Linear regression to radii of multiple circles

[Nick.Kallas]

Hi,
I am trying to simulate muon paths through drift tubes and I have ran into a problem performing a linear regression. I have generated simulated muon trajectories in 2 dimensions and they passes through my simulated drift tubes represented as black circles with a '+' in the center. As the trajectories passes through the tubes they leave an omnidirectional radius represented as colored circles. Each color corresponds to a different trajectory. I then take these radii and add noise to them simulating real world effects. Using these noisy radii I need to reconstruct the most probable path that the muon took.

Basically I have a number of circles that I need to fit a tangent line to. If anyone could help point me in the right direction it would be greatly appreciated.

https://decibel.ni.com/content/servlet/JiveServlet/showImage/105-24702-34909/MUON+RUN.jpg

 

[chiro]

Hey Nick.Kallas.

Are you trying to fit a linear regression on your entire set of simulated data?

If this is the case, then I would suggest you use a GLM where you have discrete measurements for each corresponding "row" of circles (tubes) and in this context you will have four variables corresponding to the four rows.

Then you fit the model using a statistics program (SAS, R, whatever) and you will get an equation that fits the rows.

You'll probably find that you get a lot of dependencies (since it is a straight line) and you can eliminate the dependencies in a few ways.

The first way I would suggest is to look at Principal Component Analysis and the second way is to use back-ward selection and select the best sub-model which doesn't lose too much variability within the model.

Are you familiar with these techniques?

 

[Nick.Kallas]

I just need to fit a single trajectory at a time, sorry for the ambiguity. I need to make my own algorithm so that I can eventually implement it on my hardware and there are also other factors this algorithm needs to take into account. So I am using a single trajectories information to recreate it that is using the information from a single color radii on this simulation.

So basically I think i just need to figure out a way to apply a linear regression in polar coordinates with only radius data. I am sort of at a loss of how to do this and any pertinent literature would even be helpful.

If you want a better idea of what I am tying to do here is our projects website.
https://decibel.ni.com/content/groups/muon-detector-nmt-senior-design-team-2012-2013

 

[chiro]

Just to clarify, is the radius data the intersection distance from the centre of a drift tube that it passes through?

 

[Nick.Kallas]

the radii data is represented by the closest point along the trajectory to the center of the respective tube.

 

[chiro]

Sounds like this is going to look like a normal residual against the origin of the tube.

However I need to ask, what variables do you have in total and what are you trying to relate? (Is it angle against radii or vice-versa or something else)?