1、例1、考慮仿真對(duì)象z(k)-1.5z(k-1)0.7z(k-2)=u(k-1)0.5u(k-2)v(k)其中，v(k)是服從正態(tài)分布的白噪聲N(0,1)。輸入信號(hào)采用4階M序列，幅度為1。選擇如下形式的辨識(shí)模型z(k)a1z(k-1)a2z(k_2)=hu(k-1)b2u(k-2)v(k)設(shè)輸入信號(hào)的取值是從k=1到k=16的M序列，則待辨識(shí)參數(shù)?ls為？LS=(6T9)飛Tz為？LS=(6T9)飛Tz其中，被辨識(shí)參數(shù)心、觀測(cè)矩陣中的表達(dá)式為：a11a2b1-b21-z(3)z(4)7(16程序框圖如圖l-z(2)-z(1)u-z(3)-z(2)uz(15)-z(14)1所示。Matlab仿真

2、程序如下:圖1最小二乘一次完成算法程序框圖(3u(2)(貨)(14)LS.m%二階系統(tǒng)的最小二乘一次完成算法辨識(shí)程序，文件名:u=-1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,1,1;%系統(tǒng)辨識(shí)的輸入信號(hào)為一個(gè)周期的M序列z=zeros(1,16);%定義輸出觀測(cè)值的長(zhǎng)度f(wàn)ork=3:16z(k)=1.5*z(k-1)-0.7*z(k-2)+u(k-1)+0.5*u(k-2);%用理想輸出值作為觀測(cè)值endsubplot(3,1,1)%畫(huà)三行一列圖形窗口中的第一個(gè)圖形stem(u)%畫(huà)輸入信號(hào)u的徑線(xiàn)圖形subplot(3,1,2)%畫(huà)三行一列圖形窗口中的第二個(gè)圖形i=1:

3、1:16;%橫坐標(biāo)范圍是1到16,步長(zhǎng)為1plot(i,z)%圖形的橫坐標(biāo)是采樣時(shí)刻i,縱坐標(biāo)是輸出觀測(cè)值z(mì),圖形格式為連續(xù)曲線(xiàn)subplot(3,1,3)%畫(huà)三行一列圖形窗口中的第三個(gè)圖形stem(z),gridon%畫(huà)出輸出觀測(cè)值z(mì)的徑線(xiàn)圖形，并顯示坐標(biāo)網(wǎng)格u,z%顯示輸入信號(hào)和輸出觀測(cè)信號(hào)%L=14%數(shù)據(jù)長(zhǎng)度HL=-z(2)-z(1)u(2)u(1);-z(3)-z(2)u(3)u(2);-z(4)-z(3)u(4)u(3);-z(5)-z(4)u(5)u(4);-z(6)-z(5)u(6)u(5);-z(7)-z(6)u(7)u(6);-z(8)-z(7)u(8)u(7);-z(9)-

4、z(8)u(9)u(8);-z(10)-z(9)u(10)u(9);-z(11)-z(10)u(11)u(10);-z(12)-z(11)u(12)u(11);-z(13)-z(12)u(13)u(12);-z(14)-z(13)u(14)u(13);-z(15)-z(14)u(15)u(14)%給樣本矩陣中賦值ZL=z(3);z(4);z(5);z(6);z(7);z(8);z(9);z(10);z(11);z(12);z(13);z(14);z(15);z(16)%給樣本矩陣zl賦值%CalculatingParametersc1=HL*HL;c2=inv(c1);c3=HL*ZL;c=c

5、2*c3%計(jì)算并顯示？LS%DisplayParametersa1=c(1),a2=c(2),b1=c(3),b2=c(4)%A限中分離出并顯示2、a2、bvb2%End程序運(yùn)行結(jié)果:u=-1,1,-1,1,1,1,z=0,0,0.5000,0.2500,1,-1,-1,-1,1,-1,-1,1,10.5250,2.1125,4.3012,6.4731,6.1988,3.2670,-0.9386,-3.1949,-4.6352,6.2165,-5.5800,6.2165,-5.5800,-2.5185HL=001.0000-1.0000-0.50000-1.00001.0000-0.2500-

