Combined state and parameter estimation for not fully observable dynamic systems

Abstract

In this paper, a simple, yet novel method for state estimation and parameter identification for dynamic systems is presented. Apart from providing estimates of non-measurable state variables, the algorithm is also capable of estimating (constant) system parameters. The estimation algorithm is split in two parts. Firstly, an extended Kalman filter, whose state-space-model is augmented with quasi-linear expressions for parameter values, providing estimates for the state variables and the augmented parameter values. Secondly, a Monte-Carlo-fashioned approach, which identifies the rest of the parameter values that were not included in the augmentation of the state-space model. The MonteCarlo-approach minimizes an objective function (the error between the measured and the estimated state variable). It is shown that the algorithm is capable of estimating the state- and parameter-values in a satisfying manner. The method is best applied offline and the theoretical developments will be demonstrated in case studies.