Estimation of Spatio-Temporal Processes via Online Filtering>
Wildfire growth is typically modeled using a Partial Differential Equation (PDE) that can be solved using grid-based finite difference or finite element methods using some boundary and initial conditions. Given the geographical spread of the environment over which such events occur and with the temporal aspect factored in, data from sensing systems for such processes are very high dimensional in nature, and thus developing a filtering mechanism that incorporates sensing data for online and real-time estimation and prediction for applications can be very challenging due to the computational complexity involved. This project developed a Kalman filtering based method harnessing concepts in Proper Orthogonal Decomposition (POD) for dimensional reduction. The rationale behind the proposed approach is that methods such as the POD facilitate reduced-order modeling, thus reducing the computational complexity. Implemented in a grid-based model of the environment, the approach can eventually be integrated into Geographic Information Systems (GIS) for effective utilization of information and decision making for incident managers. Following figure shows some results and demonstrates the effectiveness in removing noise in measurements.