Minimum-Covariance Estimates of Signal Parameters

Abstract

We show the existence of the only procedure ensuring the absolute minimum of an arithmetic mean covariance in a certain parameter-variation range and coinciding identically with the algorithm for calculating the estimate minimizing the mean risk for a quadratic loss function and a uniform a priory distribution of parameters. This procedure is compared with the standard method for obtaining maximum likely estimates. In particular, it is shown that the procedure ensures a significantly smaller random scatter of estimates during the estimation of deterministic-signal parameters against the background of Gaussian interference. In the case where the estimate covariance is independent of the parameter estimated for physical reasons, the use of the above procedure with an arbitrary sample size allows us to reach the actual attainable variance bound.