Robustified Kalman Filtering Using Both Dynamic Stochastic Approximation and M-Robust Performance Index

Abstract

In this paper, the problem of designing the feasible Kalman filter under a non-Gaussian stochastic environment characterized by spiky noise or outliers has been considered. Firstly, the similarity among a class of dynamic stochastic approximation algorithms and the standard Kalmanfilter is found. Moreover, the particular dynamic stochastic approximation algorithm is derived by minimizing the generalized M-robust performance index. The adopted robust criterion represents the conditional expectation of a suitably chosen non-linear transformation of the measurement residuals, given the predicted system states and the observation sequence. The standard Kalman filtering time-update recursions are used to account for the predicted changes in the system states at each stage. Furthermore, the speed of algorithm convergence is improved by choosing the gain matrix from the minimization of an additional criterion at each stage, resulting in an approximately minimum variance algorithm. A target tracking scenery is simulated to demonstrate the practical robustness of the proposed state estimator.

Keywords

• impulsive noise
• Kalman filtering
• non-Gaussian noise
• nonlinear filters
• robust estimation
• state estimation