omoguæiti visokoprecizna mjerenja ispod razine mikrometra i udaljenosti do tisuæu kilometara u svemiru (Kozma i dr. 2007). U tom èlanku
autor je bio i R. Holzwarth, suradnik dobitnika Nobelove nagrade T. Hänscha.
I dalje ostaje dosta veliki problem odreðivanja indeksa loma svjetlosti sredstva
kroz koje prolazi optièki signal koji se pokušava riješiti na razne naèine. Za sada
postoji moguænost da æe se riješiti pomoæu spektroskopske metode (Wallerand i dr.
2008). Tom metodom odreðuje se temperatura zraka što je i najveæi problem pri
odreðivanju indeksa loma svjetlosti sredstva kroz koje prolazi optièki signal. Osim
toga tom metodom odreðuje se i vlanost zraka. Za sada ne postoje najave da æe se
i s optièkim frekvencijskim èešljem u tom dijelu uskoro postiæi veæa toènost odreðivanja indeksa loma svjetlosti sredstva kroz koje prolazi optièki signal.
Preliminarni simulirani podaci pokazuju da æe se u svemiru (vakuumu) moæi postizati vrlo visoka preciznost:
• na duljini do 10 m preciznost 20 nm21 (relativna preciznost 10–9)
• na duljini do 1000 m preciznost 150 nm (relativna preciznost 10–10)
• na duljini do 1 milion km preciznost 100 mm (relativna preciznost 10–13).
U jednom od sljedeæih èlanaka detaljnije æe biti obraðeno mjerenje duljina femtosekundnim laserima.
18
CHAMP – CHAllenging Minisatellite Payload (satelitska misija)
GRACE – Gravity Recovery And Climate Experiment (satelitska misija)
20
GOCE – Gravity field and steady-state Ocean Circulation Explorer (satelitska misija)
21
1 nm = 10–9 m
19
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
17
8. Zakljuèak
Iz izloenog se vidi da su s femtosekundnim laserima i optièkim frekvencijskim
èešljem veæ sada postignuta velika poveæanja toènosti mjerenja vremena optièkim
satovima, a uskoro æe biti omoguæeno i mjerenje razlika gravitacijskih potencijala
na površini Zemlje s centimetarskom toènošæu. Osim toga poveæat æe se i preciznost mjerenja velikih duljina u vakuumu, a moe se oèekivati s manjim zakašnjenjem i u atmosferi.
ZAHVALA. Najljepše zahvaljujemo akademiku Goranu Pichleru i profesoru Asimu Bilajbegoviæu na vrlo korisnim primjedbama, kojima su pridonijeli boljoj kvaliteti ovog rada. Takoðer zahvaljujemo Ministarstvu znanosti, obrazovanja i sporta Republike Hrvatske što je djelomièno financiralo ovaj rad, koji je izraðen u okviru projekta Razvoj znanstvenog mjeriteljskog laboratorija za geodetske instrumente br.: 007-1201785-3539.
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Frequency Comparison of Two High-Accuracy Al+ Optical Clocks, Physical Review
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Laurent, P., Santarelli, G., Clairon, A., Ertmer, W., Rasel, E., Müller, J., Iorio, L.,
Lämmerzahl, C., Dittus, H., Gill, E., Rothacher, M., Flechner, F., Schreiber, U.,
Flambaum, V., Ni, W.-T., Liu, L., Chen, X., Chen, J., Gao, K., Cacciapuoti, L., Holzwarth, R., Heß, M. P., Schäfer, W. (2009): Einstein Gravity Explorer – a medium-class fundamental physics mission, Experimental Astronomy, 23(2), 573–610,
doi: 10.1007/s10686-008-9126-5.
Švehla, D. (2008a): A novel design for a timing and navigation system, Kolloquium
Satellitennavigation, TU München, May 8, 2008,
http://www.nav.ei.tum.de/joomla/documents/up/colloquium_svehla_slides.pdf,
(04.04.2011.).
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Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
Švehla, D. (2008b): Geodesy Part of the ACES Mission: GALILEO on Board the
International Space Station, Proceedings from the ESA Conference “ACES and
Future GNSS-Based Earth Observation and Navigation”, May 26–27, 2008, TU
München, Germany,
http://www.espace-tum.de/12727-bD1lbg-~aces~start.html, (20.06.2011.).
Švehla, D. (2008c): A Novel Design for the Navigation System and Proposal to Unify the
Timing and the Positioning System Using GIOVE Follow-on, Proceedings from the
ESA Conference “ACES and Future GNSS-Based Earth Observation and Navigation”, May 26–27, 2008, TU München, Germany,
http://www.espace-tum.de/12727-bD1lbg-~aces~start.html, (20.06.2011.).
Vermeer, M. (1983): Chronometric levelling, Reports of the Finnish Geodetic Institute,
83:2, Helsinki.
Wallerand, J.-P., Abou-Zeid, A., Badr, T. i dr. (2008): Towards New Absolute Long Distance Measurement Systems in Air, NCSL International 2008 Workshop and
Symposium,
http://www.longdistanceproject.eu/files/towards_new_absolute.pdf, (04.04.2011.).
URL 1: The Nobel Prize in Physics 2005, Roy J. Glauber, John L. Hall, Theodor W. Hänsch,
http://nobelprize.org/nobel_prizes/physics/laureates/2005/hansch-autobio.html,
(07.04.2011.).
URL 2: Optical Frequency Comb,
http://www.nrc-cnrc.gc.ca/eng/projects/inms/optical-comb.html, Fig. 6,
(04.04.2011.).
URL 3: Laboratory for femtosecond spectrosccopy, Frekventni èešalj (frequency comb),
http://projekt2.ifs.hr/comb.htm, (05.04.2011.).
URL 4: The Nobel Prize in Physics 1997, Steven Chu, Claude Cohen-Tannoudji, William D. Phillips,
http://nobelprize.org/nobel_prizes/physics/laureates/1997/, (07.04.2011.).
URL 5: Planck constant, http://en.wikipedia.org/wiki/Planck_constnt, (20.04.2011.).
URL 6: Gravitational Potential,
http://en.wikipedia.org/wiki/Gravitational_potential, (24.04.2011.).
URL 7: NIST "Quantum Logic Clock",
http://www.nist.gov/pml/div688/logic_clock.cfm, (16.06.2011.).
URL 8: Pulsni_laseri_predavanje11,
http://www.fer.hr/_download/repository/pulsni_laseri-predavanje11.pdf,
(15.06.20011.).
URL 9: Mode Locking, http://www.rp-photonics.com/mode_locking.html, (24.06.2011.).
URL 10: Frequency Comparison of Two High-Accuracy Al+ Optical Clocks, C.-W. Chou, D.
B. Hume, J. C. J. Koelemeij, D. J. Wineland, T. Rosenband, A preprint is available at:
http://arxiv.org/abs/0911.4527, (15.06.2011.).
URL 11: Photonic Frontiers: Optical Clocks: Optical clocks set the pace in accurate
timekeeping,
http://www.laserfocusworld.com/articles/print/volume-45/issue-5/features/photonicfrontiers-optical-clocks-optical-clocks-set-the-pace-in-accurate-timekeeping.html,
(04.06.2011.).
Solariæ, N. i dr.: Nove revolucionarne moguænosti u geodeziji …, Geod. list 2012, 1, 1–19
19
URL 12: When should we change the definition of the second? Patrick Gill,
http://www.bipm.org/utils/common/pdf/RoySoc/Patrick_Gill.pdf, (29.06.2011.).
URL 13: Nobelova nagrada za fiziku 2005. godine, Goran Pichler,
http://projekt2.ifs.hr/documents/Nobelova%20nagrada%20za%20fiziku%202005.pdf,
(29.06.2011.).
New Revolutionary Possibilities in Geodesy
Providing the Discoveries Awarded
for Physics in 2005 and 1997
ABSTRACT. Nobel Prize for Physics in the year 2005 was awarded to Roy J. Glauber, John L. Hall and Theodor W. Hänsch in recognition of their contribution in the
field of optics. Nobel Prize for physics in 1997 was awarded to Steven Chu, Claude
Cohen-Tannoudji and William D. Phillips for the discovery and development of the
method by means of which the atoms are cooled down and trapped by laser light. The
improvements that were suggested by Theodor W. Hänsch and John L. Hall supported by the discoveries made by Steven Chu, Claude Cohen-Tannoudji and William
Phillips offer new revolutionary possibilities for significant improvement of measuring accuracy in geodesy and also in many other fields of science and application. By
means of optical clocks it will be possible to measure time even more precisely than by
atomic clocks, providing thus more precise determination of navigational satellite orbits, and consequently the positions of points on the Earth’s surface. It also opens the
possibility of determining the difference of gravitational potential between the points
on the Earth’s surface applying thereby the theory of relativity by Einstein. In this
way it will be possible to connect the heights between the continents by means of direct measurements, and also to improve the connection of levelling networks between
individual countries on the continents. More precise distance measurements will also
bi provided.
Keywords: femtolaser, frequency comb, frequency lineal, optical clock, measurement
of difference in gravitation potential.
Primljeno: 2011-07-11
Prihvaæeno: 2012-02-09
Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
21
UDK 528.088.2:528.516:514.774.8
Pregledni znanstveni èlanak
An Analysis of the Impact of Errors Occurring
in the Auxiliary Parameters while Determining
Geometric Corrections of Distance
Milan MEDVED – Velenje1, Aleksandar GANIÆ – Belgrade2,
Milivoj VULIÆ – Ljubljana3
ABSTRACT. Distance measurement results are hampered by systematic and accidental errors. The influence of systematic errors is reduced or eliminated mostly
through the entering of appropriate corrections or through the use of a particular
measurement method. A large number of different sources of corrections may be divided into three groups, namely into meteorological, geometric and projection corrections. In this paper, exclusively geometric corrections are explored. The determination of geometric corrections and the elimination of their influence upon measurement results demands knowledge or measurement of various auxiliary parameters.
Auxiliary parameters are also hampered by accidental errors, which under the law of
propagation of errors affect the precision of the distance measured adjusted for geometric corrections. These are all generally known facts, but due to reasons unknown
to the authors, the problematics exposed in this paper have not yet been treated in literature. This paper presents an analysis of the impact of auxiliary parameters on
the precision of measured distances that have been adjusted for geometric corrections. Knowing the precision of a distance adjusted in this manner is significant, as
the previously listed effects are present in the daily implementation of surveying
tasks in the field of precise geodetic measurements and in the calibration of electronic instruments used to measure distances. This paper also presents a detailed example of calculating the impact of geodetic sources and their standard deviations on the
precision of an electronically measured distance. In addition, this paper can also serve as a detailed general instruction manual for everyday professional application during precision distance measurements.
Keywords: electronic distance measurement, geometric corrections, standard deviation.
1
Ass. Prof. Dr. Sc. Milan Medved, Coal Mine Velenje, Partizanska cesta 78, SI-3320 Velenje, Slovenia,
e-mail: [email protected],
2
Assoc. Prof. Dr. Sc. Aleksandar Ganiæ, Faculty of Mining and Geology, University of Belgrade, Ðušina 7,
RS-11000 Belgrade, Serbia, e-mail: [email protected],
3
Ass. Prof. Dr. Sc. Milivoj Vuliæ, Faculty of Natural Sciences and Engineering, University of Ljubljana, Aškerèeva 12, SI-1000 Ljubljana, Slovenia, e-mail: [email protected]
22
Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
1. Introduction
Usually, slope distances are measured on the survey site. For further calculations,
it is necessary to reduce slope distances to the horizon, respectively to the projection plane (Dapo and Zrinjski 2004, Zrinjski 2010, Zrinjski and Dapo 2010). Results of distance measurements are encumbered by different systematic and accidental errors. Therefore, it is necessary to eliminate different impacts from the
results of distance measurements by the operating method or by entering appropriate corrections (Schofield and Breach 2007). With respect to the character of
the impacts existing within the results of slope distances measurements, the corrections can be divided into three groups (Rüeger 1996):
• meteorogical corrections,
• geometric corrections and
• projection corrections.
Firstly, measured distances are to be corrected based on meteorogical impacts.
The electromagnetic waves propagate through the air, which is heterogeneous,
and the speed of wave propagation depends on certain meteorogical characteristics of the atmosphere, such as: air temperature, air humidity and air pressure.
Geometric corrections are the result of the imperfection of instruments and measuring equipment, spatial distortion of the path of electromagnetic waves as well
as the position of the points in space, which includes the distance to be measured,
in relation to the instrument itself and the reflector (Hashemi et al. 1994).
The projection corrections are to be entered because of the aforementioned need
to determine the horizontal projection of the distance to be measured and its representation within the projection plane.
In order to determine the appropriate corrections, other auxiliary parameters
have to be measured on the survey site apart from the distance itself, such as for
example: air temperature, difference in altitude, height of the instrument and the
reflector (Zrinjski 2010, Zrinjski and Dapo 2010), etc. Simultaneously, the auxiliary parameters are, just like the distance itself, encumbered by accidental errors.
Pursuant to the Law on the Propagation of Errors, the precision of the measurement of auxiliary parameters affects the precision of the corrected distance. Understanding the total standard deviation of the corrected distance is very important in because not only the precision of the other parameters, but also further
field work depend on the precision of the corrected distance.
2. Geometric Corrections of the Distance
Geometric corrections of the measured distances are as follows (Zrinjski 2010):
• correction of the distance by an additive constant,
• correction of the distance by a multiplication constant,
• distance correction due to refraction,
• distance reduction.
While performing usual engineering tasks, distances are not to be corrected on
account of the impact of refraction. The reason for this is that such corrections
Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
23
have a minor influence, i.e., they are smaller than the precision of the distance
measurement itself (Saastamoinen 1964). Specifically, the value k = 0,13 has
been adopted both in Slovenia and in Serbia as the refraction coefficient for light
waves and only distances larger than 39 km are corrected for the refraction,
which is in the millimetre size range (Mrkiæ 1991).
The necessary calculations are shown using as an example a distance measured
from the point Šoštanj (The Republic of Slovenia).
Data relevant for calculation are (Kogoj 2005):
• total station: Leica TDM5000
• standard deviation of the distance measurement: 2 mm + 2 ppm
• standard deviation of the angle measurement: 1"
• additive constant: –0.8 mm
• standard deviation of the additive constant: 0.2 mm
• measured distance: 1281.0078 m
• height of the total station: 0.234 m
• height of the reflector: 1.390 m
• slope distance reduced by meteorogical corrections: 1281.0055 m
• standard deviation of the distance reduced by meteorogical corrections: 4.6 mm
• zenith distance: 86°55'48.85"
• elevation of the station: 450.990 m.
As support for this example, all computations within this paper were performed
in the program package Microsoft Office Excel using the corresponding functions,
which were specifically implemented into the program (URL 1).
3. Determination of the Distance Correction for the Additive Constant
The additive constant is the horizontal distance between the centre of the emission of electromagnetic waves and the point at which the measurement is performed (Dzierzega and Scherrer 2003). This correction includes all geometric,
electronic and linear eccentricities of both the total station and the reflector, as
well as errors that occurred because of the difference in the speed of wave propagation through the electro-optical system of the instrument and reflector, and
through the air.
The eccentricity of the total station KI is the result of the path geometry of the
reference signal and the electronic delay within the total station. It occurs
because the centre of the measurement is not positioned on the vertical axis of
total station. The eccentricity of the reflector KR is the result of the path geometry of the measuring signal through the reflector prisms. This difference occurs
because the wave reflection plane is not on the same level as vertical axis of the
reflector.
The additive constant represents the algebraic sum of the additive constant of the
total station KI and additive constant of the reflector KR:
K a = K I + K R.
(1)
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Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
where: KI = –0.8 mm and KR = 0. Thus:
Ka = –0.8 mm.
Due to the additive constant, the distance measured is shorter or longer than the
actual value. The value of the additive constant is entered into the total station
and the distance is automatically reduced or it is taken into account when further
computations are performed. The distance corrected for the additive constant Sra
amounts to:
S ra = S met + K a
(2)
Sra = 1281.0047 m.
3.1. Measurement Errors in the Input Values of the Distance Corrected
for the Additive Constant
The precision of the calculation of distance corrected for the additive constant is
affected by:
• the standard deviation of the distance reduced by the meteorogical corrections
s Smet ,
• the standard deviation of the additive constant s K a .
