Sensor Selection in Distributed Multiple-Radar Architectures for Localization: A Knapsack Problem Formulation

Abstract

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