Parameter estimation from samples of stationary complex Gaussian processes

Sampling stationary, circularly-symmetric complex Gaussian stochastic process models from multiple sensors arise in array signal processing, including applications in direction of arrival estimation and radio astronomy. The goal is to take narrow-band filtered samples so as to estimate process parameters as accurately as possible. We derive analytical results on the estimation variance of the parameters as a function of the number of samples, the sampling rate, and the filter, under two different statistical estimators. The first is a standard sample variance estimator. The second, a generalization, is a maximum-likelihood estimator, useful when samples are correlated. The explicit relationships between estimation performance and filter autocorrelation can be used to improve process parameter estimation when sampling at higher than Nyquist. Additionally, they have potential application in filter optimization.