Code phase GNSS receivers convert the measured satellite pseudoranges into estimates of the position and clock offset of the receiver, typically via an iterative, linearized least squares method. Since the pseudoranges themselves are noisy, the resulting estimates of position and time are random variables. To describe the accuracy of this solution, it is common to describe it statistically via the error covariance matrix. Rather than considering the individual elements of this covariance matrix, users frequently reduce it to a scalar performance indicator; the most common of these is the Geometric Dilution of Precision (GDOP). It is well known that the GDOP is a function of the satellite geometry; with only a few visible satellites in poor locations, the GDOP can become quite large. However, for a future with multiple, fully occupied GNSS constellations it is expected that receivers would select those satellites to track so as to achieve the best possible performance. Hence, an understanding of both how small the GDOP can be as a function of the number of satellites visible and the characteristics of the constellations that meet that bound are of value. Further, once identified, a receiver could exploit those constellation characteristics in selecting a subset of satellites. Investigating the best possible GNSS satellite constellation with respect to the GDOP is not a new problem. Recently, these authors developed achievable lower bounds to the GDOP as a function of the number of satellites; the bounds were also extended to non-zero mask angle and to multiple GNSS constellations. Further, using actual GPS satellite ephemeris data, it was shown by example that good GDOP performance resulted from constellations similar to the “best” constellations resulting from the bounds. This paper examines augmentation of the GNSS pseudoragnes with data from non-GNSS sensors; specifically, ranges. While integration of GNSS and non-GNSS sensors is not novel, the perspective in the paper is how such external sensors impact potential receiver performance (i.e. minimum GDOP) and what role they play in satellite selection. Specifically, tight lower bounds to GDOP when the GNSS is augmented by this additional measurement (barometric altimeter or a DME slant range) are presented; achievability of the bounds is also examined.
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