Least squares parameter correlation

[vibe3]

I am trying to solve a large least squares inversion (inverting data for the modeled sources), and find that my parameters describing 1 source are highly correlated with the parameters describing the second source.

Can anyone recommend a technique or reference which discusses how to reduce the correlation between parameters in a least squares system? I have already tried Tikhonov regularization (damping each set of parameters) with no luck.

 

[gonadas91]

I used Thikonov in my MSc thesis, and it is a genera method used on ill - posed problems, and it works fine. What you usually find is some correlation between a set of data (the one you one to calculate) with some "noise" of this data. Thikonov used the parameter \alpha to regularize the solution. You may calculate the residual norm (RN) between your desired data and the one you obtain. However, using Thikonov regularization means to include this regulator \alpha |S|^{2} in the residual norm and minimize it, where S is the solution. The problem with this method is a non- well stablished criterion to find the appropiate value of the parameter.

I suggest you to take a look at the L curves and S curves an its definitions,I hope I gave you a taste about it.