Robust filter for multiscale stochastic process

The problems of making the Kalman filter robust for multiscale stochastic process are considered in This work. An efficient optimal robust estimation algorithm is investigated for the multiscale autoregressive model on the dyadic tree under the condition: a state is Gaussian and the observation error is non-Gaussian. This algorithm consists of a fine-to-coarse robust filtering sweep, followed by a coarse-to-fine smoothing step. The robust Kalman filtering sweep consists of the recursive application of three steps: a measurement update step, a fine-to coarse prediction step, and a fusion step. The feasibility of the approach is demonstrated by simulation.