Robustizing Kalman filters with the M-estimating functions

This article considers a robust Kalman filter from the M-estimation point of view. Pak (Journal of the Korean Statistical Society, 27, 507–514, 1998) proposed a particular M-estimating function which has the data-based shaping constants. The Kalman filter with the proposed M-estimating function is considered. The structure and the estimating algorithm of the Kalman filter accompanying the M-estimating function are mentioned. Kalman filter estimates by the proposed M-estimating function are shown to be well behaved even when data are contaminated.