filter a sequence of coordinates
This raises many questions that you may or may not be able to answer, and this may not be helpful but hopefully it is.

Regarding the data, what are it's origins?  Is it all electronically collected or is it an amalgamation of, say delivery driver logs that could be easily falsified or recorded incorrectly? Asked another way, how do you know that the order, based on timestamps, is not correct?  

On the other hand, if you know the relationship between the points on the route, why bother with the timestamp values?  From your comments, it seems as though the participant traveled in a straight line.  If that is the case, you know the order based on the coordinates. You could order them by distance from the mean of the coordinates.

Since there is some disagreement between the "known" route and the "recorded" route I think to resolve the data you need to understand what causes this disagreement?  Is the timestamp produced by one device or multiple?  If one device, maybe someone is not driving the advertised route.  If multiple devices, maybe one is set to the wrong timezone or just has the wrong time.

Again, not really an answer, but hopefully helpful.