Data-driven spatio-temporal modeling using the integro-difference equation

Authors:
Michael Dewar;Kenneth Scerri;Visakan Kadirkamanathan
Affiliations:
School of Informatics, University of Edinburgh, Edinburgh, U.K.;Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, U.K.;Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, U.K.
Venue:
IEEE Transactions on Signal Processing
Year:
2009

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Abstract

A continuous-in-space, discrete-in-time dynamic spatio-temporal model known as the Integro-Difference Equation (IDE) model is presented in the context of data-driven modeling. A novel decomposition of the IDE is derived, leadmg to state-space representation that does not couple the number of states with the number of observation locations or the number of parameters. Based on this state-space model, an expectation-maximization (EM) algorithm is developed in order to jointly estimate the IDE model's spatial field and spatial mixing kernel. The resulting modeling framework is demonstrated on a set of examples.