A Framework for Distributed Estimation With Limited Information and Event-Based Communications

In this article, we consider the problem of distributed estimation in a sensor network, where multiple sensors are deployed to estimate the state of a linear time-invariant Gaussian system. By losslessly decomposing the 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 filters from the 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 requirements of collective system observability. Moreover, the developed results can be generalized to achieve a distributed implementation of any Luenberger observer. By solving a semidefinite programming, we further present a low-rank estimator design to obtain the (sub)optimal gains of a Luenberger observer such that the distributed estimation is realized under the constraint of message size. Therefore, as compared with existing works, the proposed algorithm is implemented with limited information since it enjoys lower data size at each transmission. Numerical examples are finally provided to demonstrate the efficacy of the proposed methods.