ECO-DKF：未知相关性下的事件触发可认证最优分布式卡尔曼滤波器
ECO-DKF: Event-Triggered and Certifiable Optimal Distributed Kalman Filter under Unknown Correlations
AI总结：
针对分布式卡尔曼滤波器的最优估计求解难与通信带宽占用高的问题，提出ECO-DKF算法，通过紧致半定规划松弛实现最优性在线认证，结合事件触发广播机制降低带宽，同时保证全局渐近稳定。
摘要：
本文提出ECO-DKF，即首个事件触发且可认证的最优分布式卡尔曼滤波器。我们的算法解决了分布式卡尔曼滤波器固有的两大核心问题：（一）完全分布式且可扩展的最优估计；（二）降低通信带宽占用。第一个问题需要求解一个NP难优化问题，现有方法通常采用松弛策略，导致无法保证原问题的最优性。仅利用一跳邻居的信息，我们提出了一种紧致的半定规划（Semi-Definite Programming）松弛方法，能够在本地在线认证松弛解是否为原NP难问题的最优解。当满足认证条件时，在可扩展性与事件触发一跳通信的约束下，ECO-DKF在平方误差意义下是最优的，且该估计器是全局渐近稳定的。针对第二个问题，我们基于松弛优化的输出设计了事件触发机制。最终得到的基于广播的算法能够节省通信带宽，无需独立通信链路，也避免了同一时刻内的多次信息交互，同时保留了滤波器的最优性与稳定性特性。
英文摘要：
This paper presents ECO-DKF, the first Event-Triggered and Certifiable Optimal Distributed Kalman Filter. Our algorithm addresses two major issues inherent to Distributed Kalman Filters: (i) fully distributed and scalable optimal estimation and (ii) reduction of the communication bandwidth usage. The first requires to solve an NP-hard optimisation problem, forcing relaxations that lose optimality guarantees over the original problem. Using only information from one-hop neighbours, we propose a tight Semi-Definite Programming relaxation that allows to certify locally and online if the relaxed solution is the optimum of the original NP-hard problem. In that case, ECO-DKF is optimal in the square error sense under scalability and event-triggered one-hop communications restrictions. Additionally, ECO-DKF is a globally asymptotically stable estimator. To address the second issue, we propose an event-triggered scheme from the relaxed optimisation output. The consequence is a broadcasting-based algorithm that saves communication bandwidth, avoids individual communication links and multiple information exchanges within instants, and preserves the optimality and stability properties of the filter.
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