97

CHAPTER 5

ANALYSIS OF SATELLITE CLOCK BIAS, CLOCK DRIFT AND RELATIVISTIC ERROR EFFECT ON THE

PSEUDORANGE AND NAVIGATION SOLUTION

5.1 INTRODUCTION

The GPS position accuracy relies on the precise knowledge of the

satellite orbits and time. Each GPS satellite carries an atomic clock to

provide precise timing information for the signals transmitted by the

satellites. The oscillator clock time and the true time differ from each other

both in scale and in origin. The typical error in GPS positioning, due to the

non synchronisation of satellite clock time to Coordinated Universal Time

(UTC) is 100 ns and the corresponding pseudorange error is 30 m. The GPS

satellites revolve around the earth with a velocity of 3.874 Km/s at an

altitude of 20,184 Km. Thus on account of its velocity, a satellite clock

appears to run slow by 7 µs per day when compared to a clock on the earth‘s

surface. But on account of the difference in gravitational potential, the

satellite clock appears to run fast by 45 µs per day. The net effect is that the

clock appears to run fast by 38 µs per day. This is an enormous rate

difference for an atomic clock with a precision of a few nanoseconds. In this

chapter, the satellite clock error and the relativistic error effect on the

navigation solutions presented in Chapter 4 are carried out by collecting

several days of dual frequency (1575.42.MHz and 1227.6 MHz) GPS receiver

98

data from the Andhra University Engineering College, Visakhapatnam

(Latitude/Longitude 17.730 N/83.320 E).

5.2 GPS ERRORS

The GPS system was designed as a one-way ranging system, where

signals are transmitted only from the satellite in the space to a passive user.

These properties are the requirement of military systems, where system

operators retain full control. In one-way ranging systems, there is an offset

between the independent satellite and receiver clocks, which translate into a

receiver position error (the receiver position being calculated from the

estimated travel time of the signal from satellite to the receiver) (Parkinson

and Spilker 1996).

GPS range measurements contain several errors, resulting from a

variety of sources. Errors in range measurements and satellite location in

the space create a range of uncertainty around the user position. The GPS

errors can arise from inaccuracies in the satellite position estimation and

satellite clock corrections (broadcast ephemerides), tropospheric, ionospheric

effects along the signal propagation path from satellite to receiver and

receiver noise generated through signal processing errors. These effects are

included in the following code based pseudorange (PR) Eq. (5.1) and carrier

phase range (Φcr) Eq. (5.2) observables. All the quantities are in units of

distance (Kaplan 2006). The carrier phase measurement is the difference in

phase between the transmitted carrier wave from the satellite and the

receiver oscillator signal at a specified epoch. The carrier phase range is

99

simply the sum of the total number of full carrier cycles between the receiver

and the satellite, multiplied by the carrier wavelength.

PR = ρ + dρ + cdtsv – cdT + iono + trop +εPR (5.1)

Φcr = ρ + dρ + cdtsv – cdT - iono + trop + εΦ + λN (5.2)

where,

ρ = geometric (or true) range

dρ = satellite ephemeris errors

dtsv = satellite clock error

dT = receiver clock error

iono = ionospheric error

trop = tropospheric error

λ = carrier wave wavelength

c = light velocity in vacuum

N = carrier phase integer ambiguity (in number of cycles)

εPR = pseudorange measurement noise

εΦ = carrier phase measurement noise

5.2.1 GPS SATELLITE CLOCKS AND TIME

GPS works by using a nominal 24 satellites constellation. These

satellites orbit around the earth and relay precise timing information from

onboard rubidium and cesium atomic clocks down to earth.

Atomic clocks

Atomic clocks are critical equipment for the satellite based navigation

systems. The difference between a standard clock in our home and an

atomic clock is that the oscillation in an atomic clock is between the nucleus

of an atom and the surrounding electronics. Atomic clock uses the

100

electromagnetic waves emitted by the atoms. The most commonly used

atomic clocks are Cesium, Hydrogen maser and Rubidium. Cesium clock has

high accuracy and good long term stability. The rubidium clock is least

expensive, compact and has good short term stability. The cesium atomic

clock is used for the purpose of establishing coordinated universal time

(UTC) standard. The UTC standard is maintained by over 250 atomic

stations around the world. The first three GPS satellites used rubidium

clocks. The Block II/IIA GPS satellites carry 2 rubidium and 2 cesium clocks

onboard. The different atomic clock standards are given in Table 5.1.

