1
Global
Fundamentals of
Positioning System (GPS)
1.1 INTRODUCTION TO GPS
The Global Positioning System (GPS) i.e., NAVSTAR GPS (Navigation Satellite Timing and Ranging
Global Positioning System) is a satellite based radio navigation system which provides precise three
dimensional (3-D) positions in terms of x, y and z i.e., latitude, longitude and altitude/height respectively
of any place/point on the globe. This information can be collected continuously throughout day and
night using a handheld GPS instrument called receiver which is just like the shape and size of a mobile
(Fig. 1.1). This space based system was developed by United States of America (USA), Department of
Defense (DoD) way back in 1973, is an all-weather, space based navigation system to meet the needs of
the USA military forces and accurately determine their position, velocity, and time (PVT) in a common
reference system, anywhere on or near the Earth on a continuous basis (Wooden, 1985). But from 1980
onwards the government made the system available for civilian uses also and now it is a dual system that
can be accessed both by military and civilian users. Nowadays GPS is on its way to be a part of our daily
lives as an essential element of the public utility and services, which we will see in the sixth chapter i.e.,
on application part of this book. There are no subscription fees or setup charges to use GPS, compared
to the setup boxes of the TV sets. If one uses two GPS receivers at the same time for one project then it
is called as differential global portioning system (DGPS). It will be discussed in detail in the next part
of the book. Differential GPS gives better accuracy, which corrects GPS signals to within an average of
three to five meters depending upon what signals it is receiving.
In the beginning in order to understand basics of GPS, the system can be categorized into five
logical steps as follows:
1. Triangulation from the satellite is the basis of the system.
2. To triangulate, the GPS measures the distance using the travel time of the radio message.
3. To measure travel time, the GPS need a very accurate clock.
4. Once the distance to a satellite is known, then we need to know where the satellite is in space.
5. As the GPS signal travels through the ionosphere and the earth’s atmosphere, the signal is
delayed.
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2
Global Positioning System (GPS): Concept, Technique and Application
Fig. 1.1 Handheld GPS
The basic aim of the very first chapter is give basic understanding of this new technique i.e.,
(i) to get the accurate position of a person or any object over and above the surface of the earth,
(ii) to survey the large land (state and nation)
(iii) navigation and tracking in the isolated area, and
(iv) to generate geo-spatial data sets for the Geographic Information System (GIS). Originally
GPS was designed as a tool for defense purposes but their civil applications have increased
tremendously.
GPS was developed with an objective to obtain accurate estimation of PVT with root mean square
(rms) errors of 10m in position (P), 0.1m/s in velocity (V) and 100ns in time (T). GPS has been planned
to give two basic services:
(a) Standard Positioning Services (SPS) for open, unrestricted civilian uses and
(b) Precise Positioning Services (PPS) exclusive for military (DoD) personals.
As an exercise the objective of GPS could be to measure the four corners of any building/plot with
GPS. The task seems simple enough and yet is quite difficult to accomplish it. This is a very common
problem with many positioning projects that have selected GPS as the source for position data. The
task is difficult because GPS depends upon the ability of the receiver antenna to “see” four or more
satellites at the same time in order to provide a position solution. Without tracking four satellites the
receiver cannot provide (without aiding) a three-dimension fix. The task of measuring the corners of
the building/plot is even more difficult because the ability to track four satellites is not enough to insure
an accurate position solution. To achieve the specified accuracies of GPS, the receiver must track four
Fundamentals of Global Positioning System (GPS)
3
satellites which are well-distributed around the sky so that the satellites measurements provide good
Geometric Dilution of Precision (GDOP) that will be discussed in the chapter 4.
1.2 HISTORY OF DEVELOPMENT OF GPS
The heavenly bodies e.g., stars in the sky were used in many centuries to set the time standards and
to locate astronomical observatories. But due to bad weather (clouds, fogs and rain) the visibility of
stars and planets is not possible so the astronomical approach to position location and navigation fails.
