A LEAST-SQUARES FORMULATION FOR STATE ESTIMATION

Abstract

A general formulation of least squares estimation is given. An algorithm with a fixed-size moving estimation window and constraints on states, disturbances and measurement noise is developed through a probabilistic interpretation of least squares estimation. The moving horizon estimator has one more tuning parameter (namely, the horizon size) than many well-known recursive filters. This parameter allows for a compromise between the computational advantages of recursive filters and the improved performance of the batch least squares estimator. Specific issues relevant to linear and nonlinear systems are discussed, with comparisons made to the Kalman filter, extended Kalman filter (EKF), and other optimization-based estimation schemes.