Estimation of complex systems with parametric uncertainties using a JSSF heuristically adjusted

In practical applications, the chances of having a mathematical model that accurately describes the dynamics of a complex real system are limited. Besides, the noise included in the measurements increases, even more, the problem of estimating the actual states of the system. It is well-known that the most recurring methods for estimating systems, in a practical way, are: Kalman Filter (KF) for linear case and the Extended Kalman Filter (EKF) for nonlinear case. Unfortunately, such estimation methods do not hold when the mathematical model and the real system do not coincide with each other. On the other hand, the James-Stein State Filter provides a robust approach to estimate linear and nonlinear systems under parametric uncertainties of the mathematical model; but, its performance degrades as the standard deviation of the measurement noise increases. Therefore, in this paper, an heuristic adjustment is proposed to improve the performance of the James-Stein State Filter (JSSF) even in the presence of measurement noise. In order to illustrate the applicability of the approach on nonlinear systems with complex dynamics, the estimation of Chen and Lorenz attractors with uncertainties in their parameters is considered.