Outlier-Resistant Localization for Smart Cities: Low-Rank Approximation-Based Approaches

Table 3

Matrix completion methods used in the simulation.

Algorithms	Description
MatrixIRLS [27]	An iterative weighted least squares (IRLS) algorithm, which can be interpreted as smoothing Newton’s method applied on a non-convex rank surrogate cost function, has the ability of escaping saddle points.
MDS-MAP [13]	The shortest path algorithm, i.e., Dijkstra, is used to estimate the missing ranging data.
AD [15]	An alternating coordinate descent method, where a single coordinate of a particular point is updated each time and the optimal solution is obtained iteratively.
Lmafit [28]	An efficient non-linear successive relaxation strategy is used, where only one linear least squares problem needs to be solved per iteration instead of singular value decomposition (SVD).
TNNR [23]	Using truncated nuclear norm (TNN) regularization, where TNN is defined as the nuclear norm subtracted by the sum of the largest few singular values.
LRM-CG [17]	The low-rank matrix completion is transformed into an unconstrained minimization problem in Riemannian manifolds. The definition of differentiability is also given, and the modified conjugate gradient algorithm is used to solve the problem.