Table 5.1 Different atomic clock standards

Atomic clock Type of standard Accuracy Stability Remarks

Cesium Primary 5×10-13 1×10-14 Excellent stability

Rubidium Secondary 5×10-11 3×10-11 Good stability

Crystal Ternary 1×10-9 1×10-12 Cheap and poor

accuracy

The GPS receiver located on or above the earth‘s surface will pick up

this time signal from at least four satellites and computes its exact position

using triangulation method. The receiver calculates the distance between

each satellite to its antenna phase center by considering how long each

timing signal takes to reach the receiver. The time taken by the signal to

travel from the satellite to the receiver is known as travel time or transit time

of the signal. The velocity of the light is multiplied by the travel time to get

the distance between the satellite and the receiver. This distance computed

is not the true range and is known as ‗pseudorange‘. Because of this, the

101

pseudorange measurement includes several errors such as satellite clock,

atmospheric errors, multipath and receiver noise. The pseudo part of the

pseudorange is mainly dependent on both the satellite and receiver clock

errors.

Among these two clock errors, satellite clock error is precisely known,

and is broadcasted in the navigation message data. The receiver clock offset

is computed as part of the navigation solution algorithm. GPS satellites use

cesium and rubidium atomic clocks onboard. These are kept within a

millisecond of the master clocks at the GPS master control station located in

Colorado Springs, Colorado. The master control station in turn keeps the

master clocks synchronized to the Coordinated Universal Time (UTC), except

that GPS time is continuous and has no leap seconds. GPS time is derived

from an ensemble of Cesium atomic clocks maintained at a very safe place in

Colorado. The GPS clock time ensemble is compared to the UTC time scale

maintained at the United States Naval Observatory (USNO) in Washington,

D.C.

GPS time differs from UTC by the integer number of leap seconds that

have occurred since the GPS time scale began on 5th/6th midnight of

January, 1980. This difference is equal to 15 s by the year 2010.

5.2.2 SATELLITE CLOCK ERROR

Satellite clock error is caused by satellite oscillator not synchronized to

the GPS time which is a true time. These errors represent the difference

102

between the time reported by the satellite and the GPS system time. The

observation equation for such satellite biased range can be written as

Pm = ρ + dtsv c (5.3)

where Pm = Measured range

ρ = True range

dtsv = Satellite clock error

c = Velocity of light

The travel time of SV signal is corrected using

t = tsv - dtsv (5.4)

As the satellite clocks use atomic clocks and significantly have better long

term drift characteristics than the receiver clocks, the clock error can be

modeled using the second order polynomial as (Rao 2010)

dtsv = af0 + af1 (t-toc) + af2 (t-toc)2 + Δtr (5.5)

where af0 = Clock bias term (s)

af1 = Clock drift term (s/s)

af2 = Clock drift rate (s/s2)

t = Satellite clock time (s)

toc = Reference epoch for the definition of the coefficients

Δtr = Correction due to relativistic effects (s)

Clock bias (af0) is the difference between the clocks indicated time and

the GPS time. The clock drift (af1) is satellite clock‘s drift from the bias. The

clock drift rate (af2) is the satellite clock drift rate from the bias. The GPS

requires all the transmitter clocks to be synchronized. In reality the GPS

satellites clocks are slowly but steadily drifting away from each other. The

GPS satellite clock bias (af0), drift (af1) and drift rate (af2) are explicitly

103

determined in the same procedure as the estimation of the satellite orbital

parameters. The behavior of each GPS satellite clock is monitored with

respect to GPS time, as maintained by an ensemble of atomic clocks at the

GPS master control station. The clock bias, drift and drift rate of the satellite

clocks are available to all GPS users as clock error coefficients broadcast in

the navigation message at the rate of 50 bps.

5.2.3 RELATIVISTIC EFFECTS

All clocks will have a different frequency in GPS orbit compared to the

frequency of an identical clock on the earth because of relativity effects. In

the day-to-day life, we are quite unaware of the omnipresence of the theory

of relativity. However it has influence on proper functioning of the GPS

system. The clock ticks from the GPS satellites must be known to an

accuracy of 20-30 ns for precise estimation of user position. However,

because the GPS satellites are constantly moving with a speed of 3.9Km/s

relative to observers on the Earth, the effects predicted by the Special and

General theories of relativity must be taken into account to achieve the 20-

30 ns accuracy.

