This paper presents a time-domain method to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data. The identified filter has the properties that its residual is minimized in the least squares sense, orthogonal to the time-shifted versions of itself, and to the given input-output data sequences. The connection between the state space model and a particular auto-regressive moving average description of a linear system is made in terms of the Kalman filter and a deadbeat gain matrix. The procedure first identifies the Markov parameters of an observer system, from which a state space model of the system and the filter gain are computed. The developed procedure is shown to improve results obtained by an existing observer/Kalman filter identification method, which is based on an auto-regressive model without the moving average terms. Numerical and experimental results are presented to illustrate the proposed method.
Improvement of Observer/Kalman Filter Identification (OKID) by Residual Whitening
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Phan, M., Horta, L. G., Juang, J., and Longman, R. W. (April 1, 1995). "Improvement of Observer/Kalman Filter Identification (OKID) by Residual Whitening." ASME. J. Vib. Acoust. April 1995; 117(2): 232–239. https://doi.org/10.1115/1.2873927
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