Thread Subject: optimization using NLS (fitting 2 curves simutaneously)-any scaling problem here?

Hi all,

I have 2 highly nonlinear objective functions x and y.
x and y both are function of parameters (a,b,c). These 3 parameters a,b,c are all between 0 and 1.

Then I have data for x and y. I call them xdata and ydata. My purpose is to adjust a,b,c to make the simulated x and y fit the xdata and ydata using nonlinear least squares.

Now the problem is all data for x is much larger than ydata. say, xdata is between 0.15-0.6. While ydata is only between 0.01-0.1. When I use fmincon to search the optimal parameters (a,b,c) to get the NLS
\sum_{i=1}^N {(xdata-x)^2+(ydata-y)^2}
where x, y, xdata, ydata are all N*1 vectors.

I find that this result is quite different with the two separate NLS result, i.e., if I run only the NLS of (xdata-x) or run only the NLS of (ydata-y). I think the problem is both x and y are depending on all three parameters. So I am confused. Do I need to take care of scaling problem here (to make ydata in a similar magnitude with xdata)? What procedure should I use? What result is correct? I am not familiar with simultaneous curve fitting. Anyone here can give some suggestions? Many many thanks in advance!!

All my best,
Amber