基于稀疏优化的空时分布密集多径信号估计方法研究

The problem of estimating the dense multipath signals is an important and hard issue to realize the target localization encountered in many fields of physics and engineering. In order to meet the demand of high resolution for dense signals appeared in many applications, this research aims to explore a sparse optimization approach to solve the estimation problem of dense signals in the spatio-temporal correlation models. This approach takes the advantage of the sparse representation model for solving the inverse problem, design the optimization conditions that is close to the characters of dense signals, and then propose a novel algorithm to estimation the dense multipath signals based on sparse optimization theory. This algorithm can reduce the effect of high correlations among dense signals, improve the computation efficiency and reduce the computation complexity by applying the methods such as stepwise regression and probability analysis, and it is benefit for applying to the real engineering. The availability and advantage of this algorithm for resolving the dense multipath signals are totally presented according to some Monte Carlo simulations with different cases. Besides, the relationship among the performance of this algorithm, the sparsity of the solution, the correlations of signals and the SNR parameter is analyzed, and thus the availability range of this algorithm is presented. The theory proof is given to illustrate the logicality of the proposed algorithm, which provides a theoretical basis for solving other similar inverse problems and working on its improvements. At last, the proposed approach is applied to a real project, that is, the low-angle target localization by radar, in order to ensure the availability of the proposed method working in the engineering.

密集多径信号估计问题是众多工程领域中实现目标定位的难点和重点。为了满足诸多领域对密集信号估计的高分辨率需求，本研究旨在探索一种基于稀疏优化的方法求解具有空时相关性的密集信号估计问题。该方法将利用稀疏表示模型对反问题的求解优势，设定符合密集信号特点的优化条件，提出一种新颖的基于稀疏优化的密集多径信号估计算法，有效削弱密集信号之间高相关性，并采用逐步回归、概率分析等手段加快计算效率，降低计算复杂度，利于它应用在实际中。通过设定多种情况的Monte Carlo仿真实验全面验证该算法对密集多径信号估计的先进性和有效性。研究中将给出算法的效果与解的稀疏度、信号之间的相关系数及信噪比等参数的关系，提出算法合理的适用范围，并从理论的角度论证算法的可靠性，为该方法用于解决类似的反问题奠定理论基础，并为其推广和改进工作提供科学判据。最后，该方法将应用于相控阵雷达信号对近地目标定位的实际数据中，验证其实用性。

本项目围绕着影响目标定位精度的空时分布密集信号估计问题展开了一系列的深入研究，为通信、雷达、声呐、地球物理、生物医学等领域的工程应用提供基础理论依据和有效的解决方案。研究中主要针对单快拍密集波达角度(DOA)估计问题、密集信号频率估计问题、密集信号的波达角度(DOA)和频率联合估计等问题，提出了多种基于稀疏优化理论的算法方案和实验分析，可以解决密集信号之间较高的空时相关性导致的估计精度大幅下降问题，克服较少的快拍数导致的统计信息不准确问题，提高多维多径信号估计精度和计算效率。.主要研究内容和重要结果包括：（1）针对单快拍密集DOA估计模型，提出了一种基于混沌序列和非常稀疏投影的测量矩阵，设计了一种两步稀疏优化求解方法，可以有效提高求解精度并降低计算复杂度。（2）针对传统方法无法解决密集分布频率的细微结构问题，分别采用稀疏优化和进化优化两种技术方案实现了有效的密集频率精确估计方法，分析了基于稀疏表示的基跟踪算法和正交匹配追踪算法对密集频率估计的求解优势，提出了一种新的基于主观概率的妥协排序方法，改善了多目标遗传规划算法的优化性能。（3）针对密集信号DOA和频率联合估计问题，通过定义方向波数、参考频率等参数来降低维度，利用稀疏优化算法对方向波数、预估计角度等参数进行估计，设计了三种基于稀疏优化的DOA-频率联合估计的求解方案，分析了不同求解方案的适用范围，通过和现有算法Monte Carlo实验对比，验证了这些方法在适用的实验背景下可以在少快拍数、低信噪比的情况下取得更优的性能。上述研究方法可以提高密集信号的超分辨精度和抗干扰能力，增强复杂密集信号环境下的信源定位精度。.项目研究过程中，发表论文12篇，其中SCI论文5篇，EI论文6篇，参加4次国际学术会议；申请发明专利3项，授权发明专利3项，培养研究生4名。