Study On Direct Positioning Method For Distributed Sources Using GAA Model

The distributed source localization is an important problem in many fields,such as communications.In practical scenarios,a source is often surrounded by many scatters,which will scatter and spread the signal in all directions in the space.The conventional point-source-model-based localization methods fail to deal with such scenarios.More appropriate localization models and methods should be set up for distributed source localization problems.Regarding the localization methods for a distributed source,Most of the existing methods are two-step ones using some special measurements that are estimated from raw received data.These two-step methods ignore the constraint that all the measurements should correspond to the same source,resulting in bad localization performance especially under low signal-to-noise ratios(SNRs).This study focuses on direct positioning estimation of a distributed source using raw received data,which can outperform the two-step localization methods.The main work includes:(1)Distributed source modelsIn view of the limitations of applying point source models for distributed source localization,the angle spread parameter is introduced to establish a distributed source model;the concepts of coherent and incoherent distributed sources are then introduced,as well as the spatial frequency model and two point source approximation model;For a incoherently distributed(ID)source that often occurs in real communication scenarios,we consider the Gaussian angle of arrival(GAA)model,which assumes that the distribution of scatters around the target source are Gaussian.We study and derive the spatial and temporal models.(2)Review on direct positioning methods for point sourcesThe fundamental theories of direct positioning estimation for point source localization are reviewed.Different from the traditional two-step positioning estimation schemes that first estimate some measurements from raw data and then estimate the source location from the measurements,the direct positioning method estimate a source directly from raw data.Transforming raw data into frequency-domain and using the maximum likelihood(ML)criterion to obtain the source location.For multi-source localization cases,the minimum variance distortionless response(MVDR)method is used to filter sources and improve the estimation resolution.The simulation results show that the direct positioning methods can get low positioning errors in low SNRs.MVDR method has good resolution.(3)Study on direct positioning methods for distributed sourceWe first generalize direct positioning methods to a distributed-source localization problem,using the GAA model to represent the received raw data and estimating the source location and scattering radius through the ML criterion.Then several sub-optimal estimators are studied for lower computational complexity at the cost of the slight localization performance degradation.We have derived the gradient-descent formulas to optimize the related cost functions,and estimate the source location iteratively.The simulation results show that the ML method has the optimal accuracy among all methods in tests and the least squares(LS)method can obtain good tradeoff between high positioning accuracy and low computation.