Kalman Filter Residual-Based Integrity Monitoring Against Measurement Faults

Abstract

This paper introduces a new Kalman filter-based method for detecting sensor faults in linear dynamic systems. In contrast with existing sequential fault-detection algorithms, the proposed method enables direct evaluation of the integrity risk, which is the probability that an undetected fault causes state estimate errors to exceed predefined bounds of acceptability. The new method is also computationally efficient and straightforward to implement. The algorithm's detection test statistic is established in three steps. First, the weighted norms of current and past-time Kalman filter residuals are defined as generalized non-centrally chisquare distributed random variables. Second, these residuals are proved to be stochastically independent from the state estimate error. Third, current-time and past-time residuals are shown to be mutually independent, so that the Kalman filter-based test statistic can be recursively updated in real time by simply adding the current-time residual contribution to a previously computed weighted norm of past-time residuals. The Kalman filter-based integrity monitor is evaluated against worst-case fault profiles, which are also derived in this paper. Finally, performance analyses results are presented for an example application of aircraft precision approach navigation, where differential ranging signals from a multiconstellation satellite navigation system are filtered for positioning and carrier phase cycle ambiguity estimation.

Reliable urban vehicle localization under faulty satellite navigation signals

“…Traditional GNSS localization approaches that rely on filter-based techniques design the measurement likelihood model under the assumption that all incorporated measurements are both independent and devoid of any faults. The probability p(ρ k t | x t ) associated with the kth measurement at time t for x t is modeled as a Gaussian distribution [7,24,41,54].…”

“…To evaluate the integrity monitoring performance of our particle filter-based method, we compared our approach against the particle filter-based Bayesian RAIM [41], which detects positioning failures based on statistics computed by integrating the J-PF probability distribution. We note that other integrity monitoring methods have been explored in research, such as methods based on Kalman filter innovations [24], however they cannot be readily applied to our particle filter setting and therefore have not been compared against.…”

New Approach for Integrity Risk Evaluation Based on Expected Acceptable Region for Carrier-Phase-Based Precise Relative Positioning

“…High integrity and high accuracy are simultaneously required for life-critical and mission-critical GNSS navigation applications, such as automatic shipboard landing (Khanafseh & Pervan, 2008;Pervan et al, 2001;Rife et al, 2009), autonomous airborne refueling (J. Hansen, N. Nabaa, R. Andersen, L. Myers, & McCormick, 2006;Samer Khanafseh, Boris Pervan, & Colby, 2005) and vehicle intelligent operation in both ground and air transportations (Joerger & Pervan, 2012;Velaga, 2012). As for shipboard landing, the requirement of accuracy and integrity risk is 0.4 m with a corresponding vertical alert limit (VAL) of 1.1m and availability of at least 99.7% (Rife et al, 2009).…”