Kalman Filter Integrity Monitoring Over Finite Time-Intervals

Matthew Marti and Mathieu Joerger

Abstract:	In this paper, we derive and analyze a Kalman filter (KF) integrity monitoring method for measurement faults occurring over a finite past-time interval. The method is intended for safety-critical navigation applications involving GNSS corrections with latency or delayed GNSS authentication, i.e., where a delayed past-time integrity guarantee is available and a current-time integrity risk bound is needed. In-between these two times, redundancy of sensor information is assumed even if all recent GNSS measurements are simultaneously faulted or spoofed, for example, using inertial measurement units (IMUs). To ensure navigation integrity, we derive a compact and recursively updated fault detector using KF innovation projections instead of the conventional normalized innovations squared (NIS) or accumulated NIS. The integrity monitor can then be tailored to the estimated state of interest, thereby providing tight integrity risk bounds while accounting for worst-case fault profiles. We evaluate this integrity risk bound in an example tight integration of GNSS and IMUs.
Published in:	Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025) September 8 - 12, 2025 Hilton Baltimore Inner Harbor Baltimore, Maryland
Pages:	291 - 310
Cite this article:	Marti, Matthew, Joerger, Mathieu, "Kalman Filter Integrity Monitoring Over Finite Time-Intervals," Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025), Baltimore, Maryland, September 2025, pp. 291-310. https://doi.org/10.33012/2025.20304
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