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465
Kamil KRASUSKI
ZESPÓŁ TECHNIK SATELITARNYCH, 08-530 Dęblin, 16 Zawiszy Czarnego St.
STAROSTWO POWIATOWE W RYKACH, WYDZIAŁ GEODEZJI, KARTOGRAFII I KATASTRU NIERUCHOMOŚCI, 08-500 Ryki, 10A Wyczółkowskiego St.
Preliminary results of DCB C1-C2 in a GPS system
Abstract
The paper present the results of studies related to estimation of
instrumental biases C1-C2 in a GPS system. The data from LAMA and
WROC reference stations in Poland were used in numerical processing,
using the least squares method in SciTEC software. The Differential Code
Biases C1-C2 were determined based on the Geometry Free linear
combination with temporal resolution of 2 hours, separately for each
station. The first results of the DCB C1-C2 were compared with theoretical
values based on monthly CODE’s product. Moreover, the theoretical
values of SDCB C1-C2 include many anomalies and the reference sum of
SDCB C1-C2 is not equal to 0. The standard deviation of the mean
difference between CODE and each station is about ±3 ns. The magnitude
order of SDCB C1-C2 for each station for each day is less than ±10 ns
with the standard deviation less than ±0.5 ns. The average values of SDCB
C1-C2 for each station were determined based on a RINEX file from 6
measurements days. The SDCB C1-C2 from each station have got similar
trends, except to the bias of SVN1, where the difference is more than 2 ns.
Generally, the mean difference of SDCB C1-C2 between the LAMA and
WROC solution is about ±1 ns. The RDCB C1-C2 are more stable than the
SDCB C1-C2, with a daily repeatability about 0.7 ns. The characteristic of
RDCB C1-C2 for each station over a few days is very irregular, with the
range of about ±1.5 ns.
Keywords: GPS, DCB, geometry-free linear combination.
1. Introduction
Since 2005, when the first Satellite Vehicle 17 (SV17) from
Block IIR-M (Replenishment and Modernized) was launched to
transmit signal L2C (C2 code on L2 frequency), a new type of
instrumental biases in a GPS system has been determined.
Especially, C2 code has been utilized to positioning augmentation
(Wang 2010, Leandro et al. 2008), but also application in time
transfer has been found. Primary, only Differential Code Biases
(DCB) P2-C2 were estimated as a difference in time transfer
between codes P2 and C2. Based on this conception, only three
scientific departments, e. g.: the Center for Orbit Determination in
Europe (CODE) (Schaer et al. 2010, Schaer 2012), the Natural
Resources Canada (NRCan) (Ghoddousi-Fard 2012) and the
University of New Brunswick (UNB) (Leandro et al. 2007, Santos
et al. 2010), estimate and provide DCB P2-C2. Moreover, C2 code
is applied in the Geometry Free linear combination to the obtained
ionosphere delay Slant TEC (STEC) and instrumental biases DCB
C1-C2. Generally the STEC parameter should be calculated based
on P1/P2 codes (Coco 1991), but also multiple codes from
different frequencies can be utilized in this processing. It can be an
important facilitation, because the STEC value from P1/P2 and
C1/C2 observations is the same parameter and only instrumental
biases are shifted relative to each other.
Usually, instrumental biases are divided into two types:
Satellites DCB and Receivers DCB (e. g. C1-C2). The
instrumental biases of each type (also SDCB C1-C2) are defined
as the difference of the transmission time between observations on
the 1st frequency (e. g. C1 code) and the 2nd frequency (e. g. C2
code) from each satellite to the receiver (Lin 2001, Øvstedal 2002)
and depend on the stability of onboard atomic clocks. The
instrumental biases RDCB (e. g. C1-C2) are determined as the
difference of the time travel between both observations from the
antenna channel to the hardware of the receiver (Hong 2007).
A few factors influence the RDCB C1-C2 value, e. g.: the type of
a receiver antenna, the type of a receiver, the hardware model of
a receiver, the type of a receiver clock pattern and the cutoff
elevation in computations. The typical magnitude order of SDCB
C1-C2 is less than ±10 ns (nearly ±3 m). The instrumental biases
RDCB C1-C2 should be stable over few days, but what is most
important, their values are unique for each type of the receiver.
