On-line modified least-squares parameter estimation of linear discrete dynamic systems

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Abstract
The problem of identifying a single-input, single-output linear discrete-time system, where the output data are corrupted by additive noise, is considered. Use is made of the fact that a consistent estimator may be obtained by compensating an asymptotic bias on the least-squares estimator. The algorithm proposed in this paper is useful in the case when the variance of the noise is not known and on-line computation is required. It is shown that the algorithm generates an estimate asymptotically equivalent to that which minimizes an approximation to the sum of squared output errors. The minimization problem can be reduced to the eigenvalue problem. The experimental results of digital simulation are presented to illustrate the usefulness of the approach and to verify the validity of the theoretical discussions. A comparison with the instrumental variable method proposed by Wong and Polak (1967) is also made. The experimental comparison shows that the performance of the proposed estimator is comparable to that of the optimal on-line instrumental variable method.

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