Location Finding and Positioning Errors
Location Estimate Accuracy
The position of the GPS receiver is found by trilateration. The distance of the unknown point (receiver location) from three known points (three satellites) is measured. The distance is calculated using the time it takes for a signal to reach the receiver and the velocity of electromagnetic waves in free space. A fourth satellite is used to correct for the clock bias because the clock in the receiver is not accurate enough.
The major sources of error in a position calculation are estimated in the table below. A discussion of each of the error sources is included in the next section.
Error Source |
Estimated Error (m) |
Satellite Clock Error |
3.5 |
Ephemeris Error |
4.3 |
Ionospheric Delay |
0.3 |
Tropospheric Delay |
0.1 |
Receiver Noise |
3.08 |
Multipath |
0.5 |
RMS Range Error |
6.37 |
The 2DRMS accuracy figure is then calculated with:
2DRMS = 2 * HDOP (~1.5) * Range Error = 19.11 m
95% of all measurements yield a position within 19.11 m of the true location of the receiver. This design figure is better than the Earth GPS system (28.6 m).
Error Sources
Satellite clock error
Due to the similarity between the Mars Positioning System’s configurations to the system on Earth, the satellite clock error is taken to be 3.5 m. [1]
Ephemeris errors
The Earth GPS system’s ephemeris data is considered good for 30 days, and the Mars Positioning System ephemeris data is updated every 21 days; the altitude of the GPS satellites in the two systems are also comparable (Earth system: 20200 km vs Mars system: 17700 km). Therefore, it is reasonable to estimate the ephemeris error to be comparable to 4.3 m. [1]
Ionospheric delay
Trans-ionospheric delay was studied using recent results from the radio science experiment onboard the Mars Global Surveyor (MGS) spacecraft and a photochemical model of Mars’ ionosphere. At GPS frequencies, the Mars ionosphere would cause approximately 0.3 m of error. [2]
Tropospheric delay
In a paper published in The Proceedings of IEEE, the troposphere of Mars, because of its low density, was shown to have essentially no effect on the propagation loss between points on the surface or near the surface. A value of 0.1 m is included in the calculation as an estimate. [3]
Receiver noise
The position location process requires an accurate measurement of the time of arrival of the code sequence at the receiver. Using the following equation: δt ≈ [Bn (S/N)^1/2]^-1 and a time averaging factor of half of a second. The upper-bound estimated error is 3.08 m. [1]
Multipath
GPS signals can also be affected by multipath issues, where the radio signals reflect off surrounding terrain; buildings, canyon walls, hard ground, etc. These delayed signals can cause inaccuracy, with the worst being inside a metropolitan area. With a lack of metropolitan buildings on Mars, the worst-case multipath error estimate is taken to be 0.5 m, approximately half of the error on Earth. [1]
References
[1] T. Pratt, C. W. Bostian, and J. E. Allnutt, Satellite Communications. Wiley, 2002.
[2] M. Mendillo, X. Pi, S. Smith, C. Martinis, J. Wilson, and D. Hinson, “Ionospheric Effects Upon a Satellite Navigation System at Mars,” Radio Science, July 2003.
[3] C. E. Francis, "The Electromagnetic Propagation Characteristics of Venus and Mars," Proceedings of the IEEE, vol. 53, no. 9, p. 1216 - 1221, Sept. 1965.