GIS@development September 2000; An Appraisal of GPS Related Errors

Abstract
The GPS provides position of a point on the surface of the earth with high degree of speed and accuracy. However, the GPS measurements are also fraught with all kinds of errors. The gross and random errors in GPS measurements can be treated in the same way as in any other surveying technique. To study the effect of systematic errors, it is necessary to understand the error sources and their effect on the measurements. In this paper, a brief evaluation of the various error sources and their effect on GPS measurements has been provided.

Introduction
Now a days, Global Positioning System (GPS) is being used for a variety of applications such as control surveys and mapping, photogrammetry, remote sensing, aircraft route navigation, crustal movement studies, glaciology etc. It is a satellite-based positioning system that provides 3 dimensional position, velocity and time with high degree of accuracy. There are 24 satellites revolving in six orbital planes. The atomic clock in each satellite generates a fundamental frequency of 10.23 MHz from which two frequencies (f1 = 1575.42 MHz and f2 = 1227.6 MHz) are created. A Pseudo Random Noise (PRN) code, also called C/A (Clear Acquisition) code, is modulated on the f1 frequency. Another more precise P (Precision or protected) code is modulated on both f1 and f2 frequencies.

The accuracy of GPS depends on the quality of the two basic measurements namely pseudorange and carrier phase, and the satellite ephemeris data. In addition, fidelity of the underlying physical model that relates various parameters is also relevant. All these activities may be fraught with errors that may lead to the degradation in the quality of GPS observations. Some of these errors may have systematic effect while others may have random effect. Systematic effect may change from one survey epoch to another due to the change in the error characteristics or the geometry of the satellites and thus need to be modeled perfectly (Chrzanowski and Chen, 1994). Random effects can not be modelled analytically and hence may be distributed or adjusted within a set of GPS observations. It is very important that the behaviour of various types of errors in the GPS observations is understood properly so as to derive accurate and meaningful results from these.

The main objective of this paper is to apprise the user with the various types of errors that may creep in during the GPS measurement process and to suggest possible remedies to reduce the effect of these errors.

GPS Observations
GPS provides two services, Standard Positioning Service (SPS) and Precise Positioning Service (PPS). PPS is intended for military and selected government agencies whereas SPS is available to all civilians worldwide with no restriction on its use. The SPS can provide predictable accuracy of 100m in horizontal and 156m in vertical whereas PPS can provide 22m in horizontal and 28m in vertical planes. Access to the PPS position services is controlled through two cryptographic features denoted as Anti-Spoofing (AS) and Selective Availability (SA). AS is a mechanism to defeat deception jamming (Kaplan, 1996). Deception jamming is a technique whereby ranging codes, navigation data, carrier frequencies from one or more satellites are replicated with the intention to deceive the user's receiver. SA is implemented to deny full system accuracy to the users by intentionally dithering the satellite's clock. It also induces errors into the broadcast navigation data. Nevertheless, there are two basic GPS observables for both PPS and SPS users,

Pseudorange
Carrier phase

Pseudorange is a measure of the distance between satellite and the receiver's antenna and is computed from travel time of the codes. The travel time is measured by correlating identical PRN codes generated by the satellite with those generated internally by the receiver. The satellite and receiver clock offset, atmospheric delay, reflection (multipath) delay etc. tend to corrupt the true range (also referred to as geometric range) measurement. The corrupted range measured by GPS receiver is called Pseudorange. It includes the total time offset due to various error sources such as atmospheric effect, receiver noise, multipath, hardware delay and the SA.

The carrier phase is the difference between the receiving satellite phase (as sensed by the receiver's antenna) and the phase of the internal receiver oscillator at the epoch of measurement (Leick, 1995). These measurements also carry with them various errors such as atmospheric error, multipath error, clock offset etc.

The data in the form of these observables are collected using one or the other GPS surveying technique namely point positioning and relative or differential positioning. In point positioning, a single GPS receiver located on an unknown point is used to determine its three dimensional coordinates (X, Y, Z) with reference to the center of earth in WGS 84 system. In this technique, the accuracy of the position depends on the length of station occupation time of the receiver and the accuracy of the satellite ephemeris.

In differential positioning, two or more GPS receivers receive signals from the same set of satellites simultaneously. One receiver is always positioned on a known point called reference station. The observations to obtain the position of other unknown points called rover stations are processed with respect to the reference station. The accuracy obtained in relative positioning is much higher than that in point positioning because errors common to both receivers get cancelled. There are many ways to perform relative positioning that may be broadly categorized into static and kinematics positioning.