To overcome this problem an electro-system commonly called as Long Range Navigational System
(LORAN) was developed. It is the first true all weather system that has been developed to find out the
true position of a receiver. This is based on the principle that if two radio transmitters are located at known
position and each transmits a short pulse in synchronization being received by a receiver, the separation
in the time of arrival of two pulses could be determined a line of position (a hyperbola) characteristics
of the time interval between the received pulses. In this way, either from three synchronized ground
stations or from two sets of transmission stations, two lines of position are obtained, leading to a point
of intersection, and that is the unique location of the receiver.
Fig. 1.2 GPS satellite in space
Later on, Omega Systems (i.e., using continuous radio waves) LORAN C etc., were developed
based on the principles of synchronization of the ground stations. But these systems provide only two
dimensional data i.e., can give position in latitude (X) and longitude (Y) but not altitude (Z). With the
passage of time US (DoD) and NASA since the early 1960 demonstrated the space based positioning
system i.e., Navy Navigation Satellite System (TRANSIT system) first of its kind were used after the
development of satellites. This is based on the principles that if the ephemeris of a satellite is known,
the position of any receiver can be determined by observing the Doppler Shift in the signals broadcast
by the satellite even it is also a 2-D system. So there was a need for a radio system that can give 3-D
position of a receiver that lead to the development of GPS (Fig. 1.2).
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Global Positioning System (GPS): Concept, Technique and Application
American nuclear submarines in the 1960’s were having a difficult time to find positions, quickly
and accurately. They knew target coordinates, ballistics, and missile trajectory but the essential element
in the fire control solution i.e., current submarine coordinates was not known. The solution for that was
to create orbiting satellites network that transmitted position information (3 D) to a worldwide nuclear
submarine fleet. So in the year 1970, US Congress authorized the U.S. Department of Defense (DoD) to
develop the NAVSTAR GPS system at an estimated cost of $13 billion (Rs. 5,200 Crores) at that time.
Previously we call it Navigation satellite timing and range (Navstar) now GPS. Its real development was
started in 1973 and the satellites were launched in separate blocks. First four satellites were launched in
1978 and the Full Operational Capacity (FOC) was reached on July 17, 1995.
1.3 DEVELOPMENT OF THE TRANSIT SYSTEM
The TRANSIT satellite system was developed by the Applied Physics Laboratory at the Johns Hopkins
University for the use of the U.S. Navy. Development of the TRANSIT system began in 1958, and a
prototype satellite, Transit 1A, was launched in September 1959 but the satellite failed to reach orbit.
Then a second satellite, Transit 1B, was successfully launched on 13th April 1960. The first successful
tests of the system were made in 1960, and the system entered Naval service in 1964. It is noteworthy
that surveyors used Transit to locate remote benchmarks by averaging dozens of Transit fixes, producing
sub-meter accuracy. In fact, the elevation of Mount Everest was corrected in the late 1980s by using a
Transit receiver to re-survey a nearby benchmark.
The TRANSIT system was made obsolete by the Global Positioning System (GPS) and ceased
navigation service in 1996. Improvements in electronics allowed the GPS system to effectively take
several fixes at once, thereby greatly reducing the complexity of deducing a position. In addition the
GPS system uses many more satellites than were used with TRANSIT, allowing the system able to be
used continually, whereas TRANSIT provided a fix only every hour or more. After 1996, the satellites
were kept in use as space borne ‘mailboxes’ and for the Navy’s Ionospheric Monitoring System.
1.4 WHY DO WE NEED GPS TODAY?
The need and use of GPS is increasing today day by day at a very fast rate and the main advantages that
can be put in this support are as follows:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
(xi)
(xii)
(xiii)
Applications in n number of fields’ e.g., military, crime, civilian and planning etc.
Very precise and accurate positions can be obtained
Provide the service to an unlimited number of users and signals are free of cost
Very useful for remote and inaccessible areas where ground survey is not possible
Distances up to thousands of kilometers can be measured
In surveying GPS has revolutionized and has replaced the conventional methods of surveying
All weather operation
Day and night operation
Round the clock availability
Inter-visibility between points is not required
Can generate huge geo-spatial data base
Economical system that could save > 50% of the total cost
Fast system and it could save 75% time.
