Robust Graph Localization for Underwater Acoustic Networks

We consider the problem of robust localization of a set of underwater network nodes, based on pairwise distance measurements. Localization plays a key role in underwater network optimization, as accurate node positioning enables location-aware scheduling, data routing, and geo-referencing of the collected underwater sensor data. State-of-the-art graph localization approaches include variations of the classical multidimensional scaling (MDS) algorithm, modified to handle unlabelled, missing, and noisy distance measurements. In this paper, we present MAD-MDS, a robust method for graph localization from incomplete and outlier corrupted pair-wise distance measurements. The proposed method first conducts outlier excision by means of Median Absolute Deviation (MAD). Then, MAD-MDS performs rank-based completion of the distance matrix, to estimate missing measurements. As a last step, MAD-MDS applies MDS to the reconstructed distance matrix, to estimate the coordinates of the underwater network nodes. Numerical studies on both sparsely and fully connected network graphs as well as on data from past sea experiments corroborate that MAD-MDS attains high coordinate-estimation performance for sparsely connected network graphs and high corruption variance.