6、0.50001.0000-1.0000-0.5250-0.25001.00001.0000-2.1125-0.52501.00001.0000-4.3012-2.11251.00001.0000-6.4731-4.3012-1.00001.0000-6.1988-6.4731-1.0000-1.0000-3.2670-6.1988-1.0000-1.00000.9386-3.26701.0000-1.00003.19490.9386-1.00001.00004.63523.1949-1.0000-1.00006.21654.63521.0000-1.00005.58006.21651.0000

7、1.00004.3012,6.4731,6.1988,3.2670,-0.9386,-3.1949,-4.6352,ZL=0.5000,0.2500,0.5250,2.1125,-6.2165,-5.5800,-2.5185Tc=-1.5000,0.7000,1.0000,0.5000Ta1=-1.5000a2=0.7000b1=1.0000b2=0.500010-I口IJISTEMPLOTOFINPUTMSERIES-10乙5101510|BBB0WAVEOFMEASUREMENTSOFOUTPUT-100246810121416100II,IISTEMPLOTO:MEASUREMEN-So

8、fOUTPUT-100246810121416圖2最小二乘一次完成算法仿真實(shí)例中輸入信號(hào)和輸出觀測(cè)值從仿真結(jié)果表1可以看出，由于所用的輸出觀測(cè)值沒(méi)有任何噪聲成分，所以辨識(shí)結(jié)果也無(wú)任何誤差。表1最小二乘一次完成算法的辨識(shí)結(jié)果參數(shù)aa2b1b2真值-1.50.71.00.5估計(jì)值-1.50.71.00.5例2根據(jù)熱力學(xué)原理，對(duì)給定質(zhì)量的氣體，體積V與壓力P之間的關(guān)系為PVa=P，其中口和P為待定參數(shù)。經(jīng)實(shí)驗(yàn)獲得如下一批數(shù)據(jù)，V的單位為立方英寸，P的單位為帕每平方英寸。V54.361.872.488.7118.6194.0P61.249.537.628.419.210.1試用最小二乘一次完成算法確定

9、參數(shù)”和P。首先要寫(xiě)出系統(tǒng)的最小二乘表達(dá)式。為此，把體積V與壓力P之間的關(guān)系曠”=2改為對(duì)數(shù)關(guān)系，即，logP=ToW+logP。此式與式z(k)=h4)8+e(k),對(duì)比可得:z(k)=logP,hk)=-logV1,0=alogPT0例2的Matlab6.0程序如下。%實(shí)際壓力系統(tǒng)的最小二乘辨識(shí)程序，文件名：LS2.mclear%工作間清零V=54.3,61.8,72.4,88.7,118.6,194.0,P=61.2,49.5,37.6,28.4,19.2,10.1%賦初值并顯示V、P%logP=-alpha*logV+logbeita=-logV,1alpha,10g(beita)=H

10、L*sita%注釋P、V之間的關(guān)系fori=1:6;Z(i)=log(P(i);%循環(huán)變量的取值為從1到6,系統(tǒng)的采樣輸出賦值End%循環(huán)結(jié)束ZL=Z%Zl賦值HL=-log(V(1),1;-log(V(2),1;-log(V(3),1;-log(V(4),1;-log(V(5),1;-log(V(6),1%Hl賦值%CalculatingParametersc1=HL*HL;c2=inv(c1);c3=HL*ZL;c4=c2*c3%計(jì)算被辨識(shí)參數(shù)的值%SeparationofParametersalpha=c4(1)%U為c4的第一個(gè)元素beita=exp(c4(2)%P為以自然數(shù)為底的c4

