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

Moving-horizon state estimation is addressed for discrete-time linear systems with disturbances acting on the dynamic and measurement equations. In particular, the measurement noises can take abnormal values, usually called outliers. For such systems, one can adopt a Kalman filter with estimate update that depends on the result of a statistical test on the residuals. As an alternative to such a method, we propose a robust moving-horizon estimator. Such a method provides estimates of the state variables obtained by minimizing a set of least-squares cost functions by leaving out in turn all the measurements that can be affected by outliers. At each time instant, the estimate that corresponds to the lowest cost is retained and propagated ahead at the next step, where the procedure is repeated with the new batch of measures. The stability of the estimation error for the proposed moving-horizon estimator is proved under mild conditions concerning the observability of the free-noise dynamic equations and the selection of a tuning parameter in the cost function. The effectiveness the proposed method as compared with the Kalman filter is shown by means of simulations on a simple example.