State estimator design for chaotic systems with piecewise linear and polynomial type nonlinearities

Tongyan Zhai, Marquette University


This work presents novel techniques for state estimation of nonlinear stochastic systems, specifically chaotic stochastic systems, as well as their application to chaotic communication systems. The performance of the Extended Kalman Filter based state estimation of first order nonlinear dynamic systems is evaluated, a categorization technique is derived in terms of the upper bound on the absolute values of the derivatives of nonlinear functions. This performance evaluation method brings insight into the convergence property of the estimation error variance from the system nonlinearity. Also, robustness of the Extended Kalman Filter to under- and over-estimation of parameters is investigated. Several nonlinear estimation algorithms of varying degrees of complexity are developed, which depend on the use of linear and quadratic functions of current and past measurements for suboptimal and optimal performance. In addition to these estimators for scalar models, a Current Output Filter is also developed in order to carry out state and parameter estimation for multidimensional chaotic stochastic systems. The estimation performance of these estimators is theoretically analyzed and compared with the classical nonlinear estimation algorithm, Extended Kalman Filter. The estimation techniques proposed in this work are employed for estimating the state/parameters of chaotic systems to demodulate chaotically modulated digital signals.

Recommended Citation

Zhai, Tongyan, "State estimator design for chaotic systems with piecewise linear and polynomial type nonlinearities" (2008). Dissertations (1962 - 2010) Access via Proquest Digital Dissertations. AAI3306526.