A combinatorial optimization framework for subset selection in distributed multiple-radar architectures

Widely distributed multiple radar architectures offer parameter estimation improvement for target localization. For a large number of radars, the achievable localization minimum estimation mean-square error (MSE), with full resource allocation, may extend beyond the system predetermined performance goals. In this paper, a performance driven resource allocation scheme for multiple radar systems is proposed. The number of transmit and receive radars employed in the estimation process is minimized by effectively selecting a subset of active radars such that the required MSE performance threshold is attained. As the goal is to obtain a performance level with the lowest cost, in terms of active system elements, the problem is formulated in a combinatorial optimization framework as a knapsack problem (KP). The Cramer-Rao bound (CRB) is used as a performance metric. Cost parameters, representing operational cost or any other utilization constraints on the radars, are associated with each of the radars. These are incorporated in the KP formulation, as decision making factors in the selection process. Radar subset selection is implemented through a heuristic algorithm, successively selecting radars that minimize the performance gap between the temporal CRB and a given MSE goal. The proposed algorithm offers considerable reduction in computational complexity when compared with an exhaustive search. By minimizing the number of operational radars needed to complete the task, this concept introduces savings in both communication link needs and central processing load, in addition to the operational ones.