| We develop methods to detect and localize particle-emitting sources using detector arrays that are inspired by biological compound eyes. The sources of interest may be optical, nuclear, or cosmic; they emit particles such as visible photons, neutrons, protons, or charged particles. Our results may have wide applications to artificial vision, which can be important in robotics (robot vision) or medicine (e.g., artificial eyes for the blind); security, where the detection of nuclear materials is needed; or astronomy. This dissertation consists of three parts. First, we detect a far-field particle source using two directional detector arrays: cubic and spherical. We propose a mean-difference test (MDT) detector, analyze its statistical performance, and show that the MDT has a number of advantages over the generalized likelihood-ratio test (GLRT). Second, we localize the source by proposing a novel biologically inspired detector array, whose configuration generalizes the compound eye of insects. This array combines the advantages of compound eyes (e.g., large field-of-view) and human eyes (e.g., high angular resolution). Based on a statistical model of the array measurements, we analyze the array performance by computing the Cramer-Rao bound (CRB) on the error in estimating the source direction. We also derive lower bounds on the mean-square angular error (MSAE) of the source localization and investigate the MSAE of two source-direction estimators. Numerical examples, including the optimal array design, are presented to further illustrate the array performance. Third, we derive a statistical angular resolution limit (ARL) on resolving two closely spaced point sources in a three-dimensional frame, which is applicable to various measurement models (e.g., radar, sonar, or astronomy). Using the asymptotic analysis of the GLRT, we derive the ARL with constraints on the probabilities of false alarm and detection. Our results give explicit analytical expression for the ARL that is proportional to the square root of the CRB on the angular source separation, or equivalently to the lower bound on the MSAE. |
