Sparsity-Aware Multi-Source TDOA Localization

The problem of source localization from time-difference-of-arrival (TDOA) measurements is in general a non-convex and complex problem due to its hyperbolic nature. This problem becomes even more complicated for the case of multi-source localization where TDOAs should be assigned to their respective sources. We simplify this problem to an $\ell_1$-norm minimization by introducing a novel TDOA fingerprinting and grid design model for a multi-source scenario. Moreover, we propose an innovative trick to enhance the performance of our proposed fingerprinting model in terms of the number of identifiable sources. An interesting by-product of this enhanced model is that under some conditions we can convert the given underdetermined problem to an overdetermined one that could be solved using classical least squares (LS). Finally, we also tackle the problem of off-grid source localization as a case of grid mismatch. Our extensive simulation results illustrate a good performance for the introduced TDOA fingerprinting paradigm as well as a significant detection gain for the enhanced model.