  This paper addresses the Sensor Network Localization (SNL) problem using
received signal strength. The SNL is formulated as an Euclidean Distance Matrix
Completion (EDMC) problem under the unit ball sample model. Using the
Burer-Monteiro factorization type cost function, the EDMC is solved by
Riemannian conjugate gradient with Hager-Zhang line search method on a quotient
manifold. A "rank reduction" preprocess is proposed for proper initialization
and to achieve global convergence with high probability. Simulations on a
synthetic scene show that our approach attains better localization accuracy and
is computationally efficient compared to several baseline methods.
Characterization of a small local basin of attraction around the global optima
of the s-stress function under Bernoulli sampling rule and incoherence matrix
completion framework is conducted for the first time. Theoretical result
conjectures that the Euclidean distance problem with a structure-less sample
mask can be effectively handled using spectral initialization followed by
vanilla first-order methods. This preliminary analysis, along with the
aforementioned numerical accomplishments, provides insights into revealing the
landscape of the s-stress function and may stimulate the design of simpler
algorithms to tackle the non-convex formulation of general EDMC problems.
