Comparison of total least squares and instrumental variable methods for parameter estimation of transfer function models

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Abstract
The estimation of the parameters of a transfer function model is considered. Relationships between the total least squares (TLS) and instrumental variable (IV) approaches are outlined. Both methods are able to compute strongly consistent parameter estimates. TLS can be considered as a variation on the IV method where the IV are functions of the time instant and the estimated model parameters. TLS computes strongly consistent estimates of the true model parameters if the outputs and possibly the inputs are independently disturbed by discrete, stationary white noise with zero mean and equal variance. The IV need not be generated. Hence TLS is much simpler to use but more restrictive (IV allows arbitrary noise models) and computationally not so attractive. Next, simulation results are presented comparing the short sample accuracy properties of both methods. When the outputs and possibly the inputs are disturbed by stationary zero mean while noise, TLS outperforms the ordinary IV methods. The accuracy becomes comparable by extending the IV sufficiently. The superiority of TLS is particularly clear in cases where the zeros of the polynomial operating on the outputs are close to the unit circle or where both the inputs and outputs are noisy.

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