Abstract
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.
Highlights
Process and measurement noise estimation is a task worthy of attention, and it has wide applications in many fields, such as battery condition estimation, multifrequency signal estimation, oil seismic exploration, and image processing [1,2,3,4,5]
This is the idea of the extended Kalman filter (EKF), which was originally proposed by Stanley Schmidt, so that the Kalman filter could be applied to nonlinear spacecraft navigation problems [13]
For the nonlinear hybrid systems with continuous-time dynamic and discrete-time measurements, white noise estimators for process and measurement noises were designed in this paper
Summary
Process and measurement noise estimation is a task worthy of attention, and it has wide applications in many fields, such as battery condition estimation, multifrequency signal estimation, oil seismic exploration, and image processing [1,2,3,4,5]. The nonlinear system is approximated to the linear system by real-time linear Taylor approximation; EKF is designed based on KF This is the idea of the EKF, which was originally proposed by Stanley Schmidt, so that the Kalman filter could be applied to nonlinear spacecraft navigation problems [13]. It can be seen from the above discussion that the research on white noise estimation of linear systems has been relatively mature, but there are few studies on the white noise estimation of nonlinear systems; reports on the white noise estimation of continuous discrete hybrid nonlinear systems are even less
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