Physics-driven quantized consensus for distributed diffusion source estimation using sensor networks

Abstract

Sensor networks are important for monitoring several physical phenomena. In this paper, we consider the monitoring of diffusion fields and design simple, yet robust, sensing, data processing and communication strategies for estimating the sources of diffusion fields under communication constraints. Specifically, based on our previous work in the area, we firstly show how sources of the field can be recovered analytically through the use of well-chosen sensing functions. Then, by properly extending this scheme to our sensor network setting, we design and propose an effective diffusion field sensing strategy. Next, we introduce a physics-driven quantized gossip scheme, as a joint information processing and communication strategy for handling the network communication constraints: i.e. when a sensor can only communicate with a small subset of nodes over links with a finite capacity. Combining the proposed strategies allows us to develop a fully distributed algorithm for recovering sources of diffusion fields using sensor networks. Numerical simulation results are presented in order to evaluate the effectiveness and robustness of our algorithm.

A Sampling Framework for Solving Physics-Driven Inverse Source Problems

“…This is the fundamental idea behind Cadzow-like [54] algorithms common in the FRI literature. Furthermore, these approaches are most effective when the noise in H is white, so we first need to apply a noise prewhitening transform similar to the approach in [43].…”

“…1) Recovering an unknown number of sources: By combining the observations in Remark 1 with the fact that the singular value decomposition of the multilevel Hankel matrix H (or H ) also encodes information about M -i.e. most dominant singular values are due to the sources-an iterative estimation scheme similar to those in [37], [43] can be devised. The scheme relies on finding a time interval over which only a fixed number of field sources are active.…”

Solving inverse source problems for linear PDEs using sparse sensor measurements

“…See for example, [4], [24]. Therefore, given such a sequence R(k) applying Prony's method to it solves the ISP of interest.…”

Distributed Source Identification by Two-Hop Consensus Dynamics with Uniform Time-Varying Communication Time-Delays

“…We show that the multi-agent system can estimate the initial distribution of the 2-D diffusion phenomena by the proposed 2-hop consensus dynamics with communication time-delays. In contract to the existing consensus-based source identification methods by [16], [17], and [21], the proposed method explicitly considers the effects of the multi-hop communication and communication time-delays which are unavoidable for large-scale sensor networks.…”

“…For a distributed source identification problem, Cao et al proposed a distributed sequential convex combination method with the advection-diffusion model [16]. Murray-Bruce and Dragotti considered a consensus-based distributed source identification problem by the quantized gossip algorithm [17].…”