How to do least square error estimation to find the coeffcient values for a quadratic type equation with set of constraints on coefficients

I have measured and actual values need to find the values of a,b,c.

for y=ax^2+bx+c

constraints are: a+b+c=1

0<a<1, 0<b<1,0<c<1

Answer 1

[Just Manuel]

I love this answer from Star Strider: https://ch.mathworks.com/matlabcentral/answers/126146-curve-fitting-without-the-toolbox

This allows you to fit any curve with vanilla matlab.

You just need to write a function that constrains your parameters and your own cost function.

Try this:

% i don't know your data, so i'll demonstrate fitting a second
% order over an inverse cosine
x = -1:0.01:1;
y = 1 - cos(x .* 1.5);

% define 2nd order polynomial function
fun = @(b, x) b(1) .* x.^2 + b(2) .* x + b(3);

% i use square to constrain parameters to be positive
% and divide by the sum to have the parameters to sum up to 1
constrainParams = @(b) b.^2 ./ sum(b.^2);

% cost function to optimize is just a least square function
cost = @(b) sum((fun(constrainParams(b),x) - y).^2);

% find parameters using fminsearch (in the domain of all real
% numbers) with an initial guess (probably you have one that
% fits your data).
b = fminsearch(cost, [1 0 0]);

% then you just have to apply the constrain function to those
% parameters
params = constrainParams(b);

% there you have a, b and c
a = params(1);
b = params(2);
c = params(3);

% quickly verify it with a plot
plot(x,y, x,fun(params, x));

Cheers

Manuel

[Just Manuel]

Dear @ @MAHANTESH CHIKKADESAI

Please accept the answer, if it was of use to you.

Cheers

Manuel