Robust estimation of LP parameters in white noise with unknown variance

The problem of robust estimation of the linear prediction (LP) parameters for an autoregressive process (AR) in white noise is addressed in this paper. The classical solution to this problem involves using the p low-order Yule-Walker equations and subtracting an estimate of the noise variance from the main diagonal of the correlation matrix. However, this approach lacks robustness against possible oversubtraction of the noise variance. In such a case, the resulting estimate of the correlation matrix won´t constrain to be positive-definite. The main contribution of this paper is the combination of an appropriate noise variance estimator with an effective processing scheme to circumvent the problem mentioned above. The noise variance, which determines the bias in the standard least-squares criterion, is estimated using the overdetermined normal equations, the truncated singular value decomposition and the correlation matching property. It is shown that for an AR process in additive white noise, the present method performs better than that proposed by the authors in previous related work.