Perspective Chapter: Approximate Kalman Filter Using M-Robust Estimate Dynamic Stochastic Approximation with Parallel Adaptation of Unknown Noise Statistics by Huber’s M-Robust Parameter Estimator

Abstract

The problem of designing a feasible adaptive M-robustified Kalman filter in a case of a thick-tailed Gaussian environment, characterized by impulsive noise-inducing observation and innovation outliers, and/or errors in mathematical model-inducing structural outliers, has been considered. Firstly, the time-varying criterion is used to generate a family of dynamic stochastic approximation algorithms. The M-robust estimate stochastic approximation is derived by minimizing the minimum variance criterion, the estimates of the latter being combined with the one-step minimum mean square error prediction to design M-robust estimate Kalman filter. Finally, the latter is combined with the Huber moving window M-robust parameter estimator of the unknown noises statistics, in parallel with the M-robust state estimation to design an adaptive M-robust estimate Kalman filter. Simulated maneuvering target tracking scenario revealed that the proposed adaptive M-robust estimate-based Kalman filter improves significantly the target estimation and tracking quality, being effective in suppressing multiple outliers with contamination degrees less than thirty percent. Moreover, the achieved improvement comes with additional computational efforts. However, these efforts are usually not significant enough to prevent real-time application.