A Temporal Algorithm for Satellite Subset Selection in Multi-Constellation GNSS

GNSS receivers convert the measured pseudoranges from the visible GNSS satellites into an estimate of the position and clock offset of the receiver. For various reasons receivers might want to process only a subset of the visible satellites; it would be desired, of course, to use the best subset. In general, selecting the best subset is a combinatorics problem; selecting m objects from a choice of n allows for ((m)(n)) potential subsets. And since the typical performance criterion (e.g. Geometric Dilution of Precision) is nonlinear and non-separable in the satellites' locations in the sky, finding the best subset is a brute force procedure; hence, a number of authors have described sub-optimal algorithms for choosing satellites. This paper revisits this problem, especially in the context of multiple GNSS constellations. The paper begins with a review of the existing subset selection algorithms. We note that all of these algorithms are what might be called "snapshot" in nature, selecting a subset for a single, fixed skyview of satellites. Through an example with the GPS constellation, we examine the time-sequential, or temporal, characteristics of the best subset selection noting: That the best subset at a particular point (snapshot) in time is also the best subset for a significant time interval around that point (typically measured in minutes). That the changes in the best subset over time are primarily, but not always, due to the loss or gain of a satellite crossing the horizon (or, more precisely, the receiver's mask angle). Based upon these observations this paper develops several time-sequential, or temporal, algorithms that attempt to track the optimum subset of satellites over time at low computational cost. The accuracy and complexity of the algorithms are assessed with GPS constellation data. On a larger scale, these algorithms are then tested on combined GPS, GLONASS, and Galileo constellations with the resulting performance compared to optimal solutions found via exhaustive search.