多传感器分布式协方差信息融合Kalman滤波理论

对于带多传感器和带相关噪声的线性离散时变随机控制系统,基于按矩阵加权、按对角阵加权和按标量加权的三种最优信息融合规则,提出了相应的三种分布式最优信息融合Kalman估值器,可统一处理融合滤波、预报和平滑问题。为了计算最优加权,提出了计算局部估计误差协方差公式。作为特殊情形,还提出了定常系统的稳态最优信息融合Kalman估值器,其中用解Lyapunov方程计算局部估计误差协方差。同集中融合Kalman估值器相比,可减小计算负担。同单传感器Kalman估值器相比,可提高精度。它们构成了统一和通用的分布式协方差信息融合Kalman滤波理论。

Multisensor Distributed Fusion Kalman Filtering Theory Based on Covariance Information

For the linear discrete time-varying stochastic systems with multisensor and with correlated noises, based on three optimal information fusion rules weighted by matrices, diagonal matrices, and scalars, respectively, the corresponding distributed optimal information fusion Kalman estimators is presented, which can handle the fused filtering, prediction, and smoothing problems in a unified framework. In order to compute the optimal weights, the formulas of computing the local estimation error covariances are presented. As a special case, the steady-state optimal information fusion Kalman estimators are presented for the time-invariant systems, where the local estimation error covariances are computed by solving the Lyapunov equations. Compared with the centralized Kalman estimators, they can reduce the computational burden. Compared with the single-sensor Kalman estimators, their accuracy is improved. They constitute a unified and general distributed Fusion Kalman filtering theory based on covariance information.