带有色观测噪声的广义系统Kalman滤波器

Kalman Filter with Coloured Observation Noises for Descriptor Systems

对于带多传感器的广义线性离散随机系统,应用奇异值分解,并通过对观测方程的状态变换,将带有色观测噪声的系统变换为等价的带相关噪声的两个降阶多传感器子系统。应用Kalman滤波方法,在线性最小方差按块对角阵加权融合准则下,提出了按矩阵加权融合降阶广义Kalman滤波器,可减少计算负担和改善局部滤波精度。为了计算最优加权,给出了局部滤波误差协方差阵的计算公式,证明了融合器和局部滤波器之间的精度关系。一个MonteCarlo仿真例子说明了其有效性。

For the linear discrete stochastic descriptor systems with multisensor, using the singular value decomposition, by means of a linear transformation of the observation equation, the system with coloured observation noises is converted into two equivalent reduced-order subsystems with correlated noises. Based on Kalman filtering method, fusion reduced-order descriptor Kalman filters weighted by matrices is proposed under the linear least variance optimal fusion criterion by block-diagonal matrices. The computational burden can reduce, and can improve the local filtering accuracy. In order to compute the optimal weights, the formulas of computing the cross-covariantes matrices among local filtering errors are presented. The accuracy relations among fusers and local filters are proved. A Monte Carlo simulation example shows its effectiveness.