Errors in GPS Observations and their correction
The errors in GPS observations like any other field surveying technique may be broadly categorised as,

Gross errors
Systematic errors
Random errors

Gross Errors
Gross errors are the result of blunders or mistakes that occur due to carelessness of the observer. Some of the reasons causing the gross errors in GPS observations are,

Loss of lock to a few satellites for some time due to the presence of a dense tree, tall building or any other obstruction close to GPS antenna.
Corruption of GPS signals due to any power line or similar object having magnetic characteristics near the observation point.
Improper levelling and/or centering of receiver antenna.
Errors in measuring height of antenna center from ground.

To remove or minimize the effects of blunders, skilled observers should be employed for taking GPS observations with due precautions related to the above error sources. If the observations still contain blunders, these may be treated as outliers and must be rejected using some rejection criteria such as three-sigma criterion (Mikhail and Gracie, 1981).

Systematic Errors
Systematic errors are so called because they occur according to some deterministic system that can be expressed by some functional relationship. The GPS errors having systematic behaviour can be classified into three categories,

Satellite related errors
Receiver related errors
Signal propagation errors

Satellite related errors
The satellite related errors originate either directly from the satellite or are found to be a part of satellite transmitted signals. These include errors due to satellite orbit and selective availability (SA) etc. Some of these errors are be described in the following,

Satellite clock errors
Satellites contain atomic clocks that control all onboard timing operations including broadcast signal generation. Although the clocks are highly stable, these may deviate up to one millisecond from GPS time. This deviation is known as satellite clock error. It is usually estimated at the Master Control Station and the required correction is broadcast to the satellite. Since the signals transmitted from satellite to the receiver are corrected for this error, the user need not be concerned about this (Kaplan, 1996).
Orbital error Satellite moves in a predefined orbit that is normally estimated from the satellite ephemeris data. Any deviation from this orbit is known as orbital error. The true orbit of the satellite could be estimated provided earth was the only celestial body acting on the satellite and if non-gravitational forces like air-drag and radiation pressure did not exist. However, these forces do exist and, therefore, the true orbit can not be determined. The precision of the estimated orbit depends upon the quality of the ephemeris data. As a result a number of orbits have been estimated (Table 1). It can be seen that in estimating a particular orbit errors ranging from � 0.1m to �3m can be introduced. Any error in orbit determination will result into errors in coordinates of the points. It may however be mentioned that for usual surveying and navigation works, broadcast orbit is generally used.
Selective Availability (SA) This is the largest error source for SPS users and is intentionally induced by the Department of Defense, USA, to degrade the user's navigation solution. The degradation is accomplished by dithering the satellite clock and manipulating the broadcast ephemeris data. However, since SA is generated at the transmission side (satellite), it will have same effect on the measurements taken by different receivers from the same satellites at the same instant. Therefore, SA can be eliminated using differential GPS surveys.

Receiver Related Errors
This group of errors originates from the receiver due to multipath effects, antenna phase center variations etc. The common receiver related errors are,

Phase center variation (PCV)
Phase center is a position (point) in GPS antenna at which the difference between the phase generated by satellite and the receiver is measured. The phase center depends upon the type of antenna used, the GPS signals and their directions etc.

The antenna PCV occurs due to any electrical activity in the immediate vicinity of the antenna. For satellite antenna, phase center is not direction dependent because only the rays pointing towards the earth are relevant. However, in case of receiver antenna, GPS signals come from different directions. This direction dependence of phase center is known as antenna PCV. Satellite antenna PCV is assumed to be same for L1and L2 carriers whereas the receiver antenna PCV is not (Rothacher and Mervart, 1996).

The major impact of PCV on GPS results is elevation dependent. When different types of antenna are used simultaneously, the bias in relative station height may reach to a value of 10 cm independent of the baseline length. For same type of antennas, the main effect of antenna PCV amounts to a scale factor in the network of up to about 0.015 ppm. There are two methods in use today to determine the PCV of geodetic GPS antennas; the anechoic chamber measurements and the determination of PCV from processing GPS data (Rothacher et al., 1995).
Multipath errors
Satellite signals can arrive at the receiver via multiple paths due to reflection from an object close to antenna and/or from the ground. The reflected signals are more likely to interfere with the direct signals from the satellite when satellite signals are received at low elevation. The impact of multipath depends on factors such as the strength and the delay of the reflected signal as compared to the direct signal, the attenuation characteristics of the reflector, and the quality of the measuring technique (Leick, 1995). Thus, the multipath not only distorts the PRN code and navigation data but also the phase of the carrier itself.

