有偏卡尔曼滤波及其算法

The Biased Kalman Filter and Algorithm

从理论角度分析了观测矩阵的复共线性对卡尔曼滤波的影响,并在均方误差最小意义下,给出了一种有偏卡尔曼滤波算法。分别对观测矩阵和观测量施加扰动进行了试验和分析,证明观测矩阵的病态性会对卡尔曼滤波估计造成严重危害。数值模拟结果表明,本文算法能够有效改善观测矩阵病态性对卡尔曼滤波估计的影响,提高解算质量。

Kalman filter is one of the most common ways to deal with dynamic data and has been widely used in project fields.However,the accuracy of Kalman filter for discrete dynamic system is poor when the observation matrix is ill-conditioned.Therefore,the method for overcoming the harmful effect caused by ill-conditioned observation matrix in discrete dynamic system is studied in this paper.The causes of the ill-conditioned observation matrix and its effect on Kalman filter are analyzed.Biased Kalman filter and its algorithm are proposed by combining the biased estimation and Kalman filter in the sense of mean square error（MSE）.The methods of choosing biased parameter in the new algorithm is proposed.By separately exerting some disturbance on the observation matrix and observation vector,two simulations are carried out.The experimental results show that the traditional Kalman filter is inaccurate when the observation matrix is ill-conditioned,and the biased Kalman filter is more accurate than the traditional one in terms of MSE.