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Fundamentals of Global Positioning System (GPS)
1.5 BASIC WORKING PRINCIPLES OF GPS
he basic concept behind GPS is rather simple. If the 3 GPS satellites locations are known then the
T
position of a point (x, y, z) on the Earth (a GPS receiver) can be calculated using the three distances
equations from the unknown satellites locations by applying well-known concept of resection. The
distance between the receiver and a satellite is measured in terms of transit time (T) of the signal
multiplied by the velocity of light (c). In order to measure the true transit time of a satellite and the
receiver must be maintained in synchronization. Therefore, Rubidium and Cesium clocked are used
in the satellite to measure very precise timing i.e., accuracy of 3 nanoseconds (0.000000003, or three
billionths of a second).
ll GPS satellites continuously transmits radio signal, it consists of two carriers, two codes and a
A
navigational message (Fig. 1.3). The moment we switch on a GPS receiver, it picks up signals coming
from GPS satellites through receiver’s antenna and processes it using its inbuilt software. The outcome
of this processing give the distances to the GPS satellites through digital codes (pseudo-range) and the
coordinates of the satellite through the navigation message.
All GPS satellites circle our earth twice a day in a very precise orbit and transmit signal information
to earth i.e., to a receiver. GPS receivers take this information and use triangulation to calculate the
user’s exact location. Essentially, the GPS receiver compares the time a signal was transmitted by a
satellite with the time it was received. The time difference tells the GPS receiver how far away a satellite
is. Now, with distance measurements from a few more satellites, the receiver can determine the user’s
position and display it on the receiver screen.
Satellite
L1 and L2
downlink
SV correction
data uplink
Master control station
DSCS
DSC
S
Schriever AFB
Monitor station
Ground antenna
Fig. 1.3 GPS working principles
A GPS receiver must be locked on to the signal of at least three satellites to calculate 2-D position
(latitude and longitude) and track movement. With four or more than 4 satellites in view, the receiver
can determine the user’s 3-D position (latitude, longitude and altitude). So minimum four satellites are
needed to find coordinate of place on the earth. Signal reception from more satellites increases position
accuracy. Once the user’s position has been determined, the GPS unit can calculate other secondary
information, such as speed, bearing, track, trip distance, distance to destination, sunrise and sunset
time etc.
To get the exact point of any place at any point of time GPS uses simple triangulation method. One
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Global Positioning System (GPS): Concept, Technique and Application
can find any points on the earth if given distances from three other points are known. You use get signal
from only one satellite that will tells you that you are 10 kms from Delhi Fig. 1.4 (a). If you use two
satellites then the second satellite may tell that you are 10 kms away from Agra Fig. 1.4 (b). The third
satellite may tell you that you are 10 kms from Ajmer Fig. 1.4 (c). And once you have a fourth satellite
you can determine the exact location and height at a particular place Fig. 1.4 (d).
Delhi
10 kms
Delhi
Agra
(a)
(b)
or
Delhi
Delhi
(c)
Agra
Ajmer
Agra
Delhi
Agra
Ajmer
(d)
Fig. 1.4 Tracking the position on earth GPS triangulation
1.6 TRIANGULATION
For several centuries the propagation of the datum, and the primary means of determining precise
relative coordinates of a network of control points, was by means of triangulation. In this a network of
points was established on hilltops, and their coordinates determined by the principles of trigonometry
using the following data:
I. the given coordinate of one point (the origin station),
II. the azimuth of one line (one end of which was the known point),
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Fundamentals of Global Positioning System (GPS)
III. the distance between two points in the network, and
IV. measurement of the included angles within the triangles formed by the points in the network.
The angles were measured using a theodolite, and because the points had to be visible from at least
two other points, the spacing of these points was likely to be of the order of a few tens of kilometres at
the most. Once these primary points were established, a similar technique could be used to “intersect”
any other point of interest.
Triangulation techniques were favoured by most of the surveyors because angular measurement
using a theodolite was a far easier and more accurate measurement to make than distance. Herculean
efforts were expanded simply to measure occasional “baselines” of about 10 km length using specially
manufactured wooden or metal bars. These bars (around 2m in length) had to be carefully handled, and
laboriously placed end-to-end in order to span the distances required.
