Moving data window-based partially-coupled estimation approach for modeling a dynamical system involving unmeasurable states

The simultaneous parameter and state estimation for a multi-input multi-output (MIMO) state space system from a set of measurement data is taken into account in this paper. Firstly, in line with the number of the system outputs, the considered MIMO system is transformed to some subsystems, which lessens the dimensions and the number of the parameters to be estimated. Secondly, by designing the moving data window that contains the latest batch of collected data, we develop a moving data window-based partially-coupled average extended stochastic gradient algorithm for parameter estimation. Thirdly, once the parameter estimates are obtained, a new state filter is designed to produce the estimates of the unmeasurable states by means of the Kalman filtering principle. Then we propose a combined state filtering and moving data window-based partially-coupled average extended stochastic gradient (CSF-MDW-PC-A-ESG) algorithm to produce the estimates of the parameters and states simultaneously. To reveal the superiority of the CSF-MDW-PC-A-ESG algorithm, a combined state filtering and partially-coupled average extended stochastic gradient (CSF-PC-A-ESG) algorithm is given to make a comparison. Finally, the effectiveness and superiority of the proposed CSF-MDW-PC-A-ESG algorithm are proved in a simulation example. The results from the illustrative example show that the CSF-MDW-PC-A-ESG algorithm is effective to produce the estimates of the parameters and states and that the CSF-MDW-PC-A-ESG algorithm has the higher efficient data utilization, the more accurate parameter estimation capability and the better model fitting ability than the CSF-PC-A-ESG algorithm.