Enhanced edge kernel estimation for robust positioning

We consider a localization problem of multiple sources from range and angle measurements. To exploit the heterogeneity of the information we formulate the problem as an optimization over an edge-kernel matrix, in which angle and distance information are decoupled. The algorithm consists of estimating the Euclidean structure of the network by means of the angle-kernel (Euclidean kernel derived from angle information only) and, recovery the unknown positions by means of a weighted linear least square optimization. Based on recent advances of robust principal component analysis applied to low-rank matrix recovery, we show how to improve the estimation of the angle-kernel and how to construct an effective angle-distance weighing strategy that uses the noise subspace of the angle kernel to mitigate the errors in the angle measurements and small-scale analysis to increase robustness to range errors. Our results show the advantage of the proposed nuclear-norm optimization over classical spectrum truncation (E-MDS) and a SDP-based formulations of the problem.