I really didn’t mean this discussion to degrade into a discussion about how GPS works or why it kinda sucks for our purposes but since we’re riding this snowball straight to hell, we may as well see how close we can get. If you really want to understand the issues with positional GPS, I would suggest picking up the book “Understanding GPS, Principles and Applications.” It is *not* light reading but it is the best reference I’ve seen so far. It took me a good 6 months to properly get through it but I had to look up a lot of stuff referenced from the book. I am not smart man, but I know what love is…
The abridged Cliff’s Notes version in shorthand tells us that the source of the “wandering” is due to many factors. GPS relies heavily on time stamping and even something simple as a slight mismatch between the crystals driving the clocks on the satellites versus the ones in our receivers are enough to throw the entire thing off a few meters. Once you start factoring in the continually changing atmospheric conditions and a host of other issues, it’s somewhat amazing it works at all!
I did some experiments and observed a drift of roughly 30 feet over a period of a few hours. What does that mean? Not much by itself, actually. What is important is that the “drift” had a nearly constant motion moving the observed position by anywhere from 0.5 to 1.5 feet per second. The speed of the “drift” is highly dependant on location and environment but that number turns out to be fairly representative of other’s observation. Another property of the “drift” is that it never wanders off too far from its true location.
Suddenly the “drift” is an entity! Let’s call him Bob. Bob is a heavy drinker. Bob got into some trouble with the law a while back and they put him in the middle of a circle. The circle isn’t really shaped like a circle but it is close enough. The circle’s size changes all the time but it is generally in the 60-foot diameter range. In the middle of the circle is a “device” that is linked to the ankle bracelet Bob is wearing. As Bob moves further away from the center, the “device” sends a signal that shocks Bob with increasing intensity.
The center of the circle is supposed to be Bob’s true location. But Bob is restless-- and drunk. Bob is a little numb (drunk, remember!) so he doesn’t really feel the shock of his ankle bracelet until he gets closer to the edges of his circle of confinement. The shock naturally guides Bob back towards the center but even if he hits it spot on, he doesn’t stay there very long. Bob is a drunk with a bad caffeine habit! It really doesn’t matter why Bob moves about like he does, the question is can we sit him still long enough to get something useful out of him?
Well, we can’t really sit him still without sobering him up. Sobering him up would require very expensive rehab and is hard to justify. I mean, come one, it’s just Bob! Bob gets no love. So what can we do? Let’s use Bob in an experiment. Bob won’t mind! We are going to build a container big enough to house Bob and his circle so we can move him around. Think “Bob in a petrie dish”. Bob’s “device” is naturally located in the center of the petrie dish and we are going to move that center point along a pre-defined path. Meanwhile, Bob is busy wandering around inside his circle and we are going to record his position at set intervals like, say, 10 times a seconds.
The result? Bob finally passed out from all the drinking. But before he did that, we managed to record his path along with the true path we moved the center of his circle along. So what do we know about Bob and the path he took? Remember, we were moving Bob and Bob was moving himself to generate the path. Bob is a bastard for making our lives difficult! We’ll get back at him eventually.
OK, so Bob started somewhere within his circle. Where? It doesn’t really matter as long as we record it. A tenth of a second later, we record his position again. Now in that time, we moved the petrie dish slightly and Bob moved as well. Now this is key, remember when we said that Bob is moving around pretty slowly? How slowly exactly? In general, he moves around at about 1/2 mph. That’s pretty slow. Bob doesn’t really have a predicable pattern but as long as we are moving faster than a walking speed, Bob’s movement gets lost in the noise. Think about it in these terms: in the 1/10 of a second between sample times, Bob won’t move more than a couple of inches in most of the worst cases. Under just good conditions, Bob’s movement is limited to around an inch which is very good indeed. At only 30mph, the petrie dish will move 4.4 feet in a 1/10 of a second which if Bob is messing us up by an inch, represents less than a 2% error. It gets even better as you collect data over a longer interval and explains why the course maps are at least representative of reality. They may have a little “drunken wobble” in them but it isn’t anything you can’t work around.
You can probably start to see how adding accelerometers to the mix can make things more accurate. Imagine outfitting Bob with lie detector. Every time you take a sample of Bob’s position, you ask him if he moved. Since Bob is a drunk and a notorious liar, you use the lie detector as a sanity check and adjust accordingly. For example, if the accelerometers, I mean, lie detector shows movement but yet Bob swears up and down he’s been in the same position all day, who are you going to believe? This step is definitely not necessary but it gives you a little extra piece of mind as to the validity of your results.
Is there anything else we can do? Since I’m big tease, I’ll leave you with this: Imagine if we could clone Bob. See, those sheep were handy! Seriously, think about what we could do if we had an exact copy of Bob.
Next installment: Cloning Bob and the big accuracy wrap up.
Jim
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