GPS Always Overestimates Distances (i-programmer.info)

mikejuk writes: Have you had a suspicion that your GPS app is overestimating the distance traveled? It is something that runners and walkers complain about a lot. If so, you are probably correct -- but the reason isn't an algorithmic glitch. The answer lies in the statistics, and it is a strange story. If you make a measurement and it is subject to a random unbiased error, then you generally are safe in assuming that the random component will make the quantity larger as often as it makes it smaller. Researchers at the University of Salzburg (UoS), Salzburg Forschungsgesellchaft (SFG), and the Delft University of Technology have done some fairly simple calculations that prove that this is not the case for GPS distance measurement. Consider the distance between two points — this is along a straight line, and hence it is the shortest distance. Now add some unbiased random noise, and guess what? This tends to increase the distance. So unbiased errors in position give rise to a biased overestimate of the distance. There is an exact formula for the bias and in some cases it can be more than 20%. Is there a solution? Perhaps using velocity measurements and time to work out distance is better — it isn't biased in the same way, but how accurate it could be remains to be seen. So when your fitness band tells you you have run a 4-minute mile — don't believe it.

Comments

Simple problem with a simple solution

[carlhaagen]

As a sailor who use GPS alongside traditional navigation: stop using devices that poll and insert a new leg on your route every 5 seconds. If you lower the polling frequency to f.e. every 1 or 2 minutes this problem goes away. I realize that this doesn't work for people who insist on taking their morning run zig-zagging through city blocks.

Re:Simple problem with a simple solution

[Aighearach]

http://www.adafruit.com/datash...

That's the cheapo GPS chip that makers are using. ~$40 on a breadboad module, but more like $5 as an OEM part. Calculates and stores "up to 3 days" of satellite position, then uses a lookup table. That is part of why new units still take a long time to get a cold fix; they're calculating satellite positions.

This has been a standard feature since around 10-15 years ago when they started advertising improved urban accuracy. If you're not predicting locations, you'd have to do a cold fix every time you walked past a building! It would be basically unusable downtown. Like in the old days! Back then it was also largely unusable in the forest; you'd have to find a clearing, or else remain stationary for a couple minutes, to get a fix on a cheap unit. That is why back then for serious outdoor use people were dropping $500 on dedicated GPS units that had the predictive routines, and regular GPS was intended mostly for highway auto use where the sky is usually visible.

Almost everything predictive uses Kalman filters. That is not a sign of low quality. It is a system of using predictions and expected error rates to overcome noise. If the result quality is low, it is not because of using a Kalman filter it is because of having a low quality prediction routine, or an inaccurate expected noise level. There is nothing about orbital mechanics or radio propagation that makes Kalman filters a poor fit; actually, it is nearly the ideal case for them; the noise will have a Gaussian distribution.

Perhaps this explains my Garmin

[suprcvic]

I began running 5ks recently and the watch consistently reports my distance as 100 - 150 meters short of 5k when I finish. It is also fairly inaccurate in reporting my current pace particularly when I've turned a corner or made any kind of deviation from a straight line really. I've been running long enough at this point to know when I'm running a 9 minute/km pace (yeah, I'm a turtle) but my watch will occasionally say I'm running a 7 minute km.