The standard deviation of DCB C1-C2 is most important in the
Ionosphere-Free linear combination, because it determines the
accuracy order of the receiver clock. Currently (2014 year) the
number of GPS satellites, whose transmitted civil signal C2 equals
to 12, is less than 40% of the full GPS constellation. It also makes
a problem, mainly in computation processing, when using the data
from a single station. Sometimes one or more satellites from
Block IIR-M (or IIF) are not available, which causes the change in
the DCB C1-C2 value for the other satellites. Major significance
in DCB C1-C2 determination will have to be applied to technical
infrastructure of IGS stations in the Multi-GNSS Experiment
(MGEX) campaign. New type of receivers include channels
reserved for the L2C code (Montenbruck et al. 2014). More
information about the MGEX campaign is available at the
website: http://www.igs.org/mgex.
In this paper, SDCB C1-C2 and RDCB C1-C2 are estimated,
using the least squares method. All computations were executed in
SciTEC software, whose source code was written in Scilab 5.4.1
language. The temporal resolution of the proposed mathematical
model for a single session is equal to 2 hours. The description of
the mathematical model is located in the second section and called
„Estimation of DCB C1-C2”. The results of studies are presented
in the third section „Experiments and Results”, and the last section
of the paper contains some conclusions.
2. Estimation of DCB C1-C2
The Geometry Free linear combination is applied to estimation
of the ionosphere parameter (STEC or VTEC) and instrumental
biases DCB C1-C2. The basic equation for code and phase
observations can be described as follows:
C4  C1  C2 
40.28   f12  f 22 
L4  L1  L2  
f12  f 22
 STEC  C   SDCBC1C 2  RDCBC1C 2 
40.28   f12  f 22 
f12  f 22
(1)
 STEC  B4
where: C4 , L4 - index of the code and phase Geometry Free linear
combination; C1 , C2 - code observations; L1 , L2 - phase observations;
f1 , f 2 - 1st and 2nd frequency in the GPS system; STEC - slant TEC;
STEC  F  VTEC ; TEC - electrons concentration in the ionosphere;
C - speed of light; SDCBC1C 2 , RDCBC1C 2 - instrumental biases for
satellites and receivers; B4 - float ambiguity.
The code observations in equation (1) include the instrumental
biases DCB C1-C2. The C4 term is charged with measurements
noise, as below:
M C 4  M C21  M C2 2
(2)
where: MC1, MC2- measurement noise for C1 and C2 observations.
If the MC1 and MC2 parameters are expressed by the elevation
angle, then:
2
2
a 
 a 

MC4  
  k 

sin
sin
e
e C 2

C1 
(3)
a
a
, MC2  k 
, a- mean error of the
sin e
sin e
pseudorange for C1 and C2 code, a=3 m, e- elevation angle,
where: M C1 
466
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e>100, k- scaling factor for observations on the 2nd frequency in
2
 f 
the GPS system, k   1  .
 f2 
In connection with equation (3), the magnitude order for the C4
index is between about 6 meters (on the zenith direction, e=90)
and 34 meters (for satellites with e=100). This difference is the
major reason for the fact that a few anomalies between the DCB
values from other stations can be seen. Moreover, equation (3)
presents only the empirical solution of measurements noise in the
Geometry Free linear combination. Especially, a new civil L2C
code is still in the testing phase and the optimal model of the
pseudorange standard deviation has not been implemented yet. In
the case of the L4 term, the measurements noise in the code
observations is smoothed based on equation (4) (Arikan et al.
2008, Nohutcu 2009):
C4sm  C4  L4  B4  C   SDCBC1C 2  RDCBC1C 2 
(4)
The measurements noise in the L4 combination can be limited,
as in equation (5):
L4 
C4sm
 L4  B4   STEC  C  ( SDCBC1C 2  RDCBC1C 2 ) (5)
n
n - numbers of measurements,
B4 - mean ambiguity,
VTEC - vertical TEC,
F - mapping function (Choi et al. 2013, Choi et al. 2011),
2
 R

F  cos z '  1  sin 2 z '  1  
 sin z  ,
RH

z ' - zenith angle at the IPP,
z  90  e ,
R - Earth radius, R=6371 km (Liu et al. 2010),
H - ionosphere height, H=450 km (Kao et al. 2013).
Equation (5) is the final equation for determination of the
instrumental biases DCB C1-C2. Additionally, the ambiguity term
from the phase observations is eliminated as a float component.
