Modelling search with a binary sensor utilizing self-conjugacy of the exponential family

In this paper, we consider the problem of an autonomous robot searching for a target object whose position is characterized by a prior probability distribution over the workspace (the object prior). We consider the case of a continuous search domain, and a robot equipped with a single binary sensor whose ability to recognize the target object varies probabilistically as a function of the distance from the robot to the target (the sensor model). We show that when the object prior and sensor model are taken from the exponential family of distributions, the searcher's posterior probability map for the object location belongs to a finitely parameterizable class of functions, admitting an exact representation of the searcher's evolving belief. Unfortunately, the cost of the representation grows exponentially with the number of stages in the search. For this reason, we develop an approximation scheme that exploits regularized particle filtering methods. We present simulation studies for several scenarios to demonstrate the effectiveness of our approach using a simple, greedy search strategy.