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In this paper we consider a diffusion field induced by multiple point sources and address the problem of reconstructing the field from its spatio-temporal samples obtained using a sensor network. We begin by formulating the problem as a multi-source estimation problem - so estimating source locations, activation times and intensities given samples of the(More)
We consider diffusion fields induced by a finite number of spatially localized sources and address the problem of estimating these sources using spatiotemporal samples of the field obtained with a sensor network. Within this framework, we consider two different time evolutions: the case where the sources are instantaneous, as well as, the case where the(More)
Sensor networks are becoming increasingly prevalent for monitoring physical phenomena of interest. For such wireless sensor network applications, knowledge of node location is important. Although a uniform sensor distribution is common in the literature, it is normally difficult to achieve in reality. Thus we propose a robust algorithm for reconstructing(More)
Numerous physical phenomena are well modeled by partial differential equations (PDEs); they describe a wide range of phenomena across many application domains, from modeling EEG signals in electroencephalography to, modeling the release and propagation of toxic substances in environmental monitoring. In these applications it is often of interest to find the(More)
In this contribution, we implement a fully distributed diffusion field estimation algorithm based on the use of average consensus schemes. We show that the field reconstruction problem is equivalent to estimating the sources of the field, and then derive an exact inversion formula for jointly recovering these sources when they are localized and(More)
—Partial differential equations are central to describing many physical phenomena. Moreover in many applications these phenomena are observed through a sensor network, with the aim of inferring its underlying properties. Here we present a new framework for analysing fields governed by linear partial differential equations. The framework leverages from(More)
We present a framework for estimating non-localized sources of diffusion fields using spatiotemporal measurements of the field. Specifically in this contribution, we consider two non-localized source types: straight line and polygonal sources and assume that the induced field is monitored using a sensor network. Given the sensor measurements, we(More)
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