Least-Mean-Square Receding Horizon Estimation

Abstract

We propose a least-mean-square (LMS) receding horizon (RH) estimator for state estimation. The proposed LMS RH estimator is obtained from the conditional expectation of the estimated state given a finite number of inputs and outputs over the recent finite horizon. Any a priori state information is not required, and existing artificial constraints for easy derivation are not imposed. For a general stochastic discrete-time state space model with both system and measurement noise, the LMS RH estimator is explicitly represented in a closed form. For numerical reliability, the iterative form is presented with forward and backward computations. It is shown through a numerical example that the proposed LMS RH estimator has better robust performance than conventional Kalman estimators when uncertainties exist.