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The context is autonomous bearings-only tracking of a single appearing/disappearing target in the presence of detection uncertainty (false and missed detections) with observer control. The optimal tracking method for this problem in the sequential Bayesian estimation framework is the Bernoulli filter. Observer control is based on previously acquired measurements and is formulated as a partially observable Markov decision process (POMDP) where future actions are ranked according to their associated reward. The paper develops a sequential Monte Carlo implementation of the Bernoulli filter and the reward based on an information theoretic criterion.