John David (JD) Quartararo and Steven E. Langel, The MITRE Corporation

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Approved for Public Release; Distribution Unlimited. Public Release Case Number 19-3796 NOTICE This technical data was produced for the U. S. Government under Contract No. FA8702-20-C-0001, and is subject to the Rights in Technical Data-Noncommercial Items Clause DFARS 252.227-7013 (FEB 2014) ©2020 The MITRE Corporation. ALL RIGHTS RESERVED. Detecting Slowly Accumulating Faults Using a Bank of Cumulative Innovations Monitors in Kalman Filters John David (JD) Quartararo, Dr. Steven E. Langel, The MITRE Corporation 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 loosely and tightly coupled GPS+inertial EKFs, 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 computational requirements and implications for mitigation are discussed. Modern navigation systems are increasingly utilizing multiple sensors for positioning, navigation and timing, most often beginning with a global navigation satellite system (GNSS) receiver and an inertial measurement unit (IMU). The EKF remains the most widely used filter for multisensor fusion, and much effort has been devoted to designing optimal navigation algorithms under nominal conditions. However, additional sensors provide more than improved accuracy and availability of navigation. They can also be cross-checked against each other to detect the presence of faulty measurements. This paper focuses on quantifying the ability of an IMU to detect slowly accumulating GPS measurement faults. We use the GPS+IMU sensor suite for demonstrative purposes, but the techniques developed in the paper extend naturally to EKFs that utilize any number of sensors. Some examples of slowly accumulating measurement faults may include GPS satellite clock anomalies and incorrect orbit ephemeris parameters broadcast by the satellites [2]. Because it can be difficult to model the behavior of these faults over time, we focus on fault detection algorithms that make no assumptions regarding the temporal behavior of measurement faults. A commonly used fault detection technique that is agnostic to the fault profile is innovations monitoring. In [1], a monitor is developed that accumulates innovations over time to provide the capability of detecting slowly growing GPS measurement faults. A practical but often overlooked aspect of innovations-based fault detection is the impact of real-world model uncertainty. A main contribution of this work is the conclusion that the cumulative innovations monitor becomes increasingly sensitive to model uncertainty as the accumulation interval increases. In response, this work proposes a novel implementation of innovations monitoring that uses a bank of finite-length cumulative monitors to mitigate the adverse effects of real-world model uncertainty. These effects become extremely important for longer-duration runtimes which may last for tens of minutes or hours and the monitor bank provides a practical solution to this problem. A complicating factor in the analysis of fault detection performance for cumulative innovations approaches is that until a detection is declared, which may be seconds or minutes from the initial onset of an accumulating measurement fault, the filter ingests faulty measurements which induce a bias in the state estimate error. This feedback effect complicates a purely analytic approach to the analysis of false alarm and missed detection rates because effects on the EKFs linearization point must also be considered. Therefore, the monitor bank concept was studied using a novel extension of traditional covariance analysis and in a high-fidelity Monte Carlo simulation testbed using the GNSS Test Architecture (GNSSTA) [3]. The results indicate significant improvement using the monitor bank approach to detect slowly accumulating measurement faults over the single cumulative monitor for a runtime of 30 minutes. We describe the 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, fusion filter architectures (loosely and tightly coupled GPS C/A code + inertial EKFs), and IMU quality (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 algorithm 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. References [1] C. Tanil, S. Khanafseh, M. Joerger and B. Pervan, "Sequential Integrity Monitoring for Kalman Filter Innovations-Based Detectors," Proceedings of the 31st International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2018), Miami, FL, 2018, pp. 2440-2455. [2] U. I. Bhatti and W. Y. Ochieng, “Failure Modes and Models for Integrated GPS/INS Systems,” The Journal of Navigation 60 (2007): 327 – 348. [3] The MITRE Corporation, "Global Navigation Satellite System Test Architecture," [Online]. Available: http://gnssta.mitre.org. [Accessed 6 Sep 2019].