How to match noisy GPS data to a known route?

I have:
∙ A known running route as a sequence of lat/lon coordinates
∙ GPS observations from a runner (noisy, ~5-10m error)
∙ Timestamps for each GPS point
I need to snap each GPS observation to the most likely position on the route, accounting for:
∙ GPS error (observations don’t fall exactly on the route)
∙ Realistic movement constraints (can’t move 100m in 1 second)
∙ Following the route in order
What algorithm should I use for this? And what python libraries might be best suited?