The impact of the distance reduced by the meteorogical correction Smet on the distance corrected for additive constant Sra is obtained when the partial derivative
upon the variable Smet is derived from Equation (2) and then multiplied by the
standard deviation of the distance reduced by meteorogical correction s Smet .
Standard deviation of the distance reduced by meteorogical correction was computed previously and amounts to s Smet = 4.6 mm.
I Smet =
¶S ra
× s Smet = s Smet
¶S met
(3)
I Smet = 4.6 mm
The impact of the error of the additive constant Ka on the distance corrected for
the additive constant Sra is obtained when the partial derivative upon the variable
Ka is derived from Equation (2) and then multiplied by the standard deviation of
the additive constant s K a .
The standard deviation of the additive constant was determined by the manufacturer of the total station and reflector and amounts to s K a = 0.2 mm.
IK a =
¶S ra
×sKa = sKa
¶K a
I K a = 0.2 mm
(4)
Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
25
3.2. Standard Deviation of the Distance Corrected for Additive Constant
The standard deviation of the distance corrected for the additive constant is derived from the square root of the sum of squares of the impact:
• the distance reduced by meteorogical correction I Smet determined according to
the equation (3),
• additive constant I K a determined according to the equation (4).
s 2Sra = I S2met + I K2 a = s 2Smet + s 2K a
(5)
s Sra = 4.6 mm
4. Determination of the Distance Correction Based
on the Multiplication Constant
The multiplication constant q is the result of a change in the oscillation frequency
of quartz within the total station, which is a cause for distances different from actual values being obtained (Dzierzega and Scherrer 2003). One of the methods to
determine the multiplication constant is to measure a particular, conditionally
taken as accurate, distance using the total station the multiplication constant of
which is to be determined.
The distance corrected for the multiplication constant is calculated by using the
equation:
S r = q × S ra
(6)
Sr = 1281.0047 m.
The multiplication constant for the total station used in the example amounts to
q = 1.
4.1. Errors in the Measurement of the Input Values of Distance Corrected
for the Multiplication Constant
The precision of the calculation of distance corrected for the multiplication constant is affected by:
• the standard deviation of the multiplication constant sq,
• the standard deviation of the distance corrected for the additive constant s Sra .
The impact that the multiplication constant q has on the distance Sr is obtained
when the partial derivative upon variable q is derived from Equation (6) and then
multiplied by standard deviation sq.
The standard deviation of the multiplication constant amounts to sq = 0.002 mm/m.
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Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
Iq =
¶S r
× s q = s q × S ra
¶q
(7)
I q = 2.6 mm
The impact that the distance corrected for the additive constant Sra has on the
distance corrected for the multiplication constant Sr is obtained when the partial
derivative upon the variable Sra is derived from Equation (6) and then multiplied
by the standard deviation of the distance corrected for the additive constant s Sra .
The standard deviation of the distance corrected for the additive constant (5) is
s Sra = 4.6 mm.
I Sra =
¶S r
× s Sra = s Sra × q
¶S ra
(8)
I Sra = 4.6 mm
4.2. Standard Deviation of the Distance Corrected for the Multiplication Constant
Standard deviation of the distance corrected for the multiplication constant is derived from the square root of the sum of squares of the impact:
• the multiplication constant Iq determined according to Equation (7),
• the distance corrected for the additive constant I Sra determined according to
Equation (8).
s 2Sr = I q2 + I S2ra
(9)
s Sr = 5.3 mm
5. Determination of the Distance between the Centres of Reference Points
It is necessary to convert the slope distance Sr, preliminary corrected for the
meteorogical correction and the additive and multiplication constant, to the distance Sk between centres of stabilized endpoints of the distance measured (17).
These calculations are to be performed using one of two following methods:
• based on the measured zenith distance,
• based on the known elevations of endpoints on a line segment.
The equation used to calculate the distance Sk also contains the radius of the
Earth’s curvature R at a reference point (station). First, the Earth’s radius at the
reference point Šoštanj has to be calculated, as well as the impact of the error of
the radius on the precision of the distance measured.
Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
27
6. Determination of the Earth’s Radius at the Reference Point
The Earth’s datum level is defined by the reference ellipsoid of revolution for the
specific region. Based on the given ellipsoid, the mean radius of the Earth’s curvature R is calculated. The magnitude of the radius at some particular point depends on the semi-major and semi-minor axis of the ellipsoid of revolution as well
as on the ellipsoidal width of the reference point according to the equation:
R=
a4
2
é
( a 2 - b 2 ) cos 2 j ù
b ê1 +
ú
b2
û
ë
(10)
2
where:
a = 6378137.000 m – semi-major axis of the ellipsoid of revolution,
b = 6356752.314 m – semi-minor axis of the ellipsoid of revolution,
j = 46°20' – ellipsoidal width of the reference point.
The semi-major and semi-minor axes refer to the Geodetic Reference System 1980
– GRS80 ellipsoid.
In this example, the Earth’s radius at the reference point Šoštanj is:
R = 6379097.775 m.
6.1. Errors of the Input Values Affecting the Radius R
The precision of calculation of the Earth’s radius is affected by:
• the standard deviation of the ellipsoidal width at the chosen point sj,
• the standard deviation of the semi-major axis of the ellipsoid of revolution sa,
• the standard deviation of the semi-minor axis of the ellipsoid of revolution sb.
The ellipsoidal width of Slovenia is one degree; hence, the same radius can be
used throughout the country, considering the fact that its value does not affect significantly the calculation of distances. The impact of the ellipsoidal width j on
the radius R is obtained when the partial derivative upon the variable j is derived
from Equation (10) and then multiplied by the standard deviation value of the ellipsoidal width sj.
The standard deviation value of the ellipsoidal width of the chosen point is
sj = 30'.
Ij =
¶R
×sj =
¶j
a 4b2
[ b + ( a - b 2 ) × cos 2 j]2
b 2 + ( a 2 - b 2 ) × cos 2 j
s j ( a 2 - b 2 ) × sin 2j
2
Ij = 373.5686 m
2
(11)
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Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
The impact that the semi-major axis of the ellipsoid of revolution a has on the radius R is obtained when the partial derivative upon the variable a is derived from
Equation (10) and then multiplied by the standard deviation of the semi-major
axis of the ellipsoid of revolution sa.
The standard deviation of the semi-major axis of the ellipsoid of revolution is
sa = 0.5 mm.
Ia =
¶R
×sa =
¶a
s a × 2a 3 × b 4 × sin2 j
[ b + ( a - b ) × cos j]
2
2
2
2
3
a 4b2
2
2
[b + ( a - b 2 ) × cos 2 j]2
(12)
Ia = 0.5 mm
The impact that the semi-minor axis of the ellipsoid of revolution b has on the radius R is obtained when the partial derivative upon the variable b is derived from
Equation (10) and then multiplied by the standard deviation of the semi-minor
axis of the ellipsoid of revolution sb.
The standard deviation of the semi-minor axis of the ellipsoid of revolution is
sb = 0.5 mm.
Ib =
¶R
×sb =
¶b
a 4b2
[ b 2 + ( a 2 - b 2 ) × cos 2 j]2
2
2
- b [ b + ( a - b 2 ) × cos 2 j]
s b × [ b 2 + ( a 2 - b 2 ) × cos 2 j]
(13)
Ib = 2.2 · 10–2 mm
6.2. Standard Deviation of the Earth’s Radius in Reference Point
The standard deviation of the Earth’s radius R at the reference point is derived
from the square root of the sum of squares of the impact:
• the ellipsoidal width Ij determined according to Equation (11),
• the semi-major axis of the ellipsoid of revolution Ia determined according to
Equation (12),
• the semi-minor axis of the ellipsoid of revolution Ib determined according to
Equation (13).
s R2 = I j2 + I a2 + I b2
(14)
sR = 373.5686 m
7. Calculation of the Distance Sk Based on the Measured Zenith Distance
The calculation of the slope distance Sk is necessary because of the different
heights of the total station and reflector, i.e., because of their different vertical distance from the ground. The measured distance corrected for the additive and
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Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
multiplication constant must be converted into the slope distance existing between the very centres of the stabilized reference points. Therefore this type of distance may be called the stone-stone distance.
The slope distance Sp at the height the total station above sea level is given by:
S p = S r - ( l - i) × cos z r +
( l - i) × sin z r
2S r
(15)
Sp = 1280.9432 m.
It is necessary to convert the distance Sp at the altitude of total station into the
reference point elevation:
Sk = S p -
i× S p
R+ Hi + i
.
(16)
By replacing Equation (15) with Equation (16) and after re-arrangement, the
equation for the slope distance at the elevation of the reference point is obtained:
Sk =
( R + H i)[ 2S r2 + 2S r( i - l) cos z r + ( l - i) sin z r ]
2S r( R + H i + i)
(17)
Sk = 1280.9432 m.
7.1. Errors in the Input Values Affecting the Slope Distance Sk Determined
by Means of Zenith Distance
The precision of the calculation of the slope distance Sk determined by means of
zenith distance is affected by:
• the standard deviation of the distance corrected for the multiplication constant s Sr ,
• the standard deviation of the altitude of the total station si,
• the standard deviation of the altitude of the reflector sl,
• the standard deviation of the zenith distance s z r ,
• the standard deviation of the elevation of a station s H i ,
• the standard deviation of the Earth’s radius sR.
The impact that the distance corrected for the multiplying constant Sr has on the
slope distance Sk calculated based the zenith distance is obtained when the partial derivative upon the variable Sr is derived from Equation (17) and then multiplied by the standard deviation of the distance corrected for the multiplication
constant s Sr .
The standard deviation of the distance corrected for the multiplication constant
(9) is s Sr = 5.3 mm.
I Sr =
s S ( R + H i)[ 2S r2 + ( i - l) sin z r ]
¶S k
× s Sr = r
¶S r
2S r2 ( R + H i + i)
I Sr = 5.3 mm
(18)
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Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
The impact that the altitude of the total station i has on the slope distance Sk calculated on the basis of the zenith distance is obtained when the partial derivative
upon the variable i is derived from Equation (17) and then multiplied by the standard deviation of the altitude of the total station si.
The standard deviation of the altitude of the total station is the result of the error
in the measurement of the altitude and it amounts to si = 1mm.
Ii =
¶S k
( R + H i)[( R + H i + l)( 2S r cos z r - sin z r) - 2S r2 ]
×si = si ×
¶i
2S r( R + H i + i) 2
(19)
Ii = 5.3 · 10–2 mm
The impact that the altitude of the reflector l has on the slope distance Sk calculated based on the zenith distance is obtained when the partial derivative upon the
variable l is derived from Equation (17) and then multiplied by the standard deviation of the altitude of the reflector sl.
The standard deviation of the altitude of the reflector is the result of the error in
the measurement of the altitude and amounts to sl = 1 mm.
Il =
¶S k
s ( R + H i)(sin z r - 2S r cos z r)
×sl = l
¶l
2S r( R + H i + i)
(20)
Il = 5.3 · 10–2 mm
The impact that the zenith distance zr has on the slope distance Sk calculated based on the zenith distance is obtained when the partial derivative upon the variable zr is derived from Equation (17) and then multiplied by the standard deviation
of the zenith distance s z r .
The standard deviation of the zenith distance is determined based on an a-posteriori evaluation of the precision of the measurements performed and it amounts
to s z r = 5".
Iz r =
s z ( i - l)( R + H i)( 2S r × sin z r + cos z r)
¶S k
× szr = - r
¶z r
2S r( R + H i + i)
(21)
I z r = 2.8 · 10–2 mm
The impact that the elevation of the station Hi has on the slope distance Sk calculated based on the zenith distance is obtained when the partial derivative upon
the variable Hi is derived from Equation (17) and then multiplied by the standard
deviation of the altitude of the station s H i .
The standard deviation of the elevation of the station is the result of the levelling
error and it amounts to s H i = 20 mm.
Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
s H i × i [ 2S r2 + 2S r( i - l) cos z r + ( l - i) sin z r ]
¶S k
IHi =
× s Hi =
¶H i
2S r( R + H i + i) 2
31
(22)
I H i = 1.5 · 10–10 mm
The impact that the Earth’s radius R has on the slope distance Sk calculated based on the zenith distance is obtained when the partial derivative upon the variable R is derived from Equation (17) and then multiplied by the standard deviation
of the Earth’s radius sR.
The standard deviation of the Earth’s radius (14) is sR = 373.5686 m.
IR =
s R × i [ 2S r2 + 2S r( i - l) cos z r + ( l - i) sin z r ]
¶S k
×sR =
¶R
2S r( R + H i + i) 2
(23)
IR = 2.8 · 10–6 mm
7.2. Standard Deviation of the Slope Distance Sk
The standard deviation of the slope distance Sk calculated based on the zenith distance (17) is derived from the square root of the sum of the squares of the impact
of:
• the distance corrected for the multiplication constant I Sr determined according
to Equation (18),
• the altitude of the total station Ii determined according to Equation (19),
• the altitude of the reflector Il determined according to Equation (20),
• the zenith distance I z r determined according to Equation (21),
• the elevation of the station I H i determined according to Equation (22),
• the impact of the Earth’s radius IR determined according to Equation (23).
s 2Sk = I S2r + I i2 + I l2 + I H2 i + I z2r + I R2
(24)
s Sk = 5.3 mm
7.3. Determination of the Point Elevation of the Reflector
The point elevation of the reflector is to be determined according to the following
equation:
H l = ( R + H l) 2 - R
(25)
( R + H l) 2 = ( R + H i) 2 + S k2 + 2S k ( R + H i) cos z r,
(26)
whereby:
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Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
hence, after the replacement, the following equation is obtained:
H l = ( R + H i) 2 + S k2 + 2S k ( R + H i) cos z r - R.
(27)
The point elevation of the reflector Hl amounts to:
Hl = 519.715 m.
7.4. Error in the Measurement of the Input Values on the Determination
of the Point Elevation of the Reflector Hl
The precision of the determination of the point elevation of the reflector Hl is
affected by:
• the standard deviation of the elevation of the station s H i ,
• the standard deviation of the slope distance s Sk ,
• the standard deviation of the Earth’s radius sR,
• the standard deviation of the zenith distance s z r .
The impact that the elevation of the station Hi has on the point elevation of the
reflector Hl is obtained when the partial derivative upon the variable Hi is derived
from Equation (27) and then multiplied by the standard deviation of the altitude
of the station s H i .
The standard deviation of the elevation of the station is the result of the levelling
error and amounts to s H i = 20 mm.
IHi =
s H i ( R + H i + S k × cos z r)
¶H l
× s Hi =
¶H i
( R + H i) 2 + S k2 + 2S k ( R + H i) × cos z r
(28)
I H i = 20.0 mm
The impact that the slope distance Sk has on the point elevation of the reflector
Hl is obtained when the partial derivative upon the variable Sk is derived
from Equation (27) and them multiplied by the standard deviation of the slope distance s Sk .
The standard deviation of the slope distance (24) is s Sk = 5.3 mm.
I Sk =
s Sk [ S k + ( R + H i) × cos z r ]
¶H l
× s Sk =
¶S k
( R + H i) 2 + S k2 + 2S k ( R + H i) × cos z r
(29)
I Sk = 0.3 mm
The impact that the Earth’s radius R has on the point elevation of the reflector
Hl is obtained when the partial derivative upon the variable R is derived
from Equation (27) and then multiplied by the standard deviation of the Earth’s
radius sR.
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The standard deviation of the Earth’s radius (14) is sR = 373.5686 m.
IR =
é
ù
¶H l
R + H i + S k × cos z r
ú
× s R = s Rê
1
2
2
¶R
ê
ú
ë ( R + H i) + S k + 2S k × ( R + H i) × cos z r
û
(30)
IR = 7.5 · 10–3 mm
The impact that the zenith distance zr has on the point elevation of the reflector
Hl is obtained when the partial derivative upon the variable zr is derived from
Equation (27) and then multiplied by the standard deviation of the zenith distance s z r .
The standard deviation of the zenith distance is determined based on the a-posteriori evaluation of the precision of the measurements performed and amounts to
s z r = 5".
