TDOA-Based Robust Sound Source Localization With Sparse Regularization in Wireless Acoustic Sensor Networks

Time difference of arrival (TDOA) measurements, which are contaminated by large values of error, known as outliers, would have a significant impact on the accuracy of sound source localization (SSL) in wireless acoustic sensor networks (WASNs). Few techniques are reported in the literature to tackle SSL in WASNs by taking TDOA outliers into consideration. To mitigate the effect of outliers on the accuracy of SSL, we propose outlier-resistant robust sound source localization (RSSL) algorithms based on sparse regularization using an unsynchronized network of microphone arrays. The TDOA errors are divided into two components: a) energy-bounded inliers and b) outliers. Assuming that outliers are sparse in the measurement set, we formulate the RSSL problem as that of minimizing the number of outliers, mathematically, a $\ell _{0}$ (pseudo)-norm optimization problem with non-convex constraints. Five sub-optimal RSSL solvers are derived, among which the first two solvers are applicable to the scenario involving only outliers while the last three solvers concentrate on the scenario incorporating both outliers and inliers. In common, these solvers exploit a convex approximation technique called Concave Convex Procedure to dispose of the non-convex constraints. Differently, the first solver approximates the original $\ell _{0}$ (pseudo)-norm cost function with the $\ell _{1}$ norm while a concave surrogate function is adopted in the second solver to yield a tighter approximation to the $\ell _{0}$ (pseudo)-norm. Apart from the application of these two approximation techniques, the third and fourth solvers relax the non-convex $\ell _{2}$ norm constraint with the $\ell _{\infty }$ norm. The fifth solver is dedicated to the $\ell _{1}$ norm regularization problem with the Lasso formulation, which is equivalent to the M-estimator of Huber’s function solved via the iteratively reweighted least squares paradigm. Experimental results validate the effectiveness and robustness of the proposed algorithms.