An analytical subspace-based robust sparse Bayesian inference estimator for off-grid TDOA localization

To locate multiple sources through time-difference-of-arrival (TDOA) measurements, existing algorithms generally require the matching relationship between measurements and the corresponding sources. In this paper, we propose a new Bayesian learning method for cases where the matching relationship is not given and off-grid error is considered. To achieve this, first we propose a new basis generator, which casts the localization problem within the Bayesian learning scheme. Then, we modify the existing sparse Bayesian inference (SBI) approaches and explore the priors on fingerprinting weights, resulting in two intermediate algorithms. On these foundations, a subspace-based robust SBI (SRSBI) algorithm is proposed as the core of this paper. SRSBI is highlighted by its ability to work free from iteration when estimating off-grid targets. What' more, SRSBI offers considerable robustness against initial guesses of hyper-parameters. Numerical simulations demonstrate the superiority of SRSBI in terms of accuracy, robustness and speed, compared to the other reported ones.