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1、系统辨识上机实验报告广义递推最小二乘辨识一、实验目的1通过实验掌握广义最小二乘辨识算法；2运用MATLAB编程，掌握算法实现方法。二、实验原理广义最小二乘法的根本思想是基于对数据先进行一次滤波预处理，然后利用普通最小二乘法对滤波后的数据进行辨识。如果滤波模型选择得适宜，对数据进行了较好的白色化处理，那么直接利用普通最小二乘法就能获得无偏一致估计。广义最小二乘法所用的滤波模型实际上就是一种动态模型，在整个迭代过程中不断靠偏差信息来调整这个滤波模型，使它逐渐逼近于一个较好的滤波模型，以便对数据进行较好的白色化处理，使模型参数估计称为无偏一致估计。理论上说，广义最小二乘法所用的动态模型经过几次迭代调
2、整后，便可对数据进行较好的白化处理，但是，当过程的输出噪信比比拟大或模型参数比拟多时,这种数据白色化处理的可靠性就会下降。此时，准那么函数可能出现多个局部收敛点，因而辨识结果可能使准那么函数收敛于局部极小点上而不是全局极小点上。这样，最终的辨识结果往往也会是有偏的。其收敛速度比拟慢，需要经过屡次迭代计算，才能得到较准确的参数估计值。一般情况下，经过屡次迭代后，估计值便会收敛到稳态值。但在某些情况下（如噪声比拟低时）存在局部极小值，估计值不一定收敛到准那么函数的全局极小值上。为了防止参数估计值收敛到局部极小值，最好选定初值接近最优解，一般可以用最小二乘法的批处理估计值作为初值。如果系统是时变的，
3、或为了克服数据饱和现象，可以在两次RLS算法中分别引进遗忘因子。三、实验内容数据获取实验数据按照表10-1,为二阶线性离散系统的输入输出数据数据处理为了提高辨识精度，实验者必须对原始数据进行剔除坏数据、零均值化、工频滤波等处理。实验进行了白化滤波处理。辨识算法利用处理过的数据（取适当的数据长度），选择某种辨识方法（如RLS递推最小二乘法、RELSRlV或RML等参数估计算法及F-检验或AlC定阶法），估计出模型参数和阶次，同时分析辨识结果。本实验采用广义递推最小二乘法进行系统辨识。三、广义递推最小二乘法（RLS）原理广义最小二乘法是用迭代的松弛算法对最小二乘估计的一种改良，它的根本思想是引入一
4、个白化滤波器，把相关噪声转换为白噪声，基于对观测数据先进行一次滤波处理然后利用普通最小二乘法对滤波后的数据进行辨识。广义最小二乘法的计算步骤如下：1给定初始条件：包括给定的输入输出数据或者产生的数据序列，初始状态矩阵PO,被辨识参数的初始值（取一个充分小的实向量），滤波器参数与矩阵初值。2利用式Z（Q=C（z-z（Q=C（z）（Q计算滤波后的输入输出序列。3对于二阶离散系统，利用式号优）=-2/（4-1）,-2/（2-2）,勺伏一1）,勺（2-2）7构造（女）。4利用三个式子递推计算辨识矩阵*）5利用式ee）=z（幻-力（幻仇幻计算贸&）,并根据小伏）=-也-1）,-6（&-2）7构造4（幻。
5、6利用三个式子递推计算。（幻。7返回第二步进行迭代计算，直至获得满意的辨识结果。四、实验步骤输入输出数据：u=1.147,0.201,-0.787,-1.584-1.052,0.866,1.152,1.573,0.626,0.433.- 0.958,0.810,-0.044,0.947,-1.474,-0.719,-0.086,1.099,1.450,1.151.0.485,1,633,0.043,1.326,1.706,-0.340,0.890,0.433,-1.177,-0.390.- 0.982,1.435,-0.119,-0.769,-0.899,0.882,-1.008,-0.844
6、,0.628,-0.679.1.541,1.375,-0.984,-0.582,1.609,0.090,-0.813,-0.428,-0.848,-0.410.0.048,-1.099,-1.108,0.259,-1.627,-0.528,0.203,1.204,1.691,-1.235.- 1.228,-1.267,0.309,0.043,0.043,1.461,1.585,0.552,-0.601,-0.319.0.7440.829,-1.626,-0.127,-1.578,-0.822,1.469,-0.379,-0.212,0.178.0.493-0.056,-0.1294,1.228
7、,-1.606,-0.382,-0.229,0.313,-0.161,-0.810.- 0.2770.983,-0.288,0.846,1.325,0.723,0.713,0.6430.463,0.786.1.161,0.850,-1.349,-0.596,1.512,0.795,-0.713,0.453,-1.604,0.889.-0.938,0.056,0.829,-0.981,-1.232,1.327,-0.681,0.114,-1.135,1.284.-1.2010.758,0.590,-1.007,0.390,0.836,-1.52,-1.053,-0.083,0.619.0.840
8、-1.258,-0.354,0.629,-0.242,1.680,-1.236,-0.803,0.537,-1.100.1.417,-1.024,0.671,0.688,-0.123,-0.952,0.232,-0.793,-1.138,1.154.0.206,1.196,1.013,1.518,-0.553,-0.987,0.167,-1.445,0.630,1.255.0.311,-1.726,0.975,1.718,1.360,1.667,1.111,1.018,0.078,-1.665.-0.760,1.184,-0.614,0.994,-0.089,0,947,1.706,-0.39
