[论文解读] Randomized Consensus based Distributed Kalman Filtering over Wireless Sensor Networks

Jiahu Qin, Wang Jie+2 more|arXiv (Cornell University)|Oct 5, 2018

Distributed Control Multi-Agent Systems参考文献 36被引用 4

一句话总结

本文提出了一种基于随机gossip协议的分布式卡尔曼滤波算法，适用于无线传感器网络，使每个传感器仅通过本地邻居信息即可估计系统状态，从而降低通信和能耗成本。该方法实现了均方收敛，并在能量和资源受限条件下，估计精度优于非合作式分布式滤波。

ABSTRACT

This paper is concerned with developing a novel distributed Kalman filtering algorithm over wireless sensor networks based on randomized consensus strategy. Compared with the centralized algorithm, distributed filtering techniques require less computation per sensor and lead to more robust estimation since they simply use the information from the neighboring nodes in the network. However, poor local sensor estimation caused by limited observability and network topology changes which interfere the global consensus are challenging issues. Motivated by this observation, we propose a novel randomized gossip-based distributed Kalman filtering algorithm. Information exchange and computation in the proposed algorithm can be carried out in an arbitrarily connected network of nodes. In addition, the computational burden can be distributed for a sensor which communicates with a stochastically selected neighbor at each clock step under schemes of gossip algorithm. In this case, the error covariance matrix changes stochastically at every clock step, thus the convergence is considered in a probabilistic sense. We provide the mean square convergence analysis of the proposed algorithm. Under a sufficient condition, we show that the proposed algorithm is quite appealing as it achieves better mean square error performance theoretically than the noncooperative decentralized Kalman filtering algorithm. Besides, considering the limited computation, communication, and energy resources in the wireless sensor networks, we propose an optimization problem which minimizes the average expected state estimation error based on the proposed algorithm. To solve the proposed problem efficiently, we transform it into a convex optimization problem. And a sub-optimal solution is attained. Examples and simulations are provided to illustrate the theoretical results.

研究动机与目标

• 解决无线传感器网络中分布式卡尔曼滤波面临的可观测性受限与动态网络拓扑的挑战。
• 通过避免集中式处理并最小化数据交换，降低每个传感器的计算与通信负担。
• 设计一种鲁棒且可扩展的滤波框架，适用于具有任意连通性的能量受限自组织传感器网络。
• 优化传感器调度策略，在资源受限条件下最小化平均期望状态估计误差。
• 为随机信息交换与状态更新机制建立概率意义上的理论收敛保证。

提出的方法

• 采用随机gossip协议，使每个传感器在每个时间步随机选择一个邻居进行信息交换。
• 将基于一致性框架的卡尔曼滤波动态与本地测量值和邻居数据相结合，更新状态估计。
• 将误差协方差演化建模为随机过程，利用矩阵理论与压缩映射原理，在期望意义下分析收敛性。
• 采用对称随机权重矩阵，确保分布式估计过程中的一致性与稳定性。
• 将传感器调度优化问题转化为凸规划问题，以寻找最小化期望估计误差的次优解。
• 应用迹不等式与条件期望技术，证明期望误差协方差被限制在集中式情况之下。

实验结果

研究问题

• RQ1 在相同资源约束下，分布式卡尔曼滤波算法能否实现优于非合作式分布式滤波的均方估计性能？
• RQ2 如何在保持估计精度与对拓扑变化的鲁棒性的同时，最小化无线传感器网络中的信息交换？
• RQ3 当更新以随机方式随时间发生时，何种条件可确保分布式滤波算法的均方收敛性？
• RQ4 在能量受限网络中，如何优化传感器调度以最小化平均期望状态估计误差？
• RQ5 所提出的算法是否能在无需完整网络知识或集中协调的情况下，维持在任意连通网络中的性能？

主要发现

• 在充分条件下，所提算法在均方误差性能上优于非合作式分布式卡尔曼滤波。
• 误差协方差矩阵以随机方式演化，且通过压缩映射论证证明了其在期望意义下的收敛性。
• 期望误差协方差的迹被上界限制在集中式误差协方差的迹之内，确保了估计质量的保持。
• 推导出用于最小化平均期望状态估计误差的凸优化公式，实现了高效的次优传感器调度。
• 理论分析证实，即使在任意网络连通性与随机通信模式下，该算法仍能保持稳定与一致性。
• 仿真结果验证了理论分析，展示了在实际无线传感器网络场景中，估计精度与能效的显著提升。