  Distributed cooperative localization in wireless networks is a challenging
problem since it typically requires solving a large-scale nonconvex and
nonsmooth optimization problem. In this paper, we reformulate the classic
cooperative localization problem as a smooth and constrained nonconvex
minimization problem while its loss function is separable over nodes. By
utilizing the structure of the reformulation, we propose two novel scaled
proximal alternating direction method of multipliers (SP-ADMM) algorithms,
which can be implemented in a distributed manner. Compared with the classic
semi-definite programming relaxation techniques, the proposed algorithms can
provide more accurate position estimates with significantly lower computation
complexity. The associated theoretical analysis shows that our algorithms
{\blue globally converge to a KKT point} of the reformulated problem and a
critical point of the original problem, with a favorable sublinear
$\mathcal{O}\left(1/T\right)$ convergence rate, where $T$ is the iteration
counter. Numerical experiments have consistently shown that the proposed
SP-ADMM algorithms are superior to state-of-the-art methods in terms of
localization accuracy and computational complexity across all tested scenarios,
varying network size, number of anchors, average number of neighbors, and noise
variance levels.
