基于不等式约束的稀疏程度未知条件下自适应滤波算法研究

Adaptive filter has been a strong tool in signal processing and control area. In many applications, the unknown system response is sparse, such as echo channel, satellite communication channel etc. Convergence performance of sparse filtering algorithms is improved by using sparsity. However, there are two problems in existing sparse algorithms. First, the performance of algorithm relies on the sparsity of the unknown system, which is often unknown in reality. Second, in these algorithms, L1 norm of the step size vector is a constant to ensure the stability, which restricts the algorithm performance. Aiming at these two problems, adaptive filtering algorithms based on inequality constraint for unknown sparse system is studied in this project. Through establishing a cost function unrelated with system sparsity, and by using inequality constraint, a theoretical optimal step size vector iteration method is obtained. Then reasonable assumptions and approximations are used to obtain an approximately optimal but practicable method. Finally, the relation between the parameters of the algorithm and the performance are derived and discussed, and parameter choices are guided according to the discussion to facilitate its application.

自适应滤波器是信号处理和自动控制应用领域强大的工具。在许多应用中，系统冲击响应呈稀疏性，如声学回声信道、卫星通信信道等，稀疏自适应滤波算法利用这一特性提高了算法的收敛性能。然而现有的稀疏算法大都存在以下两个问题：第一，算法实际性能对于待辨识系统冲击响应稀疏程度有一定的要求，而实际应用中系统稀疏程度差异较大且未知。第二，在这些稀疏自适应滤波算法中，为保证稳定性，一般采用迭代步长矢量L1范数恒定的约束，限制了算法的收敛速度。针对这两个问题，本项目拟开展待辨识系统冲击响应稀疏程度未知条件下自适应滤波器快速收敛方法研究。主要研究思想为，通过建立与系统稀疏性无关的代价函数，采用迭代步长矢量L1范数的不等式约束，从理论上获得最优步长矢量迭代方法；然后通过合理的近似和假设获得实际可用的近似最优步长矢量迭代方法；最后通过理论分析获得算法参数与滤波器性能之间的关系，为算法提供参数选择依据，促进其实际应用。

自适应滤波器在通信、雷达、声纳、导航、地震学和金融工程等领域都有着广泛的应用。在许多应用中，待辨识系统冲击响应呈稀疏性，如声学回声信道、卫星通信信道等，稀疏LMS算法利用这一特性提高了算法的收敛性能。本项目开展待辨识系统冲击响应稀疏程度未知条件下的自适应滤波器快速收敛方法研究。其根本思想为,通过建立与系统稀疏性无关的代价函数，采用迭代步长矢量L1范数的不等式约束，提高稀疏程度未知条件下自适应滤波器的收敛速度。项目主要开展了稀疏自适应滤波算法研究，提出多种稀疏自适应滤波算法，包括带个体活化因子的比例NLMS算法，Krylov子空间变换域变阶数LMS算法，Krylov子空间变换域凸联合的自适应LMS算法，分布式网络稀疏算法等，提高了稀疏自适应滤波算法的收敛速度。.项目同时还对非线性滤波和自适应网络滤波算法开展了研究，提出了多种非线性滤波算法，提高滤波精度，扩展了自适应滤波研究领域，丰富了自适应滤波器基础理论。.依托项目共发表或被接收论文二十余篇，授权专利两项，申请专利多项。申请并获得中国博士后科学基金特别资助一项。出版译著一部。