Fit to find the value of an unknown parameter

Question

Tomer 2020-3-24

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https://ww2.mathworks.cn/matlabcentral/answers/512603-fit-to-find-the-value-of-an-unknown-parameter

评论： Tomer 2020-3-25

Hi. I want to determine the value of a paramter (H) using a fit to measurements. I am assuming a list of H values.

A=0.1; 
B=0.5; 
C=100;
x; % x - coordinates
P1; % Measured data
H=0.0001:0.00005:0.05; % Assuming some values of H
for i=1:length(H)
    i
    P2=H(i)*(((1/A)*log(x.*H(i)/C))+B); % Estimation
    R2(i)=rsquared(P1,P2) % Calculating the R2 value using rsquared function
end

I want the same number of P2 estimations as the number of assumed H values. I don't get it here. I want to save the values of R2 and select the value of H which gives R2=0.95.

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Answer 1

Stephan 2020-3-24

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https://ww2.mathworks.cn/matlabcentral/answers/512603-fit-to-find-the-value-of-an-unknown-parameter#answer_421687

在 MATLAB Online 中打开

Try to optimize with least squares:

A=0.1;
B=0.5;
C=100;
% Range for H
lb = 0.0001;
ub = 0.05;
best_H = fminbnd(@(H)sseval(H,x,P1,A,B,C),lb,ub)
P2 = best_H*(((1/A)*log(x.*best_H/C))+B)
function sse = sseval(H,x,P1,A,B,C)
    sse=sum((H*(((1/A)*log(x.*H/C))+B)-P1).^2);
end