Model-based solution techniques for the source localization problem

This paper studies the problem of using point sensor measurements to locate a point source in a class of distributed systems described by partial differential equations (PDEs). Assuming that a priori knowledge of system dynamics is available, three model-based approaches are developed for this problem: off-line numerical computation of the time-response data at the sensor(s) resulting from each possible source location and function of source strength; spatial and time discretization of the PDE model; and off-line solution of a dual (forward) PDE problem based on the dual system model. In each case, a particular algorithm is presented, and an analysis of appropriate sensor placements and the minimal number of sensors required is given. In all three approaches, a minimal amount of online processing is required. The relative advantages and shortcomings of the three approaches are discussed and are demonstrated by applying them to the two-dimensional heat conduction problem