ROBUST PARAMETRIC AND NONPARAMETRIC TECHNIQUES FOR SYSTEM IDENTIFICATION
Abstract
Estimating the impulse response of linear systems from input-output measurements has various applications in Signal Processing. The problem is ill-posed especially when the length of the observations is of the order of the effective length of the impulse response. In this study various parametric and nonparametric methods for this estimation problem are developed and compared with the existing methods. Two nonparametric methods for estimating the impulse response are developed--one based on minimizing the estimated mean squared error of prediction and the other based on the Bayesian approach. These methods give much better estimates of the impulse response than the usual constrained least squares method. The method based on the Bayesian approach needs more work because the estimates are biased; as a remedy, better priors for the noise variance are suggested. All of these nonparametric methods depend directly or indirectly on good estimates of the noise variance. Noise variance estimation has proven to be a difficult task when the distribution of noise is not known precisely, particularly, in problems where the noise distribution may be considered approximately Gaussian. However, a noise variance estimation method based on a Jackknife type scheme is developed, the estimates from which have much better properties than the estimates from the usual method based on the (chi)('2) statistics. Parameterizing the impulse response significantly reduces the number of variables, and this is especially advantageous in implementing nonlinear estimation techniques. Nonlinear estimation techniques are almost essential when designing procedures which are robust with respect to distributional uncertainties. A robust method based on the use of the minimax approach for fitting the data to a special case of the ARMAX model is developed. The impulse response estimates from this method are much more robust than those obtained from the method of fitting the data to the same model using the usual quadratic criterion.
Degree
Ph.D.
Subject Area
Electrical engineering
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