Special relativity predicts that moving satellite clocks will appear to

tick slower than non-moving ones. Because of the slower ticking rate due to

the time dilation effect of their relative motion, the special relativity predicts

that the on-board atomic clocks on the satellites fall behind clocks on the

ground by about 7 µs per day.

104

General relativity predicts that clocks experiencing the stronger

gravitational field will tick at a slower rate. As such, when viewed from on or

near the surface of the Earth, the clocks on the satellites appear to be

ticking faster than identical clocks on the ground. A calculation using

General relativity predicts that the clocks onboard a GPS satellite should get

ahead of ground-based clocks by 45 µs per day. This second effect is six

times stronger than the time dilation experienced above.

The combination of these two relativistic effects results that the clocks

on-board each satellite should tick faster than identical clocks on the ground

by about 38 µs/day (45µs -7µs =38µs). If these effects are not properly taken

into account, a navigational fix obtained based on the GPS constellation

would be false after only 2 minutes, and errors in global positions would

continue to accumulate at a rate of about 10 Km each day. Relativity is not

just some abstract mathematical theory. Understanding it is absolutely

essential for the global navigation system to work properly.

When the satellite is at perigee point, the satellite velocity is higher

and the gravitational potential is lower because of which the satellite clocks

run slower. In contrast, when the satellite is at apogee, the satellite velocity

is lower and the gravitational potential is higher, and so the satellite clocks

run faster. The relativistic error can be modeled as

)sin( kr EAFet (5.6)

where, Δtr = Relativistic error term

105

2

2

CF

µ = Earth‘s gravitational constant=3.986005×1014 m3/s2 C = Speed of light F = - 4.442807633×10-10 s/ m1/2

e = Satellite orbital eccentricity A = Semi major axis of the satellite orbit and

Ek = Eccentric anomaly of the satellite orbit

Correlating the satellite clock for relativistic effect will result in a more

accurate estimation of the time of transmission by the user. Due to rotation

of the earth during the signal transmission time, a relativistic error is

introduced, which is called the sagnac effect. During the propagation time of

the SV signal, a clock on the surface of the earth will experience a finite

rotation with respect to the resting reference frame at the geocentre. If the

user receiver experiences a net rotation away from SV, the propagation time

will increase and vice-versa (Boubeker et. al., 2005).

The satellite correction parameters are estimated using a curve fit to

the predicted estimates of the actual satellite clock errors, but during this

computation, some residual error remains. This residual clock error (𝜹t)

results in ranging errors that typically vary from 0.3 to 4.2 m, depending on

the type of GPS satellite and age of the broadcast data. The range errors on

the pseudorange measurement due to residual clock errors are generally the

smallest following a control segment uploads to a satellite, and they slowly

degrade over time until the next upload (Akim and Tuchin 2002).

The satellite clock error (dtsv), symmetrically affects all the measurements

made to satellite, by any GPS receiver making a measurement at the same

106

time. Hence, satellite clock error (dtsv) is spatially correlated at an epoch and

this property can be exploited to overcome the effect of this bias (Boubeker

et. al., 2005).

5.3 RESULTS

The GPS data required for investigating the satellite clock and

relativistic error impact on the proposed navigation solution was collected

from a newly installed dual frequency GPS receiver (NovaTel make DL-V3) at

Andhra University College of Engineering, Visakhapatnam, NGRI, Hyderabad

and IISc, Bangalore stations. The data corresponds to 15th February, 2010.

The actual position coordinates of the receiver located at Visakhapatnam are

X=706970.909 m, Y=6035941.022 m and Z=1930009.582 m. The variation

of mean anomaly for SV PRN 31 over a day is shown in Fig. 5.1. The

variation of eccentric anomaly for the same satellite is shown in Fig. 5.2. The

ephemeris required for the computation of mean anomaly and eccentric

anomaly values are transmitted by the satellite in the navigation data for

every two hours. The mathematical formulae used in the computation of

mean anomaly and eccentric anomaly are given below.

kk ntMM 0 (5.7)

sink k kE M e E with, Eo = Mk (5.8)

From Fig. 5.1 and Fig. 5.2 it is clear that the mean anomaly (mean

value=-3.088 rad) and the eccentric anomaly (mean value=3.194 rad)

remains same for two hours and they change for every two hours. Fig. 5.3

shows the satellite clock bias variation over a day for the same satellite. This

107

value (-5.136e-05 s) also remains same for two hours and changes every two

hours. Variation of satellite clock drift over a day is shown in Fig. 5.4. From

Fig. 5.4, it is clear that the satellite clock drift value (1.592e-12 s/s) remains

same for the entire day for SV PRN 31. The satellite drift rate value in the

navigation data for SV PRN 31 is zero.

