Two nonparametric methods for identifying the impulse response of linear systems

This paper addresses the problem of impulse response identification using nonparametric methods. Although the techniques developed herein apply to the truncated, untruncated, and circulant models, we focus on the truncated model which is useful in certain applications. Two methods of impulse response identification will be presented. The first is based on the minimization of the C
L
statistic, which is an estimate of the mean-square prediction error; the second is a Bayesian. approach, For both of these methods, we consider the effects of using both the identity matrix and the Laplacian matrix as weights on the energy in the impulse response. In addition, we present a method for estimating the effective length of the impulse response. Estimating the length is particularly important in the truncated case. Finally, we develop a method for estimating the noise variance at the output which is needed in the approach involving the C
L
statistic. Often, prior information on the noise variance is not available, and a good estimate is crucial to the success of estimating the impulse response with a nonparametric technique.