Optimization of parameters in template matching

I have a signal that looks like this:, and a template like this: . I want to optimize the parameters of my template function so that it fits well with the peak in the original signal. Right now I am using a function "correlationfitting" to try finding the place where the template and signal is most similar, and fmincon in order to optimize the parameters. The first three parameters are parameters of the template function, p is an offset parameter, and minID is where the function correlationfitting finds the highest similarity.

It does not work however, and I would greatly appreciate any tips or help.

Apologies for long or unclear question, thanks in advance!

x0 = [alpha lambda mu p minID];
A = -eye(5);
b = [0 0 0 0 0];

y = fmincon(@(x)costfunc(sensornr, bolusnr, x),x0,A,b);
alpha_opt = y(1);
lambda_opt = y(2);
mu_opt = y(3);
p_opt = y(4);
t_opt = y(5);


function sim_value = similarity(vec1, vec2)
    sim_value = sum(vec1.*vec2)/(norm(vec2)*(norm(vec1)));
end

function sim_values = correlationfitting(raw_data,template_data)
    sim_values = zeros(length(raw_data),1);
    for i=1:(length(raw_data)-length(template_data)+1)
        raw_chunk = raw_data(i:i+length(template_data)-1);
        sim_values(i) = similarity(raw_chunk,template_data);
    end
end

function cost = costfunc(sensor_values, bolustime, x)
    alpha = x(1);
    lambda = x(2);
    mu = x(3);
    p = x(4);
    t_min = x(5);
    t = 1:1:61;
    template = alpha.*exp(lambda)/mu.*(lambda.*mu./(2.*pi.*t)).^(1/2).*exp(-lambda./2.*(t./mu+mu./t));
    
    raw_data = read_raw(sensor_values, bolustime);
    raw_dataadjusted = raw_data -p;
    
    simvals = correlationfitting(raw_dataadjusted, template');
    cost = -simvals(round(t_min)); 
end

[Vinayak]

Hi Jarl, it might be more helpful if we have some data to reproduce on our end.

Answer 1

[Catalytic]

  cost = interp1( -simvals, t_min,'cubic');