带相关噪声异步采样系统的分布式最优线性递推融合估计

对带相关噪声的异步均匀采样线性离散系统, 研究了分布式最优线性递推融合预报和滤波问题. 通过引入 满足伯努利分布的随机变量将系统同步化, 给出了局部Kalman预报器和滤波器. 分别推导了局部估值间的互协方 差阵、分布式最优线性融合估值与局部估值间的互协方差阵. 提出了分布式最优线性递推融合预报器和滤波器. 与 局部估值按矩阵加权的分布式融合估计算法相比, 所提出的算法具有更高的估计精度, 但与集中式融合相比有精度 损失. 为了进一步提高估计精度, 又提出了带反馈的分布式最优线性递推融合预报器和滤波器, 证明了带反馈的融 合估计与集中式融合估计具有相同的精度. 仿真例子验证了所提算法的有效性.

Distributed optimal linear recursive fusion estimation for asynchronous sampling systems with correlated noises

The distributed optimal linear recursive fusion prediction and filtering problems are studied for asynchronous uniform sampling linear discrete-time systems with correlated noises. By introducing Bernoulli distributed random variables, the asynchronous system is synchronized and then the local Kalman predictor and the filter are given. Crosscovariance matrices between local estimates and those matrices between the distributed optimal linear fusion estimate and local estimates are derived, respectively. The distributed optimal linear recursive fusion predictor and the filter are presented. Compared with the existing distributed fusion estimates by matrix weighting local estimates, the proposed algorithms have higher estimation accuracy. However, they have accuracy losses compared with the centralized fusion estimates. In order to further improve estimation accuracy, the distributed optimal linear recursive fusion predictor and the filter with feedback are also presented. It is strictly proved that the fusion estimates with feedback have the same accuracy as the centralized fusion estimates. A simulation example demonstrates the effectiveness of the proposed algorithms.