You can achieve more accuracy with a combination of the following strategies.
As mentioned in other Answers, you can store the position of the mobile
every X seconds(say 10 seconds) using GPS and measure the
consecutive time between the points.
Also when the user makes quick turns, make sure to read that by
using Magnetic Sensor values too, so in such event, decrease the
"timing between position storing" to say 1-2 seconds(Will be needed for accuracy)
As a final step, use Map data(such as Google Maps etc.) to make sure
you are being tracked properly(if on road).
And then sum up all the values to get the accurate distance.
P.S. I gave information about the strategies alone since I'm not sure about its implementation in Android(or iOS).
Hope this helps :)
