An iterative computational method for determining the value function of an optimal control problem, related to target tracking, is presented. The target is assumed to be located in a fixed known position in space, but its identity (hostile or friendly) is known only with a prior probability. An observation of the target can be made at any location, and its error has position-dependent probability. The objective is finding the optimal navigation and observation strategy which leads to a final decision (i.e., the target is friendly or hostile), The value function is shown to be the unique viscosity solution of a variational inequality Furthermore it is the unique fixed point of a nondecreasing concave operator.