To reduce multipath, the antenna may be placed above the highest reflector so that the reflected waves may be prevented to arrive from and above the horizon. Some antenna may be attached with a ground plane with absorbent material to reduce these unwanted reflections. Therefore, the choke ring antenna may be preferred over micro-strip antenna to combat the effect of multipath error. It may, however, be mentioned that the multipath effect is likely to get canceled in the single difference observable for the same type of antenna.
Cycle slips
Often, due to the temporary blockage of the transmitted signals from a satellite, the receiver may loose lock to the satellite. In view of this, the receiver may miss some of the whole cycles in the signal. A cycle slip may be defined as a change of integer ambiguity (i.e., whole cycles) by an unknown integer number from one epoch to the next. The reasons for the occurrence of cycle slips may be the low signal strength, possible rotation and inclination of the antenna in the kinematic mode, obstructions around antenna and low satellite elevation.

There is no analytical method that can determine the integer correction at the cycle-slips all by itself. Therefore, a combination of different measurements may be taken into account to detect cycle slips. For example, a method of double difference can be used (Bock et al., 1989). In this method, carrier phase measurements are obtained by differencing two single difference carrier phase measurements for two satellites. By doing this, all error effects, except atmospheric effects, are cancelled. As stated earlier a cycle slip leads to a change in integer ambiguity by an unknown integer number between two epochs. The characteristic of a cycle slip is that all observations taken after the cycle slip are shifted by the same integer amount. A cycle slip can thus be detected from triple differences obtained from two double differences. There are a few other methods for cycle slip detection and correction as reported by Bock et al. (1989).
Receiver clock error
Inside the receiver, a coded ranging signal (identical to satellite generated code) is generated. There is usually a shift in time until both codes achieve relation. If the satellite clock and the receiver clock are perfectly synchronised, the correlation process yields true propagation time. However, receiver clock will generally have a bias from satellite clock that causes error in the propagation time and pseudorange. This error can be eliminated partially by conducting differential surveys.

Signal Propagation Error
Before reaching the receiver, the signals from satellites travel through the atmosphere. Atmosphere is usually subdivided into two main shells; ionosphere and trophosphere. The troposphere and ionosphere causes the signal propagation delay of the measurements. In case of pseudoranges, the numerical values of both tropospheric and ionospheric corrections are always positive. In case of carrier phase observation the ionospheric term has a negative value because the carrier phase advances due to ionosphere (Leick, 1995).

Ionospheric errors
Ionosphere is the upper part of the earth's atmosphere and is located approximately between 70 km and 100 km above the earth. Ionosphere may be described by the electron density in units of electron per m3 and its effect on radiowave propagation depends on total electron content (Rothacher and Mervart, 1996). Irregularities in the ionosphere produce short-term signal variations resulting into a large number of cycle slips. The effect of ionosphere on the signals can be eliminated by generating new frequencies from the two basic carriers; L1 and L2. Some derived frequencies are,
Ionosphere- free linear combination (L3)
A linear combination of the carrier phase observations L1 and L2, by using either zero or double difference measurements (L3) can be formed. It is often called 'ionosphere- free' combination because the ionospheric path delay is practically eliminated. This linear combination is also true for phase measurements.

Melbourne-Wubbena Linear Combination
This is a linear combination of both carrier phase and code measurements. Besides eliminating the effect of the ionosphere, it also eliminates the error due to geometry, clock and troposphere.
Tropospheric errors
It is the lower part of the Earth's atmosphere which extends from the Earth's surface to an altitude of 40 Km. As troposphere is a neutral atmosphere, the signal propagation depends mainly on the temperature, pressure, and water vapour content of the atmospheric layers. Troposphere is a non-dispersive medium for radiowaves upto frequencies of about 15 GHz. Tropospheric refraction is thus identical for both GPS carriers L1 and L2. An error of 1% in the relative humidity may result into an error of 1cm in height measured from GPS. Therefore, the tropospheric delay needs to be modelled properly. There are different analytical models to determine the tropospheric delays. A few of them are Saastamoinen model, Modified Hopfield model, Simplified model and Melbourne-Wubbena Linear combination. More models may be available in future but usually Saastamoinen model is applied to account for tropospheric refractions (Rothacher and Mervart, 1996).

