Origin of colour belt system(s)

Each style of martial art seems to have a belt or sash colour system, and I'd love to know a little more about this historical origin. Did each style independently begin, or did one start and the others follow? Why do martial artists wear belts or sashes anyway?

Can anyone point me to some definitive resources about this history?

I found this very interesting document about karate belts, but it doesn't mention its relationship with other martial arts disciplines. http://ift.tt/2iDQVfr