Multi-moment statistical characterization and nonlinear filtering of chaos (Q2842728)

The authors present results of investigation on multi-moment statistical characteristics of chaos as a degenerated Markov process. The proposed approach to find multi-moment statistical properties of chaos-multi-moment cumulant (covariance) functions of higher order is a generalization of the ``degenerated cumulant equations'' method proposed by the authors (see, for example [\textit{V. Kontorovich} and \textit{Z. Lovtchikova}, ``Cumulant analysis of strange attractors: theory and applications'', Rec. Adv. Nonlin. Dyn. Synch. Stud. Comput. Intelligence 254, 77--115 (2009)]). These multi-moment cumulants functions are applied to describe a generalization of Stratonovich-Kushner equations (SKE) for the optimum algorithm of nonlinear filtering of chaos. As a practical example, a new modified extended Kalman filtering algorithm is proposed. Characteristics of the filtering fidelity and the algorithm complexity of this algorithm are practically the same as the ``classic'' one-moment extended Kalman filtering algorithm.