Constrained Probabilistic Search for a One-Dimensional Random Walker


This paper addresses a elementary search problem in which a searcher subject to time and energy constraints tries to find a mobile target. The target's motion is modeled as a random walk on a discrete set of points on a line section. At every time step, the target chooses one in all the adjacent nodes at random and moves there. We tend to study 2 detection models. Within the no-crossing model, the searcher detects the target if it's on the identical node or if it takes the same edge at the identical time. Within the crossing model, detection happens only if the target lands on the same node at the identical time. For the no-crossing model, where move and keep actions could have different prices, we tend to gift an optimal search strategy below energy and time constraints. For the crossing model, we have a tendency to formulate the matter of coming up with an optimal strategy as a partially observable Markov call method (POMDP) and solve it using strategies that reduce the state-space illustration of the belief. The POMDP solution reveals structural properties of the optimal resolution. We tend to use this structure to style an economical strategy and analytically study its performance. Finally, we tend to gift preliminary experimental results to demonstrate the applicability of our model to our tracking system, that is used for finding radio-tagged invasive fish.

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