Signal Clustering Using Bayesian Inference (SCUBI): A Bayesian Approach to Choosing Consistent GNSS Signals

Jerome M. Shapiro

Abstract:	GNSS receivers need to be able to exclude faulty navigation signals to ensure accurate PNT determination. These faults can be the result of satellite errors, multipath interference, or deliberate spoofing of multiple signals. A new method for determining consistent sets of global navigation satellite system (GNSS) signals in the presence of faults is presented. A consistent set is defined as having residuals with small magnitudes for each measurement, where a residual is the difference between an actual measurement and a predicted measurement obtained by applying the set’s position-velocity-time (PVT) solution to the pseudorange and pseudorange rate equations for a single signal. Bayesian inference is used to score sets using the posterior log-probability ratio (LPR), which is a metric that is monotonic with the posterior probability that the set is true, where truth here means that each signal in the set comes from a direct line-of-sight (LOS) reception from an actual GNSS satellite rather than a spoofed signal, multipath or a fault. Two algorithms are derived. The first one scores many clusters of 5 signals and sorts them by posterior LPR. The second algorithm takes some of the most promising clusters and attempts to enlarge the cluster using a Bayesian cost function of expected root-mean-square position error. This const function weights the benefit in reduced geometric dilution of precision (GDOP) obtained by adding a true signal against the risk that the added signal is false. An experimental example illustrates the algorithms’ operation.
Published in:	Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021) September 20 - 24, 2021 Union Station Hotel St. Louis, Missouri
Pages:	3307 - 3321
Cite this article:	Shapiro, Jerome M., "Signal Clustering Using Bayesian Inference (SCUBI): A Bayesian Approach to Choosing Consistent GNSS Signals," Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, Missouri, September 2021, pp. 3307-3321. https://doi.org/10.33012/2021.17950
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