The Global Positioning System
Introduction
1. There had been a requirement for a world wide based navigational aid with an accuracy of a few meters for quite some time. With the introduction of global postioning system, this requirement has been very closely met. The development of nav star GPS is a real time postion fixing system and is a more accurate navigational aid than any other existing system with world coverage. As per the plan an absolute accuracy of 100m will be available to general users of all the countries and an accuracy of 16 m to the US & NATO military and other authorised users.
2. Besides position fixing in three dimension (longitude, latitude and altitude above sea level) GPS provides the user with velocity information and with Universal time coordinated. The construction and working principle of GPS will be covered under the following heads:-
(a) GPS Satellite orbits
(b) General description
(c) GPS position fixing
(i) GPS clocks
(ii) Determining the position of a satellite
(iii) Equations for ranging
(iv) Determination of the user’s position
(v) Determination of the user’s velocity
(d) Satellite frequencies
(e) Accuracy of GPS
(f) Other existing and future satellite systems
GPS Satellite Orbits
3. There are 18 satellites in this system which circle the earth in orbit with a period of 12 sidereal hours. The satellite travels at a velocity of 3.9 km/sec at an altitude of 20200km. The advantage of such a great altitude is that the orbits will be less affected by irregularities caused by the unequal distribution of masses in the earth.
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GPS measures the velocity of the user by means of the doppler effect. For this application the greater altitude is a disadvantage because the doppler curves becomes flatter, thus affecting the accuracy of the measurements. As near the centre of the orbit, there is almost no doppler effect.
4. The 18 satellite constellation is configured in six orbital planes of three satellites each, in addition there are 3 satellites orbiting in space, which can be made operational by radio commands from Earth. These 3 sattelites basically work as a back up system. All satellites have a propulsion system to maintain orbit postion and for stability control. The three satellites in each orbit are equally 2
spaced with an angle of 120 deg between the plane. The angle between each of the 6 orbit planes and the equatorial (the inclination) is 55 deg. The difference between the successive orbit plane is 60 deg. In this arrangement the earth makes one revolution each sidereal day around its north south axis. In that time each satellite completes two orbits. After a north ward heading satellite passes the equator, a southward heading satellite will pass the equator. When the satellite has made an orbit, the earth has rotated 90 deg. The satellite of subsequent planes are staggered by 40 deg.
5. The GPS satellite configuration will enable users at any point on or near the surface of the earth to obtain their position by continuously receiving direct line of sight navigation signals from at least four satellites.
General Description
6. The basic principle of this system is that the satellites in the orbit each radiate a series of precisely timed radio signals which are received by an user after a delay due to the travel time and with the knowledge of the position of the satellite at the moment of transmission, calculates his distance from each and thus his position:
The GPS has three segments :-
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(a) The space segment.
(b) The control segement.
(c) The user segment.
(a)The space segment: It consists of the constellation of satellites.
(b)The control segment: The control segment has currently 4 monitor stations. More stations are being set up, one in the Atlantic area, one in the Pacific area and one at Diego Suare an island in the Indian Ocean. The master control station (including the data upload station) is located at Colorado Springs in the US. The monitor stations track the satellites by receiving their broadcast signals when they are in view.
(c)The user segment. The user segment includes ground based, marine,airborne or space platforms, equipped with GPS receiver/ processors, capable of receiving atleast four satellites signals simultaneously or sequentially. The receiver will select which 4 satellites to track to provide the best geometry for accurate pos’n fixing. As the satellites cont their orbits, the receiver will drop one satellite with marginal geometry, as soon as a different satellite with better geometry becomes available.
7. Technical Data
(a) Wt of each nav star satellite = 850 kgs
(b) Orbit ht = 20,200kms
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(c) Expected operational life of each satellite = 7 1/2 years.
GPS Position Fixing
8. For simplicity, we assume that the position of a satellite is known and that satellite and user/receiver are equipped with clocks which are synchronised. When the satellite transmits a signal at a known time on the users’s clock, and the user receives the signal `t’ seconds later, the travel time is `t’ sec and the distance travelled
is c x t (where C = 3×10 m/s Sp of radio signal).
The locus of the user’s position on earth is a sphere with a radius R = c x t whose centre is at the time it transmitted the signal. The intersection curve between this sphere and the earth is a small circle whose centre is the point where a line from the satellite to the centre of the earth intersects the earth’s surface. Simultaneous application of this type of range measurement from a second satellite provides the user with a locus, which is a second small circle. This circle intersects the first circle at two points. P, one of which is the user’s position. Normally these two positions are far enough apart to avoid ambiguity.
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9. By using two satellites there will be two unknown travel times. At first sight it appears that two satellites will be sufficient to determine latitude and longitude. However, there is a third unknown in the equations, the user’s clock error with respect to the satellite’s clock. Therefore distance to 3 satellites are required. On ships the ht above mean sea level is always known but for an airborne user or a user on land this ht must also be determined. So a min of 4 satellites are reqd. The geometry of the satellites should be such that the angle bet’n the LOPS is 90 degs, to obtain a better accuracy.
