Low-rank Matrix Recovery Algorithm And Its Application In Rechargeable Wireless Sensor Networks

Low Rank Matrix Recovery(LRMR),a key technique in large-scale data processing,has been widely used in the field of data mining,machine vision,image processing,and so on.The environment of Rechargeable Wireless Sensor Networks(RWSN)is complex,it is necessary to decrease processing of nodes location and trajectory information,and improve capability of noise immunity.However,the classic LRMR algorithms guarantee accuracy effectively,only if matrix elements are sufficient or noise matrix is sparse,which lead to poor effect in the process of nodes localization and trajectory fitting.So,an improved LRMR algorithm is proposed that can be applied to nodes localization and trajectory fitting based on the classic models of LRMR.The main research contents and innovations are as follows:(1)The LRMR algorithms are analyzed and improved.The LRMR model includes Matrix Completion(MC)and Robust Principal Component Analysis(RPCA),which can be solved by Alternating Direction Method of Multipliers(ADMM)algorithm respectively.Then the MC using ADMM(MC-ADMM)and RPCA using ADMM(RPCA-ADMM)algorithms are obtained.MC-ADMM is sensitive to noise,as well as RPCA-ADMM requires a high number of known matrix elements,so an improved LRMR algorithm is proposed.Based on the combination of RPCA and MC,in order to highlight the low-rank and sparsity of the matrix better,the norm of low-rank matrix and sparse matrix are weighted separately,and to enhance the Gaussian noise immunity performance,the F norm of Gaussian noise matrix is taken as a new regular term.Then the new model of Regularized Weighted Incomplete RPCA(RWIRPCA)is established,solved by ADMM algorithm,which named as RWIRPCA-ADMM algorithm.The simulation results show that the proposed RWIRPCA-ADMM algorithm can reconstruct the low-rank matrix in the presence of both low sampling rate and mixed noise accurately and efficiently.(2)Application on RWSN static nodes localization based on RWIRPCA is studied.In order to solve the two major problems of insufficient distance data and noise pollution in common localization algorithms,RWSN static nodes localization method based on RWIRPCA is proposed.The low-rank character of the distance matrix between nodes has been proved,and the reconstruction of noisy and partial distance matrix is modeled as a RWIRPCA problem.Then,the classical multi-dimensional scaling(MDS)technique is used to convert the relative distance into nodes coordinates.The simulation results show that with partial known distance between nodes,RWIRPCA can realize accurate positioning under the conditions of noise-free,sparse noise,Gaussian noise even mixed noise.(3)Application on RWSN mobile nodes trajectory fitting based on RWIRPCA is studied.In order to reduce energy consumption caused by transmission of trajectory information of mobile nodes as well as enhance the system's ability to deal with noise,RWSN mobile nodes trajectory fitting method based on RWIRPCA is proposed.RWIRPCA-ADMM is used to recover the sampling matrix with noise by taking advantage of the low-rank feature of nodes position moving information matrix,and then the nodes original trajectory is fitted.The simulation results show that RWIRPCA-ADMM can not only fit trajectory accurately at low collecting rate,but also remain stable results under the condition of complex noise interference,reducing the amount of system trajectory information sending while improving the fitting accuracy.