Blind collaborative 20 questions for target localization

We consider the problem of collaborative target localization by several observers, called players, where the reliability of each player is unknown. As in our previous work [1] we formulate this problem as a 20 questions game with noise for collaborative players under a minimum entropy criterion. We extend the setting of [1] to the case where the players' error channels have unknown crossover probabilities. First, we use dynamic programming to characterize the structure of the optimal policy for constructing the sequence of questions. This generalizes the multiplayer policies derived in [1] for the known error channel setting. Second, we prove a separation theorem showing that a sequential bisection scheme achieves the same performance as the optimal joint queries. This generalizes the separation theorem recently derived for the known error channel case in [1]. Third, we derive bounds for the maximum entropy loss per iteration. Finally, we show that even for the one-dimensional case, the optimal query policy for the unknown error channel is not equivalent to a probabilistic bisection policy. This framework provides a methodology for simultaneous sequential estimation of target location and learning the error channels associated with the players.