A Monitor for Correlated Kalman Filter Innovations

Tucker Haydon, Connor Brashar

Abstract:	A novel monitor is introduced to detect correlations in a Kalman filter’s pre-fit measurement innovations. The two primary innovation monitors used today – innovations Snapshot and Sequence monitors – are excellent tools for detecting system faults and biases. These monitors, however, are insensitive to correlations between a Kalman filter’s innovations – a key metric in evaluating and validating system assumptions and performance. A new monitor is proposed which is specifically sensitive to these correlations. The monitor evaluates the sample covariance matrix of a Kalman filter’s innovations over a finite horizon and employs a hypothesis test to determine if a modeling fault has occurred. The monitor is theoretically developed and then validated with two simulations. In the first simulation, correlated random samples are drawn from a multivariate Gaussian distribution, and it is demonstrated that the proposed monitor raises a true-positive flag significantly more often than standard Snapshot and Sequence monitors while maintaining the same false-positive ratio. In the second simulation, a Monte Carlo evaluation of a simple, two-dimensional, GNSS-like example is presented wherein the presented monitor effectively detects correlation modeling errors while a Sequence monitor does not. The proposed correlation monitor has potential applications in atmospheric monitoring, navigation receiver clock monitoring, and GNSS anti-spoofing among others – essentially any application in which correlated faults can occur.
Published in:	Proceedings of the 35th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2022) September 19 - 23, 2022 Hyatt Regency Denver Denver, Colorado
Pages:	3820 - 3832
Cite this article:	Haydon, Tucker, Brashar, Connor, "A Monitor for Correlated Kalman Filter Innovations," Proceedings of the 35th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2022), Denver, Colorado, September 2022, pp. 3820-3832. https://doi.org/10.33012/2022.18567
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