A caster wheel ('roulette pivotante' in french accoring to leo.org) in its simplest form is a shopping trolley wheel. The wheel will, in steady state, point along the velocity vector of the mounting location w.r.t. ground. The transient slip angle can be found using the angle and rate measured by the trailing arm and the vehicle velocity as measured by the rotating wheels.
I drew up a design for this while I was still in university but never had the time to make it. The concept can be found here:
https://1drv.ms/b/s!AioEiFs0jfZSgVc5hbwAOWexfqFI
The design was made to have the CG of the trailing arm assy along the vertical pivot axis but the counter balance the Doug mentioned were to be included in the green plate in front of the pivot if any corrections were required.
I've seen a similar concept used in the cottage industry too where its more accurate at low speeds than the GPS based systems which cost 50k+. I know my old uni trialled a similar concept last year. I will let them elaborate if they want.
You still need a gyro though to transform the slip angle from the measurement point to the CG and front and rear axles for cornering compliance analyses.
I doubt the idea can be any good though because my track record is nothing special. My FSAE team always came last and every shool I went to in my life was demolished shortly after I left.
In terms of definitions the slip angle is, in my opinion, unambiguously defined in Milliken, Guiggiani, Pacejka, ISO 8855 and SAE J670e. Clear as a dogs donger in my opinion - I don't get what all the fuss is about.