Maximum-likelihood spectral estimation

Abstract

A description has been given of some signal processing methods in large array seismology. The optimum detector for a known signal in additive Gaussian noise was shown to consist of the tandem combination of appropriate time delays, maximum-likelihood filter, noise whitening filter, matched filter, and a threshold comparator. The maximum-likelihood filter plays an important role in determining the structure of the optimum detector. This filter also provides a minimum-variance unbiased estimate for the input signal when it is not known, which is the same as the maximum-likelihood estimate of the signal if we have Gaussian noise.

If the noise is stationary in both time and space then it can be characterized by a frequency wave number power spectral density function. The performance of array processing filters, such as the maximum-likelihood filter, is relatively simple to explain in terms of the structure of this function.