A Robust Constrained Total Least Squares Algorithm for Three-Dimensional Target Localization with Hybrid TDOA–AOA Measurements

Three-dimensional (3D) target localization by using hybrid time difference of arrival (TDOA) and angle of arrival (AOA) measurements from multiple sensors has been an active research area for several decades due to its extensive applications in various fields. For this nonlinear estimation problem, the pseudolinear system of equations constructed by using the measurements generally acts as the basis of numerous localization algorithms. In this paper, we aim to improve the performance of 3D TDOA–AOA localization by introducing the constrained total least squares (CTLS) framework wherein the inherent characteristics of the pseudolinear equations can be properly taken into consideration. On the basis of the total least squares model, the CTLS model for 3D TDOA–AOA localization is established by imposing the inherent characteristics of the pseudolinear equations as additional constraints. Then, the multi-constraint optimization problem in CTLS model is solved by using an iterative algorithm based on successive projections. Extensive numerical simulations are accomplished for evaluating the performance of the proposed CTLS algorithm. The results show that the proposed algorithm gives moderate accuracy enhancement with acceptable computational cost, and more importantly, it is more robust to large measurement noise than the compared algorithms.