A derivative-free Kalman Filtering approach for sensorless control of nonlinear systems

Abstract

It is known that for linear systems subject to Gaussian measurement or process noise the Kalman Filter is the optimal state estimator, since it results in minimization of the trace of the estimation error's covariance matrix. For nonlinear systems, subject to Gaussian noise one can use the generalization of the Kalman Filter as formulated in terms of the Extended Kalman Filter (EKF). The Extended Kalman Filter is based on a linearization of the systems' dynamics using a first order Taylor expansion. Although EKF is efficient in several estimation problems, it is characterized by cumulative errors due to the gradient-based linearization 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 Extended Kalman Filtering the paper proposes a derivative-free Kalman Filtering approach which is suitable for sensorless control for a class of nonlinear systems. The considered systems are first subject to a linearization transformation and next state estimation is performed by applying the Kalman Filter to the linearized model. Unlike the EKF, the proposed method provides estimates of the state vector of the nonlinear system without the need of derivatives and Jacobians calculation. As application example state estimation-based control of a nonlinear DC motor model is considered.