Location is one of the basic information required for underwater optical wireless sensor networks (UOWSNs) for different purposes, such as relating the sensing measurements with precise sensor positions, enabling efficient geographic routing techniques, and sustaining link connectivity between the nodes. Even though various 2-D UOWSNs’ localization methods have been proposed in the past, the directive nature of optical wireless communications and 3-D deployment of sensors require to develop 3-D underwater localization methods. Additionally, the localization accuracy of the network strongly depends on the placement of the anchors. Therefore, we propose a robust 3-D localization method for partially connected UOWSNs, which can accommodate the outliers and optimize the placement of the anchors to improve the localization accuracy. The proposed method formulates the problem of missing pairwise distances and outliers as an optimization problem, which is solved through half quadratic minimization. Furthermore, analysis is provided to optimally place the anchors in the network, which improves the localization accuracy. The problem of optimal anchor placement is formulated as a combination of Fisher information matrices for the sensor nodes where the condition of D-optimality is satisfied. The numerical results indicate that the proposed method outperforms the literature substantially in the presence of outliers.
As the centralized localization methods are based on dimensionality reduction techniques which require all of the pairwise distance estimations between the nodes, robust matrix completion methods are needed to estimate the missing pairwise distances and remove the outliers. A number of researchers have provided theoretical constraints about the matrix rank, sampling scheme, and missing rate to effectively complete a matrix in low rank. In general, matrix completion schemes can be classified into three classes. The first class consists of matrix factorization based schemes where the missing entries of a partially filled matrix of size @math and rank @math are estimated from the product of two matrices @math and @math @cite_56 @cite_15 . Matrix completion schemes based on matrix factorization are non-convex and they require prior information about the rank of the matrix. The authors in @cite_17 have dynamically adjusted the rank of the matrix to estimate the missing elements via matrix factorization. The matrix completion problem in @cite_17 is formulated as a non-linear successive over relaxation problem which is solved by using linear least square method.
@cite_15 @cite_17 @cite_56
2060204507 2119556711
The matrix completion problem is to recover a low-rank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclear-norm minimization which requires computing singular value decompositions—a task that is increasingly costly as matrix sizes and ranks increase. To improve the capacity of solving large-scale problems, we propose a low-rank factorization model and construct a nonlinear successive over-relaxation (SOR) algorithm that only requires solving a linear least squares problem per iteration. Extensive numerical experiments show that the algorithm can reliably solve a wide range of problems at a speed at least several times faster than many nuclear-norm minimization algorithms. In addition, convergence of this nonlinear SOR algorithm to a stationary point is analyzed. Matrices that can be factored into a product of two simpler matrices can serve as a useful and often natural model in the analysis of tabulated or high-dimensional data. Models based on matrix factorization (Factor Analysis, PCA) have been extensively used in statistical analysis and machine learning for over a century, with many new formulations and models suggested in recent years (Latent Semantic Indexing, Aspect Models, Probabilistic PCA, Exponential PCA, Non-Negative Matrix Factorization and others). In this thesis we address several issues related to learning with matrix factorizations: we study the asymptotic behavior and generalization ability of existing methods, suggest new optimization methods, and present a novel maximum-margin high-dimensional matrix factorization formulation. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)