Optimal reassignment-based complex nonlinear processing of vector discrete-continuous Markovian random processes

Abstract

Methods of the Markovian estimation theory are applied to the synthesis of optimal and quasi-optimal algorithms that involve time-stepped reassignment of the values of the parameters of conditional a posteriori probability densities of filtered continuous processes. The algorithms are intended for nonlinear processing of a vector discrete-continuous Markovian random process whose continuous component is a vector diffusion Markovian process and whose discrete component is a two-component vector, each component of which is characterized by a simple several-position Markovian chain. It is assumed that one group of simultaneously processed signals is observed against the background of colored (time-correlated) noise, while the other group is observed in the presence of white Gaussian noise. Basic analytic relationships and the corresponding block diagram of a system for quasi-optimal complex nonlinear processing of signals typical of the GLONASS, GPS, Galileo, and QZSS satellite navigation systems and such satellite mobile-communications systems as the Globalstar system are presented.