A receding-horizon estimator for discrete-time linear systems

The problem of estimating the state of a discrete-time linear system can be addressed by minimizing an estimation cost function depending on a batch of the recent measurement and input vectors. This problem has been solved by introducing a general receding-horizon objective function that includes also a weighted penalty term related to the prediction of the state. For such an estimator, convergence results and unbiasedness properties have been proved. The issues related to the design of this filter are discussed as far as the choice of the scalar weight in the cost function is concerned. The performance of the proposed receding-horizon filter has been evaluated by means of both theoretical results and simulations.