Multi-domain adaptive parameter estimation

Expressions are developed for obtaining an estimate of a set of related signal parameters which is optimal in the sense that the estimates are unbiased in the absence of background interference and minimum variance for a background whose statistics are specified. When these are not known a-priori the estimator may be implemented adaptively using an iterative algorithm or by matrix estimation and inversion. For the latter approach probability density distributions are presented for the parameter estimates when signal and background have Gaussian statistics. The expressions are similar in form to those which have been developed for single parameter estimation. Finally, an approach to adaptive frequency and bearing estimation is presented as an example of multiple parameter estimation, and expressions for the probability density distributions and moments of the estimates are presented.