自适应滤波的几种算法的仿真.pdf

自适应滤波器中 几种算法的仿真研究 电信科学技术研究院 JJC 摘 要 自适应过程是指按照某种准则，通过自身与外界的接触，改变自身的性质或性能，以达 到一种滤波效果的最优化，如自动增益控制，自适应均衡等。自适应滤波过程在当代雷达数 据处理、高速数据接入、数据实时处理、最优线性滤波等领域具有举足轻重的作用。 自适应滤波过程常用两种线性自适应算法，一种是随机梯度算法，如LMS, NLMS, 仿 射投影滤波器，DCT-LMS ，GAL (gradient-adaptive lattice algorithm)，块LMS ，子带LMS 等。 通过迭代和梯度估值逼近维纳滤波，其性能准则是集平均的均方误差。另一种是最小二乘算 法，如标准RLS ，平方根RLS ，快速RLS 等。基于最小二乘的算法通过使误差平方的加权 和最小求最优权值，其性能准则是时间平均的均方误差。RLS 算法可以被看作是Kalman 滤 波的一种特殊形式。本文是关于两种算法的仿真研究，得出各自的和关联的性能特点。 关键词：自适应 随机梯度算法 最小二乘算法 Abstract Self-adaption is a kind of filtering process which could change its own properties or performances through contacting outer environment. Its purpose is to make the filtering results the best. For example, Automatic Gain Control (AGC) and Self-adaptive Equalization belong to the kind of process. Self-adaption is pretty important to processing radar data, xDSL, real-time processing, optimal liner filtering and so on. Self-adaption could be realized with the method of two liner forms. One of them is stochastic gradient method, such as LMS, NLMS, DCT-LMS, GAL, block LMS, sub-band LMS, etc. Its thought is approaching Wiener Filtering by iteration way and gradient evaluating way. The performance principle is the minimum mean square (MMS) of collection average. The other algorithm is least square method, like basic RLS, square root RLS, fast speed RLS and so on. Its thought is to find the optimal weigh by making the total of error square which is relative to the weighs minimum. The performance principle is the minimum mean square of time sequence average. RLS could be seen as one particular form of Kalman filtering. The