Iz r =
s z r ( R + H i) × S k × sin z r
¶H l
× szr = ¶z r
( R + H i) 2 + S k2 + 2S k ( R + H i) × cos z r
(31)
I z r = 31.0 mm
7.5. Standard Deviation of the Point Elevation of the Reflector
The standard deviation of the point elevation of the reflector Hl determined by
Equation (27) is derived from the square root of the sum of the squares of the impact:
• of the elevation of the station I H i determined according to Equation (28),
• of the slope distance I Sk determined according to Equation (29),
• of the Earth’s radius IR determined according to Equation (30),
• of the zenith distance I z r determined according to Equation (31).
s 2H l = I H2 i + I S2k + I R2 + I z2r
(32)
s H l = 36.9 mm
8. Calculation of the Distance Sk Based on the Known Elevation Between
the Endpoints on the Line Segment
The reduction is performed based on the known elevation between the endpoints
on the line segment to be measured. The elevation between points is obtained by
means of geometric or trigonometric levelling. The method of trigonometric levelling is applied on steep and overgrown terrains, because in these cases, it is simpler to obtain differences in altitude using this method than by using the geometric levelling method, which is applied on an even and smooth terrain.
The slope distance is to be calculated because the total station and the reflector
are positioned at different altitudes, respectively at the different vertical distan-
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Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
ces from the ground. It is therefore necessary to convert the measured distance
into the slope distance between the centres of the stabilized reference points.
Such a distance is, therefore, called the stone-stone distance.
This method of calculation implies that the elevation between the endpoints is
known, however, it is necessary to calculate the difference in altitude between the
total station and the reflector according to the equation:
DS =
( i - l)( H l - H i) ( i - l) 2 ( i + l)
× Sr
2S r
2R
Sr
(33)
DS = –0.0627 m.
The slope distance is to be calculated according to the equation:
S k = S r + DS
(34)
Sk = 1280.9420 m.
8.1. Errors of the Input Values Affecting the Slope Distance Sk Determined
based on the Known Elevation Between the Endpoints
The precision of the slope distance Sk determined based on the known elevation
between the endpoints is affected by:
• the standard deviation of the distance corrected for the multiplication constant s Sr ,
• the standard deviation of the altitude of the total station si,
• the standard deviation of the altitude of the reflector sl,
• the standard deviation of the elevation of the station s H i ,
• the standard deviation of the point elevation of the reflector s H l ,
• the standard deviation of the Earth’s radius sR.
The impact that the distance corrected for the additive constant Sr has on the slope distance Sk calculated based on the known elevation between the endpoints is
obtained when the partial derivative upon the variable Sr is derived from Equation (34) and then multiplied by the standard deviation of the distance corrected
for the multiplication constant s Sr .
The standard deviation of the distance corrected for the multiplication constant
(9) is s Sr = 5.3 mm.
I Sr =
s S [( i - l)( 2H i - 2H l + i - l) × R + S r2 ( 2R - i - l)]
¶S k
× s Sr = r
¶S r
2S r2 R
(35)
I Sr = 5.3 mm
The impact that the altitude of the total station i has on the slope distance Sk calculated based on the known elevation between the endpoints is obtained when
the partial derivative upon the variable i is derived from Equation (34) and then
multiplied by the standard deviation of the altitude of the total station si.
Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
35
The standard deviation of the altitude of the total station is the result of the error
in the measurement of the altitude and amounts to si = 1 mm.
Ii =
¶S k
s [ S 2 + 2R( H i - H l + i - l)]
×si =- i r
¶i
2S r R
(36)
Ii = 5.5 · 10–2 mm
The impact that the altitude of the reflector l has on the slope distance Sk calculated based on the known elevation between the endpoints is obtained when the
partial derivative upon the variable l is derived from Equation (34) and then multiplied by the standard deviation of the altitude of the reflector sl.
The standard deviation of the altitude of the reflector is the result of the error in
the measurement of the altitude and amounts to sl = 1 mm.
Il =
¶S k
s [ 2R( H i - H l + i - l) - S r2 ]
×sl = l
¶l
2S r R
(37)
Il = 5.5 · 10–2 mm
The impact that the elevation of the station Hi has on the slope distance Sk calculated based on the known elevation between the endpoints is obtained when the
partial derivative upon the variable Hi is derived from Equation (34) and then
multiplied by the standard deviation of the elevation of the station s H i .
The standard deviation of the elevation of the station is the result of the levelling
error and amounts to s H i = 20 mm.
IHi =
s H i ( l - i)
¶S k
× s Hi =
¶H i
Sr
(38)
I H i = 1.8 · 10–2 mm
The impact that the point elevation of the reflector Hl has on the slope distance
Sk calculated based on the known elevation between the endpoints is obtained
when the partial derivative upon the variable Hl is derived from Equation (34)
and then multiplied by the standard deviation of the point elevation of the reflector s H l .
The standard deviation of the point elevation of the reflector (32) is s H l = 36.9 mm.
IHl =
s H l ( i - l)
¶S k
× s Hl =
¶H l
Sr
(39)
I H l = 3.3 · 10–2 mm
The impact that the Earth’s radius R at the reference point has on the slope distance Sk calculated based on the known elevation between the endpoints is obtai-
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Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
ned when the partial derivative upon the variable R is derived from Equation (34)
and then multiplied by the standard deviation of the Earth’s radius sR.
The standard deviation of the Earth’s radius (14) is sR = 373.5686 m.
IR =
¶S k
s ( i + l) × S r
×sR = R
¶R
2R 2
(40)
IR = 9.5 · 10–6 mm
8.2. Standard Deviation of the Slope Distance Determined Based
on the Known Elevation between the Endpoints
The standard deviation of the slope distance Sk determined based on the known
elevation between the endpoints (34) is derived from the square root of the sum of
the squares of the impact:
• of the distance corrected for the additive constant I Sr determined according to
Equation (35),
• of the altitude of the total station Ii determined according to Equation (36),
• of the altitude of the reflector Il determined according to Equation (37),
• of the elevation of the station I H i determined according to Equation (38),
• of the point elevation of the reflector I H l determined according to Equation (39),
• of the Earth’s radius IR determined according to Equation (40).
s 2Sk = I S2r + I i2 + I l2 + I H2 i + I H2 l + I R2
(41)
s Sk = 5.3 mm
9. Conclusions
This paper shows, both theoretically and on a practical example, the impact of
accidental errors of parameters while determining geometric corrections of distances measured.
The measured distance used in the example had, after reductions for the meteorogical corrections, a standard deviation of 4.6 mm. After the geometric corrections
were entered, its standard deviation amounted to 5.3 mm. This means that the
standard deviation from the example was increased by 15.2% due to the input of
the geometric corrections.
This increase in the standard deviation is the result of the impact of the error of
the multiplication constant Iq = 2.6 mm. This means that while entering the geometric corrections, full attention must be paid to the multiplication constant and
its determination. The other influences are significantly lower (in the order of the
one-hundredth of millimetre), while some influences, such as the impact of the error of the elevation of the station and the impact of the error in determining the
Earth’s radius, are so small that practically it is not necessary to take them into
consideration while processing the distances measured during daily engineering
work.
Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
37
The determination of geometric corrections for the measured distances could be
significant when performing a critical engineering task in which highly accurate
measured distances are desired. This primarily refers to deformation monitoring
in highly complicated terrain sites where accessibility is impossible. The equations shown enable simple implementation within appropriate software and the
successful determination of the standard deviation of a measured distance, for
which the geometric corrections had been determined, and this paper could serve
as a general guideline for surveying professionals.
The equations, however, also enable the inverse procedure, or to be precise, they
enable the a priori definition of the precision required for the measurement of auxiliary parameters in order to keep the total standard deviation of distances within permissible limits. Knowledge of the impacts enables their practical implementation during the optimization of distance measurement for achievement of
the specified precision. The detection of the impacts that significantly affect the
precision of the distance corrected for geometric sources enables the required precision of the measurement of auxiliary parameters to be defined, which bring
such corrections to light.
References
Dzierzega, A., Scherrer, R. (2003): Measuring with Electronic Total Stations, Survey
Review, 37 (287), 55–65.
Dapo, M., Zrinjski, M. (2004): Underground Geodetic Basis of the Tunnel ''Mala Kapela'', Geodetski list, Vol. 58 (81), No. 2, 117–132.
Hashemi, K. S., Hurst, P. T., Oliver, J. N. (1994): Sources of Error in a Laser Rangefinder, Review of Science Instruments, 65 (10), 3165–3171.
Kogoj, D. (2005): Merjenje dolin z elektronskimi razdaljemeri, Fakulteta za gradbeništvo in geodezijo, Oddelek za geodezijo, Ljubljana.
Mrkiæ, R. (1991): Geodetska metrologija, Nauèna knjiga, Beograd.
Rüeger, J. M. (1996): Electronic Distance Measurement: An Introduction, Springer-Verlag, Berlin/Heidelberg.
Saastamoinen, J. (1964): Curvature Correction in Electronic Distance Measurement,
Bulletin Géodésique, 73 (1), 265–269.
Schofield, W., Breach, M. (2007): Engineering Surveying, Imprint Butterworth-Heinemann, Elsevier, UK.
Zrinjski, M. (2010): Defining the Calibration Baseline Scale of the Faculty of Geodesy by
Applying Precise Electro-Optical Distance Meter and GPS, PhD Thesis, Faculty of
Geodesy, University of Zagreb, Zagreb.
Zrinjski, M., Dapo, M. (2010): Geodetic Basis of the Longest Tunnel in the Republic
of Croatia, Survey Review – Directorate of Overseas Surveys, Vol. 42, No. 318,
345–358.
URL 1: Milivoj Vuliæ, Distance reductions,
http://www.geo.ntf.uni-lj.si/mvulic/udf/Distance_reductions.xla, (23.03.2009).
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Medved, M. i dr.: An Analysis of the Impact of Errors Occurring …, Geod. list 2012, 1, 21–38
Analiza utjecaja pogrešaka pomoænih velièina
pri odreðivanju geometrijskih popravaka duljina
SAETAK. Rezultati mjerenja duljina optereæeni su sustavnim i sluèajnim pogreškama. Utjecaj sustavnih pogrešaka smanjuje se ili eliminira najèešæe unošenjem odgovarajuæih popravaka ili metodom mjerenja. Veliki broj razlièitih izvora popravaka
moe se podijeliti u tri skupine, i to: meteorološke, geometrijske i projekcijske popravke. U ovom radu obraðene su samo geometrijske popravke. Odreðivanje geometrijskih popravka i eliminiranje njihovih utjecaja iz rezultata mjerenja zahtijeva poznavanje ili mjerenje razlièitih pomoænih velièina. Pomoæne velièine su, takoðer, optereæene sluèajnim pogreškama koje prema zakonu o rasprostiranju pogrešaka utjeèu i
na toènost duljine popravljene za geometrijske popravke. Ovo su opæe poznate èinjenice, ali iz autorima nepoznatih razloga, problematika izloena u ovom radu nije do
sada tretirana u struènoj literaturi. U radu je prikazana analiza utjecaja pomoænih
velièina na toènost mjerene duljine koja je popravljena za geometrijske popravke.
Poznavanje toènosti ovako popravljene duljine je vano, jer su navedeni utjecaji svakodnevno prisutni pri realizaciji geodetskih zadataka iz podruèja preciznih geodetskih mjerenja, kao i pri umjeravanju elektronièkih instrumenata za mjerenje duljina. Takoðer, prikazan je i detaljan primjer raèunanja utjecaja geometrijskih izvora
i njihovih standardnih odstupanja na toènost elektronièki izmjerene duljine. Stoga,
rad moe posluiti i kao detaljne, opæe upute za svakodnevnu profesionalnu primjenu prilikom preciznih mjerenja duljina.
Kljuène rijeèi: elektronièko mjerenje duljina, geometrijske popravke, standardno
odstupanje.
Primljeno: 2011-05-25
Prihvaæeno: 2012-02-22
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
39
UDK 528.4:347.214.2:332.74:510.6:519.86
Struèni èlanak
The Application of Intelligent Techniques
for Massreal Estate Appraisal
Miroslav KUBURIÆ – Subotica1, Goran ÆIROVIÆ – Belgrade2
ABSTRACT. The paper reviews the concept of mass appraisal of real estate, within
which, besides defining the basic concepts, a comparative analysis is carried out of
different international experiences related to this issue. The normative and institutional order of the subject area is analyzed in a test area, while the concept of evaluating spatial units as a base of massreal estate appraisal and the field of their use are
also defined. The essence of a valuation model of spatial units is defined, based on
the principle of case based reasoning (CBR) and logical aggregation (LA), and the
mathematical basis for the proposed model is given for anticipating the average price
of real estate within spatial units. In the proposed model, spatial units are described,
that is, the method of their normalization and their granulation into groups. Individual attributes and groups are allocated appropriate weight by which their individual and group significance are defined within the framework of the integral model,
and finally, testing of the model was carried out in a test area.
Keywords: evaluation of spatial units, mass appraisal of real estate value, case-based reasoning, logical aggregation.
1. Introduction
One of the fundamental reasons for establishing cadastral records, and thus the
generator of geodesy, is the objective and fair administration of tax policy. From
its conception to the present, the national spatial data infrastructure is one of the
most important factors in the implementation of this policy. Adjusting to the real
needs of their users, without deviating from their basic principles, cadastral records, particularly in developed countries, are constantly evolving. Valuing real
estate is one of its attributes which has been expanding more and more in recent
years.
1
Miroslav Kuburiæ, PhD, Geod. Eng., Faculty of Civil Engineering Subotica, University of Novi Sad, Kozaraèka
2a, RS-24000 Subotica, Serbia, e-mail: [email protected],
2
Prof. Goran Æiroviæ, PhD, Civ. Eng., Faculty of Technical Science, University of Novi Sad, Trg Dositeja Obradoviæa 6, RS-21000 Novi Sad, Serbia, e-mail: [email protected]
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Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
Real estate in the development of human civilization also has particular significance and can be considered as multi-spectral. Ownership of land or buildings, or
their use, has a direct existential connection with their owner. That connection is
often materialized as a relationship with the historical past or family inheritance,
existential security, or position.
Alone its value is, in broad terms, the monetary value which the real estate can
make on the market at the moment of its sale, and on the other hand it is the total resulting value of all of the most significant attributes that affect its value.
Astronomical leaps and unexpected collapse of the real estate market are just a
few of the factors which support the thesis that real estate value is an integral
function of the value of its attributes, some of which often remain unknown even
to the greatest experts.
One of the preconditions to successfully modelling the process of mass appraisal
of real estate value is defining the field of its application, and selecting the criteria and methodology for the appraisal are directly related to the size of its domain. Namely, the greater the population of buildings for the mass appraisal, as a
result of the expansion of its field of application, the more complicated and complex the number of criteria, the methodology and the modelling become. Hence,
the integral model must be broken down into its own subsystems, in order for it
on one hand to be universally applicable, and on the other hand, to a model which
not only recognizes the relevant attributes of each property being valued, but also
assigns characteristics to the area in which that property is located.
The universal model of mass appraisal of real estate value in a particular country
must in essence be functional, practically applicable, consistent and adaptable to
the real conditions and trends in the real estate market. It must also recognize all
relevant factors which influence the price of real estate in each spatial unit, and
at the same time preserve all of the essential features of that area and use them
in the process of determining the average price of real estate within it. Thus, one
important task in modelling the mass appraisal of real estate is assessing the influence of an area on the real estate within it, as well as describing the given area
with a sufficient number of attributes in order to determine the relation between
the values of these attributes and average property prices in each spatial unit.
By describing the middle set of attributes, and using the known data on the average prices of property within it, a base of known cases can be formed–knowledge
that will serve as a standard for pricing properties in any area, which can also be
described by means of an identical set of attributes. Using logical aggregation or
aggregate measures of similarity, that is by determining the measure of similarity
between the assessed spatial units and representatives from the list of known
cases, the most likely value of the average price of real estate can be anticipated.
Namely, we can consider an aggregate measure of similarity as a point in n-dimensional real vector space, where the distance of the rectangular projection
point from the point of origin for each axis is equal to the value of a partial measure of similarity for each attribute. On the basis of the distance from the point of
origin, the overall measure of similarity to the list of known cases for the spatial
unit concerned can be determined, and on the basis of the measure of similarity,
the average price of property within it can be anticipated.
