Estimation of the mixing kernel and the disturbance covariance in IDE-based spatiotemporal systems

Abstract

The integro-difference equation (IDE) is an increasingly popular mathematical model of spatiotemporal processes, such as brain dynamics, weather systems, disease spread and others. We present an efficient approach for system identification based on correlation techniques for linear temporal systems that extended to spatiotemporal IDE-based models. The method is derived from the average (over time) spatial correlations of observations to calculate closed-form estimates of the spatial mixing kernel and the disturbance covariance function. Synthetic data are used to demonstrate the performance of the estimation algorithm.

Estimation and Identification of Spatio-Temporal Models with Applications in Engineering, Healthcare and Social Science

“…The estimated algorithm based on spatial correlation technique was further developed to solve general IDE model of the form described in equation 8 (Aram and Freestone, 2016). This work does not provide an estimate of the spatial field, however, if one is interested in the field reconstruction, the kernel estimate can be used as an initialisation for state-space estimation frameworks developed by Dewar et al (2009); Scerri et al (2009), improving the speed and the convergence of the estimation procedure.…”