Second-Order EKF White Noise Estimator Design for Hybrid Systems
Second-Order EKF White Noise Estimator Design for Hybrid Systems
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DOI：
10.3390/sym13112044
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发表时间：
2021-10
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影响因子：
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通讯作者：
Yuxiang Liang;Huihong Zhao;Yunlong Shang;Hailong Meng
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文献类型：
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作者：
Yuxiang Liang;Huihong Zhao;Yunlong Shang;Hailong Meng
扩展卡尔曼滤波器（EKF）具有广泛的应用（特别是在动力电池管理系统中），市场份额迅速增加。该算法以对称损失函数（均方误差）最小为目标，在电池状态估计中具有较高的精度和效率。本文研究了基于二阶扩展卡尔曼滤波的非线性连续-离散系统测量白色噪声估计问题。首先通过二阶泰勒级数展开近似和使二阶项近似等于估计误差方差的函数，将白色噪声滤波器和平滑器的设计转化为线性估计问题。其次，基于卡尔曼滤波（KF）理论的投影公式和随机向量二次和四次乘积迹的期望引理，推导了二阶EKF。然后，为了生成滤波和平滑形式的白色噪声估计器，我们使用新息方法导出了递归解。最后通过数值算例验证了该方法的有效性。
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.