Unknown source in spatially distributed systems: Identifiability analysis and estimation

Point source estimation aims to detect and localize a concentrated diffusive source as well as to estimate its intensity and induced field from pointwise-in-time-and-space measurements of sensors spread over the area to be monitored. The space–time dynamics of the diffused field is modeled by an advection–diffusion–reaction partial differential equation (ADR PDE) and a finite element (FE) method is adopted in order to spatially discretize the ADR PDE model. Source identifiability, i.e. the ability to detect the source and uniquely identify its location and intensity, is analyzed in a system-theoretic framework by providing sufficient conditions in terms of rank tests on suitable polynomial matrices. Further, a novel finite element multiple model (FE-MM) filtering approach to source estimation is presented. The approach consists of running a bank of FE Kalman filters, each conditioned to the source being placed in a given element of the FE mesh, and then combining the estimates of such filters in order to produce estimates of the source location and intensity as well as of the diffusing field. The effectiveness of the proposed source estimation algorithm is demonstrated via simulation experiments in both cases of motionless source of unknown position and mobile source.