Optimal Placement of the Receivers for Multistatic Target Localization

In this paper, we propose a numerical method for the optimal placement of the receivers in a multistatic target localization system (with a single transmitter and multiple receivers) in order to improve the achievable target estimation accuracy of time-sum-of-arrival (TSOA) localization techniques, for 2D and 3D scenarios. The proposed algorithm is based on the principle of block majorization minimization (block MM) which is a combination of block coordinate descent and majorization-minimization (MM) methods. More precisely, we formulate the design objective for the placement of sensors performing TSOA measurements using $A-$ and $D-$ optimality criteria, and propose an iterative algorithm to find the optimal solution by first splitting the design variable into M blocks (where M is the number of receivers) and then applying the principle of MM on each block. The proposed method can additionally handle the cases where the transmitter also acts as a receiver. The framework can also be applied to the case of non-uniform noise variances at the receivers. Several numerical simulation results are included to show the benefits offered by the developed design algorithm.