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Efficient employment of imperfect search sensors in complex environments

Abstract : Defense planners must strive to develop and incorporate new, efficient procedures to allocate scarce resources in varied complex environments. We consider two discrete-time, discrete-space search effort allocation situations. Both involve the employment of an imperfect sensor, which is subject to both false-positive and false-negative errors. The area of interest, comprised of several disjoint area-cells, contains a single target of interest. In the first situation, the target moves according to a Markovian transition matrix, which is unknown to the sensor operator. The objective is to estimate the target's steady-state distribution, using only the sensor's detection signals and knowledge of its false-positive and false-negative rates. The second situation considers a stationary target, wherein the objective is to determine the area-cell occupied by the target, in the fewest expected number of investigations, to within certain operator-prescribed error tolerances. We develop an adaptive algorithm based on stochastic approximation for the first situation, and show that the resultant rate of error in determining target presence/absence in any area-cell converges to zero at the fastest possible rate. We propose a sequential elimination procedure for the second situation, which provides an efficient determination of target location and guarantees its error rate not to exceed the operator-prescribed tolerance.