Using Least Squares for curve fitting in Matlab
1) Form a matrix, A of order $m$ x $3$, such that:

$$A=\left[f(x) \ \ g(x) \ \ h(x)\right]$$

where $f(x), g(x)$ and $h(x)$ are three column vectors such that each column is a sample of component guassian at $x$.  

2) Form a column vector, $b$ of your original Gaussian pulse of order m.

3) Solve the system $x=((A'*A)^{-1}*A')*b$, where $x$ is your desired set of coefficients of order $3$ x $1$, that would minimize the error in the least square sense.