However, cycle slips in the phase observations must be detected
and repaired (Jin et al. 2012). The unknown parameters in
equation (5) are estimated using the least squares method (Sanz
Subirana et al. 2013), as below:
AQ  l  v
(6)
Measurement Automation Monitoring, Oct. 2015, vol. 61, no. 10
in relation to them. A similar approach can be utilized in a local
network of receivers. One receiver is selected as a reference with
the known value of the RDCB parameter and for other receivers,
the unknown RDCB are determined using the Single Difference
method (Ma et al. 2003, Hong et al. 2008).
3. Experiment and results
In this section all experiments and results are published and
analyzed. The raw GPS observations from two Polish reference
stations (LAMA and WROC) were taken in the studies. The
LAMA and WROC stations are a part of the ASG-EUPOS system
in the area of Poland and they are included in the IGS service.
From all receivers of ASG-EUPOS, only LAMA and WROC
station can collect and register the civil L2C code. The basic
equipment of LAMA and WROC station is a dual-frequency
multiplexing receiver LEICA GRX1200+GNSS and LEICA
GR25, respectively. Each receiver can track GPS/GLONASS
constellation satellites and in the case of WROC station, also
GALILEO satellites. Both receivers are classified as the C1/X2
type of receivers (Dach et al. 2007). In practice, they can only
repair the precise P code on the 2nd frequency using the crosscorrelation technique. The WROC site makes it possible to receive
the civil C/A code on the 5th frequency in the GPS system. The
observations data for each station in RINEX format were
downloaded from the website http://igs.bkg.bund.de/file/
rinexsearch/. The precise ephemeris data from the CODE Center
Analysis (from website ftp://ftp.unibe.ch/aiub/CODE/2014/) were
utilized for calculations, e. g. mapping function, elevation,
azimuth, Ionosphere Pierce Points. The interval of observations in
RINEX was set up to 30 seconds. The observations with the
elevation angle above 10 were taken in computations. The
mapping function was modeled using Single Layer Model with the
ionosphere height about 450 km (Grejner-Brzezinska et al. 2004,
Wielgosz et al. 2003). Cycle slips were detected and repaired in
the 3-degree processing (Ionosphere-Free, Geometry Free and
Melbourne-Wübbena solutions), similar like in gLAB software
(Sanz Subirana et al. 2011). Computations were realized in a static
mode using the zero difference approach. Station coordinates from
the RINEX header for all the time of numerical processing were
constant. Computations were executed in SciTEC software at the
temporal resolution of 2 hours for 12 observation sessions. The
unknown parameters were estimated in each session in an iterative
process based on the least squares method. The final results of the
instrumental biases DCB C1-C2 after 24 hours were presented as
the average values. Also the standard deviation was obtained for
each biase. Moreover, the DCB C1-C2 values were written in the
universal ”*.DCB” format, as in Figure 1.
where: A - matrix of the coefficients, matrix with dimension (n, u),
u - number of the unknown parameters, Q - unknown parameters,
Q  VTEC , SDCBC1C 2 , RDCBC1C 2  , l - observations vector,
T
v - residuals vector.
The matrix A has got rank deficient, equals one (Choi et al.
2012, Camargo et al. 2000). Additionally, the matrix of normal
equations (N) is singular and the determinant of the matrix N is 0.
Usually one constraint is recommended to eliminate the columns
rank deficient in the matrix A. The proposed constraint depends on
the relation between the Satellites DCB that the reference sum of
SDCB C1-C2 amounts to 0 (Schaer 1999), as follows:
Fig. 1. Example file of the DCB C1-C2 data for LAMA station
m

SDCBC1C 2  0
(7)
1
where: m- number of the unknown SDCB C1C2.
Another constraints can be applied also, e. g. one or more SDCB
are stable over 24 hours and the rest of SDCB biases is estimated
The “*.DCB” format should be considered as a sub-product of
the IONEX format but sometimes is a part of the IONEX file
(Schaer et al. 1997). The standard “*.DCB” format includes
a header and a section with data, as in Figure 1.
