Iterative Estimation of Location and Trajectory of Radioactive Sources With a Networked System of Detectors

We consider the problem of estimating the parameters (location and intensity) of multiple radioactive sources using a system of radiation detectors. The problem formulated as maximum likelihood estimation (MLE) requires the optimization of a high-dimensional objective function and presents significant computational challenges. We propose Fisher's scoring iterations approach (a special case of Newton's iterative method) for finding the MLE. While being computationally scalable, an inherent problem with this approach is finding good initial estimates specifically when multiple sources are present. We propose an expectation maximization (EM) based approach which finds the approximate distribution of the source intensity in space. Peaks in this distribution are used as initial estimates of the parameters to bootstrap the iterative MLE procedure. Next, we consider the problem of estimating the trajectory of a moving and maneuvering source. Since a priori motion model cannot be assumed, the trajectory is approximated as a set of points which again presents a high dimensional estimation problem. The trajectory estimation is posed as a constrained weighted least squares problem which is iteratively solved using the Interior Point Method (IPM). Simulation results are presented which illustrate the behavior and performance of our proposed approaches.