10 11 12 13 14 15 16 17-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

GPS Time in Hours

Mean

an

om

aly

in

Rad

ian

s

Fig. 5.1 GPS time vs. Mean anomaly

10 11 12 13 14 15 16 172

2.5

3

3.5

4

4.5

5

5.5

GPS Time in Hours

Eccen

tric

an

om

aly

in

Rad

ian

s

Fig. 5.2 GPS time vs. Eccentric anomaly

SV PRN No. 31

Min.: 2.097 rad at 10:00:00 Hrs

Max.: 5.236 rad at 16:00:30 Hrs

Mean: 3.194 rad σ = 0.905 rad σ2 = 0.82

SV PRN No. 31

Min.: -4.191 rad at 10:00:00 Hrs

Max.: -1.04 rad at 16:00:30 Hrs

Mean: -3.088 rad σ = 0.91 rad σ2 = 0.828

108

10 11 12 13 14 15 16 17-5.1365

-5.136

-5.1355

-5.135

-5.1345

-5.134

-5.1335

-5.133

-5.1325x 10

-5

GPS Time in Hours

Sate

llit

e c

lock b

ias i

n S

eco

nd

s

Fig. 5.3 GPS time vs. Satellite clock bias

10 11 12 13 14 15 16-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1x 10

-11

GPS Time in Hours

Sate

llit

e c

lock d

rift

in

Seco

nd

s

Fig. 5.4 GPS time vs. Satellite clock drift

SV PRN No. 31 Min.: -5.136e-05 s at 10:00:00 Hrs

Max.: -5.132e-05 s at 16:00:30 Hrs Mean: -5.135e-05 s

σ = 9.875e-09 s σ2 = 9.753e-17

SV PRN No. 31 Min.: 1.592e-12 s/s at 10:00:00 Hrs Max.: 1.592e-12 s/s at 10:00:00 Hrs

Mean: 1.592e-12 s/s σ = 7.275e-27 s/s σ2 = 5.292e-53

109

10 11 12 13 14 15 16 17-2

-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

-8

GPS Time in Hours

Rela

tivis

tic e

rro

r in

Seco

nd

s

Fig. 5.5 shows the variation of relativistic error for 17 hours duration

of GPS time for the same day. This also remains same for two hours and

changes every two hours. The mean relativistic error observed is -4.054e-09

s and the minimum and maximum values observed are -1.564e-08 s and

1.737e-08 s respectively.

Fig. 5.5 GPS time vs. Relativistic error

The variation of the satellite clock error over a day is shown in Fig. 5.6.

This satellite clock error is used in correcting the pseudoranges to the

satellites from the user. From Fig. 5.6, we can observe that unlike other

parameters it varies continuously over the day because it is not the

parameter which is transmitted by the satellite. The satellite clock error is

estimated using Eq. (5.5).

SV PRN No. 31 Min.: -1.564e-08 s at 14:00:30 Hrs

Max.: 1.737e-08 s at 16:00:30 Hrs Mean: -4.054e-09 s

σ = 1.364e-08 s σ2 = 1.863e-16

110

10 11 12 13 14 15 16 172

2.1

2.2

2.3

2.4

2.5

2.6x 10

7

GPS Time in Hours

Pseu

do

ran

ge o

bserv

ed

on

L1 d

ue t

o C

/A c

od

e (

m)

10 11 12 13 14 15 16 17-5.137

-5.136

-5.135

-5.134

-5.133

-5.132

-5.131

-5.13x 10

-5

GPS Time in Hours

Sate

llit

e c

lock e

rro

r in

Seco

nd

s

Fig. 5.6 GPS time vs. Satellite clock error

The pseudorange of SV PRN 31 observed on L1 due to C/A code over a

day is shown in Fig. 5.7.

