One problem with using GPS coordinates is that they (obviously) are not accurate. If you are travelling in a straight line, the GPS coordinates might show you travelling on a zig-zag path, hence returning a greater distance travelled than the true distance. Even with good GPS accuracy this error can be significant. Using less coordinates could result in a more accurate calculation, or not.
What you need is a way to smooth the GPS path plotted, with due consideration to your required accuracy (again a trade-off).
My first thought is to break the points into groups, and fit line segments to each group (look up "linear regression"). Then find where each consecutive line-pair overlap to define each line segment. Then simply sum the line segment lengths.
You could curve-fit segments, but that's much more intense mathematically, and might not yield a better result (and which curve formula to use?). There may be better mathematical ways I'm not aware of.
Hope this helps.
