To investigate what's wrong with LSQLIN, we'll probably need to see your code, your data, and an explanation of what the terminology "curve x_model" means.
However, if your 180 equality constrains are of the form x(i)=c(i) where the c(i) are known values, then there's no apparent reason to be using LSQLIN, unless the constraints x>=0 that you added later are eventually going to become important.
With these equality constraints, you really only have 192 unknown x(i) and can re-write your equations as a square system
where A_square is 192x192. You claim that A_square is full rank. If you are right, then
is the solution. Even if it is not, then pinv(A_square)*b_square should easily give you one of the non-unique solutions.
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