9、5,1.222,-1.351.0.231,1,425,0.114,-0.689,-0.704,1.070,0.262,1.610,1.489,-1.602.0.020,-0.601,-0.020,-0.601,-0.235,1.245,1.226,-0.204,0.926,-1.297;figure(l);stem(u)gridontitle(图1输入信号)y=1.3813.7942.481-0.280-2.742-1.5542.1292.6913.4272.199.1.679-1.2491.3710.6373.131-0.8190.2351.2622.8493.374.2.3460.6643
10、.0150.5612.2713.6500.6252.3050.3641.857.- 0.912-1.5471.9400.262-0.379-0.1763.7200.058-0.7521.983.- 0.9233.3614.240-0.074-0.4813.7802.1370.0860.638-0.971.- 0.9290.679-0.664-0.4331.570-2.785-1.1530.8193.4844.091.- 2.375-2.561-2.7782.9111.3620.7353.1183.7702.381-0.812.- 1.6350.5891.550-3.410-1.249-3.69
11、2-2.3582.552-0.2280.554.2.1782.4710.743-0.0042.504-3.204-1.800-1.2840.1590.426.0.0590.3952.371-0.1572.2483.2972.3292.7802.3751.873.2.4113.9282.846-2.215-1.1043.4602.8830.245-0.231-2.963.2.072-0.845-0.0741.0372.468-3.6792.149-0.0811.639-1.291.2.548-1.6812.3072.227-1.5580.0082.055-1.102-1.4270.350.2.7
12、362.965-2.346-1.5100.809-0.5922.706-1.9412.2752.802.- 1.3372.091-2.5850.0131.2170.691-0.4912.1140.333-0.482.3.3882.0823.7974.0795.0361.250-1.019-0.160-3.2011.161.3.9261.789-2.7032.1255.0544.6785.236-0.2412.1520.356.- 3.5192.2131.527-1.2062.1510.2641.5952.864-0.5391.982.- 3.104-0.2642.4330.009-1.360-
13、0.5213.3191.4453.1053.783.- 1.973-0.138-0.452-0.586-4.045-1.7432.5773.8490.3671.324;初始值设置，包括被辨识参数的初始值、误差序列以及滤波器参数初值；迭代循环，辨识参数更新，根据误差调整滤波器参数，迭代计算被辨识参数，直至参数符合条件或迭代次数到。计算数据与图形显示，包括辨识参数辨识过程以及误差的收敛情况。五、运行结果显示1输入数据：2被辨识参数：辨识结果：ans=-0.42510.01161.8869-0.54643被辨识参数误差的收敛情况：六、实验源程序%递推的广义最小二乘法进行参数估计clear;close
14、all;display。广义递推最小二乘辨识);u=1.147,0.201,-0.787,-1.584-1.052,0.866,1.152,1.573,0.626,0.433.- 0.958,0.810,-0.044,0.947,-1.474,-0.719,-0.086,1.099,1.450,1.151.0.485,1.633,0.043,1.326,1.706,-0.340,0.890,0.433,-1.177,-0.390.- 0.982,1.435,-0.119,-0.769,-0.899,0.882,1.008,-0.844,0.628,-0.679.1.541,1.375,-0.9
15、84,-0.582,1.609,0.090,-0.813,-0.428,-0.848,-0.410.0.048,-1.099,-1.108,0.259,1.627,-0.528,0.203,1.204,1.691,-1.235.- 1.228,-1.267,0.309,0.043,0.043,1.461,1.585,0.552,-0.601,-0.319.0.7440.829,-1.626,-0.127,-1.578,0.822,1.469,0.379,0.212,0.1780.493-0.056,-0.1294,1.228,-1.606,-0.382,-0.229,0.313,-0.161,-0.810.-0.2770.983,-0.288,0.846,1.325,0.723,0.713,0.6430.463,0.786.1.161,0.850,-1.349,-0.596,1.512,0.795,-0.713,0.453,-1.604,0.889.-0.938,0.056,0.829,-0.981,-1.232,1.327