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Usually, the header part describes the type of DCB, data of
creating the DCB file and the name of organizations creating the
DCB file. The DCB and standard deviation values for each
satellite and receiver are presented in Section 3. The basic unit of
DCB is 1 ns (about 30 cm). The magnitude order for SDCB C1-C2
is less than ± 10 ns (nearly ± 3 m). The value of the RDCB
parameter is unique for each type of the receiver. In this paper, for
LAMA and WROC station, the RDCB parameter is positive,
between 5 and 16 ns. The mean errors for each DCB are less than
0.5 ns (about 15 cm).
The DCB C1-C2 formats are not available as the final product
for utilization in absolute positioning. Most organizations (e. g.
CODE (Schaer 2008), JPL (Wilson et al. 1993), gAGE
(Hernández-Pajares et al. 1998), ESA (Feltens et al. 2006))
provide only DCB P1-P2 and, if possible, also the DCB P1-C1
and DCB P2-C2 files. The DCB P1-P2 products can be found at
the website: ftp://cddis.nasa.gov/pub/gps/products/ionex/. The
CODE Center Analysis availables its DCB products on-line in
service: ftp://ftp.unibe.ch/aiub/CODE/2014/. It is a big problem
because the results of DCB C1-C2 presented in the paper cannot
be compare with outer solutions. The author suggests
determination of theoretical values of SDCB C1-C2 using CODE’s
products, as below:
CODE
CODE
SDCBCth1C 2  SDCBPCODE
1P 2  SDCBP1C1  SDCBP 2C 2
467
Exactly 8 GPS satellites have got the negative index of SDCB
C1-C2 and only 4 satellites have got a positive value. The
reference sum of SDCB C1-C2 cannot be 0, because the sum of
SDCB P1-P2 and P1-C1 for 12 GPS satellites is different than 0.
In this paper, the reference sum of SDCB C1-C2 equals 36.650 ns.
The theoretical values of SDCB C1-C2 from Table 1 were
compared with DCB C1-C2 from LAMA and WROC station from
SciTEC software in Figure 2. The vertical axis describes the
values of SDCB C1-C2 and the horizontal axis gives the SV
number for each satellite. Additionally, the result of SDCB C1-C2
for SVN30 was removed, because observations from its satellite
are not available in RINEX files for LAMA and WROC stations.
Both 3 curves in Figure 2 have got the same trends, but SDCB
C1-C2 results from CODE are shifted in relation to WROC and
LAMA values. The WROC and LAMA solutions are represented
as the average biases from six measurement days (between 83 to
88 day of 2014 year). The mean value and the reference sum of
SDCB C1-C2 for LAMA and WROC station is 0, which causes
that the constraint in equation (7) from Section 2 is true. The
magnitude order of SDCB C1-C2 for the LAMA station is
between 6.249 ns (SVN17) and 7.528 ns (SVN25). In the case of
the WROC station, the maximum and minimum values of SDCB
C1-C2 are about 6.069 ns (SVN17) and 7.845 ns (SVN25),
respectively.
(8)
where: SDCBCth1C 2 - theoretical value for SDCB C1-C2, SDCBPCODE
1P 2 instrumental biases SDCB P1-P2 from CODE, applied as the final
- instrumental biases SDCB P1-C1 from
product, SDCBPCODE
1C 1
- instrumental
CODE, applied as the final product, SDCBPCODE
2C 2
biases SDCB P2-C2 from CODE, applied as the final product,
SDCBCCODE
- instrumental biases SDCB C1-P2 from CODE, not
1P 2
prefer as the final product.
The proposed solution for theoretical SDCB C1-C2 based on
monthly products from CODE and currently (2014 year) can be
applied for 12 GPS satellites (SV1, SV5, SV7, SV12, SV15,
SV17, SV24, SV25, SV27, SV29, SV30 and SV31). The results of
SDCB C1-C2 (in ns) of March 2014 are presented in Table 1.
Tab. 1. Monthly theoretical SDCB C1-C2 values based on CODE’s products
(from March 2014)
SV Number
Theoretical SDCB C1-C2, ns
1
 9.088
5
 0.246
7
1.237
12
1.156
15
 0.131
17
0.756
24
 8.270
25
 9.117
27
 6.635
29
 0.624
30
 7.505
31
1.817
Mean value of SDCB C1-C2
Reference sum of SDCB C1-C2
 3.054
 36.650
The mean value for the theoretical SDCB C1-C2 is 3.054 ns
(about -90 cm). The maximum and minimum values of SDCB
C1-C2 are referenced for G31 (1.817 ns) and G25 (9.117 ns)
satellites, respectively.
