Probabilistic search: a Bayesian approach in a continuous workspace

This thesis considers the problem of modeling search for a single, non-moving target in a continuous environment, where the search agent's only observations are obtained from a binary sensor. To model this problem, the widely used Bayesian filtering approach is employed to obtain the general filtering equations for the posterior distribution representing the object's location over the workspace. Given a likelihood and prior belief belonging to the exponential family class, while using this class's self-conjugacy property, an exact, finite representation of the object posterior is explicitly derived. Though complexity issues may render this exact representation infeasible for computation, regularized particle filtering is utilized to yield a continuous approximation of the object belief. To demonstrate the validity of the search model, a gradient-ascent search strategy is applied with care taken to avoid local maxima. This is done with multiple simulations for various prior distributions. Finally, future work is described for search applications and approximation schemas relevant to the structure of the search model presented