Hi,
Looks like you have an over-determined system with 2 unknowns 'sigma1' and 'sigma2' and a number of equations. Simplifying the details, you have equations of the following form:
A1x + B1y = C1
A2x + B2y = C2
where x and y are the unknowns, and A1, A2, B1, B2 and C1, C2 are vectors of known observations.
As I understand, there can be two ways to solve for x and y:
1. You solve x and y as vectors: in that case, you can take one observation from each vector giving you:
a1x + b1y = c1
a2x + b2y = c2
where a1, a2, b1, b2, c1, and c2 are scalar values. If we create a matrix P = [a1 b1; a2 b2] and Q = [c1 c2], the left divide operator '\' solves the system of linear equations using least square errors:
[x, y] = P\Q;
Repeating the above for all 'n' values (assuming the vectors Ai, Bi and Ci are of length 'n'), we can find n values for x and y.
2. You solve only one value of x and one value of y: in that case, let's say the above system of linear equation becomes:
Ax + By = C
where A = [A1; A2], B = [B1; B2] and C = [C1; C2].
P = [A B] would be now 2nx2 matrix where A1 and A2 are each nx1 vector (same with Bi).
Now the solution would be:
[x, y] = P\Q; % Q = C
You can find more information on left divide (\) or mldivide in the following documentation link: http://www.mathworks.com/help/matlab/ref/mldivide.html
