Lunar surface navigation is an important area of research, with the need to define the architecture of how science rovers, manned sortie missions, manned outpost missions, and lunar surface operations will perform navigation. Decisions need to be made as to what navigation aids these vehicles will use to gain knowledge of their lunar surface position. One idea that was investigated at the NASA Glenn Research Center was the use of a constellation of satellites around the Moon providing continuous global coverage. The Lunar-Based Lunar Surface Navigation Analysis characterized the performance of four types of satellite constellations that could be placed around the Moon. The constellations were designed to implement continuous communication and navigation over the entire lunar surface. Constellations included inclined Walker, inclined elliptical, Lang-Meyer, and polar orbit orientations.
Two forms of navigation were investigated: one-way and two-way navigation. The Global Positioning System (GPS) is considered to be a one-way navigation system because signals are only broadcast in one direction. In the one-way navigation system, the user receives broadcast pseudorange signals from satellites and determines their own position and time bias on the basis of pseudorange and range-rate measurements.
One-way navigation system; pr, pseudo-range; 
, range rate.
Long description of figure 1.
Two-way navigation system; r, range; range rate.
Long description of figure 2.
The two-way navigation method would eliminate the need to determine time bias, because the time-stamped signal would be retransmitted back to the source for processing. In the two-way system, the user retransmits broadcast range signals from satellites and determines their own position on the basis of range and range-rate measurements.
Two metrics used to characterize the navigation performance of the constellations were system availability (SA) and system latency (SL), both of which utilize the Dilution of Precision (DoP) technique. DoP is a high-level geometrical analysis of the view angles, from the user to the satellites in view, which is used to determine the effect of geometrical spacing on solution error. This can take several forms depending on the state variables being analyzed. One-way navigation methods, called Geometrical DoP (GDoP), require solving for a topocentric Cartesian position and time. In comparison, two-way navigation methods, called the Positional DoP (PDoP), only solve for a topocentric Cartesian position.
The SA and SL metrics compared the DoP results with a threshold. In the SA analysis, the DoP results, with a given integration latency, were compared with a threshold of 10, and the number of instances where the DoP was less than the threshold was weighted spatially to determine the overall SA. In the SL analysis, integration latency was increased until the SA was 90 percent of the DoP results, from which the integration latency was spatially weighted to determine the overall SL. These metrics were analyzed with 5°, 10°, and 15° minimum elevation angles from the lunar surface points.
SA results for the Polar 6/2/1 satellite constellation.
Long description of figures 3 and 4.
SL results for the Polar 6/2/1 satellite constellation.
Long description of figures 3 and 4.
The study concluded that the Polar 12/4/1 constellation had the best performance, as it also had the most satellites in the constellation. The recommended constellation was the Polar 8/2/1 because it could degrade to the Polar 6/2/1 if a failure was present. The Polar 6/2/1 was an acceptable constellation on the basis of performance and latency results.
The Lunar-Based Lunar Surface Navigation Analysis effort is managed under the Space Communications and Data Systems Project at Glenn. The work was performed in-house by members of the Communications Systems Integration Branch in Glenn’s Communications Technology Division.
Find out more about the research of Glenn’s Communications Technology Division: http://ctd.grc.nasa.govLast updated: December 28, 2007
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