Second-Order EKF White Noise Estimator Design for Hybrid Systems

The extended Kalman filter (EKF) has a wide range of applications (especially in power battery management systems) with a rapidly increasing market share. It aims to minimize the symmetric loss function (mean square error) and it has high accuracy and efficiency in battery state estimation. This study deals with the second-order extended Kalman filter-based process and the measurement white noise estimation problem for nonlinear continuous-discrete systems. The design of the white noise filter and smoother were, firstly, converted into a linear estimation problem by the second-order Taylor series expansion approximation and the function that makes the second-order term approximately equivalent to the estimation error variance. Secondly, based on the projection formula of the Kalman filtering (KF) theory and the Lemma of expectation for quadratic and quartic product traces of random vectors, the second-order EKF was derived. Then, to generate white noise estimators in the forms of filtering and smoothing, we derived a recursive solution, using an innovation method. Finally, a numerical example is given to show the effectiveness of the proposed method.