Point source estimation via finite element multiple-model Kalman filtering

Point source estimation consists of detecting and localizing a concentrated diffusive source as well as estimating its intensity and induced field from pointwise-in-time-and-space measurements of sensors deployed over the area of interest. The spatiotemporal dynamics of the diffused field is modeled by a partial differential equation (PDE) and a finite element (FE) method is employed for spatially discretizing the PDE model. Source identifiability, i.e. the possibility of detecting the source and uniquely identifying its location and intensity, is analysed in a system-theoretic framework. Further, a novel multiple model filtering approach to source estimation is presented and its effectiveness is demonstrated via a simulation experiment.