Research Of Algorithms And Application Of Distributed Compressive Sensing Based On Joint Sparseness

With the rapid development of information technology and computer network technology,compressed sensing theory has attracted more and more attention.Unlike the traditional Shannon-Nyquist sampling theorem,compressed sensing reduces the sampling rate of signals by finding sparse solutions of underdetermined linear systems.On the basis of compressed sensing theory,distributed compressed sensing theory makes full use of the correlation between signals and internal signals to reconstruct multiple signals in order to further reduce the sampling rate of signals.Distributed compressed sensing compresses multiple signals independently at the coding end and combines multiple signals at the decoding end for recovery.In this paper,a Joint-Sparsity Adaptive Matching Pursuit(Joint-SAMP)algorithm is proposed based on distributed compressed sensing theory.Based on this algorithm,a DCS-Data Acquisition Method for Smart Grid and a DCS-Urban Traffic Volume Estimation Method are designed.The detailed research contents of this paper are summarized as follows:(1)In order to solve the problem of unknown signal sparsity when reconstructing signals in practical applications,a joint-SAMP algorithm for joint sparsity adaptive matching pursuit in distributed scenarios is proposed.This algorithm combines the sparse adaptive matching pursuit algorithm(SAMP)of compressed sensing theory,and uses distributed compressed sensing theory to reduce the requirement of signal measurement by means of both the internal correlation structure and the correlation structure between signals.In the iteration cycle,the new residual is compared with the old residual as the stopping condition of the algorithm.The stopping condition of the algorithm is independent of the sparseness of the signal and does not need the prior information of the sparseness of the signal.It is suitable for distributed scenarios that satisfy the hybrid support set model.The algorithm reduces the data acquisition rate by reconstructing multiple signals jointly,and makes full use of the correlation between signals.The experimental results show that the proposed algorithm can reduce the data acquisition overhead without using the sparseness of the signal as a priori information and ensuring the accuracy of data recovery.(2)In order to solve the problem that the overhead of data storage and transmission in smart grid brings enormous pressure to the system,a data acquisitionmethod for smart grid(DCS-ASMSG)based on distributed compressed sensing theory is designed.This method reduces the data transmission and storage overhead by utilizing the correlation between the data in the smart grid intermediate station and the data between the intermediate station and the smart grid intermediate station.And a sparse matrix for power data acquisition based on K-SVD(K-Singular Value Decomposition)algorithm is designed.This method combines the joint sparse adaptive matching pursuit algorithm proposed in this paper to restore the signal.The sparsity of power data is verified by simulation experiments.The experiment shows that K-SVD algorithm can well sparsely represent power data.The designed DCS-smart grid data acquisition method can guarantee the accuracy of data reconstruction and reduce the data transmission overhead.The amount of data transmitted by the method is only 25.69% of the original data.(3)To solve the high cost of infrastructure deployment and maintenance in traditional road condition estimation,a DCS-Urban Traffic Volume Estimation Method(DCS-UTVEM)based on distributed compressed sensing theory is designed.This method utilizes the correlation of speed at the same time between different roads in urban road traffic estimation and the correlation of speed of each road in a period of time to estimate the traffic condition of urban roads based on distributed compressed sensing theory.In this paper,an estimation model of traffic condition estimation method is designed.In this model,the detected vehicle sends its position and speed updates(or detection data reports)to the monitoring center periodically through data services such as GSM/GPRS.According to the received reports,the monitoring center uses distributed compressed sensing technology to estimate the traffic condition of road network.Then,the multiple linear regression(MLR)model is used to capture the relationship between road conditions and sparsely express the speed signal.This method combines the joint sparse adaptive matching pursuit algorithm proposed in this paper to restore the estimated signal.Experiments verify the validity of the traffic condition estimation model designed in this paper,and prove that this method can achieve accurate and scalable traffic flow estimation only by using sparse probes.A small number of detected vehicles can bring good estimation performance and lower system operation cost.