11、的第二個(gè)元素的指數(shù)程序運(yùn)行結(jié)果：V=54.3000,61.8000,72.4000,88.7000,118.6000,194.0000P=61.2000,49.5000,37.6000,28.4000,19.2000,10.1000ZL=4.1141,3.9020,3.6270,3.3464,2.9549,2.3125HL=-3.99451.00001-4.12391.0000-4.28221.0000-4.48531.0000-4.77581.0000,-5.26791.0000Jc4=1.4042、9.6786alpha=1.4042beita=1.5972e+004仿真結(jié)果表明，用最小二

12、乘一次完成算法可以迅速辨識(shí)出系統(tǒng)參數(shù),即=1.4042,=1.5972e+004例3考慮圖3所示的仿真對(duì)象，圖中，v(k)是服從N(0,1)分布的不相關(guān)隨機(jī)噪聲。且11、G(z-)-B(z),N(z-),D(z),A(z-C(z)111_2_1A(z-)=1-1.5z-+0.7z=C(z-)B(z-)=1.0z,0.5z-_1D(z-)=1經(jīng)過(guò)計(jì)算，得到系統(tǒng)真實(shí)的模型：z(k)-1.5z(k-1)0.7z(k-2)=u(k-1)0.5u(k-2)v(k)選擇圖3所示的辨識(shí)模型。仿真對(duì)象選擇如下的模型結(jié)構(gòu)z(k)a1z(k-1)a2z(k-2)=biu(k-1)du(k-2)v(k)其中，v(k

13、)是服從正態(tài)分布的白噪聲N(0,1)。輸入信號(hào)采用4位移位寄存器產(chǎn)生的M序列，幅度為0.03。圖3最小二乘遞推算法辨識(shí)實(shí)例結(jié)構(gòu)圖最小二乘遞推算法辨識(shí)的Malab6.0程序流程如圖4所示。下面給出具體程序。%最小二乘遞推算法辨識(shí)程序，在光盤(pán)中的文件名：RL3.mclear%青理工作間變量L=15;%M序列的周期y1=1;y2=1;y3=1;y4=0;%四個(gè)移位寄存器的輸出初始值fo門(mén)=1:L;%開(kāi)始循環(huán)，長(zhǎng)度為L(zhǎng)x1=xor(y3,y4);%第一個(gè)移位寄存器的輸入是第三個(gè)與第四個(gè)移位寄存器的輸出的“或”x2=y1;%第二個(gè)移位寄存器的輸入是第一個(gè)移位寄存器的輸出x3=y2;%第三個(gè)移位寄存器的輸

14、入是第二個(gè)移位寄存器的輸出x4=y3;%第四個(gè)移位寄存器的輸入是第三個(gè)移位寄存器的輸出y(i)=y4;%取出第四個(gè)移位寄存器的幅值為0和1的輸出信號(hào),即M序列ify(i)0,5,u(i)=-0.03;%如果M序列的值為1,辨識(shí)的輸入信號(hào)取“-0.03”elseu(i)=0.03;%如果M序列的值為0,辨識(shí)的輸入信號(hào)取“0.03”end%小循環(huán)結(jié)束y1=x1;y2=x2;y3=x3;y4=x4;%為下一次的輸入信號(hào)做準(zhǔn)備end%大循環(huán)結(jié)束，產(chǎn)生輸入信號(hào)ufigure(1);%第一個(gè)圖形stem(u),gridon%顯示出輸入信號(hào)徑線(xiàn)圖并給圖形加上網(wǎng)格z(2)=0;z(1)=0;%設(shè)z的前兩個(gè)初始

