Robust-resistant spectrum estimation

Abstract

Conventional spectrum estimates of both the smoothed-periodogram and autoregressive variety lack robustness toward outliers in the original data. Outliers and other local perturbations are modeled by non-Gaussian additive noise, which is zero most of the time. Correspondingly, the lack of robustness of the conventional estimates of the spectrum manifest not only inflated variances but also damaging asymptotic biases. This paper discusses robust-resistant methods of spectrum estimation which do not suffer in this way. The main approach involves "data cleaning" by either one-sided or two-sided outlier interpolators based on autoregressive approximations. The autoregressive coefficients are themselves estimated robustly in an iterative loop along with the data-cleaning operation. The well-cleaned data are then used along with the autoregressive model to form smoothed spectral density estimates via prewhitening. Study of the so-called "linear part" of the nonlinear outlier interpolator algorithm shows that considerable bias reduction is realizable through use of the robust procedure. Some examples of applications of the robust methodology are presented. Special considerations for real-time processing and large data sets are discussed. Extensions of the method to cross-spectrum estimation, missing data, and irregularly spaced data problems are briefly mentioned.