A Derivative-Free Kalman Filtering Approach to State Estimation-Based Control of Nonlinear Systems

For nonlinear systems, subject to Gaussian noise, the extended Kalman filter (EKF) is frequently applied for estimating the system´s state vector from output measurements. The EFK is based on linearization of the systems´ dynamics using a first-order Taylor expansion. Although EKF is efficient in several problems, it is characterized by cumulative errors due to the gradient-based linearization it performs, and this may affect the accuracy of the state estimation or even risk the stability of the state estimation-based control loop. To overcome the flaws of EKF, it has been proposed to use the unscented Kalman filter (UKF) as a method for nonlinear state estimation, which does not introduce linearization errors. Aiming also at finding more efficient implementations of nonlinear Kalman filtering, this paper introduces a derivative-free Kalman filtering approach, which is suitable for state estimation-based control of a class of nonlinear systems. The considered systems are first subject to a linearization transformation, and next state estimation is performed by applying the standard Kalman filter to the linearized model. Unlike EKF, the proposed method provides estimates of the state vector of the nonlinear system without the need for derivatives and Jacobians calculation and without using linearization approximations. The proposed derivative-free Kalman filtering approach has been compared to EKF and UKF in the case of state estimation-based control for a nonlinear DC motor model.