15、值為零fork=3:15;%循環(huán)變量從3到15z(k)=1.5*z(k-1)-0.7*z(k-2)+u(k-1)+0.5*u(k-2);%輸出采樣信號(hào)end.工作間清零給M序列的長(zhǎng)度L和移位寄存器的輸入賦初始值第四個(gè)移位寄存器的輸出取反，并將幅值變?yōu)?.03得到辨識(shí)系統(tǒng)的輸入信號(hào)樣本值畫(huà)出辨識(shí)的輸入信號(hào)徑線(xiàn)圖形十產(chǎn)生輸出采樣信號(hào)S給被辨識(shí)參數(shù)8和P賦初值T按照式(4.95)的第二式計(jì)算K(k)按照式(4.96)的第一式計(jì)算Q(k)十一按照式(4.94)的第三式計(jì)算P(k)計(jì)算被辨識(shí)參數(shù)的相對(duì)變化量-NrTjjjjjjZ分離參數(shù)畫(huà)出被辨識(shí)參數(shù)e的各次遞推估計(jì)值圖形畫(huà)出被辨識(shí)參數(shù)日的相對(duì)誤差的圖形

16、7ZET(結(jié)束)圖4最小二乘遞推算法辨識(shí)的Malab6.0程序流程圖%RLS遞推最小二乘辨識(shí)c0=0.0010.0010.0010.001;%直接給出被辨識(shí)參數(shù)的初始值，即一個(gè)充分小的實(shí)向量p0=10八6*eye(4,4);%直接給出初始狀態(tài)P0,即一個(gè)充分大的實(shí)數(shù)單位矩陣E=0.000000005;糠相對(duì)誤差E=0.000000005c=c0,zeros(4,14);%被辨識(shí)參數(shù)矩陣的初始值及大小e=zeros(4,15);騎目對(duì)誤差的初始值及大小fork=3:15;%開(kāi)始求Kh1=-z(k-1),-z(k-2),u(k-1),u(k-2);x=h1*p0*h1+1;x1=inv(x);%開(kāi)

17、始求K(k)k1=p0*h1*x1;%求出K的值d1=z(k)-h1*c0;c1=c0+k1*d1;%求被辨識(shí)參數(shù)ce1=c1-c0;%求參數(shù)當(dāng)前值與上一次的值的差值e2=e1./c0;%求參數(shù)的相對(duì)變化e(:,k)=e2;%把當(dāng)前相對(duì)變化的列向量加入誤差矩陣的第k列c0=c1;%新獲得的參數(shù)作為下一次遞推的舊參數(shù)c(:,k)=c1;%把辨識(shí)參數(shù)c列向量加入辨識(shí)參數(shù)矩陣的第k列p1=p0-k1*h1*p0;%求出p(k)的值p0=p1;%給下次用ife2c=r0.001000.0010-0.4984-1.2328-1.4951-1.4962-1.4991-1.4998-1.49990.0010

18、00.00100.0010-0.23500.69130.69410.69900.69980.69990.001000.25091.24971.06651.00171.00201.00020.99990.9998L0.00100-0.24890.75000.56680.50200.50160.50080.50020.50020.030.030.020.01-0.01-0.02-0.03IdentificationPrecision300200-Convergenceofbl100-100rConvergenceofa2-200-300Convergenceofb2-400Convergenceo

19、fa1-5005Fig.3IdentificationError1015最小二乘遞推算法的參數(shù)辨識(shí)仿真-1.5000-1.5000-1.5000-1.4999-1.49990.70000.70000.70000.7000-0.70000.99990.99990.99990.99990.99990.50000.50000.50000.50000.5000000-499.42001.47340.21280.00070.00200.00040.00000000-235.9916-3.94160.00420.00700.00120.000100249.86123.9816-0.1466-0.06070

20、.0003-0.0018-0.0003-0.000100-249.8612-4.0136-0.2443-0.1143-0.0007-0.0016-0.0012-0.00010.00010.0000-0.0000-0.00000.00000.0001-0.00000.00000.00000.00000.00010.00000.00000.0000-0.0000-0.00040.0000-0.00000.0000-0.0000表2最小二乘遞推算法的辨識(shí)結(jié)果a1a2b1b2真值-1.50.71.00.5-1.49990.70.99990.5000仿真結(jié)果表明，大約遞推到第十步時(shí)，參數(shù)辨識(shí)的結(jié)果基本達(dá)

