Martographers
Mars' leader in Global Positioning
"If you're on Mars, we'll find you!"
Locationing
The Martian positioning system has location errors similar to the Earth based global positioning system with some important differences. Major error sources in this system are from the satellite clock, ephemeris errors, ionospheric and tropospheric error and receiver noise [1].
Satellite clock error is a major error source in our system with an expected error of 3.5m. Ephemeris errors create approximately 4.3m of error. In our system we have no selective availability, and so the position location requires an accurate measurement of the time of arrival of code sequence at the receiver. The accuracy with which a timing measurement can be made on a single pulse is given approximately as Δt= 1/(Bn*sqrt(S/N)) in seconds where Δt is the RMS timing error, Bn is the noise bandwidth of the RF channel and S/N ratio is the signal-to-noise power ratio for the pulse in the noise bandwidth[1]. RMS error of Δt will be decreased by a factor of nearly 20, so for a 10dB SNR and 6MHz noise bandwidth, values from our system, the measurement accuracy is expected to be approximately 0.8m.
Propagation of waves in ionosphere is another source of error. Due to changes in properties of these media, the expected wave velocity in the receiver becomes different from the actual wave velocity. This difference degrades accuracy in a location estimation. However, scientific studies show that ionospheric effects are not a big concern unless very high accuracy (<1m) position estimation is needed. Recent studies suggest a range error close to 0.4m [2].
Tropospheric delay is another issue to consider in a positioning system. Studies show that the troposphere of Mars, due to its low density, has nearly no impact on propagation of electromagnetic waves [3].
There will also be some dilution of precision (DOP) factors in our MPS. The important ones will be horizontal, vertical, and geometric DOP[1]. Depending of the alignment of satellites in sky, these error sources will gain or lose their impact. In our system we expect to minimize these dilutions of precisions with our designed constellation of visible satellites.
In conclusion, taking into account all possible error sources, RMS range error is expected to be 5.6m.
References:
[1] T.Pratt and E. Allnutt ,Satellite Communications. John Wiley&Sons, 2003.
[2] M.Mendillo and X.Pi , “Ionospheric effects upon a satellite navigation system at Mars”,Radio Science, vol.39,2004.
[3] C.E.Francis ,”The electromagnetic propagation characteristics of venus and mars”, Proceedings of the IEEE, vol.53, Sept. 1965.