I get from a specific experiment 3 outputs. Each is the information of some physical quantity in the direction x,y or z. The way we extract the information from those signals is by fitting.
In the data extracted from fitting, some parameters depend only on the direction of the physical quantity we want to measure, and some others depend on the whole system or on the scalar value of the physical quantity (common attributes). Statistically, it's preferred to do a simultaneous fit for all the directions. This is what my boss told me.
What he said sounds right, but technically, it's pretty hard to fit the 3 data sets together, because the function is already pretty complicated with 7 parameters in each direction, and combining the 3 together will just complicate stuff, and my fit doesn't converge when doing them simultaneously. I'm using Levenberg-Marquardt's algorithm.
The question is, is there anything I could do in the individual results of the fit, to obtain the result of a simultaneous fit? In other words, how can I avoid simultaneous fitting and obtain its statistical advantage?
And if simultaneous fitting is the only solution I have, what does taking 3 data sets to a simultaneous fit entail? how will that scale the fitting parameters (Chi^2, weighting, tolerance ...etc)?
I'm fitting using a program I wrote myself with C++.
Thank you for any efforts.