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Imagine that I have collected a large set of GPS tracks of objects moving from A to B, and for the sake of simplicity assume they avoid obstacles in a consistent way, so that their path is just "noisy", but not very different.

Are there any algorithms that average those paths to a path that is "representative" of the path all users took?

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though technically not an average, a douglas reduction might work for what you need, getting rid of all the points that are inside a given "cross track" error.

it's a widespread algorithm, so every language or GIS software has an implementation.

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