21、到穩(wěn)定狀態(tài)，即a1=-1,4999,a2=0.7000,bi=0.9999,b2=0.5000。此時(shí)，參數(shù)的相對(duì)變化量EM0.00000000S從整個(gè)辨識(shí)過(guò)程來(lái)看，精度的要求直接影響辨識(shí)的速度。雖然最終的精度可以達(dá)到很小，但開(kāi)始階段的相對(duì)誤差會(huì)很大。例四：考慮圖4所示的仿真對(duì)象，圖中，v(k)是服從N(0,1)分布的不相關(guān)隨機(jī)噪聲。+圖4增廣最小二乘法辨識(shí)實(shí)例結(jié)構(gòu)圖N(z)D(z),C(z)1、G(z),b(z)1A(z-)fA(z)=1-1.5aiz-1+0.7Z-2=C(z11)B(z-1)=1.0z-10.5z-2I1-1-2D(z1)=1-z10.2z2工作間清零)給M序列的長(zhǎng)度L賦值

22、t用4位移位寄存器產(chǎn)生幅值為1的輸入信號(hào)t產(chǎn)生隨機(jī)噪聲信號(hào)畫(huà)出輸入信號(hào)徑線(xiàn)圖形及隨機(jī)噪聲圖形十產(chǎn)生輸出采樣信號(hào)t給被辨識(shí)參數(shù)日和p賦初值I-1I按照式(4-153)的第二式遞推計(jì)算K(k)tJ按照式(4-152)的第一式遞推計(jì)算8t-按照式(4-154)的第三式遞推計(jì)算P(k)計(jì)算系統(tǒng)的實(shí)際輸出響應(yīng)及模型的響應(yīng)計(jì)算被辨識(shí)參數(shù)的相對(duì)變化量斂滿(mǎn)足要求？N不顯示被辨識(shí)參數(shù)、辨識(shí)精度、輸出采樣、系統(tǒng)實(shí)際輸出、模型輸出畫(huà)出被辨識(shí)參數(shù)0的各次估計(jì)值及其誤差畫(huà)出系統(tǒng)的實(shí)際輸出、輸出采樣及模型輸出(停機(jī)j圖增廣最小二乘遞推算法辨識(shí)的Malab6.0程序流程圖模型結(jié)構(gòu)選用如下形式：z(k)a1z(k-1)a2(

23、k-2)=b1u(k-1)b2u(k-2)v(k)d1V(k-1)d2(v(k-2)增廣最小二乘辨識(shí)程序流程上圖所示Matlab6.0程序如下%增廣最小二乘辨識(shí)程序clearL=60;%4位移位寄存器產(chǎn)生的M序列的周期y1=1;y2=1;y3=1;y4=0;%4個(gè)移位寄存器的輸出初始值fori=1:L;x1=xor(y3,y4);%第一個(gè)移位寄存器的輸入信號(hào)x2=y1;%第二個(gè)移位寄存器的輸入信號(hào)x3=y2;%第三個(gè)移位寄存器的輸入信號(hào)x4=y3;%第四個(gè)移位寄存器的輸入信號(hào)y(i)=y4;%第四個(gè)移位寄存器的輸出信號(hào)，M序列，幅值0和1,ify(i)0.5,u(i)=-1;%M序列的值為1時(shí)

24、，辨識(shí)的輸入信號(hào)取“-1”elseu(i)=1;%M序列的值為0時(shí)，辨識(shí)的輸入信號(hào)取“1”endy1=x1;y2=x2;y3=x3;y4=x4;%為下一次的輸入信號(hào)準(zhǔn)備endfigure(1);%畫(huà)第一個(gè)圖形subplot(2,1,1);%畫(huà)第一個(gè)圖形的第一個(gè)子圖stem(u),gridon%畫(huà)出M序列輸入信號(hào)v=randn(1,60);%產(chǎn)生一組60個(gè)正態(tài)分布的隨機(jī)噪聲subplot(2,1,2);%畫(huà)第一個(gè)圖形的第二個(gè)子圖plot(v),gridon;%畫(huà)出隨機(jī)噪聲信號(hào)u,v%顯示輸入信號(hào)和噪聲信號(hào)z=zeros(7,60);zs=zeros(7,60);zm=zeros(7,60);zm

