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摘 要

最小二乘(RLS)法是一种典型的有效的数据处理方法。由著名学者高斯在1795年提出，他认为根据所获得的观测数据来推断未知参数时，未知参数最可能的值是这样一个数据，即它使各项实际观测值和计算值之间的差的平方乘以度量其精度的数值以后的和为最小。这就是著名的最小二乘法。自适应滤波算法根据的最佳准则为最小均方误差准则。自适应算法的目标在于，使滤波器输出与需要信号的误差的平方的统计平均值最小。这个准则根据输入数据的长期统计特性寻求最佳滤波。最小二乘法对不同的数据组导出不同的“最佳”滤波器。因而常说最小二乘法导出的最佳滤波器是“精确”的。递推最小二乘法(RLS)是最小二乘法的一类快速算法。

本文基于matlab进行仿真，研究不同输入和信噪比滤波器的性能。通过对比实验，分析收敛性和滤波效果，确定了滤波器正则化系数的选取，信噪比高正则化系数选取小正常数，反之取大正常数。对不同类型滤波器输入信号独立实验，周期型号和非周期信号的滤波器效果都较好，但周期信号的滤波效果更好。但从程序的运行时间上看，其复杂度高，计算量比较大。

关键词：自适应滤波器，最小二乘法，matlab仿真

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Abstract

Least squares (RLS) method is a kind of typical effective data processing method. Gauss proposed in 1795 by famous scholars, he thinks, according to the observed data to infer unknown parameter is obtained, the unknown parameters is the most possible values that a data, which make the actual observed value multiplied by the square measure of the difference between calculated value and the accuracy of numerical and later to a minimum. This is the famous least-square method.Adaptive filtering algorithm based on optimum criterion for the minimum mean square error criterion. Adaptive algorithm's goal is to make the filter output and signal statistical average of the squared error is minimal. The criteria according to the long-term statistical characteristics of the input data for optimal filter. Least squares method for different data sets derived different "best" filter. Thus derived the optimum filter often say least-square method is "accurate". Recursive least squares (RLS) is a fast algorithm of the least-square method.

this paper studies the performance of the filter input and SNR and simulation based on matlab. Convergence analysis and filtering effect by experiment, confirmed the filter selection of regularization coefficient, high SNR regularization coefficient selected normal number, instead take dazheng constant. For different types of filter input signal independent exper