Distributed and Recursive Parameter Estimation in Parametrized Linear State-Space Models

TL;DR

This paper introduces a distributed recursive estimation algorithm for parameter identification in sensor networks observing spatio-temporal state-space processes, with proven convergence and practical application to gas-leak source localization.

Contribution

It proposes a novel incremental recursive prediction error algorithm that combines distributed and online estimation properties with general convergence guarantees.

Findings

Algorithm successfully estimates parameters in simulated scenarios.

Convergence conditions are established and verified.

Application to gas-leak source identification demonstrates practical utility.

Abstract

We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is perturbed by random noise and parametrized by an unknown parameter. To estimate the unknown parameter from the measurements that the sensors sequentially collect, we propose a distributed and recursive estimation algorithm, which we refer to as the incremental recursive prediction error algorithm. This algorithm has the distributed property of incremental gradient algorithms and the on-line property of recursive prediction error algorithms. We study the convergence behavior of the algorithm and provide sufficient conditions for its convergence. Our convergence result is rather general and contains as special cases the known convergence results for the incremental versions of the least-mean square algorithm. Finally, we use the algorithm developed in this paper to identify the source of a gas-leak (diffusing source) in a closed warehouse and also report numerical simulations to verify convergence.