Multi-Constellation GNSS: New Bounds on DOP and a Related Satellite Selection Process

GPS receivers convert the measured pseudoranges from the visible GPS satellites into an estimate of the position and clock offset of the receiver. For various reasons receivers might only track and process 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 (n) potential subsets. And since the GDOP performance criterion is nonlinear and non-separable, 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, for the GDOP and PDOP criteria. Included are a discussion of optimum constellations (based upon parallel work of these authors on achievable lower bounds to GDOP and PDOP), musings on how the non-separableness of DOP makes it impossible to rank order the satellites, and a review/discussion of subset selection algorithms. Our long term goal is the development of better selection algorithms for multi-constellation GNSS.