Estimation of Efficiency of Nonlinear Filtering Algorithms under Influence of the Correlated non-Gaussian Multiplicative Noise

We obtained the recurrent equations describing the quasi-optimal algorithm for estimating the correlated multiplicative noise with an arbitrary probability density function, the components of which describe the structure of the of nonlinear block of the signal and the structure of the of nonlinear block of the envelope (amplitude) of the processed signal. We obtained the structure diagram of the demodulator constructed using the above mentioned recurrent equations. This diagram consists of two channels: the channel of evaluation formation of the demodulated parameter and the channel of gain formation. It is shown that the above diagram models the estimation formation of the demodulation information parameter and it is a nonlinear non-stationary discrete tracking system. It is noted that the synthesized algorithms for the estimation of the information process include characteristics of the nonlinear transformation of the signal amplitude, which, in turn, are determined by the probability density function of the multiplicative noise. It is shown that the optimal processing efficiency of the information process in correlated multiplicative noise, the probability density function of which in general case differs from Gaussian, and completely determined by Fisher information matrices. It is shown that accounting for correlation properties of multiplicative noise can significantly improve the accuracy of estimation of an information component.