Search strategies for radar target localization

In this thesis we consider a discretized version of the problem of optimal beam-forming, or radar transmit and receive pattern design. This is done for stationary radar target localization in the presence of white Gaussian noise while the target is equally likely to be in one of M discrete two-dimensional cells. This work falls under the area of optimal search, which addresses optimal allocation of effort in search problems. This arises in many areas such as the radar target localization problem that we address here, fault location in circuits, localization of mobile stations in wireless networks and Internet information searches.; We propose two new approaches for beam-form design in target localization problems. The first is a finite-horizon approach in which we design the beam-form off-line with the goal of minimizing the probability of error after exactly L observations. We choose to maximize an objective function that is a point-wise infimum of all Kullback-Leibler Information Numbers (KLINs) between the M hypotheses. The second is an adaptive approach in which the beam-form is optimized after each observation to minimize the probability of incorrectly localizing the target after the next observation is acquired. In general, the adaptive approach has a better performance than the finite-horizon one. Both approaches provide an optimal trade-off between available resources, like time and signal to noise ratio (SNR), and performance.; We also proposed a novel hierarchical radar target localization scheme in which the search cells are logically arranged as an m-ary search tree. Off-line allocation of available observations among the tree levels reduces to the Knapsack problem. We introduce an unconstrained solution that serves as a benchmark for the other approaches. In another approach we impose a constraint that allows us to dynamically allocate the available observations. Under this setup we propose two strategies. The first is based on the use of the multi-hypothesis sequential probability ratio test (MSPRT). The second is a look-ahead strategy which gears the search based on the expected probability of error for the next observation. In conclusion, the hierarchical localization scheme offers means to capitalize on available SNR to reduce search time.