Stochastic Cramer Rao bounds for non-Gaussian signals and parameters
Weibo Liang, MICHAEL T. MANRY, Qiang Yu, Michael S. Dawson, A.K. Fung · 2002
In minimum mean square estimation, an estimate /spl theta/' of the random parameter vector /spl theta/ is obtained from an input vector y. We develop bounds on the variances of elements of /spl theta/'-/spl theta/ for the case where input signal vector y and the parameter vector /spl theta/ are non-Gaussian. First, we use linear transformations to obtain a new parameter vector /spl phi/ from /spl theta/ and a new input vector x from y. These new vectors are approximately Gaussian because of the central limit theorem, so stochastic Cramer-Rao bounds on the variance of /spl phi/'-/spl phi/ are tight. Lastly, bounds on variances of elements of /spl theta/-/spl theta/ are obtained.