A Framework for Distributed Estimation with Reduced Communication via Event-Based Strategies

TL;DR

This paper introduces a novel event-based distributed estimation framework for sensor networks that reduces communication load while maintaining stability and accuracy, applicable to general Luenberger observers.

Contribution

It proposes a lossless Kalman filter decomposition and a decoupled local filtering and synchronization approach, enabling stable, low-communication distributed estimation.

Findings

Lower data transmission per sensor compared to existing methods

Framework guarantees stability under minimal network conditions

Optimal observer gains derived via SDP for efficient estimation

Abstract

This paper considers the problem of distributed estimation in a sensor network, where multiple sensors are deployed to infer the state of a linear time-invariant (LTI) Gaussian system. By proposing a lossless decomposition of Kalman filter, a framework of event-based distributed estimation is developed, where each sensor node runs a local filter using solely its own measurement, alongside with an event-based synchronization algorithm to fuse the neighboring information. One novelty of the proposed framework is that it decouples the local filter from synchronization process. By doing so, we prove that a general class of triggering strategies can be applied in our framework, which yields stable distributed estimators under the minimal requirements of network connectivity and collective system observability. As compared with existing works, the proposed algorithm enjoys lower data size for each transmission. Moreover, the developed results can be generalized to achieve a distributed implementation of any Luenberger observer. By solving a semi-definite programming (SDP), we further present a low-rank estimator design to obtain the optimal gain of Luenberger observer such that the distributed estimation is realized under the constraint of message complexity. Numerical examples are finally provided to demonstrate the proposed methods.