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

Abstract

In this paper, 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 semi-definite programming (SDP), 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.

Fixed-time and robust distributed state estimation for fractional-order linear systems based on fractional-order modulating functions

“…, 4, let i denote zero-mean white Gaussian noises with the Signal-to-Noise Ratio (SNR) of 30dB, holding the conditions (C 4 )-(C 5 ). In this case, according to Theorem 2, we employ our developed estimators (17) with the FOMFs (25) to estimate each node's observable states. Subsequently, by applying Theorem 4, the estimation for the entire state can be obtained.…”

“…This facilitates parameter designs and reduces the efforts for estimations and communications. Recently, the filter proposed in [15] has been further developed for distributed estimation with limited information and event-based communications [17].…”

“…Significantly, the majority of existing works presented by [6]- [17] were for IOSs, which typically cannot be directly extended to fractional cases. However, fractional-order calculus can offer a more precise characterization of the longmemory property of various processes [18]- [21], making it suitable for describing certain engineering systems.…”