GPS goes martian: nav/com for a red planet; Researchers assess the performance of a proposed Martian satellite positioning system, calculate inter-satellite and satellite-ground ranges and range rates, and finally predict the ability of Mars exploratory vehicles—the Netlanders—to position themselves by observing passing satellites

GPS World,  June, 2004  by Kyle O'Keefe,  Gerard Lachapelle,  Susan Skone

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To compute these figures of merit, the Mars Network constellation is simulated for one sol. Satellite orbits were computed using a GPS almanac-like representation, that is, six Keplerian parameters plus the secular drift of the right ascension of the ascending node. In the simulation, landed elements were located at 5 degree intervals in latitude and longitude and with each making one observation once every three minutes. The landed elements have an elevation mask of 10 degrees. Each landed element is estimating its three dimensional position using two-way observations.

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Figure 2 shows the instantaneous availability, or number of satellites in view, at the start of the simulation, after 15 minutes and after 30 minutes. This figure shows an interesting effect of the Mars Network constellation design. At the initial epoch, one of the two near-equatorial satellites is co-located with two of the near polar satellites. The other two near-polar satellites are at their most northerly and southerly latitudes respectively. For a very brief period, there are three satellites in view for users in this part of the equatorial region. However, 15 minutes later, the two near-polar orbiting satellites have ascended and descended, leaving only one satellite in view for most users, with smaller regions with two satellites in view and an even smaller region with three in view. After 30 minutes, the polar satellites have switched places and there are again three satellites in view at another location along the equator.

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This initial phasing, with regions with three satellites simultaneously in view near the equator, will not last as the ascending nodes of the two near-equatorial satellites will drift at a different rate than those of the near-polar satellites. However, there will still be intermittent two-satellite coverage near the equator provided by pairs to near-polar satellites.

Figure 3 show the minimum, mean, maximum number of satellite passes per sol as a function of user latitude for the entire constellation, and for a single near-equatorial and a single near-polar satellite. Each satellite makes 11 orbits of the planet per sol. Every location on Mars receives between 20 and 44 satellite passes per sol.

The two near equatorial satellites are visible on every pass to all users located below 15 degrees latitude, and are not visible at all to users above 40 degrees. The four polar satellites are visible to users at all latitudes, though the number of return visits per sol increases from between two and four per sol at the equator to 11 per sol at the poles. Users at 35 degrees have the poorest overall coverage, averaging 22 passes per sol. The mean number of observations per sol as a function of latitude is shown in Figure 4. Comparing this figure to Figure 3 shows that a typical pass results in four or five observations, that is, a typical pass lasts between 12 and 15 minutes.

Availability and pass statistics provide some indication of the global coverage of a satellite constellation, but do not assess the quality of the geometry of the navigation solution or provide an estimate of achievable positioning accuracy.