离散卡尔曼滤波器滤波精度与噪声统计模型准确度的关系

The relation between the accuracy of discrete - time Kalman filter and accuracy of noise statistic

针对多维渐近稳定线性离散系统，推导了使用不准确的初始条件和噪声统计的卡尔曼滤波器实际估计误差协方差矩阵，并基于该矩阵分析了滤波精度与模型精度的关系，指出使用非准确的初始条件和噪声统计模型仍能构造出与最优卡尔曼滤波器等效的滤波器。组合导航系统的仿真验证了文中的结论。

The actual estimation error covariance matrix of the Kalman filter(KF) using incorrectinitial conditions and noise covariance is derived for multidimensional asymtotically stablediscrete linear system and is used to analyze the relation between filtering accuracy and modeling accuracy. It is indicated that the KF using incorrect initial conditions and noisecovariance can be made equivalent to the optimal KF using correct ones. The conclusions areverified by simulation on integrated navigation system.