含噪声驱动阵的相关噪声卡尔曼滤波及稳定性

摘要

探讨相关噪声下离散时变线性系统的卡尔曼滤波模型.借助广义逆和最小模最小二乘解的思想,在Frobenius范数意义下,获得基于偏差最优估计的转换系数矩阵,将相关噪声系统转化为不相关噪声系统,获得相应的卡尔曼滤波模型.理论上,在误差协方差矩阵有界前提下,获证该滤波模型是全局渐近稳定的,数值实验获该模型的合理性.理论和实验结果表明,该模型是稳定的,且可有效解决含相关噪声和时变量测噪声驱动阵的离散时变系统的状态估计问题.%The Kalman filter of the discrete time-varying linear system with correlated noise is investigated. First, we obtained the transformation coefficient matrix based on minimizing the deviation of optimal estimation under Frobenius norm, with the help of the theory of the generalized inverse and minimum modulus least square solution. This helps us transform the system with correlated noise into one with uncorrelated noise. Second, the resultant Kalman filter, which is rational with the experiment, is proven to be globally asymptotically stable, provided that the error covariance matrix and the derived state matrix are bounded and inverse respectively. Theoretical and experimental results show that the proposed Kalman filter is not only stable, but can effectively estimate the state of the original system with the correlated noise and time-varying observation noisy matrix.