Minimum Mean-Squared-Error Estimation in Nonlinear Problems with Gaussian Inputs.

摘要

In this report, general theorems for estimation of nonlinear functions of Gaussian random processes are developed. Based on these general theorems, minimum mean-squared-error nonlinear estimators for the time average autocorrelation function and the time average power spectral density function of a sample function of a random process are formulated. Examples and performance curves are given for both stationary and nonstationary processes. Additional nonlinear estimators are analyzed, with emphasis on nonergodic situations such as those that occur when an observation interval is finite, and these estimators are shown to be capable of outperforming the minimum mean-squared-error estimator on a single trial basis.