I am trying to develop an electronic that tracks a barbell movement from the side or underneath during lifting movements such as squat, bench press, deadlift, clean and jerk, and snatch.
The idea is to use either ping sensor to triangulate (may need more than 1), or IR camera/IR transmitter to achieve this. I prefer not to use accel/gyro as they prove to be very inconsistent in these type of settings.
Definitely go with a camera. Or multiple cameras. I think that is the only choice that will give you real-time tracking. If you can use reflective tape markers and an IR source near the camera that will save you from having to make a bunch of active markers. It will also allow you to track more points, like elbow and knee joints.
Having said that, it puts the project well outside the capability of the Arduino UNO. If you need something compact and relatively inexpensive, the RaspberryPI should be capable enough.