Fig. 2. SDCB C1-C2 values based on the CODE, LAMA and WROC solution
The mean differences of SDCB C1-C2 between the CODE and
each station are better visualized in Figure 3. In three cases, the
differences of SDCB C1-C2 between the CODE and each station
are greater than 3 ns, e. g. for SVN1 (adequately 6.780 and 4.294
ns), SVN17 (adequately 5.493 and 5.313 ns) and SVN27
(adequately 3.212 and 3.217 ns).
The other GPS satellites (more than 70%) gave the mean
differences of SDCB C1-C2 smaller than 3 ns. Especially, the
mean differences of SDCB C1-C2 are less than 2 ns for 4 satellites
(SVN7, SVN25, SVN29 and SVN31) for each comparison. The
standard deviation results are very similar to the mean differences
of SDCB C1-C2. The three satellites (SVN1, SVN17 and SV2N7)
for LAMA-CODE difference and 5 satellites (SVN1, SVN15
SVN17, SVN24 and SVN27) for WROC-CODE difference have
the standard deviation greater than ±3 ns. However, for the
LAMA-CODE difference (for SVN1 and SVN17 satellites) and
for the WROC-CODE difference (for SVN1 satellite), this error is
greater than ±5 ns. The standard deviation values are less than ±2
ns only for SVN25 and SVN29 satellites, which corresponds to
less than 20% of all the standard deviation results. The average
value of the standard deviation for each comparison is about
±3.030 and ±2.989 ns, respectively.
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468
Measurement Automation Monitoring, Oct. 2015, vol. 61, no. 10
each solution. The range of the RDCB parameter for the LAMA
solution is between 15.067 ns and 13.274 ns, for the WROC
solution 6.993 ns and 5.345 ns, adequately. The daily repeatability
of each RDCB bias is below 1 ns and amounts to about 0.7 ns.
Tab. 3. Mean values of RDCB C1-C2 for each station over a few measurement days
Fig. 3. Mean difference of SDCB C1-C2 between the CODE and each stations
The relations between the average biases from the LAMA and
WROC stations are expressed in Table 2. The mean results of
SDCB C1-C2 from each station are very similar, except G01
satellite, where the difference between the LAMA-WROC
solution is larger than 2 ns. It can be a consequence of fewer
numbers of L2C observations in the RINEX and LAMA station
compared to the WROC station. The minimum difference of
LAMA-WROC solution is equal 1.027 ns for G05 satellite. The
mean differences of SDCB C1-C2 (LAMA-WROC) for the rest of
satellites are less than ±1 ns (see Table 2). The average value of
the standard deviation of SDCB C1-C2 for the LAMA and WROC
solution is about ±0.766 and ±0.626 ns, respectively. In the case of
the LAMA solution, three values of the standard deviation are
larger than ±1 ns, e. g. ±1.306 for G01 satellite, ±1.047 for G17
satellite and ±1.149 for G27 satellite. More than 70% of standard
deviations of SDCB C1-C2 in the LAMA station are smaller than
± 1 ns. The minimum value of the standard deviation of SDCB
C1-C2 in the LAMA station equals ±0.492 ns (for G07 and G12
satellites). For the WROC station, all the results of the standard
deviation of SDCB C1-C2 are smaller than ±1 ns, with the
magnitude order between ±0.990 ns (for G01 satellite) and ±0.235
ns (for G25 satellite), respectively.