Almost overnight the technique of triangulation was superseded by the techniques of traversing and
trilateration (Fig.1.5). Trilateration is similar to triangulation except that instead of measuring the angles
within the chain of triangles, the distances are measured. The technique of Traversing, on the other hand,
requires that both distances and angles are measured. A characteristic of all three of these terrestrial
methods is that the stations whose coordinates are being determined must be visible from the measuring
stations, and therefore the coordinates which are so derived are all relative quantities (Chris, 1999).
C
A
D
B
(a)
A
(b)
B
B
F
D
X
E
A
(c)
C
Y
Fig. 1.5 The Principles of (a) Triangulation, (b) Trilateration and (c) Traversing
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Global Positioning System (GPS): Concept, Technique and Application
1.7 THE CONCEPTS OF PARAMETER ESTIMATION
In GPS observation we measure range and phase data that are related to the positions of the ground
receiver, satellites and other quantities but how we can obtain the “best” position of any of the above
that is key issue in measurement using GPS. There are two styles of estimation (appropriate for geodetic
type measurements), one is the parametric estimation where the quantities to be estimated are the
unknown variables in equations that express the observables, the second is the condition estimation
where conditions can be formulated among the observations (http://web.ics.purdue.edu).
All parametric estimation methods can be broken into the following steps:
(i) Observation equations: Equations that relate the parameters to be estimated to the observed
quantities (observables) e.g., relationship between pseudorange, receiver position, satellite
position, clocks, atmospheric and ionospheric delays.
(ii) Stochastic model: Statistical description that describes the random fluctuations in the
measurements (and may be the parameters).
(iii) Inversion that determines the parameters values from the mathematical model consistent with
the statistical model.
1.8 GPS SATELLITE CONSTELLATION
The system consists of 24 satellites (21 active and 3 active spare), all are placed in near circular orbits at
an altitude of 20,200 km, above the earth’s surface (Fig. 1.6). These satellites are arranged in 6 circular
orbital plains which are labeled A to F. These are inclined at an angle of 55°. These satellites have 12
hour periods, so that at least 4 satellites are available for observations for positioning on ground, sea,
or in the air at any time throughout the year and anywhere in the world. These satellites are traveling at
speeds of roughly 7,000 miles per hour. GPS satellites are powered by solar energy. They have backup
batteries onboard to keep them running in the event of a solar eclipse, when there’s no solar power, small
rocket boosters are there on each satellite which keep them flying in the correct path. A GPS satellite
weighs approximately 9,000 kg and is about 17 feet across with the solar panels which are extended on
two sides.
Fig. 1.6 GPS satellite constellation
Fundamentals of Global Positioning System (GPS)
9
These satellites are grouped into 3 different types according to their development and launch as
follows:
Block I : Developmental or Research and Development Satellites
Block II : Production or Operational Satellites
Block IIR : Replenishment Satellites
The first Block of satellites 1–11 were launched during 1978 and 1985 and were placed in two orbital
planes. These were initially developmental satellites with a life of about 5 years but it could last more than
5 years. The second Block II, production satellites were launched in 1989 with life of 7 years. The third
Block IIR of 20 satellites i.e., the replenishment were launched after 1996 that replaces the Block II
satellites when ever there is need.
As discussed above the GPS satellites are in nearly circular orbits and have been designed keeping
in view the following facts (Rizos, 1999):
• Their orbital period is approximately 11 hrs 58 mins, so that each satellite makes two revolutions
in one sidereal day i.e., the period taken for the earth to complete one rotation about its axis
with respect to the stars.
• At the end of a sidereal day i.e., 23 hrs 56 mins in length, the satellites are again over the same
position on earth.
• Reckoned in terms of a solar day i.e., 24 hrs in length, the satellites are in the same position in
the sky about four minutes earlier each day.
• The orbit ground track approximately repeats each day, except that there is a very small drift of
the orbital plane to the west which is arrested by periodic manoeuvres.
