DocumentCode :
738341
Title :
Estimating Localized Sources of Diffusion Fields Using Spatiotemporal Sensor Measurements
Author :
Murray-Bruce, John ; Dragotti, Pier Luigi
Author_Institution :
Dept. of Electr. & Electron. Eng., Imperial Coll. London, London, UK
Volume :
63
Issue :
12
fYear :
2015
fDate :
6/15/2015 12:00:00 AM
Firstpage :
3018
Lastpage :
3031
Abstract :
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 sources decay exponentially in time after activation. We first derive novel exact inversion formulas, for both source distributions, through the use of Green´s second theorem and a family of sensing functions to compute generalized field samples. These generalized samples can then be inverted using variations of existing algebraic methods such as Prony´s method. Next, we develop a novel and robust reconstruction method for diffusion fields by properly extending these formulas to operate on the spatiotemporal samples of the field. Finally, we present numerical results using both synthetic and real data to verify the algorithms proposed herein.
Keywords :
algebra; diffusion; wireless sensor networks; Green second theorem; Prony method; algebraic methods; diffusion fields; generalized samples; localized source estimation; sensing functions; source distributions; spatiotemporal sensor measurements; wireless sensor networks; Approximation methods; Equations; Estimation; Mathematical model; Robustness; Sensors; Spatiotemporal phenomena; Prony's method; Spatiotemporal sampling; diffusion fields; finite rate of innovation (FRI); sensor networks;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2015.2419187
Filename :
7078935
Link To Document :
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