New state estimator of nonlinear discrete-time systems

In this paper, a new technique is developed to estimate the states of both deterministic and stochastic discrete‐time nonlinear systems. The stochastic system can be uncertain. The corrupting input and/or the output noise vectors may be either Gaussian or non‐Gaussian zero‐mean sequences. The proposed filter is based on pole placement technique, in which a set of constraints are imposed of the estimated outputs. The stability of the estimator is rigorously analyzed. An extension to the developed estimator is proposed to deal with constrained estimation problems. To illustrate the effectiveness and simplicity of the developed technique, illustrative examples are presented. Simulations results show that, for the deterministic case, the developed procedure leads to better results when compared with High‐gain observer, Thau's filter, and the Iterative Regularized Least Square estimator. On the other hand, for the stochastic case, the proposed estimator is superior to the extended Kalman filter and the iterative constrained estimator (ICE) with non‐ideal situations where the statistics of the noise signals and/or the system parameters are unknown, or the noise signals are non‐Gaussian.