An innovation representation for nonlinear systems with application to parameter and state estimation

An innovation model is derived for a nonlinear stochastic system described by a state variable representation. The problem of state and system parameter estimation is solved through identification of the innovation model. A recursive prediction error (RPE) algorithm is derived for the joint system parameter and state estimation through minimization of the innovation variance (MIV). The algorithm is robust against the use of an erroneous model. Convergence and stability properties of the algorithm are also analyzed. In order to ensure stability, the algorithm needs an on-line stability check at each iteration. 1. Introduction LINEAR MODELS are very popular to simplify the analysis and design of control systems. Linear representations could be over simplifications for the phenomena they describe. Controller design based on an oversimplified model not only leads to performance deterioration, but may also make the controlled system unstable. As a result, the analysis and design of nonlinear systems are of importance to system and process control engineers. This paper considers the on-line state and parameter estimation problem of nonlinear systems in the presence of modeling errors and/or measurement noise. The most popular method of state estimation in nonlinear systems is the extended Kalman filter (EKF) (Jazwinski, 1970). The extensions include linearization at different stages of the algorithm, model linearization and the jump matrix method. All of these methods assume that the covariances of the noise processes are known. It is well known that the performance of EKF deteriorates or may even diverge in the case of erroneous models. A state estimation procedure for nonlinear systems is presented through an innovation representation. An innovation model is derived for nonlinear stochastic systems given by a state variable description. The innovation representation is exact when the state equation is nonlinear but the output equation is linear. The state estimation problem is solved through identification of the innovation gain. A recursive prediction error (RPE) algorithm (Ljung and Soderstr6m, 1983) is derived for joint state estimation and innovation gain identification through minimization of the innovation variance (MIV). It does not require the knowledge of the noise covariances. Since the algorithm is based upon direct minimization of the