TOA Localization in DDM-NLOS Propagation Environments: A Robust Optimization Approach

In the presence of occlusion, the non-line-of-sight (NLOS) error has been proven to satisfy a distance-dependent model (DDM). However, existing DDM-based Time-of-Arrival (TOA) localization methods overfit due to their dependence on the exact linear coefficients in the model or assume that the linear coefficients are the same in all paths. In response to the defect, we represent the linear coefficients in matrix form and resort to robust optimization. Subsequently, we construct a second-order cone (SOC) programming with the linear coefficients matrix. To obtain a tractable robust optimization problem, we first convert the SOC constraint to a semi-definite cone (SDC) constraint using the Schur complement. Then, we decompose the SDC constraint with auxiliary variables. For the nonconvexity introduced by the linear coefficients matrix, we use Cauchy-Schwarz inequality and norm compatibility to eliminate the linear coefficients matrix. Finally, we convert a non-convex problem into a solvable semi-definite programming (SDP) problem. This study considers the linear coefficients as matrix variables, making the estimates accurate in densely cluttered environments and independent of precisely priori information about the linear coefficients. Simulations and experiments show better localization accuracy in complex environments than state-of-the-art algorithms.