Data filtering-based parameter and state estimation algorithms for state-space systems disturbed by coloured noises

Ting Cui, Feng Ding, Ahmed Alsaedi and Tasawar Hayat

International Journal of Systems Science, 2020, vol. 51, issue 9, 1669-1684

Abstract: In this paper, the combined parameter and state estimation issues of state-space systems are considered, and the process noises and observation noises are supposed to be coloured noises. By utilising the data filtering technique, we transform the original state-space system into the filtered system for eliminating the interference of the coloured noise in the state equation, and then we derive a filtering-based extended stochastic gradient (F-ESG) algorithm to estimate the system parameters. For estimating the unmeasurable states, we derive a new state estimator by using the preceding parameter estimates to take the place of the unknown system parameters in the Kalman filter. Furthermore, we propose a filtering-based multi-innovation extended stochastic gradient (F-MI-ESG) algorithm to achieve the higher parameter estimation accuracy. Finally, we provide two simulation examples to test and compare the performance of the proposed algorithms. The simulation results indicate that the F-ESG algorithm and the F-MI-ESG algorithm are effective for parameter estimation, and that the F-MI-ESG algorithm is able to achieve more accurate parameter estimates than the F-ESG algorithm.

Date: 2020
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DOI: 10.1080/00207721.2020.1772403

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