Surveying: Capter-1: Satellite Dependent Errors In GPS Signals

Satellite dependent: Ephemeris errors and orbit perturbations, Forces on GPS satellites, Effects of orbital bias, Types of satellite ephemerides, Satellite clock bias, Selective availability, Receiver dependent: Receiver clock bias, Cycle slip, Selective availability (SA), Observation.

Types of satellite ephemerides:

Ephemeris is generally refers to a table or computerized records of the position of naturally occurring astronomical objects, as well as artificially satellites in space in a time. The satellites in their orbits slightly get shifted from their theoretical positions due to some gravitational influences by solar bodies in solar system. These shifts are very difficult to predict, and are generally fall in the range of 0.5m. These astronomical satellite positions basically derived from the timings of their eclipses in the shadow of Jupiter.

The satellite orbital information can be collected in two different classes

1.      Broadcast ephemerides, which are based on the previous tracking information, available to all users at the time of GPS observations. This ephemeris information is available in satellite navigation message, computation are made in the master control station by having use of tracing data obtained from 5 monitoring stations.

Regarded to this ephemeris’s accuracy, some effects can be seen

1. Effect of accuracy of procedure adopted in orbit computation; P-code seudo-range data is used in the computation, although signal tracking geometry is not so strong to provide best results.
2. Errors associated with the unpredictable satellite orbital motion during upload.
3. Effect of selective availability, included the intentional degradation in related broadcast ephemeris parameters within the navigation message. The error induced has high variability in magnitude as possible as 100m or more.  

The accuracy provided by broadcast ephemeris data is below 10m for single navigation message, and better then 5m when daily 3 updates has performed.

2.      Post processed ephemerides, which representation data of orbit, valid only for period of time for which tracking data covered. More accurate than the broadcast ephemerides, having an accuracy level below the meter level.  To get these high accuracy ephemerides there are two requirement 

1. Network of tracking stations and
2. An orbit processing facility.

After the mid 1980’s it become easier to establish a bigger tracking network, because since then there have been tracking networks organized on regional, continental and global bases. These networks were operated for scientific, private and/or government initiatives, as well as military purposes. Some networks have operated intermittently, for specific geodetic applications; others were organized on a semi-permanent basis. Several of these networks were the first examples of international civilian cooperation in the field of GPS ground infrastructure.

Ephemeris errors and orbit perturbations:

Ephemeris errors and orbit perturbations are the inconsistency or difference between the true position of satellite or its orbit and its broadcast ephemeris. These positions are recorded as a function of time in broadcast navigation message. The prediction of these positions, are done on the basis of the previous GPS observations at ground control stations. This ephemeris information for determining GPS satellite positions is produced from the tracking data collected by five monitoring stations of satellite control segment. Data obtained, is processed at MCS (Master Control Station) and navigation satellite information is uploaded to every satellite. The associated errors in satellite position prediction are transmitted to the user in the satellite data message and are available to the GPS users at the time of the observation.

This discrepancy can be parameterized in a number of ways, but a common way is via the three orbit components: along-track, cross-track and radial.  In the case of GPS satellites the along-track component is the one with the largest error.

Figure 1: Satellite ephemeris bias

Reference: http://www.gmat.unsw.edu.au/snap/gps/gps_survey/chap6/623.htm

The ephemeris errors and perturbation are very much influence because of the influence of the some forces, which can be listed as below:

1.      Central gravitational attraction forces

2.      Non-central gravitational forces (perturbing forces)

These forces are very difficult to calculate, and thus the ephemeris errors are very tough to eliminate. The first force is very large in magnitude (about 3order larger) in comparison of all other perturbation forces in solar system.

Ephemeris error are basically satellite dependent and are most difficult to model, correct and eliminate because of failure in prediction of effect of above mention force directly and magnitude on the predicted orbit of satellite.

Forces on GPS satellites:

Mainly acing forces on GPS satellites are classified as below;

1. Central gravitational attraction force
2. Non-central gravitational forces (perturbing forces)

Perturbing force is a combined effect of various solar forces caused by various solar bodies and effects that can further be summarized as;

1. Non central gravitational forces
2. Third body effects like gravitational attration of sun, moon, and other solar planes near and farther to satellite location
3. Atmospheric drag force
4. Solar radiation pressure force
5. Magnetic forcesVariable part of earth gravitational field arising from tidal and other deformations of solid earth and ocean.

Figure 2: Forces on satellite

Some of the forces mention above are significantly affect the theoretical position of satellite in their predicted orbit and influences the shift in location orbit and satellite position. Pre described satellite motion is mainly function of the central gravitational force, hence it is very much concerned of it.

Effects of orbital bias:

These are the effects which are

1.      Associated with computational accuracy of procedure which is used to calculate the orbital location and associated velocity using P-code pseudo-range data, with a weaker tracking geometry because of tracking station located in equatorial belt. In this case accuracies better than 5m can be achieved.

2.      Resulted from the unpredictability in the orbital motion during the period since uploaded. These are essentially prediction errors, which has varying magnitude from meter level to some tens of meters.

3.      Introduction of selective availability caused intentional degradation of broadcast ephemeris parameters; inducing highly variable orbital errors.

4.      Dependent on the ephemerides errors which are influence by

a.      Location and number of tracking stations

b.      Orbital force model

c.       Geometry of satellites in space

5.      Ephemeris errors are uncorrelated between satellites and affect both code and phase measurements. Ephemeris errors are liable to introduce equal error shift in calculated absolute positions.

