Multi‐moment statistical characterization and nonlinear filtering of chaos

Abstract

Purpose

The purpose of this paper is to provide the results of investigation of multi‐moment statistical characteristics of chaos and apply them to improve the accuracy of nonlinear algorithms for chaos filtering for real‐time applications.

Design/methodology/approach

The approach to find multi‐moment statistical properties of chaos‐multi‐moment cumulant (covariance) functions of higher order is a generalization of the previously proposed (by the authors) “degenerated cumulant equations” method. Those multi‐moment cumulants functions are applied in the generalization of the Stratonovich‐Kushner equations (SKE) for the optimum algorithm of nonlinear filtering of chaos as well as for synthesis of the quasi‐optimum algorithms.

Findings

Results are presented to investigate the multi‐moment statistical properties of chaos and formulate the theoretical background for synthesis of multi‐moment optimum and quasi‐optimum algorithms for nonlinear filtering of chaos with the improved accuracy in the presence of additive white noise.

Originality/value

The paper presents new theoretical results of the statistical description of chaos, previously partially reported only from experimental studies. A novel approach for chaos filtering is also presented. The proposed approach is dedicated to further improvement of the filtering accuracy for the case of low (less than one) SNR scenarios and is important for implementation in real‐time processing. As an important practical example, the new modified EKF algorithm is proposed with the rather opportunistic characteristics of the filtering fidelity together with algorithm complexity – practically the same as the “classic” one‐moment EKF algorithm.

Citation

Kontorovich, V. and Lovtchikova, Z. (2013), "Multi‐moment statistical characterization and nonlinear filtering of chaos", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32 No. 3, pp. 885-900. https://doi.org/10.1108/03321641311305818