Kalman Filter With Recursive Covariance Estimation-Sequentially Estimating Process Noise Covariance
Kalman Filter With Recursive Covariance Estimation-Sequentially Estimating Process Noise Covariance
复制标题
具有递归协方差估计的卡尔曼滤波器 - 顺序估计过程噪声协方差
DOI：
10.1109/tie.2014.2301756
复制
发表时间：
2014-11-01
影响因子：
7.7
通讯作者：
Wang, Bo
中科院分区：
文献类型：
--
作者：
Feng, Bo;Fu, Mengyin;Wang, Bo
人们发现卡尔曼滤波器在广阔的领域中很有用。然而，众所周知，标准卡尔曼滤波器的成功使用受到对模型结构先验信息和过程统计信息以及测量噪声的严格要求的极大限制。一般来说，过程噪声的协方差矩阵比测量噪声的协方差矩阵更难通过常规实验确定，因为过程噪声与系统动力学的内在耦合性无法通过收集大量传感器数据直接获得过程噪声的统计特性。考虑到这种广泛应用的背景，本文介绍了一种算法——递归协方差估计(RCE)算法，用于从被噪声破坏的信号样本中估计未知的噪声协方差矩阵。基于这一思想，针对一类过程噪声协方差矩阵完全未知的离散时间线性时不变系统，提出了一种新的卡尔曼滤波算法，即带有RCE的卡尔曼滤波器，以解决在没有过程噪声统计信息的情况下进行状态估计的难题，并通过严格的稳定性分析表明，当协方差矩阵为过程噪声是完全已知的。大量的仿真研究也验证了理论结果和所提出算法的有效性。
The Kalman filter has been found to be useful in vast areas. However, it is well known that the successful use of the standard Kalman filter is greatly restricted by the strict requirements on a priori information of the model structure and statistics information of the process, and measurement noises. Generally speaking, the covariance matrix of process noise is harder to be determined than that of the measurement noise by routine experiments, since the statistical property of process noise cannot be obtained directly by collecting a large number of sensor data due to the intrinsic coupling of process noise and system dynamics. Considering such background of wide applications, this paper introduces one algorithm, recursive covariance estimation (RCE) algorithm, to estimate the unknown covariance matrix of noise from a sample of signals corrupted with the noise. Based on this idea, for a class of discrete-time linear-time-invariant systems where the covariance matrix of process noise is completely unknown, a new Kalman filtering algorithm named, Kalman filter with RCE, is presented to resolve this challenging problem of state estimation without the statistical information of process noise, and the rigorous stability analysis is given to show that this algorithm is optimal in the sense that the covariance matrix and state estimations are asymptotically consistent with the ideal Kalman filter when the exact covariance matrix of process noise is completely known a priori. Extensive simulation studies have also verified the theoretical results and the effectiveness of the proposed algorithm.