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
41
Based on analysis of the real estate market, on the national spatial data infrastructure and on relevant data from other sources, it is possible on one hand to
assess the value of some spatial units for all of the defined attributes, and on the
other hand on the basis of the market to define the average price of property in it.
On the foundation of this data a database of knowledge can be formed, or a base
of known cases which can still be used for anticipating the price of property in
other spatial units. Namely, by using interpolative Boolean algebra and logical
aggregation as aggregation operators for measuring similarity, one or more similar spatial units are found on the basis of the input data values of all attributes,
based on predefined criteria, the average prices of which are used as a basis for
anticipating the most probable average price of property in a given spatial unit.
Valuation of property usually takes place in developed market economies, and
Serbia, realistically, is only at the beginning of this. Methodological inconsistency,
institutional conflict and uncoordinated jurisdiction are only some of the characteristics which inevitably imply the previous statement for the test area.
The field of application of the assessment results is a multidimensional space using this information mostly for economic purposes. Providing funding, investment decision making, statistical or financial reporting, making business decisions, legal practice, business insurance and implementation of fiscal policy are
just some of the areas for which estimating real estate value provides data, on the
basis of which important and often difficult decisions are made. The concept of
market value is as difficult to unambiguously define a show well the procedure for
estimating suitable real estate is performed.
2. Models of Mass Appraisal of Real Estate Value
As with most estimates that a man makes each day, so it is with estimating the
value of real estate. Behind the overall rating which is defined either numerically
or semantically (linguistically), in fact, hides, a multi-criterial analysis and the
optimization of different criteria. Although the individual is not usually aware of
them, and although they would be hard to define, the criteria taken into account
on that occasion are not only numerous, but in this thinking process their ranking is also carried out. However, an attempt to carry out an objective estimate in
one thinking process on the basis of different criteria would more often than not
be futile without some of the known methods of operational research – soft computing – that is, artificial intelligence.
The number of criteria on the basis of which to describe or estimate a property is
very large, and together they are intended to represent their constructional, economic, social, ecological and other aspects. We are contemporaries of the fact that
not only for the time function but also for the location, the evaluation criteria are
subject to certain modifications, that is, adapting the basic requirements of the
average buyer on the property market.
It is not surprising that buildings which are identical in terms of their technical
construction criteria have different market values in different locations. There
are also places or even regions which, because of their basic economic, demographic, sociological and other characteristics have identical real estate values for
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Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
similar properties. Looking only through the prism of estimation, and frequency
of operation, supply and demand, and therefore the price of real estate show that
there are other relevant criteria that significantly influence the value, which will
be discussed in the following consideration.
It is also important to emphasize the fact that certain features that affect property value in one place may be irrelevant in another place. For example, if a populated area is near a highway, by means of which it has a good connection with a
major national or international road corridor, the value of land in its vicinity directly relates to its distance from that highway, a potential factor which can justify investment in it economically. However, if there is no such traffic route in the
vicinity of a populated area, then it is an irrelevant criterion for all property in
that area. A similar example can be given for the water, rail, sport recreation, spa,
air and educational facilities which characterize or do not characterize a place.
2.1. Cost method
One of the basic principles of this methodological approach is to determine the objective price, that is the cost of building the property, that is replacement theory.
The logical foundation of this approach is reflected in the statement that the uninformed buyer in the open real estate market could pay a higher price for a property than the actual cost of its construction. It can be seen immediately that in
this methodological approach the time factor is neglected, as well as many other
components, some of which can and others which cannot be defined quantatively,
that is in terms of currency units, and which would definitely be used up during
its construction, and fictively miss the profit from the eventual use of the existing
building.
Bearing in mind its basic methodological approach, the cost method can be considered as effective when estimating the value of newly constructed buildings or
buildings which are not affected by the time factor, or for buildings whose exploitation period does not have to be considered as a component that affects its depreciation. This method could also be considered as suitable when estimating property for which it is difficult to assess the benefit gained from its being rented out,
or for cases in which the assessor does not have all the information about the cost
of similar or identical properties in the locality, that is, when it is impossible from
the base of known cases to find any kind of analogy with the property in question,
and on the basis of that draw a conclusion about its value.
The cost method is used for estimating industrial, agricultural and other real estate, as well as being the dominant and only method for state administration procedures and court proceedings (Miladinoviæ 2009).
2.2. Mass appraisal of real estate value
Consistently following the basic idea of establishing cadastral records and the corresponding requirements of modern society where real estate is a very important
aspect of everyday life, the modern cadastral records of developed countries across
the whole world are introducing models of mass appraisal (mass estimation) of
real estate within the framework of their everyday activities (Miladinoviæ 2009).
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
43
Modern technical and technological developments, the development of information technology in the administration of large amounts of data in real time, modern methods of acquiring large amounts of good quality and relevant geospatial
data, operational research methods, artificial intelligence and multicriteria optimization have created the necessary preconditions for the mass appraisal of real
estate value.
Georeferencing a large amount of heterogeneous spatial data, its statistical quality control, as well as relational searches within geoinformational systems have
only further accelerated and facilitated the application of mass appraisal of real
estate, made opportunities in the functioning of tax administration and facilitated
its connection with other public bodies.
The intention of implementing of tax policy in modern society is that taxation on
the basis of property ownership is based on determining the actual, objective market value in the shortest possible time period. One of the requirements is also for
the best possible quality control methodology on the basis of statistical evaluations, as well as the need for a flexible and universal system, practically applicable for the implementation of fiscal policy.
Mass appraisal finds its role primarily in forming initial or reference values, while
the methodology of individual estimates is used to survey the peculiarities and
characteristics of a particular property in order to define its real value, which
serves as the tax base. For quality and objective implementation of fiscal policy,
in addition to the qualitative methods of mass that is individual estimation, an
indispensible component is the administrative skill necessary for managing the
human and physical resources of the tax department and the quality assurance at
every level of the mass appraisal process.
One of the fundamental differences between mass and individual appraisal is that
the mass model has to examine the wider context and defines the characteristics
which influence the formation of real estate values over a larger area. Thus, appraisal refers to group rather than to individual properties, and the task of the assessor is to identify and recognize the common features of a large number of properties, that is, he must be capable of developing, supporting and explaining standardized adjustments to the model of appraisal, as well as using class, type of
building, environmental and other groups of real estate.
The next important difference between these two methods is that the quality control of the appraisal results is carried out in different ways. Namely, individual
estimates relate to a specific property which an individual or a small group of individuals are interested in, the result of which can be compared with the research
or analysis for similar, that is, comparable sales of similar property.
For mass appraisal, quality testing is carried out using statistical methods. The
subject of mass appraisal is a larger amount of real estate, and therefore the number of interested clients is larger – tax payers, who must on one hand be satisfied
or at least unharmed, and on the other hand the model must be consistent and
universally applicable throughout the whole area in which the tax policy is implemented under the auspices of an identical legal framework.
Unlike individual appraisal, it is almost impossible in this day and age to consider
the methodology of mass appraisal without computer support. It not only reviews
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Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
relevant criteria more objectively in a wider context, but is also fast and efficient
in its application and has effective control over its implementation as well as being reliable in the results of the model applied.
The mass appraisal system, whether computerized or manual, consists of four
subsystems:
1.
2.
3.
4.
Data management system
Sales analysis system
Appraisal system
Administrative system.
The four subsystems are interdependent. The appraisal system, for example, uses
information held in the sales analysis system, and the data management system
produces output documents necessary to the administrative system for printing
tax bills.
In Serbia, the Law on State Survey and Cadastre envisages the introduction of
mass appraisal of real estate, which should be an extremely significant event in
this area and one which will give the initiative to regulate the other aspects of appraisal according to the regulations. Training personnel and establishing an association of appraisers and other institutions are tasks that lie ahead on the road to
systematic and institutional regulation of this very important area.
3. Evaluation of Spatial Units based on CBR and LA
One of the goals of the scientific research in this paper is the recognition of the
relevant features, that is, criteria of spatial units which affect the formation of
the average price of real estate within them. The intensity or value of each of
them speaks of the value of that locality from the aspect of the criterion in question, and the integration of all the individual values gives the total value.
A very important problem in determining the level of similarity is the aggregation
(fusion) of a number of attributes into one globally representative aspect – the
measure of similarity. In existing practice, the most commonly used method for
summing up the weight coefficients of partial aspects is the aggregation technique. This approach is additive, and for all cases which are not additive, it is inadequate. For example, using a weighted sum for aggregation, even in cases with
only 2 attributes (a, b), does not allow realization of the natural need for a requirement in which both attributes are important together. Among those who
study the multi-attribute decision making method, this problem is known and as
a solution, the theory of capacitance, known in the “phase-community” as phase
measures and phase integrals (Mirkoviæ et al. 2006).
In this kind of approach, additivity is a “relaxed” monotonicity for which
additivity is a special case. As a result, the range of possible applications for this
approach is considerably broader, however from a logical point of view, monotonicity still remains a strongly limiting factor, since many logical functions by
nature are not monotone. The generalized discrete Choquet integral is defined for
a general measure – non monotonicity in general. This approach includes all logical and pseudo-logical functions, but allows the use of only one arithmetic opera-
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
45
tor for interpolation purposes – the min function. Interpolative realization of
Boolean algebra (IBA) includes all logical functions and all interpolative operators (operators of a generalized product) (Mirkoviæ et al. 2006).
The proposed model, therefore, on the basis of measures of similarity between
cases (spatial units) for which the average values of real estate are determined
and representatives from the base of known cases anticipate the most likely average price. Measures of similarity are a type of evaluation function which transfers
(maps) an abstract concept into a numerical value i.e. joins values together in a
series of pairs, with the idea that a higher value indicates greater similarity, and
that value is an aggregated, composite size.
Similarity, as a complex quantity, can be expressed by means of unique values
which are reached by the aggregation of partial measures of similarity (for each of
the selected attributes-criteria). The possibilities of the logical aggregation model
extend the framework of the existing model. In most well-known models, only
trivial attributes are used, without interaction between them (without the use of
logical functions). Also, for the aggregation operator, most commonly just a normal product is used.
The logical aggregation model is generalized to allow the use of logical functions
between attributes (from a finite set of possible functions for a finite number of
attributes), as well as the use of different aggregation operators and different
generalized products–subclasses of T-norms with the full axiom of non-negativity
(Radojeviæ 2006).
In addition, a measure of aggregation does not have to be either additive or monotone. Determining partial measures of similarity is a trivial task for the evaluator, since there are references for comparisons performed in one-dimensional
space for the values of each individual attribute, so expert knowledge is not necessary in the way that it is for absolute (primary) evaluation.
The implementation of logical aggregation is possible within the concept of CBR
in the phase of aggregating the data–determining the measure of similarity.
3.1. Model based on the Concepts of CBR and LA
Matrix O represents the knowledge base which consists of the spatial units – prototypes for which the average property prices in them are known. Thus, the cases
consist of a set of attributes whose values are information carriers about the
problem and corresponding average prices, and is the information carrier regarding the solution to the problem. Each prototype O j represents a case – a vector
which consists of normalized attribute values aij Î [ 0 1], and the average price of
real estate c j. The case index is j. The attributes are defined as:
$O j"aij, i Î (1, ¼ k)
(1)
For determining the average price in spatial unit Ox it is necessary to normalize
the attribute values in the same way as was done in the knowledge base. Then the
measure of similarity m j is determined with prototypes from the knowledge base.
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Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
The measure of similarity is an aggregate size. It is a result of the aggregation of
individual (partial) similarity measures for each attribute separately.
A partial measure of similarity is actually a measure of logical equivalence. An appropriate aggregation for the values of similarity measures is:
m ij = ( aij Û aix ) Ä = [( aij Ç aix ) È (Caij Ç Caix )]Ä = 1 - aij - aix + 2aij Ä aix
Ä := min (2)
Since this is aggregation of the same attribute (high positive correlation), for a
generalized product, we use the min function. The aggregation operator carries
out mapping:
Aggr:[ 0, 1]2 ® [ 0, 1]
(3)
The total similarity measure m j is gained by aggregating partial (per attribute)
measures of similarity:
m j = (Çki=1 m ij) Ä = Õi=1 m ij, Ä := +
k
(4)
Since this is aggregation of different attributes (negligible correlation), for a generalized product we use an ordinary sum. The aggregation operator carries out
mapping:
Aggr : [ 0, 1]i ® [ 0, 1]
(5)
There is a possibility of allocating weight coefficients wi to partial similarity measures m ij. A relevant total measure of similarity is then determined by the expression:
k
m j = å wi m ij;
i=1
k
å wi = 1,
i=1
wi ³ 0,
i = 1, ¼ k
(6)
There remains an open possibility of aggregating a hybrid-mixed type as required
using interpolative pseudo-Boolean polynomials. The most similar prototype
O j Î O with Ox is the one with the highest value of similarity measure m j:
$Ox "c j Î O j, O j Î O where j is chosen for m j = max
(7)
In this way, the value of the average property price is taken for a spatial unit
(case) from the knowledge base which is most similar to the input case, for which
we want to find the average price. Then these price values are assigned to the
case, the average price of which is required.
3.2. The mathematical basis for the suggested model of evaluating spatial units
The mathematical model suggested on the basis of scientific research within the
framework of this doctoral dissertation is based on the principle of case-based
reasoning in which a combination of logic and the Euclidean (L2) norm are used.
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
47
Namely, anticipation of the average price values of real estate within the framework of a spatial unit is realized on the basis of aggregate measures of similarity
between the spatial unit for which it is carried out and representatives from the
base of known cases – knowledge. Aggregate similarity measures are the integration of individual – of partial measures of similarity for each of the attributes that
describe all of the cases, and in this case a partial similarity measure is a measure
of logical equivalence. As indicated above, an appropriate aggregation operator for
the value of similarity measures is:
m ij = ( aij Û aix ) Ä = [( aij Ç aix ) È (Caij Ç Caix )]Ä = 1 - aij - aix + 2aij Ä aix ; Ä := min (8)
The total – the aggregated measure of similarity can be represented as point (O j)
in n-dimensional real vector space, where the distance of the rectangular projection point from the point of origin for each axis is equal to the value of partial
similarity measures for each of the attributes.
Using the Euclidean norm as an aggregation operator for measures of similarity actually
calculates the measure of distance of point (O j) from the point of origin as follows:
[
r j = åi=1 m ij
k
1
2 2
]
where k is the number of attributes
(9)
In the proposed model there also remains the possibility of allocating weight coefficients to each of the squares of partial measures of similarity m ij. Then the distance is defined with:
[
1
]
r j = åi=1 m ij wi 2 ; where:
k
2
k
å wi = 1, wi ³ 0, i = 1, ¼ k
(10)
i=1
Then the value of the total similarity measure is equal to the value of the logical
negation of the distance.
m j = (Ør j) Ä = 1 - r j
(11)
The most similar prototype O j Î O with Ox is the one with the greatest value of
similarity measure m j, while the greatest value of similarity measure takes the
case where the distance from the points ri j is the least.
Under the proposed model for every new case (spatial unit) which is valued, from the
knowledge base an already known case is found to which it is most similar. As described above, the similarity measures will be normed values from the interval [0.1].
However, the question is which measure of similarity is a border case for which it
can be said that a known case from the knowledge base can be used to anticipate the
average price values of real estate for the case being assessed. Within the framework
of the proposed model, in this doctoral dissertation, a minimal value of similarity
measures of 0.8 is adopted. According to this, the principle is kept by which, on the
basis of total measures of similarity, it is not necessary to find the most similar case,
but rather in determining the average price value of real estate within the frame-
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Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
work of evaluating spatial units, all known cases are used which, when evaluated,
have a total similarity measure greater or equal to the given border values.
The estimated average value of real estate prices within the framework of the assessed spatial units is not only a simple arithmetic mean of the average prices for
known cases from the knowledge base whose measure of similarity with assessment are greater than or equal to the border values, but rather, it is proportional
to it. The anticipated value is achieved using the following formula:
PRICE = åi=1 price i
n
n
( m i - 0. 8)
; where w = å( m i - 0. 8)
w
i=1
(12)
n – the number of cases from the knowledge base whose total measure of similarity to the case under assessment is greater than or equal to the border value.
