Multi-Sensor Marginalized Particle Filtering for Dynamic Source Estimation

This letter presents a marginalized particle filtering method for localizing, from sparse measurements, a moving source emitting a spatio-temporal field governed by a partial differential equation (PDE). We explicitly consider the full space-time dynamics of the field using a finite-element (FE) approximation for the spatial discretization of the governing PDE system. We propose a marginalized (or Rao-Blackwellized) formulation of the joint field and source estimation problem that leverages the conditionally linear-Gaussian structure of the system with respect to the source position and intensity. This formulation enables the estimation of field variables conditioned on each source position particle using the optimal Kalman filter. We apply this marginalized formulation to both centralized and distributed multi-sensor architectures with remarkable results in terms of monitoring performance and computational efficiency.