10. To perform the range measurements three main problems have to be solved:-
(a) To determine the relation between the user’s clock and the satellite’s clock.
(b) To measure the travel time of the signal with very high accuracy (an error of .1 micro sec corresponds to an error in the 8 -6
range measurement of ext = 3 x 10 x .1 x 10 = 30m).
(c) To inform the user of exact time the satellite transmits signals.
CLOCKS
11. The master control station, the monitoring stations and the satellites are equipped with highly stable clocks, such as caesium or hydrogen laser clocks. These clocks basically indicates the no. of cycles of an alternate current (voltage generated by an oscillator) which have elapsed since a given time, normally indicated by zero on a scale. Basically, it is the accuracy of the oscillators which determines the accuracy of the travel time measurements and thereby accuracy of the position fix. The oscillator has an extremely high
-13 frequency stability,and varies by no more than 2 x 10 cycles per day.
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Instead of measuring the time in seconds, the clock measures the time in very short time units of cycle duration of the order of -9
nano seconds(10 sec).
The user must know exactly how much the satellite clock is fast or slow with respect to his own clock. It is not possible to determine this offset by a time signals transmitted by the satellite because neither the travel time of the signal nor the relative position of the satellite and user are known exactly.
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Taking into account of accuracy required by the GPS, this time difference must be determined with an accuracy of better than .01MS.
The clock at the master control station and the monitoring stations indicate the GPS time, which is almost equal to the Universal Time Co-ordinated(UTC).
The GPS time should be considered as the standard time of the system. The time of a satellite clock is called `Space Vehicle Time'(SV time).
This time may deviate slightly from GPS time and the deviations are different for each satellite. The user’s clock is normally a quartz clock with a lower accuracy than the satellite’s clock.
Determining the position of a satellite
12. It is seen that the position of a user can be determined by ranging from 4 satellites,if the position of the 4 satellites are known at the time of transmission, conversely, if four monitor stations at known positions receive a signal by a satellite at an unknown position, the position of a satellite at the time of transmitting can be determined.
The four monitor stations do not receive a single satellite signal simultaneously, instead they receive signals from all satellites whenever possible. Each monitor station determines the arrival time of all the received satellite signals and pass this information (in GPS time) to the control station, which knows the exact position of the monitor stations. From these four positions of the monitor station, the control station can determine not only the position of the satellite in three dimensions but also the time that the signals left the satellite. From this data new future satellite positions and clock errors can be predicted and transmitted by the upload station to the satellite. The satellite will store this info in its memory and transmit it at regular intervals to the users.
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Because the altitude of the satellite is 20,200 kms the satellites can be received by the monitor stations for a long time during each orbit. This enables the control station to observe and determine its position in orbit.
Equation for Ranging
13. In the GPS system a satellite transmits a signal at a time tSV (GPS time) which is known to the user. Corrections to tsv is broadcasted by each satellite to all users. The signal’s arrival time, `tu’ at the user’s position is indicated on the user’s clock.If the user’s clock were synchronised exactly with the satellite’s clock, then the distance travelled by the signal(Range) = C x (tu – tsv)
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Since the user’s clock has an unknown error or bias with respect to the satellite’s clock.
Hence, the travel time of the signals = tu + tbias – tsv
Therefore, the distance (range) between the user and satellite = C x (tu – tsv) + c x tbias
Determination of the user’s position
14. Let us say that the user is at a point Vx, Vy, Vz and the satellite is at a range R1 position whose co-ordinates are X1, Y1, Z1. The clock bias time between user clock and GPS time = tbias then
2 2 2 2
(X1 – Vx) + (Y1 – Uy) + (Z1 -U3) = (R1 – tbias)
2 2 2
R1 – tbias = Under root (X1-Ux) + (Y1-Uy) + (Z1-Uz)
and for the second, third and fourth satellite
2 2 2
R2 – tbias = Under root (X2-Ux) + (Y2-Uy) + (Z2-Uz)
2 2 2
R3 – tbias = Under root (X3-Ux) + (Y3-Uy) + (Z3-Uz)
2 2 2
R4 – tbias = Under root (X4-Ux) + (Y4-Uy) + (Z4-Uz)
In these equations, the values for X1, Y1, Z1; X2, Y2, Z2; X3, Y3, Z3, and X4, Y4, Z4 are provided by the satellites and R1, R2, R3 and R4 are measured times. This leaves only Ux, Uy, U3 (the user’s position and Tbias (the clock bias) unknown.
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Determination of the User’s velocity
15. The carrier frequency is also employed to determine the velocity of the user by measurement of the Doppler shift. The velocity vector of a satellite at any time can be calculated by the user’s computers. This vector can be resolved into two components.
(a) in the direction of the user, whose position must be known.
(b) in a direction perpendicular to (a).
This second component does not play any further role because a speed in this direction would not bring about a Doppler shift.
Knowing the position of the user and the position and the velocity of the satellite the user’s computer can determine vector(a).
If the speed of the user towards the satellite, based on the Doppler shift measurement, is not equal to the calculated satellite speed,the difference can only have been brought about by the speed `C’
of the user towards or away from the satellite. This speed `C’ can be determined by the user’s computer.