4. Quantitative Definition of Parameters
In any procedure of multi-criteria evaluation, it is necessary, above all, to define
the criteria on the basis of which the procedure will be carried out. Each of the
criteria can have appropriate values whether they are expressed numerically or
semantically. The value of each criterion represents a score, in this case, each
spatial unit from the aspect of the criteria used to evaluate it.
In order for the process of evaluation, that is, for the assessment of the value of
each individual criterion to be implemented, it is necessary for each of them to be
described, that is, to define the method for their evaluation. The criteria used in
this scientific research are selected on the basis of two basic postulates: to better
describe the spatial units being assessed from the viewpoint of the real estate
value within them, and for the data used to evaluate the attributes to be available
from a reliable source so that when applied to future models, the same source can
be used for the actualization and modification of the suggested model.
In creating a model of mass appraisal, the criteria for evaluating spatial units,
which, according to their nature, are classified into four basic groups, which are:
natural, social and economic characteristics, or criteria which can be considered
as a corrective factor in mass appraisal.
The basic concept of establishing this model is that on the basis of the values of
all criteria for each spatial unit, as a result of the estimation, a characteristic
number normalized from 0 to 1 is achieved, which is basically a value criterion,
that is, a ranked spatial unit which should correlate with the average value of the
real estate within it.
Each group of characteristics in itself has more individual criteria or sub-criteria,
the value of which is also normalized within the framework of each group in intervals from 0 to 1. In other words, the evaluation is decomposed into several layers, and for each of these layers, normalization is carried out using a “bottom up”
principle, until one spatial unit reaches a characteristic number.
For easier and more systematic presentation below, the sub-criteria used and the
method of their normalization in individual groups are described first, followed by
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
49
a presentation of the normalization of a characteristic number of spatial units as
a result of mass appraisal.
4.1. Natural Characteristics
Among natural characteristics are those which in any environment, a man’s life
and work should not be able to influence. For the purposes of the scientific research in this paper, the following natural characteristics are used as criteria for
the evaluation of spatial units:
1.1. The ecological aspect
1.2. Distance from the capital city
1.3. Geostrategic location
1.3.1. Transport corridors
1.3.2. Bordering countries
1.3.3. Natural resources.
By considering these criteria in a slightly broader context, it is possible to come
into conflict with the previous paragraph by stating that actually, man does indirectly influence these factors.
We are contemporaries of the growing impact man has on ecology, which is unfortunately mainly negative. The expansion of cities and migration from smaller
communities to large urban centres inevitably leads to huge expansion and over
time, a change in the distance between large centres and smaller communities
must be considered. If in this regard, technical and technological progress is
taken into account, then that physical distance or difference takes on another dimension. We are also contemporaries of the fact that at different time intervals
the concept of geostrategic position has often changed in our region, and therefore the importance of its influence through history has had different intensities.
The result of the assessment, that is, evaluation of spatial units with respect to
their natural features is a real number – a normalized value which takes a discrete value in the interval from 0 to 1.
A discrete value is obtained by breaking down the evaluation criterion from the
perspective of natural features into sub-criteria, as previously shown. Each of
these sub-criteria (ecological aspect, distance from the capital city and
geostrategic position), also as a result of the evaluation of the local environment,
has as a resulting normalized value in the interval from 0 to 1. Hence, the maximum value of each of these three sub-criteria is 1. The resultant from these three
sub-criteria is calculated as the sum of these three values which are assigned appropriate weight (coefficients) as shown in the Table 1.
Table 1. Decomposition of the criterion “natural characteristics”.
Criterion
Sub-criterion
1. ecological aspect
1. Natural characteristics 2. distance from the capital city
3. geostrategic location
Value
Coef.
[0,1]
0.15
[0,0.15]
[0,1]
0.5
[0,0.5]
[0,1]
Norm. Value.
0.35
[0,0.35]
Sum=1
Sum max =1
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4.2. Social Characteristics
The social characteristics of any spatial unit, as opposed to the natural ones, include all of those traits, that is, characteristics which greatly depend on the population and their activities in that area.
For the purposes of the scientific research in this paper it was necessary to distinguish those characteristics or criteria which, from the social aspect of a spatial
unit, affect the value of the real estate in it. In this respect the criteria used to estimate or evaluate a spatial unit in the suggested model are:
2.1.
2.2.
2.3.
2.4.
Population density
Increase in the number of inhabitants
The number of employed
The educational aspect.
The evaluation value for spatial units from the aspect of social characteristics or
criteria is a normalized value – a real number from the interval from 0 to 1, which
is obtained as the sum of the normalized values of the sub-criteria broken down
in the method previously shown.
Decomposition of social characteristics (criteria) into sub-criteria: population density, increase in the number of inhabitants, the number of employed and the educational aspect has the aim of evaluating a spatial unit in the best way possible to
give the most reliable evaluation that is to obtain the most objective evaluation
possible of their influence on real estate value.
The normalized value of each sub-criterion is given a corresponding weight which
defines the influence or importance of each sub-criterion within the total assessment of the criterion in question.
The method of decomposition and evaluation of the criterion “social characteristics” is shown in the following Table 2.
Table 2. Decomposition of the criterion “social characteristics”.
Criterion
Sub-criterion
1. population density
2. Social characteristics
Value
Coef.
Norm. Value.
[0,1]
0.15
[0,0.15]
2. inc. in no of inhabitants
[0,1]
0.05
[0,0.05]
3. number employed
[0,1]
0.4
[0,0.4]
4. educational aspect
[0,1]
0.4
[0,0.4]
Sum=1
Sum max =1
4.3. Industrial Characteristics
On similar way as previously presented in the procedure of evaluating spatial
unit it could be analysed industrial characteristics as well. The method of decomposition and evaluation of the criterion “industrial characteristics” is shown in
the following Table 3.
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
51
Table 3. Decomposition of the criterion “industrial characteristics”.
Criterion
Value
Coef.
Norm. Value.
1. average earnings
Sub-criterion
[0,1]
0.4
[0,0.4]
2. agricultural development
[0,1]
0.1
[0,0.1]
[0,1]
0.2
[0,0.2]
3. Industrial 3. GDP
4. road infrastructure
[0,1]
0.1
[0,0.1]
5. tourism
[0,1]
0.2
[0,0.2]
Sum=1
Sum max =1
5. The Results of Testing the Suggested Model
Within the framework of the scientific research in this paper, the suggested
model for evaluating spatial units was tested on a sample of 30 towns equally
spaced over the whole test area. The data used in testing the application of the
model was taken mainly from official statistical data from the Serbian Statistical
Office, or from other official public sources. It should also be noted that testing
was not based on any data from 2009 or 2010.
The reason for this fact is the greatest world economic crisis since the Second
World War, as a consequence of which were large fluctuations in the real estate
market, as well as significant oscillations in the prices of the same. Significant
price fluctuations are a direct consequence of this crisis, and not any other reason, whether economic, commercial or related to any other characteristic, and
which considerably influence the market price.
Another important reason lies in the fact that this period coincides with the adoption of a new planning and construction law in Serbia, which introduces significant
changes within this field. One of the consequences of these changes is a pronounced decrease in the dynamic of constructing new residential and commercial
buildings, partly due to slow and poor implementation of the law, and the non-existence of secondary legislation, and partly because of the mentioned economic crisis.
Also, one of the political decisions of the government of the Republic of Serbia,
that by stimulating construction and intensive building of “social” housing, the
prices of which will be significantly lower than the market value, it will revive its
own economy in a period of world economic crisis. This decision significantly affects the creation of real estate market prices, which can also not be treated as
usual market characteristics.
All of the above implies that using data from the real estate market from the past
two years would call into question the quality of the model. At the same time it
would burden the results with its use, as it relates to a very specific non-standard
period which significantly deviates from the legal principles which would otherwise apply under normal circumstances.
Below are the clearly presented results of the valuation of spatial units, as well as
the anticipated average values of a square metre of real estate in them. The principle established for the purpose of this scientific research is that on the basis of the
list of known cases comprising 29 places described by a set of attributes, the price
of a spatial unit being valued is based on the values of aggregate similarity mea-
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Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
sures between the spatial units in question and corresponding representatives from
the list of known cases. Visualization of the results achieved was carried out on
thematic maps of the test area, and is presented in concise tables. For the purpose
of presentation the results of this investigation in the paper the results of evaluating of the spatial unit Savski Venac, in the Table 4 and corresponding Fig. 1.
Table 4. The results of evaluating of the spatial unit Savski Venac.
Aggregate measures of similarity
No.
Town
Average
Social
Social
Natural
DEFINI
prices
Charac- Charac- CharacTELY
teristics teristics teristics
m-0.8
Price
1.
Novi Beograd
0.943
0.985
0.853
0.939
1557
0.139
464.4
2.
Zemun
0.909
1.000
0.928
0.961
1323
0.161
456.4
3.
Savski Venac
4.
Palilula
0.961
0.781
0.934
0.867
1339
0.067
191.5
5.
Subotica
0.509
0.852
0.725
0.757
643
–0.04
6.
Zrenjanin
0.568
0.679
0.772
0.688
620
–0.11
7.
Kikinda
0.453
0.718
0.719
0.674
582
–0.13
8.
Panèevo
0.744
0.816
0.844
0.811
770
0.011
9.
Apatin
0.478
0.267
0.828
0.536
534
–0.26
2347
10. Baèka Palanka
0.476
0.346
0.766
0.530
600
–0.27
11. Novi Sad
0.608
0.912
0.855
0.842
1000
0.042
12. Ruma
0.655
0.323
0.673
0.523
744
–0.28
13. Peæinci
0.689
0.256
0.721
0.533
560
–0.27
14. Šabac
0.600
0.662
0.695
0.660
707
–0.14
15. Ub
0.502
0.446
0.610
0.511
555
–0.29
16. Smederevo
0.659
0.417
0.837
0.619
560
–0.18
17. Veliko Gradište
0.451
0.674
0.593
0.611
586
–0.19
18. Aranðelovac
0.481
0.495
0.641
0.541
618
–0.26
19. Jagodina
0.555
0.924
0.715
0.801
570
0.001
20. Bor
0.505
0.671
0.729
0.660
400
–0.14
21. Sokobanja
0.483
0.543
0.668
0.573
850
–0.23
22. Bajina Bašta
0.394
0.233
0.690
0.448
790
–0.35
23. Ivanjica
0.550
0.273
0.592
0.450
760
–0.35
24. Raška
0.504
0.380
0.652
0.500
750
–0.30
25. Kruševac
0.531
0.674
0.730
0.666
602
–0.13
26. Niš
0.534
1.000
0.728
0.846
750
0.046
27. Blace
0.497
0.282
0.601
0.444
500
–0.36
28. Pirot
0.524
0.592
0.706
0.616
655
–0.18
29. Medveða
0.481
0.233
0.648
0.447
450
–0.35
30. Vranje
0.524
0.665
0.695
0.649
563
w =
17.58
90.00
1.10
74.17
–0.15
0.466
1295.3
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
53
Fig. 1. The thematic map of the results of evaluating of the spatial unit Savski Venac.
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Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
In Table 5 is a comparative presentation of the average price values in the spatial
units where the suggested model was tested. Also presented is a comparison of
the average market prices and the price obtained by anticipation or by applying
the suggested mathematical model, in which the percentage ratio of the same is
given.
Table 5. The results of testing of the proposed model of evaluating spatial units.
No.
Town
Average prices
Values from
the model
%
Increment the
price in %
5
1.
Novi Beograd
1557
1636
105
2.
Zemun
1323
1505
114
14
3.
Savski Venac
2347
1295
55
–45
4.
Palilula
1339
1393
104
4
5.
Subotica
643
648
101
1
6.
Zrenjanin
620
562
91
–9
7.
Kikinda
582
594
102
2
8.
Panèevo
770
1001
130
30
9.
Apatin
534
642
120
20
10.
Baèka Palanka
600
647
108
8
11.
Novi Sad
1000
1228
123
23
12.
Ruma
744
616
83
–17
13.
Peæinci
560
644
115
15
14.
Šabac
707
672
95
–5
15.
Ub
555
668
121
21
16.
Smederevo
560
632
113
13
17.
Veliko Gradište
586
689
118
18
18.
Aranðelovac
618
636
103
3
19.
Jagodina
570
717
126
26
20.
Bor
400
597
149
49
21.
Sokobanja
850
634
75
–25
22.
Bajina Bašta
790
601
76
–24
23.
Ivanjica
760
611
80
–20
24.
Raška
750
629
84
–16
25.
Kruševac
602
563
94
–6
26.
Niš
750
1038
138
38
27.
Blace
500
661
132
32
28.
Pirot
655
670
102
2
29.
Medveða
450
668
148
48
30.
Vranje
563
554
98
–2
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
55
As is evident from the above table, the proposed model of evaluating spatial units,
based on the concept of case-based reasoning using interpolative Boolean algebra
and logical aggregation, confirms the scientific hypothesis that the proposed
model enables the anticipation of the average price of real estate in the test area
which is in accordance with real (market) prices with a minimum amount of 75 to
80%, and it shows a very high level of agreement between market and anticipated
prices obtained from the model.
By thorough analysis of the presented results, it can be concluded that in individual cases, the suggested model gives results which deviate significantly from the
real (market) values, which will be cause for further explanation of these anomalies.
Savski Venac. Namely, one of the extremes which reflects the significant deviations is the example of the Savski Venac Municipality, whose anticipated average
property value of 1295 makes up only 55% of the real – market value which
amounts to 2347 euros. There are a number of real reasons for this kind of anomaly. One of these certainly lies in the fact that Savski Venac is the municipality
with the highest average property price in the test area, with prices significantly
higher than any in the test area. Because the proposed model is designed to anticipate a value based on measures of similarity with known cases from the knowledge base, that is, based on the value of the same cases, it is natural to expect
that such anomalies arise. In other words, a knowledge base should be created so
that each new unknown case is resolved on the principle of interpolation, since it
is natural that in this type of model, the principle of extrapolation does not result
in the desired outcome.
On the other hand, the specificity of Savski Venac, and other Belgrade municipalities, lies in the fact that the administrative division of Belgrade into municipalities cannot be treated in the same way as other cases in the test area. The division into municipalities, in this case more than in other cases, represents an administrative boundary, but not a boundary that represents a change in ambient,
conditions, quality, comfort, culture and lifestyle. By describing and consistently
evaluating urban municipalities with a set of defined attributes and having in
mind their territorial jurisdiction, it is very easy to arrive at significant errors in
the application of the model.
Such consistent application of the evaluation of urban municipalities would ignore the fact that, for example, an important international traffic route which
passes through the centre of Belgrade represents equal quality for all of the municipalities, although administratively speaking, that same traffic route passes
through only a few of them. We can also observe the example of rivers and
streams. The Sava and Danube rivers offer a great quality of life in Belgrade, and
regardless of their administrative belonging to particular municipalities they represent not only the pride but the value of the whole city. Also, no person would
say to the residents of a particular municipality that he lives in a place that is not
a university centre, even though the whole university infrastructure is located in
just a few municipalities.
Similar examples can be given for cultural historical monuments, important hotel
accommodation, cultural, administrative, religious, sport and other urban
centres. If we added to these facts the specificities of municipalities it could mean,
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Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
for example, that an important university centre in one municipality in a street
which is on its administrative border, is opposite the street to buildings that
are in another municipality which does not have such an institution. By
consistently applying the model, buildings situated several kilometres from
an important university centre, yet belong to that municipality, will have the
same value as buildings which have that kind of centre in their municipality,
and those who administratively do not belong to that municipality, but are only
a few steps from the important centre, will not have that quality, which is a more
than obvious anomaly which should be taken into account during the evaluation
process.