6.      High measurement is less accurate because there is no satellite below the horizon. Means large error in vertical component of position. The vertical component is accurate and this amount is of the order of 2 to 3 times lesser than horizontal component accuracy.

7.      Each satellite has identical ephemeris errors associated for all users, but different users have different view angles when locating the same satellite, so its effect on range measurement a position is different.

8.      Surveys conducted by using at least 2 receivers at a time gives accurate results then the single one; both receiver have the same amount of error due to effect of orbital bias which is mainly dependent on the distance between the receivers.  If receivers are located more closely than the amount of error will have more similarity. Hence the differential GPS surveys are more reliable to give more accurate point positions.

Satellite clock bias:

For determining the accurate position of objects GPS receiver clock and satellite clock must be in the same time frame. The GPS receiver clocks are generally lacking in precise synchronization with atomic clocks (very stable and expensive clocks) of satellites.  Even these clocks are not so stable enough on their own, so cause some drift or shift of time. Thus there is a time lack in between both the clocks which introduces positional error. The ground segment continuously measures these drifts and keeps them synchronized with the system time scale within a permissible limit. The satellite clocks are not corrected physically for these drifts or shifts in time, rather some satellite broadcast correction made to compensate these drifts between satellite time and system time.  These corrections must include satellite time drifts and its derivatives, which are predicted for some time period over satellites. The corrections made here are then broadcasted within the navigation message to the user.

We can easily classified the problems related to satellites in

a.      Clock drift

b.      Relativistic effect

Clock drift: As mansion above that clock in the satellites and receiver are differ very much in their accuracy as well as materialistic character. Every atomic clock in satellite has high quality, each GPS block 2 and 2A satellites have four atomic clocks, two of them are of cesium and other two of rubidium atomic clocks. One of two cesium clocks is used for time keeping and signal synchronization because they behave better in compare of rubidium clocks, rest of two clocks are for backup.  Stability of GPS clocks basically dependence on the type of clock used in GPS bock satellite both 2 and 2A

a)     Rubidium clock: 1 to 2 parts in 10¹³ over a period of one day or about 8.64 to 17.28 ns per day

b)    Cesium clock: stability improves to 1 to 2 parts in 10¹⁴ over 10 days

c)     Hydrogen maser: 1 part in 10¹⁴

These temporally variant clock errors, which are unavoidable, are the source of significant biases. These biases are monitored by the control segment during tracking data analysis. To reduce these errors in satellite clock, corrections are made, which reduces them up to 1ms of satellite clock error to around 30ns of GPS time.

Realistic effect:  The realistic effect actually accounts for two conditions, which measuredly affect the satellite clocks’ functionality;

Firstly, the time dilation before satellite is sent to orbit; this is basically to ensure the fundament frequency. The fundamental frequency is set to little below than 10.23MHz before launch,  and it is necessary to achieve the fundamental frequency when successfully located in orbit.

Secondly, this effect attributes to eccentricity (0.02) of orbit causing time error of 45.8ns. this error automatically corrected in GPS receiver, by avoiding an error of about 14m.

Selective availability:

Selective availability is a way of the introducing positional random error in the GPS signals for the security purpose. This is a function in GPS navigation system for civilian GPS receivers. 

Each satellite is uniquely located in an orbit in space; the signals broadcasted by a satellite are unique in nature which provides time information of satellite in space.  The position of satellites at a time is recorded in GPS receivers by knowing the all information about signal propagation from satellite to receiver. Using the 4 satellite (at least 4) messages, GPS receiver calculates the time of signal propagation via atmosphere satellite to receiver and having known positions of 4 satellites it estimates the latitude, longitude and elevation of a point. Having use of selective availability on GPS receiver some un-certainties are introduced in the time measurement at the satellite, because selective availability forced to satellite to send wrong time. Although the time sent by satellite is pretty close to the real time, but not that accurate. So this inaccuracy in time makes receiver to estimate the wrong coordinates or position of object which has tried to measure. Thus the positional accuracy goes down due to the interference of selective availability.

The selective availability introduces the error in position up to 100m to the civilian navigation signals. Pseudorandom error are introduced by selective availability uses, which is produced by cryptographic algorithm from a classified seed key available only with some authorized users like government, military, etc. which uses a special type of military GPS receiver with a very controlled key system.

Before it was turned off on May 2, 2000, typical SA errors were about 50 m (164 ft) horizontally and about 100 m (328 ft) vertically.^[10] Because SA affects every GPS receiver in a given area almost equally, a fixed station with an accurately known position can measure the SA error values and transmit them to the local GPS receivers so they may correct their position fixes. This is called Differential GPS or DGPS.

Figure 3: The images compare the accuracy of GPS with and without selective availability

DGPS also corrects for several other important sources of GPS errors, particularly ionospheric delay, so it continues to be widely used even though SA has been turned off. The ineffectiveness of SA in the face of widely available DGPS was a common argument for turning off SA, and this was finally done by order of President Clinton in 2000.

DGPS services are widely available from both commercial and government sources. The latter include WAAS and the U.S. coast guard network of LF marine navigation beacons. The accuracy of the corrections depends on the distance between the user and the DGPS receiver. As the distance increases, the errors at the two sites will not correlate as well, resulting in less precise differential corrections.

( Reference: http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System )