Fig. 5.7 GPS time vs. Pseudorange observed on L1 due to C/A code

SV PRN No. 31 Min.: -5.1363e-05 s at 10:00:00 Hrs Max.: -5.1328e-05 s at 16:09:30 Hrs

Mean: -5.134e-05 s σ = 1.015e-08 s σ2 = 1.032e-16

SV PRN No. 31 Min.: 20231100 m at 11:54:00 Hrs

Max.: 25426700 m at 16:09:30 Hrs Mean: 2.215e+07 m σ = 1.6312e+06 m

σ2 = 2.6609e+12e+12

111

10 11 12 13 14 15 16 172

2.1

2.2

2.3

2.4

2.5

2.6x 10

7

GPS Time in Hours

Co

rrecte

d p

seu

do

ran

ge o

bserv

ed

on

L1 d

ue t

o C

/A c

od

e (

m)

Fig. 5.8 GPS time vs. Corrected pseudorange observed on L1 due to C/A

code

The number of satellites visible, satellite clock bias, satellite clock

drift, satellite clock drift rate and satellite clock errors estimated at a

particular epoch 10:00:00 hours are presented in Table 5.2. The

pseudorange observed on L1 due to C/A code and the corrected pseudorange

observed on L1 due to C/A code (taking satellite clock error into

consideration) and the error in range (corrected pseudorange – observed

pseudorange) due to satellite clock error are also presented in Table 5.2.

Similarly the number of satellites visible, satellite clock bias, satellite clock

drift, satellite clock drift rate and satellite clock estimated at the same epoch

along with the pseudorange observed on L2 due to P code and the corrected

pseudorange observed on L2 due to P code are presented in Table 5.3.

SV PRN No. 31

Min.: 20215700 m at 11:54:00 Hrs Max.: 25411300 m at 16:09:30 Hrs Mean: 2.214e+07 m

σ = 1.6312e+06 m σ2 = 2.661e+12

112

Table 5.2 SV PRN numbers with corresponding Satellite clock bias, clock

drift, clock drift rate and pseudorange observed on L1 (1575.42MHz) due to

C/A code

S.

No.

SV

PRN No.

Satellite clock

bias (af0) (s)

Satellite

clock drift (af1) (s//s)

Satellite

clock drift rate (af2) (s/s2)

Satellite clock

error (s)

Pseudorange

observed on L1 due to C/A code (m)

Corrected

Pseudorange observed on L1 due to C/A code

(m)

Error in

range due to satellite clock error (m)

1 3 0.00051607 5.23e-12 0 0.00051607 24146014.0 24300734.3 154720.3

2 6 0.00024922 -5.23e-12 0 0.000249185 23551751.6 23626454.1 74702.5

3 14 1.1967e-05 4.32e-12 0 1.19982e-05 21099178.4 21102774.7 3596.3

4 19 -1.57985e-5 -2.387e-12 0 -1.57985e-05 24675000.3 24670266.6 -4733.6

5 21 -4.07342e-5 -2.501e-12 0 -4.07522e-05 20907167.9 20894947.3 -12220.5

6 22 0.000179099 -9.09e-13 0 0.000179092 21637020.8 21690710.2 53689.3

7 24 0.000262568 3.297e-12 0 0.000262592 23222544.8 23301267.1 78722.3

8 26 -1.87554e-5 -3.752e-12 0 -1.87825e-05 21008229.4 21002594.4 -5635.0

9 27 0.000126352 3.411e-12 0 0.000126377 25537658.8 25575542.8 37884.0

10 30 0.000219732 3.411e-12 0 0.000219732 24438821.2 24504700.9 65879.6

11 31 -5.13638e-5 1.592e-12 0 -5.13638e-05 22753809.5 22738414.7 -15394.8

Table 5.3 SV PRN numbers with corresponding Satellite clock bias, clock

drift, clock drift rate and pseudorange observed on L2 (1227.6MHz) due to P

code

S. No.

SV PRN No.