25、d=zeros(7,60);%輸出采樣矩陣、不考慮噪聲時(shí)系統(tǒng)輸出矩陣、不考慮噪聲時(shí)模型輸出矩陣、模型輸出矩陣的大小z(2)=0;z(1)=0;zs(2)=0;zs(1)=0;zm(2)=0;zm(1)=0;zmd(2)=0;zmd(1)=0;%輸出采樣、不考慮噪聲時(shí)系統(tǒng)輸出、不考慮噪聲時(shí)模型輸出、模型輸出的初值c0=0,0010.0010.0010.0010.0010.0010.001;%直接給出被辨識(shí)參數(shù)的初始值，即一個(gè)充分小的實(shí)向量p0=10八6*eye(7,7);%直接給出初始狀態(tài)P0,即一個(gè)充分大的實(shí)數(shù)單位矩陣E=0.00000000005;咐目對(duì)誤差E=0.000000005c=c0

26、,zeros(7,14);%被辨識(shí)參數(shù)矩陣的初始值及大小e=zeros(7,15);騎目對(duì)誤差的初始值及大小fork=3:60;%開(kāi)始求Kz(k)=1.5*z(k-1)-0.7*z(k-2)+u(k-1)+0.5*u(k-2)+v(k)-v(k-1)+0.2*v(k-2);%系統(tǒng)在M序列輸入下的輸出采樣信號(hào)h1=-z(k-1),-z(k-2),u(k-1),u(k-2),v(k),v(k-1),v(k-2);%為求K(k)作準(zhǔn)備x=h1*p0*h1+1;x1=inv(x);k1=p0*h1*x1;%Kd1=z(k)-h1*c0;c1=c0+k1*d1;%辨識(shí)參數(shù)czs(k)=-1.5*z(k-

27、1)+0.7*z(k-2)+u(k-1)+0.5*u(k-2);%系統(tǒng)在M序列的輸入下的輸出響應(yīng)zm(k)=-z(k-1),-z(k-2),u(k-1),u(k-2)*c1(1);c1(2);c1(3);c1(4);%模型在M序列的輸入下的輸出響應(yīng)zmd(k)=h1*c1;%模型在M序列的輸入下的輸出響應(yīng)e1=c1-c0;e2=e1./c0;冰參數(shù)誤差的相對(duì)變化e(:,k)=e2;c0=c1;%給下一次用c(:,k)=c1;%把遞推出的辨識(shí)參數(shù)c的列向量加入辨識(shí)參數(shù)矩陣p1=p0-k1*k1*h1*p0*h1+1;%findp(k)p0=p1;%給下次用ife2u=1,-1,-1,-1,-1,

28、1,1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,-1,1,-11,1418,1.5519,1.3836,-0.7581,0.4427,0.9111,-1.0741,0.2018,0.7629,-1.2882,-0.9530,0.7782,-0.0063,0.5245,1.3643,0.4820,-0.7871,0.7520,-0.1669,-0.8162,2.0941,0.0802,-

29、0.9373,0.6357,1.6820,0.5936,0.7902,0.1053,-0.1586,0.8709,-0.1948,0.0755,-0.5266,-0.6855,-0.2684,-1.1883,0.2486,-0.1025,-0.0410,-2.2476,-0.5108,0.24920.3692,0.1792,-0.0373,-1.6033,0.3394,-0.1311,0.4852,0.5988,-0.0860,0.3253,-0.3351,-0.3224,-0.3824,-0.9534,0.2336,1.2352,-0.5785,-0.5015z=c=0.001000,001

