MATLAB: How to parametrize two parameters in an equation

Question

I have observed relative humidity and a statistical method to estimate RH. The statistical method uses two different parameters and I would like to use the observations to parametrize the two parameters (the parameters are supposed to be around 2.1 for a and 0.130 for ab).

What I have done so far is;

best_total_dist=10000000000;
best_a=100;
best_ab=100;
hum=log(rh); % rh is observed relative humidity 
for a=0:0.01:2.3
    for ab=0:0.001:0.0150
    estrh=10.^(a-(ab.*t)); % statistical method to estimate relative humidity 
    difference=estrh-hum;
    difference_sq=difference.^2;
    sum_difference=sum(difference_sq);
    if sum_difference<best_total_dist
        best_total_dist=sum_difference;
        best_a=a;
        best_ab=ab;
    end
    end
end

Where am I going wrong?

Answer 1

According to your code, the model for 'rh' (not log(rh)) is going to be

rh = exp(10.^(a-(ab.*t)))

That's a doubtful looking model to me. At t=0, it means that rh=4.7254e+54.

If I assume that you really meant,

log(rh)= a-(ab.*t)

then you could find the least squares solution by

 x=[ones(size(t)),  -t]\log(rh);
 a=x(1);
 ab=x(2);