The example of Savski Venac hides a fact that is very important to take care of
and have in mind during valuation. Namely, it is the municipality where the most
attractive locations are situated, not only in Belgrade but in the whole of the test
area, whose average property prices do not represent a quantitative manifestation
of the quality of that property, but rather that the attractiveness of the location is
more important than the place of living. Ownership of property in these locations
speaks of the financial, sociological, civil or other status of the property owner, although by evaluating these locations according to a set of proposed attributes, the
results would not reflect this. For this kind of location, an additional quality is
the absence of everything which in any other place would make its quality. By analyzing the fact that in these locations there is no major infrastructure, or significant economic, administrative, retail, university, cultural or any other centre, it is
possible to arrive at errors related to the value of real estate in them. However, it
is only in large urban centres like Belgrade in which all that is “missing” in that
location can still be found in the vicinity, that such absence can be referred to as a
quality, since if all of there attributes could not be found within a reasonable distance, it would certainly not be considered as a quality. This can be seen in the
example of some naturally more attractive locations on the periphery of Belgrade,
where property prices are significantly lower and the location is not nearly as attractive.
Bearing all of this in mind in a model, particular attention should be paid to urban centres so as not to mislead a user into using the model literally, taking into
account only the administrative and territorial aspects of municipalities.
6. Conclusions
The proposed model is tested on a limited sample, with its results confirming a
high level of correlation between the market and anticipated average price values
of real estate in the subject spatial units. Also, the tested model indicates the need
for certain specifics of a local area to be taken into particular consideration, especially when some of the attribute values are extreme, and as such dominant in the
formation of the value of real estate within that area.
This model is a good basis for solving the comprehensive problem of mass appraisal of real estate values, and its mathematical base provides a consistent approach to problem solving at all levels and should therefore be modelled and used
Kuburiæ, M. i Æiroviæ, G.: The Application of Intelligent Techniques …, Geod. list 2012, 1, 39–58
57
at all levels in the formation of a comprehensive model of the mass appraisal of
real estate values.
Testing the model confirmed the hypothesis that it is possible to conceive a model
that, for the given input values of the attributes of spatial units, finds the most
similar from the knowledgebase–prototypes, and on the basis of them assesses the
most probable average value. If it does not find a value with the given measure of
similarity, it is capable of expanding the knowledge base with the given case, so
that over time, that base would become better and more reliable.
A model conceptualized in this way is consistent in everything with the basic assumptions of this scientific research and it should serve as a starting point in the
creation of a model of mass appraisal of real estate in the Republic of Serbia, and
as such it could be universally applicable, not only in the test area, but also in a
wider context.
This model, like any other should be periodically reviewed, that is, it must comply
with all relevant factors affecting the market value of real estate including
economic, commercial, sociological, ecological, security and any other factors.
Hence, the choice of relevant attributes in all models, taking into account the
differences both in dependence on the level of generality and in the classification
of real estate, should be considered in a time function. The proposed concept of
an operative model provides flexibility and the possibility of recognizing changes
in relevant criteria values that influence the value of real estate at a given
moment.
ACKNOWLEDGEMENTS. The work reported in this paper is a part of the investigation within the research project TR 36017 supported by the Ministry for
Science and Technology, Republic of Serbia. This support is gratefully acknowledged.
References
ASA (2008): Business Valuation Standards, American Society of Appraisers, Herndon.
Delibašiæ, B. (2007): Formalizing the process of business decision making, doctoral dissertation, The Faculty of Organizational Sciences, Belgrade University, Belgrade,
(in Serbian).
Kuburiæ, M., Æiroviæ, G. (2011): Model of valuation of spatial units based on case based
reasoning as a basis for mass appraisal of real property value, Proceedings of paper,
1st Serbian Geodetic Congress, Belgrade, 419–425.
Law on the establishment of cadastral income, RS Official Gazette, No 49/92, (in Serbian).
Law on Property Taxes, RS Official Gazette, Nos 26/01, 80/02, 135/04 and 61/07, (in
Serbian).
Law on State Survey and Cadastre, RS Official Gazette, No 72/09, (in Serbian).
Law on Ministries, RS Official Gazette, Nos 65/08 and 16/11, (in Serbian).
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Miladinoviæ, M. (2009a): Valuation of Real Estate, Faculty of Civil Engineering, Belgrade University, Belgrade, (in Serbian).
Miladinoviæ, M. (2009b): Valuation of Real Estate, Proceedings of the fourth summer
school of urban planning, Association of Town Planners of Serbia, Belgrade, Zlatibor, (in Serbian).
Mirkoviæ, M., Hodoliè, J., Radojeviæ, D. (2006): Aggregation for Quality Management,
Yugoslav Journal of Operations Research 16, Number 2, 177–188.
Radojeviæ, D. (2006): Boolean frame adequate for treatment of gradation or fuzziness
equally as for two-valued or classical case, SISY 2006, 4th Serbian – Hungarian Joint Symposium on Intelligent Systems.
Radojeviæ, D. (2007): Logical Aggregation Based on Interpolative Realization of Boolean
Algebra, Eusflat Conf. (1), 119–126.
Saaty, T. L. (1972): An Eigenvalue Allocation Model for Priorization and Planning,
Energy Management and Policy Center, University of Pennsylvania.
Saaty, T. L. (1977): A Scaling Method for priorities in Hierarchical Structures, Journal
of Mathematical Psychology, 15 (3), 234–281.
Watson, I., Marir, F. (1994): Case-Based Resoning: A Review, The Knowledge Engineering Review, Vol. 9, No. 4, 335–381.
Primjena inteligentnih tehnika za masovnu
procjenu nekretnina
SAETAK. U radu je razmatran pojam masovne procjene vrijednosti nekretnina
u okviru kojega se, osim definiranja osnovnih pojmova, izvodi i paralelna analiza
razlièitih meðunarodnih iskustava vezanih uz ovu problematiku. Takoðer, analizira
se normativna i institucionalna ureðenost predmetne cjeline na testnom podruèju,
ali se definira i pojam vrednovanja prostornih jedinica kao osnove masovne procjene
vrijednosti nekretnina i polje njegove primjene. Definirana je osnova modela vrednovanja prostornih jedinica temeljenog na zakljuèivanju po principu sluèaja (ZOS) i
logièke agregacije (LA) te je dana matematièka osnova predloenog modela za predviðanje prosjeènih cijena nekretnina u okviru prostornih jedinica. U predloenom
modelu opisane su prostorne jedinice, odnosno naèin njihove normalizacije te njihova granulacija po grupama. Pojedinim atributima i grupama dodijeljene su odgovarajuæe teine kojima se definiraju njihovi pojedinaèni i grupni znaèaji u okviru integralnog modela. Na kraju je izvedeno testiranje modela na testnom podruèju.
Kljuène rijeèi: vrednovanje prostornih jedinica, masovna procjena vrijednosti nekretnina, zakljuèivanja po principu sluèaja, logièka agregacija.
Primljeno: 2011-12-19
Prihvaæeno: 2012-02-27
Geod. list 2012, 1
VIJESTI
59
EUROPSKA UNIJA UVODI SLOBODAN PRISTUP JAVNIM PODACIMA
Europska komisija usvojila je još 2003. direktivu koja propisuje temeljna naèela dostupnosti, transparentnosti i granice troškova kako bi se osigurali uvjeti za komercijalnu ponovnu
upotrebu informacija iz javnog sektora. Prijedlog za izmjenu te direktive usvojen je 12. prosinca 2011. Tom izmijenjenom direktivom Europska komisija zalae se za slobodan pristup
javnim podacima za komercijalne i nekomercijalne namjene i poziva nacionalne vlade da
slijede njezin primjer. Izraz javni podaci obuhvaæa sve informacije koje tijela javne vlasti u
Europskoj uniji proizvode, prikupljaju ili plaæaju. To ukljuèuje geopodatke, statistièke i meteorološke podatke te podatke iz javno financiranih znanstvenih projekata i digitaliziranih
knjiga iz knjinica.
Bilo tko s pristupom raèunalu treba jednostavno i lako pristupiti slobodnim javnim podacima i ponovno ih upotrijebiti. Tijela javne vlasti, èesto i nenamjerno, oteavaju pristup podacima i njihovu ponovnu upotrebu. Npr. ponekad nedostaju informacije da neki podaci postoje i da su dostupni te gdje se nalaze. Ponekad su podaci u formatima koji su neprikladni
ili skupi za upotrebu. Prepreke su i komplicirani postupci licenciranja, naknade koje treba
platiti ili ponovna upotreba ogranièena na dravne tvrtke. Mora biti omoguæena i integracija podataka u nove proizvode i usluge kojima se svakodnevno koristimo, kao što su navigacijski sustavi u automobilima, vremenske prognoze ili druge korisne primjene u tzv. pametnim telefonima.
Zalaganje za slobodan pristup javnim podacima ima i svoje ekonomsko opravdanje. Primjeri
pokazuju da je uvoðenje slobodnog pristupa javnim podacima višestruko, pa i do 10 000%,
uveæalo broj njihovih korisnika. Time se takoðer višestruko, pa i do 1000%, uveæava prihod
od poreza na ponovnu upotrebu tih podataka. Tako prikupljeni prihod od poreza mnogo je
veæi nego je bio prihod od naknada na upotrebu podataka. Velièina trišta i rast geoinformacijskog sektora pokazuju potencijal javnih podataka kao motora za stvaranje novih radnih mjesta. Njemaèko trište geoinformacija u 2007. procijenjeno je na 1,4 milijardi eura,
što je poveæanje za 50% od 2001.
Usvajanje izmijenjene direktive oèekuje se najranije krajem 2012. Drave èlanice imat æe 18
mjeseci da slobodan pristup javnim podacima uvedu u svoje zakonodavstvo. Nema, meðutim, zapreke da bilo koje tijelo javne uprave i prije tog datuma uvede poboljšanja u pristupu
javnim podacima i njihovoj upotrebi koje uvodi navedena direktiva.
U 2012. Komisija æe postaviti internetski portal za svoje podatke. Predlae se drugim institucijama EU, tijelima i agencijama da im informacije budu dostupne preko tog portala kao
jedinstvenog pristupnog mjesta EU informacijama. U 2013. Komisija æe uspostaviti paneuropski portal okupljajuæi podatke iz razlièitih drava èlanica i europskih institucija.
Izvor:
News (2011): Europe Opens Access to Public Data, GIM International Newsletter, 13/12/2011,
http://www.gim-international.com/news/id6308-Europe_Opens_Access_to_Public_Data.html.
Nedjeljko Franèula
IZLOBA DJECA TEHNOLOGIJE: ELEKTRONIÈKA RAÈUNALA
U TEHNIÈKOM MUZEJU GRADA ZAGREBA
Izloba pod nazivom Djeca tehnologije: elektronièka raèunala odrana je od 21. prosinca
2011. do 26. veljaèe 2012. u Tehnièkom muzeju Grada Zagreba. Autori izlobe bili su Vesna
Dakiæ i elimir Kozlina. Autorica likovnog postava bila je Dinka Paveliæ, a autor multimedijskog postava bio je Bojan Gagiæ.
60
Vijesti, Geod. list 2012, 1
U izdanju Tehnièkog muzeja Grada Zagreba objavljen je i katalog izlobe pod nazivom Djeca tehnologije: elektronièka raèunala (ISBN 978-953-6568-40-6), (slika 1).
Slika 1. Katalog izlobe – Djeca tehnologije: elektronièka raèunala.
Katalog izlobe obuhvaæa 108 stranica u kojem se navodi popis 114 izloaka s 49 slika u
boji. Urednica kataloga je Vesna Dakiæ, autor tekstova je elimir Kozlina, recenzent je
Draen Æika, a lektorica je Saša Vagner. Sadraj kataloga izlobe podijeljen je u sljedeæa
osnovna poglavlja:
1.
2.
3.
4.
5.
6.
7.
8.
9.
30 godina osobnog raèunala IBM-a
Pioniri današnjih raèunala
Elektronièka raèunala u Drugom svjetskom ratu
Poluvodièki materijali
Razvoj tehnologije poluvodièkih materijala
Otkriæe tranzistora
Shockley i silicijski NPN-tranzistor
Otkriæe integriranog sklopa
Prva komercijalna raèunala
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Vijesti, Geod. list 2012, 1
10.
11.
12.
13.
14.
15.
16.
17.
18.
Miniraèunala
Intel i prvi mikroprocesor
Prva osobna raèunala
Operacijski sustavi za osobna raèunala
Prièa o revoluciji amerièke jabuke
Što je elektronièko raèunalo
Osobno raèunalo IBM-a
Mooreov zakon
Širenje informatièkih znanja
Kako bi se dobio uvid o vanosti takve izlobe, navodimo saetak kataloga u cijelosti: Raèunala su naši suvremenici. Nastala su i razvijala se skupa s nama. Dok nas je prije zanimalo
od kojih se dijelova raèunalo sastoji i kako radi, današnji su korisnici više usmjereni na
moguænosti i naèin rada programa kojima se koriste, a manje na to kako raèunalo radi.
Zato raèunalo danas svatko gleda na svoj naèin: netko kao igraèku, netko kao pomoæ u poslu, a za nekoga je raèunalo osnovno sredstvo za rad. Izlobom se eli pokazati što su raèunala, od èega se sastoje i kako je tekao tehnološki razvoj. eli se pokazati ono što je pomalo
zaboravljeno, a mlaðim je korisnicima i manje poznato.
Povod za organizaciju izlobe je 30 godina od objave prvog osobnog raèunala IBM-a. Izloba
ima cilj skrenuti pozornost na èinjenice vezane uz nastanak i tehnološki razvoj, posebno današnjih osobnih raèunala. Slijedom tehnološkoga razvoja prikazani su dijelovi raèunala
koji su s vremenom postajali sve manji i sve uèinkovitiji. Naposljetku imamo raèunala mase
samo nekoliko kilograma koja su neusporedivo uèinkovitija od raèunala Eniac mase 30
tona, koje je zapremalo površinu od 120 m2.
Nekoliko izloaka treba posebno navesti jer se inaèe rijetko mogu vidjeti. Meðu njima je magnetski bubanj, naprava kakva je sluila kao vanjska raèunalna memorija prvoga komercijalnog elektronièkog raèunala. Izloena je i komunikacijska oprema koja je posluila za
uspostavu prve internetske veze u Hrvatskoj. Na izlobi je i prvo osobno raèunalo IBM-a.
Sjetit æemo se i raèunala koja su razvijena i proizvedena u Hrvatskoj i na podruèju bivše
drave na kojima smo stjecali prva praktièna informatièka iskustva.
Mladen Zrinjski i Boidar Kanajet
MAGISTRI INENJERI GEODEZIJE I GEOIFORMATIKE
Na Geodetskom fakultetu Sveuèilišta u Zagrebu, dana 9. prosinca 2011., 10. veljaèe i 24.
veljaèe 2012. godine, na sveuèilišnome diplomskom studiju geodezije i geoinformatike diplomiralo je ukupno 11 pristupnika i time stekli akademski naziv magistar inenjer geodezije i
geoinformatike, odnosno magistra inenjerka geodezije i geoinformatike.
Pregled magistara inenjera geodezije i geoinformatike:
Pristupnik
Naslov diplomskog rada
Teo Baldasar
“Praæenje sjevernoatlantske struje iz podataka
ARGO-a”
Martina Bolanèa
“Prostorna analiza zona zelenila u Kutini”
Ilija Margaretiæ
“Izrada informativne internetske interaktivne karte
za studente Sveuèilišta u Zagrebu”
Bojan Petkoviæ
“Odreðivanje horizontalnih (2D) i visinskih (1D)
pomaka HE Ðale”
Datum obrane, mentor
09. 12. 2011., prof. dr. sc. Siniša Masteliæ Iviæ
09. 12. 2011., prof. dr. sc. Siniša Masteliæ Iviæ
09. 12. 2011., doc. dr. sc. Robert upan
09. 12. 2011., prof. dr. sc. Brankica
Cigrovski-Deteliæ,
dr. sc. Mladen Zrinjski
62
Domenika Beg
“Izrada posebne geodetske podloge i problemi
koji se pri tome pojavljuju”
Mario Katièiæ
“Analiza hidrografskih mjerenja korita rijeke Drave
i Kupe”
Daria Kolak
“Kriteriji izrade elaborata PGP-a
za Šibensko-kninsku i Zadarsku upaniju”
Ines Košpo
“Komasacija dijela k. o. Stari Grad”
Ivan Nikolac
“Uspostava geodetske osnove za odreðivanje
vertikalnih pomaka Starog mosta u Sisku”
Jelena Petroviæ
“Satelitske misije CHAMP, GRACE i GOCE”
Tina Smoljan
“Uporaba programskog paketa Pointools u obradi
skeniranih objekata”
Vijesti, Geod. list 2012, 1
10. 02. 2012., prof. dr. sc. Mira Ivkoviæ
10. 02. 2012., doc. dr. sc. Almin Ðapo
10. 02. 2012., prof. dr. sc. Brankica
Cigrovski-Deteliæ
10. 02. 2012., prof. dr. sc. Siniša Masteliæ Iviæ
10. 02. 2012., prof. dr. sc. Gorana Novakoviæ
10. 02. 2012., prof. dr. sc. Tomislav Bašiæ
24. 02. 2012., doc. dr. sc. Almin Ðapo
Kratica za ovaj akademski naziv je: mag. ing. geod. et geoinf.
