Minimum variance estimator design for systems with quadratic nonlinearities

In this paper, we consider the state estimation problem for a class of nonlinear systems with second degree polynomial nonlinearities with noisy measurements. This class of nonlinearities is chosen based on the fact that they may lead to chaotic behavior for possible later use on chaotic communications applications. An unbiased state estimator is proposed having a quadratic structure and a parametric optimization problem is solved to obtain the minimum error variance. Another unbiased suboptimal estimator having a much simpler structure is proposed to provide an error performance bound on the minimum variance estimator. The performance results of these two minimum variance estimators are shown to be clearly superior to those of the extended Kalman filter for some scalar chaotic systems.