There are certain other general remarks can is very important with respect to the satellite constellation
design for navigation purposes which are as follows (Rizos, 1999):
• The higher a satellite, the longer it is visible above the horizon (the extreme case is the
geostationary satellites).
• The higher a satellite, the better the coverage due to longer fly-over passes and extended
visibility of the satellite across large areas of the earth.
• The higher a satellite, the less the rate-of-change of distance, and the lower the Doppler
frequency of a transmitted signal.
• The greater the angle of inclination, the more northerly the track of the sub-satellite point
across the surface of the earth.
• No satellite can be seen simultaneously from all locations on the earth.
• Depending on the positioning principles being employed, there may be a requirement for
observations to be made to more than one satellite simultaneously from more than one ground
station.
1.9 THE GPS SATELLITE CONFIGURATION VIEW
The GPS satellite configuration view provides current GPS satellite visibility information, illustrating
the azimuth and elevation of each GPS satellite (plotted by satellite identifier) relative to a compass
rose. The azimuth of each GPS satellite is plotted relative to true north. The elevation of each GPS
satellite, how high it is above the horizon, is plotted as the distance from the center of the compass rose.
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Global Positioning System (GPS): Concept, Technique and Application
GPS satellites immediately overhead are plotted at the center of the compass rose. GPS satellites on
the horizon are plotted at the perimeter of the compass rose. The GPS satellite configuration view also
gives Position Dilution of Precision (PDOP) value which is a unitless number that shows the quality of
a GPS position that means how good satellites are in the space when the reading of a pace is taken at a
particular place. In general, the lesser the value of PDOP the better the position data is likely to be. In
general, PDOP values of less than 4 are considered to be very good.
1.10 IMPORTANCE OF GPS SATELLITE CONFIGURATION
The importance of satellite configuration is important in terms of accuracy of data obtained from a GPS
receiver. If the satellites are scattered and more number of satellites are logged with the receiver then
the data will be better. The satellite configuration can be seen on the GPS receiver screen which shows
that how many GPS satellites are connecting or communicating with the receiver. Observer can also
read the Estimated Position Error (EPE) the main page itself. If your GPS is connecting with four or
more satellites then the EPE will be low, that means your positional data will be good. A GPS receiver’s
one of the main jobs is to locate four or more of these satellites and that depends on receiver’s capacity,
find out the distance to each, and use this data to figure out its own location. This operation is based on
a simple mathematical principle called trilateration, a system which is also used to discover the location
of lightning strikes.
1.11 GPS SATELLITE PERTURBING FORCES
Perturbing forces are external forces/influences which are acting on the orbital path of a GPS satellite or
any other satellite around an object. Some of the common perturbing forces which are observed on GPS
satellites are namely gravitational fields from the sun and other planets of the solar systems, any change
in the Earth’s gravitational field and even solar radiation etc. Gravitational fields from other celestial
bodies are called third body effects. As the satellite moves around the Earth, its orbital path is modified
by the gravitational forces from moons and planets (such as the Earth’s moon and the Sun).
The satellite orbit is also changed by fluctuations in the Earth’s gravitational field. These variations
occur due to tide changes and variations in the surface and shape of the Earth. Solar radiation is the
transferring of energy from the sun (such as in the form of photons) onto another object. Solar radiation
can influence the position of a satellite as a result of the photons hitting the satellite (radiation pressure)
when traveling from the sun and reflecting from the surface of the Earth. There is also an upward solar
pressure effect from the light that is reflected from the Earth (called the “Albedo Effect’) to the satellite.
Atmospheric drag is a force that is imposed on an object (such as an airplane or satellite) as it moves
through the atmosphere. Because GPS satellites are located well above the atmosphere of the Earth, the
atmospheric drag force is negligible. Fig. 1.7 shows how external forces may alter satellite orbits. This
diagram shows how a satellite experiences external influences from gravitational forces from the sun
and the moon. The satellite also experiences forces from photons that hit the satellite from the sun and
photons that hit the satellite as they are reflected from the Earth. This diagram also shows that variations
of the Earth’s gravitational field influence the satellite’s orbit as well.