降秩自适应滤波算法研究

对降秩自适应滤波算法进行了系统的总结和分析，推导了其相互关系。分析表明，GSC（Generalized Sidelobe Canceller）框架降秩变换自适应滤波是各种降秩自适应滤波算法的统一模型。在此基础上导出了线性约束正交投影算法。降秩多级维纳滤波器在相关意义上进行截断降秩，其降秩性能优于基于特征子空间截断的降秩方法。酉多级维纳滤波器与共轭梯度法等效，均是基于Krylov子空间截断降秩的方法，降秩性能更优。最后通过计算机仿真试验比较了各种降秩处理算法的性能。

Research on Algorithms for Reduced Rank Adaptive Filtering

Various kinds of reduced rank adaptive filtering algorithms are reviewed and analyzed systematically. The relationship between them is derived, with the result that the reduced-rank transformation adaptive filtering in the GSC structure is the uniform model for reduced rank adaptive filtering algorithms. The linearly constrained orthogonal projection algorithm is proposed as a new reduced rank processing algorithm in the linear constraints conditions. Reduced-rank Multistage Wiener Filter (RR-MWF) has better rank reduction performance than the methods based on eigen-subspace truncation. The unitary MWF (UMWF) is found to be equivalent to the conjugate gradient algorithm, both of which are based the truncation of the Krylov subspace. The rank reduction performance of the UMWF is better than one of the non-unitary MWF. The performance comparison of the reduced rank processing algorithms is carried out by computer simulations.