Research On Multiple Co-Channel Sources Localization Based On Sparse Representation

Source localization plays an important role in many fields such as defense and military applications.With the increasingly complex radiation environment,traditional single-source localization technology has been difficult to meet actual requirements,and the importance of co-channel multiple sources localization(MSL)technology has become more and more prominent.However,the MSL problem is highly non-convex and nonlinear,and thus is hard to solve directly.In recent years,sparse representation has provided a novel perspective for MSL.Based on the review of the latest research progress,this thesis abstracts the generalized MSL model from the specific MSL model,and conducts a systematic and in-depth study on the sparse representation based MSL technology under structural information mining,basis mismatch,"curse of dimensionality" and shadow fading channel.The main content of this thesis is as follows:1.A novel hierarchical greedy matching pursuit algorithm(HGMP)is proposed for structural information mining in MSL.The HGMP algorithm is composed of a global estimation layer and a sparse recovery layer,where the global estimation layer exploits the cluster structure of the residual projection to separate the signal subspace,and the sparse recovery layer use orthogonal matching pursuit algorithm(OMP)to achieve robust greedy localization in the signal subspace.Theoretical analysis shows that the proposed algorithm has linear computational complexity.Simulation results show that HGMP achieves better localization performance than the classic BP and OMP algorithm,while the computational complexity is much lower than BP.2.A parametric sparse Bayesian dictionary learning algorithm(PSBDL)is proposed to address the basis mismatch problem caused by grid mismatch and model parameter error.Firstly,we model the grid mismatch and the model parameter error problem from the perspective of parametric dictionary learn-ing.Then,the MSL problem is transformed into a joint optimization problem of parametric dictionary learning and sparse recovery,which is then solved un-der the sparse Bayesian learning framework.Finally,theoretical analysis of the computational complexity and convergence of the proposed PSBDL algo-rithm is conducted,and the effectiveness and superiority of the proposed PSBDL algorithm are verified by comparison with the classic algorithm in the simulations.Compared with traditional sparse representation based MSL algorithms,PSBDL completes the closed-loop optimization logic of dictionary learning and sparse recovery,and can effectively solve the MSL problem under basis mismatch.3.To cope with the challenges brought by the massive grid points to MSL algorithms in the large-scale high-dimensional localization scene,firstly,a sparse Bayesian learning algorithm based on fast evidence lower bound maximization(FEMSBL)is proposed for the large-scale sparse decoding problem.Theoretical analysis shows that the FEMSBL algorithm can reduce the computational complexity of the traditional sparse Bayesian learning algorithm from the second power of the grid point number to the first power.Numerical results show that the FEMSBL algorithm can efficiently solve large-scale sparse decoding problems,and alleviate the challenges brought by the "curse of dimensionality" problem.Secondly,by combining the FEMSBL algorithm with the PSBDL algorithm,a fast parametric sparse Bayesian dictionary learning algorithm(FPSBDL)that can effectively solve the large-scale high-dimensional MSL problem is proposed.Simulation results show that the FPSBDL algorithm has a significant improvement in computational efficiency and system identification ability compared with the original PSBDL algorithm.4.A novel two-stage maximum likelihood algorithm(TSML)is proposed to handle the MSL problem under shadow fading channels.In the capture stage of the TSML algorithm,by performing Taylor series expansion on the observation model,we convert the initial source parameter capture problem into a sparse recovery problem,and perform clustering and weighting on the recovery coefficient to quickly capture the initial value of the source parameter.In the tracking stage of the TSML algorithm,we use the Fenton-Wilkinson method to approximate the distribution of the observed variables,and propose a maximum likelihood estimator solved with the sequential quadratic programming(SQP)method.Theoretical analysis of the computational complexity and global convergence property of the proposed TSML algorithm is conducted,and simula-tion results verify the improved performance of the TSML algorithm compared to the existing MMSE algorithm.