Fit to find the value of an unknown parameter

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.

Answer 1

[Stephan]

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

see also:

https://de.mathworks.com/help/matlab/math/example-curve-fitting-via-optimization.html

[Tomer]

Hi, thanks for your help. I didn't follow the synatx above. When I ran it, it gave the follwoing error.

Error in sseval (line 2)

sse=sum((H*(((1/A)*log(x.*H/C))+B)-P1).^2);

Error in @(H)sseval(H,x,Pa,A,B,C)

Error in fminbnd (line 233)

x= xf; fx = funfcn(x,varargin{:});

[Stephan]

Can you attach the data?

[Tomer]

Its solved now. Thanks.