Cramer Rao maximum a-posteriori bounds for a finite number of non-Gaussian parameters

Abstract

In minimum mean square estimation, an estimate /spl theta/' of the M-dimensional random parameter vector /spl theta/ is obtained from a noisy N-dimensional input vector y. In this paper, we develop CRM bounds for the case where y and /spl theta/ are non-Gaussian and M is small. First, y is linearly transformed to x/sub /spl theta// which is approximately Gaussian because of the central limit theorem (CLT). Second, an arbitrary auxiliary signal model is introduced with Gaussian input vector x/sub d/ and Gaussian parameter vector d which are statistically independent of y and /spl theta/. Then an augmented signal model is formed with augmented input vector x/sub /spl alpha//=[x/sub /spl theta//|x/sub d/]/sup T/ and augmented parameter vector /spl theta//sub /spl alpha//=[/spl theta/|d]/sup T/. The CRM bounds for /spl phi//sub /spl alpha// are then transformed into CRM bounds for /spl theta//sub /spl alpha//. Consequently, CRM bounds on /spl theta/ can be calculated from the signal model x/sub /spl theta// as if /spl theta/ were Gaussian.