A similar measurement of two other satellite provides the user with two other velocity vectors. These three velocity vectors can then be transformed into three other vectors.
(a) directed north – south
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(b) directed east – west
(c) in the vertical directions
The three initially unknown components would require three independent equations (and three satellites) to be solved. However, the frequency is also not exactly known. Hence four equations and four satellites are necessary to determine the user’s velocity.
Satellite frequencies
16. Each satellite has an oscillator, whose frequency of 10.23 MHz is stabilised by a caesium clock. This frequency is multiplied by 154 to obtain the frequency L1 = 1575.42 MHz ( = 19cm) and by 120 to obtain the frequency L2 = 1227.6 MHz ( = 24cm).
So for navigational purposes, each satellite transmits on these two frequencies.
The paths travelled and consequently, the travel time of the signals are subjected to the refraction in the ionosphere. This implies that errors in the distance measurement will occur. Two modulations are used (a) Precise (P code)
(b) Coarse acquisition (C/A code)
(a) Precise Code (P code)
By transmitting the P code on the two frequencies L1 and L2 the convertions for these errors can be determined and applied to the travel time. Therefore the accuracy of P code is better.
(b) The Coarse acquisition Code (C/A code)
This is only transmitted on the frequency L1. Thus its accuracy is lesser than P code.
The L1 signal carries both modulations where as the L2 will carry either P/Code or C/A code but not both. The GPS applies phase modulation.
17. Four further frequencies are carried on each satellite Two S-band channels for re-freshing the pre-calculated satellite position memories and correcting the satellite clock from the ground stations, and a L-Band and a UHF channel for satellite’s second payload.
18. Coded signals: The signals transmitted by the satellite consists of a sequence of positive and negative voltages, called chips. The duration of each chip is called the chip length or chip period.
In the C/A code : the chip frequency = 1.023 MHz
chip length = 0.9975m sec
Code length or sequence length = 1 ms
Therefore a sequence consists of 1000/.9975 = 1000 chips
The sequence is repeated every ms.
In the P code : the chip frequency = 10.23 MHz
chip length = 99.75 ns(1/10 of C/A code)
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Each week at 0000 UTC Saturday/Sunday night a new sequence starts. During that week there are repetitions. This extremely long code length would make it difficult and too time consuming to find out the sequence. Therefore, every 6 secs the satellite transmitter broadcasts the time that has elapsed since the P code restored. This enables the receiver to find the appropriate part of the code faster.
19. The C/A and P code are transmitted simultaneously and continuously, using the same carrier frequency. By applying a special electronic process in the transmitter and the receiver, the receiver is able to seperate the two codes.
Accuracy
20. The basic difference between the two codes is that P code modulation sequences vary faster because of their higher chip freq of 10.2 Mega chips/sec than those of C/A code with a frequency of 1.023 mega chips/sec. Auto correlation of the P code is therefore performed with greater precision and this results in greater accuracy.
21. The fix accuracy of the P code is about 15m in latitude, longitudes and height. The accuracy of C/A code is 100m. However the accuracy in P code can be achieved to 6m and in C/A mode to 16m. Perhaps the accuracy in C/A mode may be purposely downgraded to more than 100m by reducing the stability of the clock or by changing the code. The P code will not be available to the general user. In times of war knowledge of the applied codes may only be provided to US and allied users.
The accuracy of the GPS system depends on the following :-
(a) Receiving the C/A code or the P code.
(b) The errors in the orbit prediction of the satellites.
(c) The unknown delays in the signal propagation, caused by tropospheric and ionospheric refraction.
(d) The variable errors in the travel time measurements of the coded signals between satellite and the user.
(e) The geometry of the satellite configuration at the time of the fix determination, ie, the direction of the satellite in relation to the user’s position. Each range measurement of a satellite has an error in the direction of the line between the satellite and the user.
22. Thus the Navstar GPS system is capable of :-
(a) Providing the user with longitude, latitudes and height information with velocity and GPS time.
(b) Position fix is obtained in less than .1 sec.
(c) The fix accuracy of P/Code is 15m and the Coarse acquisition code is 100m.
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(d) It can provide the information, 24 hrs in all weather.
Other existing and future Satellite Systems
(a) GLONASS
23. While the United States has developed the Navstar GPS the Russians are also developing a very similar system known as GLONASS. There are many similarities between the two systems.
The main features of GLONASS are :-
(i) The satellite constellation consists of 24 satellites in three orbital planes.
(ii) The altitude of these satellites are between 18840 and 19940 kms.
(iii)The orbital period is 11 hours and 16 minutes.
(iv) The satellite radiate L1 signal at approx 1600MHz and L2 signals at approx 1250 MHz (The L1:L2 freq = 9:7)
(v) In this system each satellite radiatesa discrete frequency for identification.
(vi) In Navstar GPS there is facility to degrade its accuracy for non-authorised users. This aspect of degrading the accuracy is not possible in the GLONASS.
(b) NAVSAT
24. The European Space Agency is developing this system which stands for Navigation by Satellites. The system is probably based on the same techniques as the Navstar GPS but is in an early state of development.
