Linear stochastic system identification using correlation techniques |
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| Authors: | Drayton D Boozer Willie L McDaniel |
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| Institution: | Teledyne Brown Engineering Research Park, Huntsville, Alabama, USA;Department of Electrical Engineering Mississippi State University, State College, Mississippi USA |
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| Abstract: | The identification of linear, discrete time, scalar output systems which are driven exclusively by white, zero mean, inaccessible noise sequences is discussed. Two principal results are presented. First, two methods (least squares and an autocorrelation technique) for identifying the system characteristic equation coefficients are compared. The least squares approach is shown to be biased except for special cases. In general, the bias cannot be removed. If the state transition matrix is of the phase variable form, bias removal requires a knowledge of the measurement noise variance and all but one of the state driving noise variances. The autocorrelation technique is not biased asymptotically and does not require a knowledge of the noise variances.Secondly, it is shown that the m2 elements of the state transition matrix cannot be identified uniquely from the scalar output sequence autocorrelation coefficients if the system order is higher than one. The implication of this uncertainty in the state transition matrix on optimal filtering of the output sequence is briefly discussed. |
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