Approximate Kalman filtering by both M-robustified dynamic stochastic approximation and statistical linearization methods

The problem of designing a robustified Kalman filtering technique, insensitive to spiky observations, or outliers, contaminating the Gaussian observations has been presented in the paper. Firstly, a class of M-robustified dynamic stochastic approximation algorithms is derived by minimizing at each stage a specific time-varying M-robust performance index, that is, general for a family of algorithms to be considered. The gain matrix of a particular algorithm is calculated at each stage by minimizing an additional criterion of the approximate minimum variance type, with the aid of the statistical linearization method. By combining the proposed M-robust estimator with the one-stage optimal prediction, in the minimum mean-square error sense, a new statistically linearized M-robustified Kalman filtering technique has been derived. Two simple practical versions of the proposed M-robustified state estimator are derived by approximating the mean-square optimal statistical linearization coefficient with the fixed and the time-varying factors. The feasibility of the approaches has been analysed by the simulations, using a manoeuvring target radar tracking example, and the real data, related to an object video tracking using short-wave infrared camera.