Tab. 2. Mean values of SDCB C1-C2 from each station over few measurement days
Mean SDCB
C1-C2
(WROC), ns
Standard
deviation of
Mean SDCB
C1-C2
(WROC) ns
SV Number
Mean SDCB
C1-C2
(LAMA), ns
Standard
deviation of
Mean SDCB
C1-C2
(LAMA), ns
1
2.307
1.306
4.793
0.990
5
1.199
0.883
2.226
0.569
7
3.054
0.492
2.921
0.832
12
3.353
0.492
3.840
0.564
15
2.203
0.752
2.810
0.556
17
6.249
1.047
6.069
0.709
24
6.118
0.566
5.508
0.470
25
7.528
0.501
7.845
0.235
27
 3.423
1.149
3.417
0.468
29
-0.296
0.578
0.138
0.499
31
3.612
0.653
3.558
0.986
The characteristic of RDCB C1-C2 over a few days is very
important for determination of the stability of this instrumental
bias. The mean value from a few days and the daily repeatability
are typical statistical parameters for underlining the changes of the
RDCB parameter. The results of RDCB C1-C2 of LAMA and
WROC station are very irregular over a few days. The mean value
of each bias equals 14.341 ns and 6.203 ns, with the standard
deviation about ±0.363 ns and ±0.386 ns, respectively. The
dispersion of RDCB C1-C2 results can reach up to ±1.5 ns for
Number of
day
RDCB of
LAMA, ns
1
15.067
0.334
6.958
0.370
2
13.274
0.383
5.345
0.394
3
14.388
0.405
6.349
0.361
4
14.252
0.343
5.696
0.377
5
14.017
0.369
5.876
0.390
6
15.046
0.344
6.993
0.421
Mean value
14.341
0.363
6.203
0.386
0.675
0.028
0.681
0.021
Daily
repeatability
Mean error
RDCB of
of RDCB, ns WROC, ns
Standard deviation
of RDCB, ns
4. Conclusions
In the paper, the results of DCB C1-C2 in a GPS system have
been presented and analyzed. The DCB C1-C2 is a new type of
instrumental biases in a GPS system. It can be calculated because
some of GPS satellites transmit a new civil signal L2C. Therefore
DCB C1-C2 are defined as a time group delay between C1 and C2
codes and they are divided into Satellites DCB C1-C2 and
Receivers DCB C1-C2. The DCB C1-C2 were estimated using the
least squares method in SciTEC software. The Geometry Free
linear combination for undifference observations was utilized as
a basic mathematical model. The raw GPS observations from the
LAMA and WROC stations were applied in computations. The
first results of SDCB C1-C2 are very irregular and include some
anomalies in the presented values. Especially, the reference values
of SDCB C1-C2 based on the CODE’s products are shifted in
relation to the LAMA and WROC solutions. What is important,
the theoretical sum of SDCB C1-C2 of the CODE solution is not
zero, but is larger than 36 ns. Moreover, the reference sum of
SDCB P1-P2 and SDCB P1-C1 from the CODE for 12 GPS
satellites is not a 0 and it is a major reason for anomalies in the
theoretical SDCB C1-C2 results. The SDCB C1-C2 for the LAMA
and WROC solutions have got similar trends, except G01 bias,
where the difference is more than 2 ns. Probably the smaller
numbers of observations in the LAMA station decided about this
event. In the case of other biases, the mean difference is about
±1 ns. Standard deviations for each SDCB C1-C2 for each day for
each station are less than ±0.5 ns, but over a few days they can
reach up to ±1 ns. In connection with these results, SDCB C1-C2
cannot be stable over a few days. The measurements noise of the
Geometry Free linear combination should be still monitored as
one of the reasons for unstable SDCB C1-C2 values. Particularly,
the equation of the pseudorange mean error has to be determined
and applied as a function of the elevation angle. Perhaps, better
results of SDCB C1-C2 will be obtained if the elevation angle
cutoff is changed, e.g. from 100 to 200. On the other hand, some
part of observations will be removed from numerical
computations. In comparison with SDCB C1-C2, RDCB C1-C2 for
each stations are more stable. The daily repeatability of each bias
after a few days is less than 0.7 ns. Similarly like in the SDCB
C1-C2 case, strange phenomena are visible in the behaviour of
RDCB C1-C2. The difference between the maximum and
minimum value of RDCB over few days can reach up ±1.5 ns.
Acknowledgements. The author would like to acknowledge BKG Service for
making available RINEX data and the CODE Analysis Center for making available
DCB and precise ephemeris products.
Measurement Automation Monitoring, Oct. 2015, vol. 61, no. 10
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_____________________________________________________
Received: 17.07.2015
Paper reviewed
Kamil KRASUSKI, MSc, eng.
Alumnus of MUT in Warsaw. Author of SciTEC
Toolbox v.1.0.0 software for determination ionosphere
parameters (currently version 1.5.0). Area of interests:
navigation, geodesy, physics. Since 2014: Team of
Satellites Techniques. Since 2015: Faculty of Geodesy,
Cartography and Cadastre in District Office in Ryki.
e-mail: [email protected]
Accepted: 01.09.2015