Nonlinear processing of nongaussian and noncoherent signals in the presence of colored noise

The problem of nonlinear processing of nongaussian and noncoherent signals is common in many applications such as remote sensing, hydroacoustics, radioastronomy and communication technologies. Optimal solution of this problem requires taking into account the space-time statistical properties of signals, medium and noise, which are usually known a priori. One of the best methods is suggested by the theory of conditional Markov processes [1-3]. Using this technique, we may describe the signal fluctuations in the form of stochastic differential equations. According to the standard procedure, to obtain the filtering algorithms, we must write the evolution equation for the conditional density functional. The disadvantage of this procedure is that we may write closed equations for the conditional density functional only for the case of signals received in the presence of white noise. In this paper on the base of the functional approach [4,5], we consider the case of signals, which are observed in the presence of colored noise only. We obtain optimal algorithms for a set of modulated signals and colored noises, including the noise described by Ornstein-Uhlenbeck process.