Multichannel spectral estimation in acoustics: A state-space approach

Abstract

Spectral estimation is a necessary methodology to analyze the frequency content of noisy data sets especially in acoustic applications. Many spectral techniques have evolved starting with the classical Fourier transform methods based on the well-known Wiener-Khintchine relationship relating the covariance-to-spectral density as a transform pair culminating with more elegant model-based parametric techniques that apply prior knowledge of the data to produce a high-resolution spectral estimate. Multichannel spectral representations are a class of both nonparametric, as well as parametric, estimators that provide improved spectral estimates. In any case, classical nonparametric multichannel techniques can provide reasonable estimates when coupled with peak-peaking methods as long as the signal levels are reasonably high. Furthermore, parametric multichannel methods can perform quite well in low signal level environments even when applying simple peak-picking techniques. In this paper, the performance of both nonparametric (periodogram) and parametric (state-space) multichannel spectral estimation methods are investigated when applied to both synthesized noisy structural vibration data as well as data obtained from a sounding rocket flight. It is demonstrated that for the multichannel problem, state-space techniques provide improved performance, offering a parametric alternative compared to classical methods.