Optimal cost allocation in centralized and decentralized detection problems

Abstract

The optimal cost allocation problem is proposed for centralized and decentralized detection systems in the presence of cost constrained measurements, where the aim is to minimize the probability of error of a given detection system under a total cost constraint. The probability of error expressions are obtained for centralized and decentralized detection systems, and the optimal cost allocation strategies are provided. In addition, special cases are investigated in the presence of Gaussian observations and measurement noise. The solutions of the proposed problems specify the optimal allocation of the cost budget among various measurement devices (sensors) to achieve the optimum detection performance. Numerical examples are presented to discuss the implications of the results.