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

• An efficient approach for identification of spatiotemporal IDE model is presented.
• A closed-form solution for the spatial mixing kernel of the IDE model is derived.
• A closed-form solution for the disturbance covariance function is calculated.
• An upper bound on the observation noise variance is computed.

The integro-difference equation (IDE) is an increasingly popular mathematical model of spatiotemporal processes, such as brain dynamics, weather systems, and disease spread. 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.