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.
A method of solution is perfect if we can forsee from the start,
and even prove, that following that method we shall attain our aim.