A Kalman-like recursive distributed optimal linear fusion predictor (RDOLFP) without feedback in the linear unbiased minimum variance sense is presented for multi-sensor discrete-time linear stochastic systems with random parameter matrices and correlated noises. Local predictions from sensors are sent to a fusion center to fuse with a prior fusion predictor. The proposed RDOLFP without feedback achieves better accuracy than distributed fusion predictors described in the literature that only weight fusion of local predictors, but worse accuracy than a centralized fusion predictor. A RDOLFP with feedback that has the same estimation accuracy as a centralized fusion predictor is also presented. Its optimality is strictly proven. The stability and steady-state properties of the proposed fusion predictors are analyzed. Distributed optimal linear fusion filters with and without feedback, based on the proposed RDOLFPs, are also presented. Two examples demonstrate the effectiveness of the proposed algorithms.

中文翻译：

---

具有随机参数矩阵和相关噪声的系统的分布式最优线性融合预测器和滤波器

针对具有随机参数矩阵和相关噪声的多传感器离散时间线性随机系统，提出了一种在线性无偏最小方差意义上没有反馈的类卡尔曼递归分布式最优线性融合预测器（RDOLFP）。来自传感器的本地预测被发送到融合中心以与先前的融合预测器融合。提出的没有反馈的 RDOLFP 比文献中描述的分布式融合预测器实现了更好的准确性，这些预测器只对局部预测器进行加权融合，但比集中式融合预测器的准确性更差。还提供了具有与集中式融合预测器相同估计精度的反馈的 RDOLFP。它的最优性被严格证明。分析了所提出的融合预测器的稳定性和稳态特性。还提出了基于所提出的 RDOLFP 的带反馈和不带反馈的分布式最优线性融合滤波器。两个例子证明了所提出算法的有效性。