Approximate Kalman Filtering Using Robustified Dynamic Stochastic Approximation Method

The problem of making the Kalman filter robust in a case of undetermined noise statistic has been considered in the paper. Firstly, the equivalence between the Kalman filter and a specific linear dynamic stochastic approximation recursive algorithm is established. In addition, the dynamic stochastic approximation algorithm is considered as a regression problem, and the regression problem is solved in a robust manner using the M-robust statistical approach. In order to improve the convergence rate, the gain matrix of the proposed state estimator is derived from the minimization of the particular criterion. A real-life example of maneuvering target tracking is considered to illustrate the usefulness of the proposed robustified Kalman filtering technique.