Moving-horizon estimation with guaranteed robustness for discrete-time linear systems and measurements subject to outliers

An approach to state estimation for discrete-time linear time-invariant systems with measurements that may be affected by outliers is presented by using only a batch of most recent inputs and outputs according to a moving-horizon strategy. The approach consists in minimizing a set of least-squares cost functions in which each measure possibly contaminated by outlier is left out in turn. The estimate that corresponds to the lowest cost is retained and propagated to the next time instant, where the procedure is repeated with the new information batch. The stability of the estimation error for the proposed moving-horizon estimator is proved under mild conditions concerning the observability of the free-noise state equation and the selection of a tuning parameter in the cost function. Robustness is guaranteed with sufficiently large outliers. The effectiveness of the proposed method as compared with the Kalman filter is shown by means of a numerical example