A class of Cramer-Rao optimal estimators for analysis of clutter

Fisher information matrix can be seen as the metric of a Riemannian manifold, Fisher-Rao metric. As such it can be evolved through Ricci flow. For the case of the estimation of two parameters, the two dimensional manifold is also conformal. In this case we show that the Cramer-Rao bound is saturated as a scalar function always exists that is a also a solution of Liouville equation. This implies that in order to have an optimal estimation of parameters one have to solve this equation. This result can be extended in higher dimensions when the Fisher information matrix can be cast into a similar form as for the two-dimensional case and the estimator vector admits a potential field. Applications of this result are wide-ranging going from tracking to control theory and clutter analysis. We present an example for the analysis of sea clutter data.