Èestitamo novim magistrima inenjerima geodezije i geoinformatike.
Mladen Zrinjski
DIPLOMIRALI NA GEODETSKOM FAKULTETU
Na Geodetskom fakultetu Sveuèilišta u Zagrebu, od 12. studenoga 2011. do 24. veljaèe
2012. godine, na sveuèilišnome dodiplomskom studiju geodezije diplomiralo je ukupno
19 pristupnika.
Pregled diplomiranih inenjera geodezije:
Pristupnik
Naslov diplomskog rada
Tomislav Bakoviæ
“Morsko-tehnièke konstrukcije”
Tihana Gripariæ
“Primjena GPS-a za potrebe izrade PGP-a”
Damjan Ivšak
“Blizupredmetna fotogrametrija u zaštiti spomenika
kulture”
Zlata Kljajiæ
“Terestrièko lasersko skeniranje utvrde Tureta”
Tomislav Mirkoviæ
“Izrada tematske karte Brodsko-posavske upanije”
Antonio Miškulin
“Zraèna laserska batimetrija”
Marija Peroš
“Utjecaj gospodarske krize na geodetsku djelatnost
u Republici Hrvatskoj”
Jasmin Tubiæ
“Fotogrametrijska izmjera secesijske fasade kuæe
Bauda u Zagrebu”
Marinko Bajica
“Atlas ivoroðenih i prekida trudnoæe po upanijama
i bolnicama od 2003.–2009. godine”
Datum obrane, mentor
09. 12. 2011., prof. dr. sc. Siniša Masteliæ Iviæ
09. 12. 2011., prof. dr. sc. Brankica
Cigrovski-Deteliæ
09. 12. 2011., doc. dr. sc. Dubravko Gajski
09. 12. 2011., prof. dr. sc. Boško Pribièeviæ
09. 12. 2011., prof. dr. sc. Stanislav Frangeš
09. 12. 2011., doc. dr. sc. Almin Ðapo
09. 12. 2011., prof. dr. sc. Boško Pribièeviæ
09. 12. 2011., doc. dr. sc. Dubravko Gajski
24. 02. 2012., doc. dr. sc. Robert upan
63
Vijesti, Geod. list 2012, 1
Boris Bijeliæ
“Karta širenja radioaktivnog zraèenja”
Goran Blaetiæ
“Izrada situacijskog plana kamena Velièanka II na
temelju 3D terestrièkog laserskog skeniranja”
Dario Dambo
“Geomagnetsko polje Hrvatske 2004–2008”
Igor Kuzmiæ
“Digitalna fotogrametrijska izmjera industrijske
arhitekture”
Ana Lubina
“Vizualizacija utvrde Prozor”
Igor Mareniæ
“Analiza poloaja dijela sjevernoatlantske struje iz
podataka projekta ARGO u programu GeoMedia”
Davor Nimani
“Trodimenzionalni model kamenoloma Vetovo”
Ines Stefanoviæ
“Slobodna programska podrška kod izrade i obrade
foto-realistiènih 3D modela”
Tomislav Šipek
“Geodetski radovi pri izmjeri DTK primjenom
CROPOS-a za potrebe katastra vodova”
Hrvoje Škarica
“Primjena CROPOS-a za potrebe izrade PGP-a”
24. 02. 2012., prof. dr. sc. Miljenko Lapaine
24. 02. 2012., prof. dr. sc. Damir Medak
24. 02. 2012., prof. dr. sc. Mario Brkiæ
24. 02. 2012., doc. dr. sc. Dubravko Gajski
24. 02. 2012., prof. dr. sc. Boško Pribièeviæ
24. 02. 2012., prof. dr. sc. Siniša Masteliæ Iviæ
24. 02. 2012., prof. dr. sc. Damir Medak
24. 02. 2012., doc. dr. sc. Dubravko Gajski
24. 02. 2012., dr. sc. Mladen Zrinjski,
prof. dr. sc. Ðuro Barkoviæ
24. 02. 2012., prof. dr. sc. Brankica
Cigrovski-Deteliæ,
dr. sc. Mladen Zrinjski
Èestitamo novim diplomiranim inenjerima geodezije.
Mladen Zrinjski
64
Vijesti Dravne geodetske uprave, Geod. list 2012, 1
REPUBLIKA HRVATSKA
Dravna geodetska uprava
HR-10000 Zagreb, Gruška 20
www.dgu.hr
OBAVLJANJE GEODETSKIH POSLOVA U OKOLNOSTIMA GOSPODARSKE KRIZE
Prema prikupljenim i upravo obraðenim podacima iz katastarskih ureda fizièke i pravne
osobe ovlaštene za struène geodetske poslove su u prošloj, 2011. godini izradile ukupno
28746 parcelacijskih i drugih geodetskih elaborata. Ovaj podatak sustavno se prati od
2002., a kretanje broja moe se vidjeti na priloenom grafièkom prikazu (slika 1).
Slika 1. Broj izraðenih geodetskih elaborata u Hrvatskoj.
Zapaa se da je u 2004. došlo do pada broja izraðenih elaborata u odnosu na 2003. godinu,
kao posljedica tada donesenih izmjena i dopuna Zakona o prostornom ureðenju i gradnji kojim su oteane, a dijelom i onemoguæene provedbe svih eljenih parcelacija. Nakon što je kolièina izraðenih elaborata premašila 32000 u 2008., pojavom gospodarske krize ovaj broj se
naglo smanjio. Ohrabruje podatak da je u 2011., nakon dvije godine opadanja tog broja, izraðeno 14% više parcelacijskih i drugih geodetskih elaborata u odnosu na 2010. godinu.
Na slici 2 prikazan je broj izraðenih posebnih geodetskih podloga od 2008. do danas. U
2011. godini izraðeno je na podruèju cijele Hrvatske ukupno 20314 posebnih geodetskih
Slika 2. Broj izraðenih posebnih geodetskih podloga u Hrvatskoj.
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65
podloga. Ovaj uradak je propisan 2007. u tada donesenom Zakonom o prostornom ureðenju
i gradnji. Kako ispravnost uklopa grafièkog prikaza stvarnog stanja na katastarski plan
potvrðuju katastarski uredi, kretanje broja izraðenih podloga je takoðer moguæe statistièki
pratiti prema podacima iz katastara.
Za razliku od djelatnosti izrade parcelacijskih i drugih geodetskih elaborata, izrada posebnih
geodetskih podloga u znaèajnijoj mjeri ovisi o graðevinskoj aktivnosti u zemlji. Stoga se na podacima o broju izraðenih podloga ogleda kriza u gradnji koja je zapoèela 2008. godine. U ovom
segmentu geodetskih poslova, kraj krize još nije razvidan. Naime, broj izraðenih podloga se
kontinuirano smanjuje, tako da je 2011. izraðeno 38% manje posebnih geodetskih podloga nego
2008. godine. Istina, broj se u posljednje dvije godine donekle stabilizirao, pa je opadanje broja
izraðenih posebnih geodetskih podloga bitno usporeno u odnosu na relaciju 2008–2009.
Zbrajanjem broja ove dvije vrste uradaka dobiva se zapravo relevantan podatak o stanju u
geodetskoj struci tijekom zadnje 4 godine, što je prikazano na slici 3. Iz grafa se moe zakljuèiti da je nakon oštrog pada u 2009., došlo do stanovite konsolidacije kolièine posla.
Ohrabruje prošlogodišnje poveæanje od 6% u odnosu na 2010., mada iskazana aktivnost još
uvijek daleko zaostaje za predkriznom 2008. godinom.
Slika 3. Ukupan broj izraðenih PGP-a i elaborata u Hrvatskoj.
Slika 4 daje prikaz pada aktivnosti, indeksiran brojem 100 u 2008. i pokazuje da je u odnosu na 2008. zadnje tri godine (2009., 2010. i 2011.) prosjeèno petina posla manje na trištu
geodetskih usluga.
Slika 4. Prikaz geodetskih aktivnosti u Hrvatskoj iskazano indeksom.
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Vijesti Dravne geodetske uprave, Geod. list 2012, 1
Kriza nije ravnomjerno pogodila sve upanije. Ova statistika temelji se na podacima iz Podruènih ureda za katastar, pa je analizu moguæe izraditi i zasebno za svaku upaniju.
Za ovu priliku izabrali smo po dvije upanije s najlošijim i najboljim pokazateljima, a pokazatelji za sve druge upanije i Grad Zagreb su negdje izmeðu navedenih primjera. Iz podataka proizlazi da je kolièina geodetskog posla najviše smanjena u Osjeèko-baranjskoj (slika
5) i Virovitièko-podravskoj upaniji (slika 6). Nakon zamalo prepolovljenog broja s 2008. na
2009. godinu, u prošloj godini u Osjeèko-baranjskoj upaniji pokazuje se blagi oporavak,
dok se broj izraðenih uradaka u Virovitièko-podravskoj upaniji i dalje smanjuje, premda u
toj upaniji smanjenje posla nije toliko izraeno kao u Osjeèko-baranjskoj.
Slika 5. Prikaz geodetskih aktivnosti u Osjeèko-baranjskoj upaniji iskazano indeksom.
Slika 6. Prikaz geodetskih aktivnosti u Virovitièko-podravskoj upaniji iskazano indeksom.
Na slikama 7 i 8 dan je prikaz kretanja broja geodetskih uradaka u dvije upanije koje najbolje odolijevaju krizi.
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Slika 7. Prikaz geodetskih aktivnosti u Šibensko-kninskoj upaniji iskazano indeksom.
Slika 8. Prikaz geodetskih aktivnosti u Istarskoj upaniji iskazano indeksom.
Šibensko-kninska upanija je jedina koja i u razdoblju krize biljei porast ukupnog
broja izraðenih elaborata i posebnih geodetskih podloga (slika 7). Kako se radi o maloj upaniji, na alost ne utjeèe znatno na ukupnu sliku stanja obavljanja geodetske
djelatnosti u Hrvatskoj. Podaci prikazani na slici 8 pokazuju izrazitu stabilnost kolièine geodetskog posla u Istarskoj upaniji, premda je u njoj 4% manje posla nego u 2008.
godini.
Ovi podaci mogu biti grubi pokazatelj i na temelju ovih kretanja moe se sagledati gospodarska aktivnost, te time i procijeniti realizacija geodetskih tvrtki, odnosno vrijednost obavljenih usluga.
Cijene izrade geodetskih elaborata i posebnih geodetskih podloga su razlièite u razlièitim
krajevima zemlje, a najviše ovise o vrijednosti nekretnina koje su predmet posla te platenoj moæi traitelja geodetskih usluga na odreðenom podruèju. Mnoeæi broj izraðenih
uradaka s prosjeènom cijenom moe se zakljuèiti da se u ovom segmentu geodetske djelatnosti obræu znatna sredstva.
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Vijesti Dravne geodetske uprave, Geod. list 2012, 1
Ovu statistiku treba sagledavati uvjetno, znajuæi da se analizirani brojevi odnose na kolièinski brojne, ali geodetske poslove manje vrijednosti. No, s druge strane, velika veæina geodetskih tvrtki bavi se upravo izradom posebnih geodetskih podloga i geodetskih elaborata, veæina èak i iskljuèivo samo time. U razmatranom sluèaju investitori su najveæim dijelom fizièke osobe koje grade ili nastoje srediti dokumentaciju i imovinsko-pravne odnose na svojoj
nekretnini.
Hori Martiniæ
PREDSTAVLJANJE MONOGRAFIJE TOPOGRAFSKE KARTE
NA PODRUÈJU HRVATSKE
Povodom obiljeavanja prvog Dana europskih geodeta i geoinformacija Dravna geodetska
uprava je, pod pokroviteljstvom ministra graditeljstva i prostornog ureðenja gospodina Ivana Vrdoljaka, predstavila 2. oujka 2012. godine u Hrvatskoj akademiji znanosti i umjetnosti monografiju Topografske karte na podruèju Hrvatske (slika 1).
Slika 1. Naslovnica monografije.
Autori monografije su dr. sc. Stjepan Æosiæ, ravnatelj Hrvatskog dravnog arhiva u Zagrebu, Mirko Aliloviæ, dipl. ing. geod., zamjenik ravnatelja Dravne geodetske uprave u miru,
prof. dr. sc. Stanislav Frangeš, redoviti profesor Geodetskog fakulteta Sveuèilišta u Zagrebu
i mr. sc. Ivan Landek, pomoænik ravnatelja Dravne geodetske uprave. Glavni urednik je
prof. dr. sc. Stanislav Frangeš.
Monografija daje pregled izrade topografskih karata od 1673. godine do danas. Sadraj monografije podijeljen je na šest poglavlja, gdje se osim uvodnog dijela i zadnjeg poglavlja, koji
tablièno prikazuju evidentirane topografske karte na podruèju Hrvatske s prikazom mjesta
èuvanja, opisuje izrada topografskih karata podijeljena u èetiri vremenska okvira. Svaki od
autora je u svom poglavlju slikovito prikazao izradu topografskih karata.
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Slika 2. Autori monografije: Frangeš, Æosiæ, Aliloviæ i Landek.
Poglavlje Topografske karte hrvatskih zemalja do poèetka 20. stoljeæa (autor Stjepan Æosiæ)
opisuje poèetke vojnih izmjera i izradu karata s topografskim obiljejima, jozefinske topografske karte, karte napoleonovog razdoblja, franciskanske i franjozefske topografske karte
i javne karte do poèetka 20. stoljeæa.
Poglavlje Topografske karte podruèja Hrvatske od 1900. do 1945. godine (autor Mirko
Aliloviæ) prikazuje tijek izrade topografskih karata razlièitih mjerila (1:25 000, 1:50 000,
1:100 000, 1:200 000, 1:300 000, 1:500 000 i druge) od strane Vojnogeografskog instituta u
Beèu, kasnije Vojnogeografskog instituta Kraljevine Jugoslavije, tijekom prvog i drugog
svjetskoga rata od strane talijana, nijemaca, engleza i drugih.
Poglavlje Topografske karte podruèja Hrvatske u razdoblju od 1946. do 1990. godine (autor
Stanislav Frangeš) opisuje izradu Osnovne dravne karte (ODK) u mjerilu 1:5000 od 1965.
do 1990. godine s preglednim kartama po godinama izrade. Zorno je opisano prikazivanje
topografskih objekata (naselja, prometnica, voda, vegetacije, reljefa, granica), kao i izrada
topografskih karata za mjerila od 1:25 000 do 1:500 000.
Zadnje poglavlje Topografske karte Republike Hrvatske poslije 1990. godine (autor Ivan
Landek) prikazuje tijek izrade Hrvatske dravne karte (HDK) i Hrvatske osnovne karte
(HOK) u mjerilu 1:5000 poslije 1990. godine s preglednim kartama po godinama izrade. Nastavno je dan prikaz razvoja CROTIS-a kao i razvoj izrade nove topografske karte u mjerilu
1:25 000 po godinama izrade za cijelo podruèje Republike Hrvatske. U tom razdoblju obnovljene su i topografske karte u mjerilu 1:100 000 i 1:200 000, izraðene vojne topografske karte 1:250 000 i pregledna topografska karta 1:500 000.
