Detecting Slowly Accumulating Faults Using a Bank of Cumulative Innovations Monitors in Kalman Filters

Abstract

Extended Kalman filters (EKFs) that monitor innovations over time have been demonstrated to be effective at detecting slowly accumulating measurement faults [1]. This paper first demonstrates that a single cumulative monitor becomes increasingly sensitive to measurement error model uncertainty as the accumulation interval increases. As a result, the monitor’s false alarm and missed detection rates can differ significantly from predefined design parameters. In response, we investigate the use of a bank of cumulative innovations monitors for measurement fault detection in multisensor navigation systems. Focusing on a tightly coupled GPS+inertial EKF, high-fidelity Monte Carlo simulation that includes real-world model uncertainty demonstrates that the monitor bank maintains tighter compliance with specified false alert and missed detection requirements. The simulations also quantify the ability of multiple monitors to reduce time-to-detect. Practical considerations including implications for mitigation are discussed. Simulation results indicate significant improvement in detecting slowly accumulating measurement faults using the monitor bank compared to the single cumulative monitor for a runtime of 30 minutes. We describe a novel covariance analysis extension method and compare the predicted performance of our method to traditional snapshot innovations monitoring and the infinitely accumulating monitor in [1]. Covariance analysis and Monte Carlo simulation results are presented for a variety of fault detection profiles and inertial measurement unit (IMU) qualities (tactical-grade and aviation-grade). Data for the time-to-detect is presented alongside the position-domain bias induced by the fault at the time of detection; generally the monitor bank can detect the presence of faulty measurements after the position-domain bias has reached only tens of meters whereas the other methods may not detect until hundreds of meters.