Random Errors
These are the errors over which the observer does not have any control. These can not be modelled and thus may not be eliminated from the observations. Therefore, these errors are distributed in the GPS observations according to some statistical laws. The amount of these errors may be determined by planning a closed GPS network. Appropriate network adjustment techniques based on least square adjustment principle can then be applied to adjust these errors.

Contribution of Different Errors in GPS Observations
From above, it is seen that the GPS observations are affected by a variety of errors. For example, in Table 2, the error contribution from various sources for both PPS and SPS pseudorange measurements has been provided. It can be seen that the cumulative effect of the GPS errors in the determination of position of a point for PPS is of the order of 6.4 m. For SPS, it may amount to 33.3 m with SA and 8.0 m without SA. It is, therefore, very important that the effect of these errors is considered properly. Gross errors can only be reduced by taking observations with due precautions. Systematic errors need to be studied and modelled carefully. Various commercial GPS processing software include many of the models required for the removal of the systematic errors. The random errors have to be adjusted by establishing a GPS control network of desired accuracy.

Conclusions
The use of different systems of GPS, for precise positioning of points in different areas of applications, is increasing day by day. There are many error sources affecting GPS measurements. Some of the errors can be minimised by adopting suitable observation techniques while others can be eliminated by using appropriate models. To adopt a suitable system, it is important that sources of errors in the system and their effect are understood properly. Depending upon the nature and the characteristics of the errors, suitable models can be framed and adopted to achieve desired accuracy.

Table-1: Estimated Quality of Orbits (Source: Rothacher and Mervart, 1996)
Orbit type	Error(m)	Delay of Availability	Available at
Broadcast Orbit	3.00	Real Time	Broadcast Message
CODE Predicted Orbit	0.20	Real time	CODE through Internet
CODE Rapid Orbit	0.10	After 16 hours	COAD through Internet
IGS Rapid Orbit	0.10	After 24 hours	IGS Data Centers
IGS Final Orbit	0.50	After 11 Days	IGS Data Centers

Table 2: PPS and SPS pseudorange error budget (Source: Kulshreshtha, 1997)
	Positional Errors(m)
Errors Positional Errors(m)	PPS	SPS
		With SA	Without SA
Satellite clock error	3.0	3.0	3.0
Orbital errors Selective Availability	4.3 -	4.3 32.3	4.3 -
Others (thermal radiation)	0.5	0.5	-
Receiver noise and resolution	1.5	1.5	1.5
Multipath errors Others (cycle slip etc.)	1.2 0.5	2.5 0.5	2.5 0.5
Ionospheric errors	2.3	5.0	5.0
Tropospheric errors	2.0	1.5	1.5
Root Sum Square Error	6.4	33.3	8.0

References

Bock, Y. and Leppard, N., 1989, Global positioning system: an overview, Proceedings of General Meeting of International Association of Geodesy, Edinburgh, UK, 57-66.
Beutler, G., Bauersima, I., Botton, S., Gurtner, W., Rothacher, M., and Schildknecht, T., 1989, Accuracy and biases in geodetic application of the GPS, Manuscripta Geodetica, 14, 28 - 35.
Chrzanowski, A. and Chen Y., 1994, Modelling of GPS systematic errors in monitroing and control surveys, Journal of Surveying Engineering, 120, 145-155.
Kaplan, E. D., 1996, Understanding GPS - principles and applications, (Boston: Artech House).
Kulshreshtha, A., 1997, GPS receiver technology overview, Paper presented at GPS National Conference, Febraury 21 --23, 1997, Kanpur.
Leick, A., 1995, GPS satellite surveying, (New York: John Wiley and Sons).
Mikhail, E. M., and Gracie, G., 1996, Analysis and adjustment of survey measurements, (New York: Van Nostrand Reinhold Company).
Rothacher, M., Schaer, S., Mervart, L., and, Beutler, G., 1995, Determination of antenna phase center variations using GPS data, Paper presented at IGS Workshop, Potsdom, Germany.
Rothacher, M. and Merrart, L. (Eds.), 1996, Manual of Bernese GPS software version 4.0, University of Bern, Switzerland.

Note:
The readers may kindly note that errors due to Selective Availability are obsolete after the announcement of Bill Clinton to discontinue Selective Availability from 1st May 2000. The paper however discusses the errors as the paper was written before the above said order. Editing of the item was not attempted as it was felt that readers be made aware of the errors that were present as a result of Selectivee Avilability.