Fitting multiple data sets to multiple functions with shared fit parameters

*To*: mathgroup at smc.vnet.net*Subject*: [mg129351] Fitting multiple data sets to multiple functions with shared fit parameters*From*: dr DanW <dmaxwarren at gmail.com>*Date*: Mon, 7 Jan 2013 00:37:54 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

I am a an experienced user of Mathematica and am used to fitting complex valued functions to data sets, but only one function at a time. I am attempting to determine the parameters in a model of a physical system (an acoustic transducer). From the model, I can determine several transfer functions over frequency or the Laplace s, and I can also measure these transfer functions on a device. This gives me, for example, three functions (which share parameters) and three data sets, and I want to find the parameters that fit all three functions to their respective data sets simultaneously. The parameters in the model are real, but the functions and data are complex. Another complication is that the data sets have different units and scales, so I will need to normalize things so \chi^2 on all curves are weighted equally. Is there a way to directly use the built in FindFit or NonlinearModelFit to solve this problem? If not, can anyone suggest how I could construct my own method using NMinimize? I would be very grateful if the group could point me toward an example where this as been done. Regards, Daniel