Consensus-Based Distributed Estimation in the Presence of Heterogeneous, Time-Invariant Delays

TL;DR

This paper introduces a consensus-based distributed estimator for sensor networks with fixed, heterogeneous, and known delays, ensuring convergence under certain conditions and reducing communication loads.

Contribution

It proposes a novel distributed estimator that accounts for fixed, heterogeneous delays and relies on distributed observability, with proven convergence over strongly-connected networks.

Findings

Estimator converges under specific delay bounds.

Distributed observability reduces communication load.

Convergence proven using augmented matrices and Kronecker products.

Abstract

Classical distributed estimation scenarios typically assume timely and reliable exchanges of information over the sensor network. This paper, in contrast, considers single time-scale distributed estimation via a sensor network subject to transmission time-delays. The proposed discrete-time networked estimator consists of two steps: (i) consensus on (delayed) a-priori estimates, and (ii) measurement update. The sensors only share their a-priori estimates with their out-neighbors over (possibly) time-delayed transmission links. The delays are assumed to be fixed over time, heterogeneous, and known. We assume distributed observability instead of local observability, which significantly reduces the communication/sensing loads on sensors. Using the notions of augmented matrices and Kronecker product, the convergence of the proposed estimator over strongly-connected networks is proved for a specific upper-bound on the time-delay.