An optimal adaptive Kalman filter
An optimal adaptive Kalman filter
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DOI：
10.1007/s00190-006-0041-0
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发表时间：
2006-07-01
影响因子：
4.4
通讯作者：
Gao, Weiguang
中科院分区：
文献类型：
--
作者：
Yang, Yuanxi;Gao, Weiguang
在鲁棒自适应卡尔曼滤波器中，关键问题是构造一个自适应因子来平衡运动模型信息和测量值对状态向量估计的贡献，以及相应的学习统计量来识别运动模型偏差。本文研究的是在状态向量可以或不能被测量估计的特定条件下的一些最优自适应因子。推导出了两个最优自适应因子，其中一个最优自适应因子要求预测残差向量的估计协方差矩阵等于相应的理论协方差矩阵。另一种方法是要求预测状态向量的估计协方差矩阵等于理论协方差矩阵。给出了两个相关的最优自适应因子。并从理论和实例两方面进行了分析比较。这表明，通过实际计算，最优自适应因子得到的滤波结果优于基于经验的自适应因子得到的滤波结果。
In a robustly adaptive Kalman filter, the key problem is to construct an adaptive factor to balance the contributions of the kinematic model information and the measurements on the state vector estimates, and the corresponding learning statistic for identifying the kinematic model biases. What we pursue in this paper are some optimal adaptive factors under the particular conditions that the state vector can or cannot be estimated by measurements. Two optimal adaptive factors are derived, one of which is deduced by requiring that the estimated covariance matrix of the predicted residual vector equals the corresponding theoretical one. The other is obtained by requiring that the estimated covariance matrix of the predicted state vector equals its theoretical one. The two related optimal adaptive factors are given. These are analyzed and compared in theory and in an actual example. This shows, through the actual computations, that the filtering results obtained by optimal adaptive factors are superior to those obtained by adaptive factors based on experience.