Predgovor monografije pripremio je bivši ravnatelj Dravne geodetske uprave prof. dr. sc.
eljko Baèiæ, a recenziju monografije proveli su prof. emeritus Nedjeljko Franèula i prof. dr.
sc. Miljenko Lapaine, koji je ujedno i lektorirao tekst. Predgovor i sadraj prevedeni su na
engleski (Corinne Enquist) i njemaèki jezik (mr. Biserka Fuèkan Driæ). Oblikovanje
tekstova i slika odradio je tehnièki urednik Ivan Grubiæ, dipl. ing. geod., a tisak u nakladi
od 1000 primjeraka izvela je tiskara Printera grupa d.o.o. iz Svete Nedelje.
Predstavljanju monografije uz ministra graditeljstva i prostornog ureðenja gosp. Ivana
Vrdoljaka i ravnatelja Dravne geodetske uprave dr. sc. Danka Markovinoviæa prisustvovali
su i brojni drugi visoki dunosnici meðu kojima su pomoænica ministrice vanjskih i europskih poslova, Andrea Metelko-Zgombiæ, gða. Zofija Mavar iz Ministarstva kulture, ravnatelj
DUZS, dr. sc. Jadran Periniæ, ravnatelj HHI, dr. sc. Zvonko Gretiæ, pomoænica ravnatelja
Dravnog zavoda za statistiku aklina Èizmoviæ i drugi.
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Slika 3. Ministar graditeljstva i prostornog ureðenja i ravnatelj DGU.
Skupu je prisustvovalo oko stotinjak gostiju koji su na kraju prigodne prezentacije dobili
primjerak monografije kao trajnu uspomenu na ovaj povijesni dogaðaj.
Slika 4. Podjela monografija.
Na kraju se zahvaljujemo svima koji su omoguæili prezentaciju i dali svoj doprinos u predstavljanju monografije Topografske karte na podruèju Hrvatske i to ministru Ivanu Vrdoljaku, dipl. ing. el., ravnatelju dr. sc. Danku Markovinoviæu, prof. dr. sc. Marijanu Heraku koji
je pozdravio goste u ime Hrvatske akademije znanosti i umjetnosti, koja nam je ustupila
prekrasan prostor Preporodne dvorane u Opatièkoj 18, glavnom uredniku monografije prof.
dr. sc. Stanislavu Frangešu, recezentu i lektoru prof. dr. sc. Miljenku Lapaineu, svim djelatnicima Sektora za topografsku izmjeru i dravne karte kao i ostalim djelatnicima Središnjeg ureda DGU.
Ivan Landek i Ivan Grubiæ
Geod. list 2012, 1
PREGLED STRUÈNOG TISKA I SOFTVERA
71
BIBLIOGRAFSKA I CITATNA BAZA SCOPUS
Scopus, komercijalna baza tvrtke Elsevier, je najveæa bibliografska i citatna baza na svijetu s alatima za pretraivanje, analiziranje i vizualizaciju dobivenih podataka. Ukljuèuje,
krajem 2011, 18 500 èasopisa od kojih 1800 s otvorenim pristupom, 425 publikacija tvrtki,
325 serija knjiga, 250 zbornika radova, 375 milijuna znanstvenih web-stranica i 24,8 milijuna patentnih zapisa. Scopus je pokrenut 2004, sadri podatke od 1966, za neke èasopise i od
1823, a citati se u bazi vode od 1996. Zahvaljujuæi Ministarstvu znanosti, obrazovanja i
sporta (MZOS) Scopus je dostupan Hrvatskoj akademskoj zajednici, a pristup je reguliran
IP adresama pa nije potrebno korisnièko ime i zaporka (http://www.scopus.com/home.ur).
Ovdje se navode samo neke moguænosti pretraivanja koje Scopus prua. Document search
omoguæuje pretraivanje po razlièitim kriterijima: nazivu èlanka, kljuènim rijeèima, autorima, prvom autoru, naslovu izvora, sveuèilištu, jeziku, ISSN-u i dr. Npr. da bi se dobili svi
radovi iz odreðenog èasopisa treba u izborniku izabrati Source Title i upisati naslov èasopisa. Dobije se ispis naslova svih radova, a u posebnim tablicama prikazuje se broj radova po
godinama, autorima, vrsti dokumenta (èlanak, izlaganje sa znanstvenog skupa, uvodnik,
prikaz i bilješka) i po znanstvenim podruèjima. Pretraivanje se stoga moe ogranièiti samo
na neku godinu, pojedinog autora, vrstu dokumenta ili znanstveno podruèje. Klikne li se na
pojedini èlanak dobije se saetak i ispis citirane literature. Poveznica View at publisher
omoguæuje pristup cjelovitom tekstu ako je èlanak objavljen u èasopisu s otvorenim pristupom ili je korisnik pretplaæen na èasopis.
Da bi se dobili radovi odreðenog autora, bolje je umjesto Document search primijeniti Autors
search. Tada, ako s istim prezimenom i istim inicijalima imena postoji više autora, Scopus
ispiše njihova prezimena, inicijale imena, za neke autore i imena, znanstveno podruèje kojim
se bave te ustanove u kojima rade pa treba samo oznaèiti o kojem se autoru radi. Ako se
traeni autor sluio s razlièitim oblicima imena, npr. s jednim ili dva inicijala, ili je radio u
više ustanova, tada treba oznaèiti sve virtualne identitete tog autora. Scopus omoguæuje i
pregled citiranosti pojedinih ili svih radova traenog autora. Oznaèe se ti radovi i klikne na
View citation overview. Dobije se pregled citiranosti svakog pojedinog rada po godinama i
ukupan broj citata. Brojevi o citiranosti ujedno su i poveznice na radove koji citiraju izabranog autora. Postoji moguænost iskljuèenja samocitata izabranog autora, ali i svih koautora.
Scopus omoguæuje i laki pregled citiranosti radova pojedinog izvora, npr. èasopisa. Na izbornoj traci treba izabrati Sources i potom u abecednom popisu izvora pronaæi traeni èasopis. Klikne li se na traeni èasopis za svaku godinu prikae se broj dokumenata i moguænost
uvida u citiranost (View citation overview). U pregledu citiranosti za svaki èlanak dan je
broj citata po godinama i ukupan broj citata te ukupan broj citata svih èlanaka objavljenih
te godine. Postoji moguænost iskljuèenja samocitata svih autora.
Scopus je u hrvatskoj znanosti vrlo cijenjena baza. Npr. u Uputama za recenzente i prosudbene skupine podruèja Tehnièke znanosti u ocjeni kompetentnosti voditelja projekata koje
financira MZOS (http://zprojekti.mzos.hr/upute/Upute_R&PS-tehnicke_HR.pdf) za ocjenu
3 voditelj projekta treba imati po 2 citata navedena u bazi Scopus ili po 1 citat u bazi Web of
Science. Za ocjenu 4 potrebna su 4 citata (Scopus) ili 2 (Web of Science) i za ocjenu 5 potrebno je 6 citata (Scopus) ili 3 (Web of Science). Za ocjenu 2 citati nisu potrebni.
Pretraili smo bazu Scopus i u tablici 1 naveli sve pronaðene univerzalne geodetske èasopise, raspon godina za koje u bazi postoje podaci i broj radova svakog èasopisa. Univerzalnim
geodetskim èasopisima smatrali smo èasopise koji objavljuju radove iz svih grana geodezije:
kartografija, fotogrametrija i daljinska istraivanja, pomorska, satelitska i fizikalna geodezija, primijenjena geodezija i geomatika.
U tablici 1 za ove èasopise upisali smo skraæene nazive dane u zagradi:
Geomatics and Information Science of Wuhan University (Geomatics… of Wuhan University)
ZfV – Zeitschrift fur Geodasie, Geoinformation und Landmanagement (ZfV – Zeitschrift fur
Geodesie…)
Journal of the Korean Society of Surveying Geodesy Photogrammetry and Cartography
(Journal of the Korean Society…).
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Pregled struènog tiska i softvera, Geod. list 2012, 1
Tablica 1. Univerzalni geodetski èasopisi u Scopusu u sijeènju 2012.
Èasopis
Raspon godina
Broj radova
1998, 2001 – 2011
2860
Journal of Geomatics
2005 – 2011
892
Acta Geodaetica et Cartographica Sinica
2005 – 2011
709
Geomatics… of Wuhan University
Survey Review
1980, 1982 – 2011
706
Geodetski vestnik
1992 – 2011
517
Geomatica
1993 – 2011
512
Journal of Surveying Engineering
1983 – 2011
491
ZfV – Zeitschrift fur Geodasie…
2002 – 2011
458
Geodesy and Cartography
2004 – 2011
419
Surveying and Land Information Science
2001 – 2011
284
Boletim de Ciencias Geodesicas
2005 – 2010
247
Journal of the Korean Society…
2005 – 2009
246
Journal of Spatial Science
2004 – 2011
167
Geodetski list
Applied Geomatics
1979 – 1983, 1985, 2008 – 2011
92
2009 – 2010
71
Neki od navedenih èasopisa izlazili su u prethodnim godinama pod drugim naslovima. Navodimo ih ako su bili ukljuèeni u Scopus (u zagradi je raspon godina za koje u Scopusu postoje podaci i potom broj radova:
• Australian Surveyor (1968 – 1971, 1975 – 2002), 472, (promijenio naslov u Journal of
Spatial Science)
• Surveying and Mapping (1969, 1972 – 1989), 254
• Surveying and Land Information Systems (1990 – 2002), 290, (oba èasopisa prethodnici
su èasopisa Surveying and Land Information Science)
• Zeitschrift fur Vermessungswesen (1979 – 1981, 1990 – 2001), 469, (promijenio naslov u
Zeitschrift fur Geodasie, Geoinformation und Land Management).
Univerzalni geodetski èasopisi koji su bili u Scopusu, ali su izostavljeni (u zagradi su godine
za koje postoje podaci u Scopusu i broj radova):
• Allgemeine Vermessungs-Nachrichten (1979 – 1980, 1988 – 1994), 219
• Bollettino di Geodesia et Science Affini (1979, 1984 – 1995), 243, (u bazi je pogrešno upisano et umjesto e)
• Geodesia es Kartografia (1979 – 1981, 1988 – 1989, 1991 – 1992, 1995 – 2007), 441
• Przeglad geodezyjny (1979 – 1981), 22.
Univerzalni geodetski èasopisi koji nisu uvršteni u Scopus:
• Geodeticky a kartograficky obzor
• Geodesia (Nederlands geodetisch tijdschrift)
• Geodetska sluba
• Geodezija i kartografija (Moskva)
• Geodezija, kartografija, zemeustrojstvo (Sofija)
• Geomatik Schweiz
• Nordic journal of surveying and real estate research
• Österreichische Zeitschrift für Vermessung und Geoinformation (VGI)
• Professional Surveyor Magazine.
Nedjeljko Franèula
Pregled struènog tiska i softvera, Geod. list 2012, 1
73
IZ STRANIH ÈASOPISA
Acta Geodaetica et Geophysica Hungarica, Vol.46, No.4., 2011.
• Exhaustive search procedure for multiple outlier detection. S. Baselga. 401.-416.
• On the determination of a new combined EGM2008 based quasi-geoid model for Hungary. Gy Tóth and E. Szûcs. 417.-430.
• A remark on the GNSS differenced phase ambiguity parameters. M. Shirazian, L. E. Sjöberg and M. Horemu. 431.-440.
• Effect of the difference between surface and terrain models on gravity field related quantities. G. Papp and E. Szûcs. 441.-456.
• A brief history of the geodetic survey of Canada. D. Nagy. 471.-480.
Allgemeine Vermessungs-Nachrichten, Vol.119, No.1., 2012.
• Vergleich photogrammetrischer und akustischer Messverfahren zur Rissdetektion bei
Belastungsversuchen im Stahlbetonbau. Robert Koschitzki, Hans-Gerd Maas.
• Eine Milliarde 3D-Punkte mit Standardhardware verarbeiten. Jan Elseberg, Dorit
Borrmann, Andreas Nüchter.
• Anwendung von UAVs in der Katastervermessung. Madeleine Manyoky, Pascal Theiler,
Daniel Steudler und Henri Eisenbeiss.
Geoinformatica, Vol.16, No.1., 2012.
• Automatic geospatial metadata generation for earth science virtual data products. Peng
Yue, Jianya Gong, Liping Di and Lianlian He. 1.-29.
• An evaluation of ontology matching in geo-service applications. Lorenzino Vaccari, Pavel
Shvaiko, Juan Pane, Paolo Besana and Maurizio Marchese. 31.-66.
• Topological operators: a relaxed query processing approach. Alberto Belussi, Barbara
Catania and Paola Podestà. 67.-110.
• Reference model for a data grid approach to address data in a dynamic SDI. Serena
Coetzee. 111.-129.
• Provably correct and complete transaction rules for updating 3D city models. Gerhard
Gröger and Lutz Plümer. 131.-164.
• The SB-index and the HSB-index: efficient indices for spatial data warehouses. SB-index
and the HSB-index: efficient indices for spatial data warehouses. Thiago Luís Lopes Siqueira, Cristina Dutra de Aguiar Ciferri, Valéria Cesário Times and Ricardo Rodrigues
Ciferri. 165.-205.
• Integrating GI with non-GI services-showcasing interoperability in a heterogeneous
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• WebGIS Performance Tests: Distributed and Centralised Work Models. Honglei Dai,
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Czech City. Vladimíra Šilhánková and Martin Maštálka.
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Vlado Cetl
PREDSTOJEÆI DOGAÐAJI
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TRAVANJ
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KOLOVOZ
Interexpo Geo-Siberia – 2012
Novosibirsk, Russian Federation, 17.-19. 4.
Web: http://geosiberia-2012.ssga.ru/
E-mail: [email protected]
XXII ISPRS 2012 Congress
Melbourne, Australia, 25. 8. – 1. 9.
Web: http://www.isprs2012-melbourne.com
E-mail: [email protected]
IGSM 2012 – 25th International
Geodetic Students Meeting
Jaén, Spain, 22.-28. 4.
Web: http://igsm2012.ujaen.es/
32nd International Geographical
Congress Cologne 2012
Cologne, Germany, 26.-30. 8.
Web: http://www.igc2012.org/
E-mail: [email protected]
Geospatial World Forum 2012
Amsterdam, The Netherlands, 23.-27. 4.
Web: http://www.geospatialworldforum.org/
E-mail: [email protected]
XVIIIth International Hydrographic
Conference
Monaco, 23.-27. 4.
Web: http://www.iho.int
E-mail: [email protected]
SVIBANJ
1st
FIG Young Surveyors Conference
Rome, Italy, 4.-5. 5.
Web: http://www.fig.net/fig2012/
E-mail: [email protected]
GeoCAD 2012
Alba lulia, Romania, 11.-12. 5.
Web: http://www.fig.net/events/2012/
/geocad2012_ alba_iulia.pdf
E-mail: [email protected]
GSDI World Conference (GSDI 13)
Québec City, Canada, 14.-17. 5.
Web: http://www.gsdi.org/gsdiconf/gsdi13/
International Symposium on
Engineering Geodesy
Slavonski Brod, Croatia, 29.-30. 5.
Web: www.hgd1952.hr
E-mail: [email protected]
LIPANJ
4th
International Conference on
Cartography and GIS
Albena, Bulgaria, 18.-22. 6.
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/4thConference/Index.html
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SRPANJ
ESRI International User Conference
San Diego, California, USA, 23.-27. 7.
Web: http://www.esri.com/events/
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RUJAN
SDI Days
Zagreb, Croatia, 25.-29. 9.
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E-mail: [email protected]
LISTOPAD
INTERGEO 2012
Hannover, Germany, 9.-11. 10.
Web: http://www.intergeo.de/en/englisch/
/index.php
E-mail: [email protected]
V. simpozij ovlaštenih inenjera
geodezije
Opatija, Hrvatska, 19.-21. 10.
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National Scientific Conference –
GEO2012
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E-mail: [email protected]
2013
ESRI International User Conference
San Diego, California, USA, 8.-12. 7.
Web: http://www.esri.com/events/uc/index.html
26th International Cartographic
Conference
Dresden, Germany, 25.-30. 8.
Web: http://www.icc2013.org/
E-mail: [email protected]
INTERGEO 2013
Essen, Germany, 8.-10. 10.
Web: http://www.intergeo.de/en/englisch/
/index.php
E-mail: [email protected]
2014
XXV FIG International Congress
Kuala Lumpur, Malaysia, 16.-21. 6.
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Mladen Zrinjski
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