Robust TDOA Source Localization Based on Lagrange Programming Neural Network

We revisit herein the problem of time-difference-of-arrival (TDOA) based localization under the mixed line-of-sight/non-line-of-sight propagation conditions. Adopting the strategy of statistically robustifying the non-outlier-resistant $\ell_2$ loss, we formulate it as the minimization of a possibly non-differentiable generalized robust cost function, which is rooted in the analog locally competitive algorithm (LCA) for sparse approximation. We then present a Lagrange programming neural network to address the optimization formulation, with the non-differentiability issues being handled by grafting thereon the LCA concept of internal state dynamics. Compared with the existing algorithms, our approach is computationally less expensive, less reliant on the use of \textit{a priori} error information, and observed to be capable of producing higher localization accuracy.