Up there in space, where the humans haven’t had an opportunity to kill each other yet, each GPS satellite orbits the earth twice every time the earth rotates once. Therefore, a satellite will repeat the same orbit twice a day, but obviously observers can only witness that when it's night time. So we have to take the scientists word on that. We refer to big GPS orbital picture (meaning all 24 moving in sequence) as the GPS constellation, despite its lack of originality. They are divided into six different orbital planes with each plane inclined 55 degrees to the equator. The image to the right, courtesy of GPS Magazine, gives you an idea of the orbital positioning.
In order to achieve the two orbits twice a day, scientists correctly calculated that they needed to be placed at an altitude of 20,200km. The satellites are equipped with thrusters that are used to ensure that they’re in the right place if they wander off the path from time to time. So, unfortunately, there are no sensational collisions going on up there that might be caught on tape. For some very precise information about the exact orbital trajectories for each satellite (at any given time), along with diagrams that explain how they are plotted, visit Wolfram Research.
Carina Software is fantastic software to use for viewing the heavens, as you can see from this great image from the perspective of the moon. Now you know the basics of how those satellites orbit so that you can better navigate down here. Look to Bright Hub's GPS & Navigation channel for reviews and information on virtually all GPS categories, makes, and models.