Aiya!!!

This is a linear combination of exponential functions! I wonder if the fminsearch function will come in handy. I've never used it though.

You'll have to set up your function as follows:

Y = X1 (a1 * V^{n1} + a2 * V^{n2} + a3 * V^{n3})

Let P=Y./X1;

So now you'll have:

P=a1*V^{n1} + a2*V^{n2}+a3*V^{n3};

Beyond that, I can't say much.

If you could provide the scenario in which you're trying to estimate this, perhaps it would help?