Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 631759, 19 pages
Research Article

Least-Mean-Square Receding Horizon Estimation

1Department of Control and Instrumentation Engineering, Kangwon National University, Samcheock 245-711, Republic of Korea
2Department of Electrical Engineering, Konkuk University, Seoul 143-701, Republic of Korea

Received 31 October 2011; Accepted 20 December 2011

Academic Editor: M. D. S. Aliyu

Copyright © 2012 Bokyu Kwon and Soohee Han. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.