Robust Kalman filter and smoothing recursive estimator for multiscale autoregressive process

A current topic of great interest is the multiresolution analysis of signals and the development of multiscale signal processing algorithms. In this paper, we focus on making the Kalman filter robust for multiscale autoregressive (MAR) model. The equivalence between the Kalman filter in optimal estimation algorithm for MAR model and a particular least squares regression problem is established. And the regression problem is solved robustly using a statistical approach named M-estimation. The robustness of the proposed approach is demonstrated with simulation.