Main-Lobe Beamwidth Constrained Target Localization Using Bistatic Range Measurements

This paper addresses the localization of a target in 3D scenarios using bistatic range measurements with a single passive receiver and multiple transmitters. The main-lobe beamwidth of the receiving antenna contains valuable
a-priori
information about the target position but is commonly overlooked. This study introduces an angular constraint to incorporate the beamwidth information into the elliptic localization, resulting in a Quadratically Constrained Quadratic Programming (QCQP) problem. A novel Two-Stage Main-lobe beamwidth Constrained Estimation (TSMCE) algorithm is proposed to solve this challenging localization problem. Theoretical analysis demonstrates that the algorithm can converge to the candidate solutions that satisfy the Karush–Kuhn–Tucker (KKT) optimality conditions. The corresponding covariance can achieve the Cramér-Rao Lower Bound (CRLB) under a small noise assumption. Numerical simulations confirm that the proposed algorithm achieves superior localization accuracy compared to other methods, particularly in the low Signal to Noise Ratio (SNR) regime. Additionally, the algorithm demonstrates fast convergence and robustness to variations in localization geometry.