30、0-0.2789-0.9025-0.9390-0.8620-1.1236-1.5000-1.5000-1.5000、0.001000,00100.0010-0.0734-0.2661-0.11990.32590.70000.70000.70000.001000,05920.45600.53000.52930.94580.54021.00001.00001.00000.001000,05720.81860.85000.86391.11571.29570.50000.50000.50000.001000,07960.73420.54170.55160.38470.24591.00001.00001

31、.00000.00100-0,0894-0.5981-0.3420-0.4456-0.4044-0.8443-1.0000-1.0000-1.0000O00100-0,0655-0.7795-0.8572-0.7412-0.4506-0.19740.20000.20000.2000e=000-279.94262.23550.0404-0.08200.30350.33500.00000.00000000-74.37642.6263-0.5495-3.71891.1479-0.00000.00000058,22126.70070.1622-0.00130.7868-0.42890.85120.00

32、000.000000-58.2212-15.30520.03840.01630.29150.1613-0.6141-0.0000-0.000000-80.5566-10.2283-0.26210.0183-0.3027-0.36073.06630.00000.000000-90.35565.6936-0.42820.3029-0.09251.08800.1844-0.00000.0000I0-66.475410,90590.0996-0.1354-0.3920-0.5619-2.01300.00000.00000,0,-0,4400,-3.9913,-5.7014,-6.9415,-7.817

33、8,-3.9097,1.4543,2.4075,3.5810,6.6598,6.0079,3.5364,2.4376,-0.0964,-2.3472,-2.3178,-4.4100,-6.9915,-6.0233,-5.8181,-3.6094,1.7476,5.5068,6.5756,8.0416,6.3933,2.3550,0.6078,-2.3342,-2.9824,-3.9807,-5.5271,-6.6924,-8.7267,-6.5221,-2.5583,2.1343,2.3062,4.1939,6.4870,6.3125,3.2878,0.8703,-3.0262,-2.7133

34、,-3.2428,-3.7807,-4.8137,-6.6618,-5.5921,-2.9025,1.1385,3.1125,3.7363,6.0362,6.7499,2.6324,0.0478zs=0,0,-0,5000,-0.8401,4.1789,4.2583,6.9212,8.3677,1.8920,-5.4182,-2.0932,-2.1863,-7.9830,-5.8500,-0.5991,-1.6810,2.3509,2.9533,0.3337,3.4925,5.9002,4.6409,6.0108,2.8415,-5.6480,-6.5369,-4.5087,-7.9595,-

35、5.4608,1.4428,0.2369,4.4268,2.3396,2.3834,4.0042,4.6696,8.9054,5.1745,0.7719,-5.4923,-1.4653,-3.1765,-7.2947,-6.4279,-0.0129,0.4961,5.6486,1.4516,1.4649,1.9010,3.0741,7.1232,5.2248,1.9393,-4.2395,-3.3718,-1.9258,6.9389,-7.3995,1.2763zm=0,0,-0,4400,-3.9913,-5.7014,-6.9415,-7.8178,-3.9097,1.4543,2.407

36、5,3.5810,6.6598,6.0079,3.5364,2.4376,-0.0964,-2.3472,-2.3178,-4.4100,-6.9915,-6.0233,-5.8181,-3.6094,1.7476,5.5068,6.5756,8.0416,6.3933,2.3550,0.6078,-2.3342,-2.9824,-3.9807,-5.5271,-6.6924,-8.7267,-6.5221,-2.5583,2.1343,2.3062,4.1939,6.4870,6.3125,3.2878,0.8703,-3.0262,-2.7133,-3.2428,-3.7807,-4.8137,-6.6618,-5.5921,-2.9025,1.1385,3.1125,3.7363,6.0362,6.7499,2.6324,0.0478130-2-430d3-1.5ionWethodFig.2Paramet20erIdentificat40ithRecursiveLeastSquaresM-0.5-0.51000201IJX1,jrvt.ipA/V1/VFig.1(1)InputSignalofMSeries20Fig.1(2)S