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Parameter estimation for a multi‐input multi‐output state‐space system with unmeasurable states through the data filtering technique

Parameter estimation is an important tool for modelling a real system. This study considers the parameter estimation problem of a multi-input multi-output state-space system with unmeasurable states. By employing the negative gradient search and cutting down redundant parameter estimates, the authors derive a partially-coupled generalised stochastic gradient (PC-GSG) algorithm to estimate the parameters. Considering the unmeasurable states, they present a new state observer which replaces the unknown parameters with their estimates to generate state estimates. By combining the PC-GSG algorithm and the new state observer, they obtain a state observer based partially-coupled generalised stochastic gradient (SO-PC-GSG) algorithm to estimate the parameters and states. In order to eliminate the interference of the coloured noise and strengthen the performance of the SO-PC-GSG algorithm, they propose a state observer based filtering PC-GSG algorithm by means of the data filtering technique. Finally, the effectiveness of the proposed algorithms is investigated in a simulation study.