LS method in idetification ,control engeeniring

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saeed
saeed 2024-5-12
回答： Aastha 2024-10-1
Hi,how are you?I have problem with that code,is about LS method with ARX model in identification,I should use xcorr command for EPS variable to compare it that how much is near to white noise ?
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saeed
saeed 2024-5-12
编辑：Sam Chak 2024-5-12
Ran in:
clc, clear, close all, N=100; e=100*randn(1,N); x=1:N; a2=0.5; a1=1; a0=2; y=a2*x.^2+a1*x+a0+e; plot(x,y,'Linewidth',2); phi=ones(N,1); Y=y'; theta_hat=phi./Y; Y_hat=phi.*theta_hat; Eps=Y-Y_hat; V0=Eps'*Eps/2; hold on, plot(x,Y_hat,'LineWidth',2); clear phi theta_hat
saeed
saeed 2024-5-12
How can I compare Eps with e by xcorr command to know that error is atleast near to white noise

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Aastha
Aastha 2024-10-1
Hi saeed,
As I understand, you want to compare the error variable “Eps" between “Y” and “Y_hat”  with the white noise realization “e” using the "xcorr" function in MATLAB. This can be done using the following code snippet:
[cross_corr, lags] = xcorr(Eps, e, 'normalized');   
You may refer to the link of MathWorks documentation for further information on “xcorr” function. Here is the link to it:
https://www.mathworks.com/help/matlab/ref/xcorr.html
The "xcorr" function computes the cross correlation between “Eps” and "e”. The "normalised" argument normalizes the sequences so that the autocorrelations at zero lag is equal to 1.
The function returns two variables, first one is “lags” which contains all the lags at which cross correlation has been computed and the second variable “cross_corr” contains the corresponding cross correlation values.
You can visualize the cross relation using the "stem" function in MATLAB. The code snippet below illustrates the same:
stem(lags,c);
For more information on “stem” function, you may refer to the documentation link below:
https://www.mathworks.com/help/matlab/ref/stem.html
I hope this helps!

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