The only way I've found is through exercise or training for a sport that requires correct movements quickly the martial arts, football, or weightlifting. Basically it comes down to first getting fundamentals downs and then your mind switching from concentrating on just movements to also picking up other information.
In football, it's learning how to run from a stance and how to block or tackle to seeing why this person is moving a certain way and how to counter it. For karate, you learn katas and after you get that down, it's almost like moving meditation because your body flows while your mind can be a million miles away. Even with running your body goes into autopilot while your mind is focused elsewhere.
If you want to increase your perception, I'd say just get into some type of fitness plan that requires explosive movements and then maybe spend a little time out your day noticing what is all around you. That way you're used to shifting your body on a moments notice and while you're in the zone, you can pick up on stuff that you've already noticed that can signal something.