We study a distributed Kalman filtering problem in which a number of nodes cooperate without central coordination to estimate a common state based on local measurements and data received from neighbors. This is typically done by running a local filter at each node using information obtained through some procedure for fusing data across the network. A common problem with existing methods is that the outcome of local filters at each time step depends on the data fused at the previous step. We propose an alternative approach to eliminate this error propagation. The proposed local filters are guaranteed to be stable under some mild conditions on certain global structural data, and their fusion yields the centralized Kalman estimate. The main feature of the new approach is that fusion errors introduced at a given time step do not carry over to subsequent steps. This offers advantages in many situations including when a global estimate in only needed at a rate slower than that of measurements or when there are network interruptions. If the global structural data can be fused correctly asymptotically, the stability of local filters is equivalent to that of the centralized Kalman filter. Otherwise, we provide conditions to guarantee stability and bound the resulting estimation error. Numerical experiments are given to show the advantage of our method over other existing alternatives.

中文翻译：

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具有解耦局部滤波器的分布式卡尔曼估计

我们研究了一个分布式卡尔曼滤波问题，其中多个节点在没有中央协调的情况下进行协作，以根据本地测量值和从邻居收到的数据来估计共同状态。这通常是通过在每个节点上运行本地过滤器来完成的，使用通过一些过程获得的信息来融合网络上的数据。现有方法的一个常见问题是每个时间步的局部过滤器的结果取决于前一步融合的数据。我们提出了一种替代方法来消除这种错误传播。所提出的局部滤波器保证在某些全局结构数据的某些温和条件下是稳定的，并且它们的融合产生集中的卡尔曼估计。新方法的主要特点是在给定时间步引入的融合误差不会延续到后续步骤。这在许多情况下提供了优势，包括仅需要以比测量慢的速率进行全局估计或存在网络中断时。如果全局结构数据能够渐近地正确融合，则局部滤波器的稳定性与集中卡尔曼滤波器的稳定性相当。否则，我们提供条件来保证稳定性并限制由此产生的估计误差。给出了数值实验以显示我们的方法相对于其他现有替代方法的优势。如果全局结构数据能够渐近地正确融合，则局部滤波器的稳定性与集中卡尔曼滤波器的稳定性相当。否则，我们提供条件来保证稳定性并限制由此产生的估计误差。给出了数值实验以显示我们的方法相对于其他现有替代方法的优势。如果全局结构数据能够渐近地正确融合，则局部滤波器的稳定性与集中卡尔曼滤波器的稳定性相当。否则，我们提供条件来保证稳定性并限制由此产生的估计误差。给出了数值实验以显示我们的方法相对于其他现有替代方法的优势。