Optimal Placement of the Receivers for Multistatic Target Localization
Ghania Fatima, Petre Stoica, Augusto Aubry, Antonio De Maio, Prabhu Babu
Abstract
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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> - and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> - optimality criteria, and propose an iterative algorithm to find the optimal solution by first splitting the design variable into <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> blocks (where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> 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.