Satellite clock bias (af0) (s)

Satellite clock drift (af1) (s//s)

Satellite clock drift rate (af2)

(s/s2)

Satellite clock error (s)

Pseudorange observed on L2 due to P code (m)

Corrected Pseudorange observed on L2 due to P

code (m)

Error in range due to satellite clock error

(m)

1 3 0.00051607 5.23e-12 0 0.00051607 24146014.0 24300734.3 154720.3

2 6 0.00024922 -5.23e-12 0 0.000249185 23551751.6 23626454.1 74702.5

3 14 1.1967e-05 4.32e-12 0 1.19982e-05 21099178.4 21102774.7 3596.3

4 19 -1.57985e-5 -2.387e-12 0 -1.57985e-05 24675000.3 24670266.6 -4733.6

5 21 -4.07342e-5 -2.501e-12 0 -4.07522e-05 20907167.9 20894947.3 -12220.5

6 22 0.000179099 -9.09e-13 0 0.000179092 21637020.8 21690710.2 53689.3

7 24 0.000262568 3.297e-12 0 0.000262592 23222544.8 23301267.1 78722.3

8 26 -1.87554e-5 -3.752e-12 0 -1.87825e-05 21008229.4 21002594.4 -5635.0

9 27 0.000126352 3.411e-12 0 0.000126377 25537658.8 25575542.8 37884.0

10 30 0.000219732 3.411e-12 0 0.000219732 24438821.2 24504700.9 65879.6

11 31 -5.13638e-5 1.592e-12 0 -5.13638e-05 22753809.5 22738414.7 -15394.8

The user position and the error in user position before and after the

satellite clock error correction is applied to both the pseudoranges are given

113

in Table 5.4. From Table 5.4, it is observed that the error has reduced

drastically with corrected pseudorange. The analyses of different parameters

corresponding to SV PRN 31 are presented in Table 5.5. The maximum

satellite clock error is found to be 5.1328e-05 s which corresponds to a

range error of 15398.4 m.

Table 5.4 The user position and the error in user position before and after

satellite clock error correction is applied to pseudoranges

S.

No.

User position

estimation using

User Position in Meters Error in Meters

X position Y position Z position X position Y position Z position

1

Pseudorange

observed on L1 due

to C/A code

(meters)

711873.642 5959315.072 1893001.288 -4902.733 76625.950 37008.294

2

Corrected

Pseudorange

observed on L1 due

to C/A code

(meters)

706953.277 6035844.981 1929978.825 17.631 96.041 30.756

3

Pseudorange

observed on L2 due

to P code (meters)

711873.220 5959319.310 1893005.642 -4902.310 76621.712 37003.939

4

Corrected

Pseudorange

observed on L2 due

to P code (meters)

706952.860 6035849.256 1929983.186 18.048 91.765 26.395

Table 5.5 The analysis of different parameters corresponding to SV PRN 31

S.

No.

Parameter Minimum

value

Maximum

value

Mean Standard

deviation (σ)

Variance

(σ2)

1 Eccentric anomaly (radians) 2.097 5.236 3.194 0.905 0.820

2 Mean anomaly (radians) -4.191 -1.040 -3.088 0.910 0.828

3 Satellite clock bias (s) -5.136e-05 -5.132e-05 -5.135e-05 9.875e-09 9.753e-17

4 Satellite clock drift (s/s) 1.592e-12 1.592e-12 1.592e-12 7.275e-27 5.292e-53

5 Relativistic error (s) -1.564e-08 1.737e-08 -4.054e-09 1.364e-08 1.863e-16

6 Satellite clock error (s) -5.1363e-05 -5.1328e-05 -5.134e-05 1.015e-08 1.032e-16

7 Pseudorange observed on L1

due to C/A code (meters)

20231100 25426700 2.215e+07 1.6312e+06 2.6609e+12

8 Corrected pseudorange

observed on L1 due to C/A

code (meters)

20215700 25411300 2.214e+07 1.6312e+06 2.661e+12

114

5.4 CONCLUSIONS

The critical application of GPS in civil aviation sector is the aircraft landing

phase which requires the statistical analysis of GPS error measurements.

The error is considered as a deviation of an estimate from a reference value,

so it is possible to determine individual errors as a function of time. In this

chapter, the behavior of satellite clock errors is studied and their impact on

timing and positioning accuracy is analyzed. The pseudorange observed on

L1 due to C/A code and pseudorange observed on L2 due to P code

measurements were processed and analysed to obtain the statistical

performances of the GPS satellite errors (ephemeris and satellite clock). From

this analysis, it is found that due to maximum satellite clock error

(51.328µs), the maximum pseudorange can go up to 15.398 Km and this will

translate into the position domain.