“Multi-moment” nonlinear filtering of chaos

It was shown in earlier works of the authors that approximate nonlinear filtering algorithms for chaos demonstrate very good filtering accuracy in low SNR scenarios. This paper is the sequel of the research related to statistical properties of chaotic signals and approximate nonlinear filtering algorithms of chaos. In this paper a novel filtering approach is presented; the proposed approach is called as "multi-moment" for the following improvement of the filtering accuracy for low SNR The general way for synthesis of the optimum and quasi-optimum filtering algorithms based on the criteria of maximum a-posteriori probability is presented, and in the following it is called as modified Stratonovich-Kushner equations (SKE) for a-posteriori Probability Density Function (PDF) and a-posteriori characteristic function. Equations for a-posteriori cumulants are presented hereafter as well and based on those equations was developed the modified EKF algorithm, based on two - moment statistics. The later demonstrates rather opportunistic characteristics for filtering accuracy practically with the same algorithm complexity as the classic EKF.