Linear Invariant Statistics for Signal Parameter Estimation

This paper presents an approach to obtain an invariant statistics for estimation interested signal parameters independently from unwanted parameters in two dimensional parameter problems. The proposed algorithm is based on the exclusion of Fisher’s information about the unwanted parameters and maintaining information about the parameter of interest. Simultaneous reduction the partial Fisher information matrices to diagonal forms provides the key steps for separation of the signal space into two orthogonal subspaces, containing Fisher’s information about different parameters. The proposed approach requires knowledge of the statistical distributions of signals of interest. The application examples with time delay and Doppler shift as the parameters are provided as a means of evidencing the advantages of the theory.