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I don't really know what's possible, and would like a pointer in the right direction.

I have measurements of time and position which could be anything from a person walking, a vehicle on a road, or in a car park, or a printer in an office. I need to work out journey times for vehicles between two points. It may be they take a meandering route, or even take days to get from A to B. Or they may be a pedestrian, or an emergency service vehicle.

I want the estimated journey time for a normal vehicle along the main route.

The detections are whenever someone is near enough to the detector, which has a particular radius. Sometimes there are very few detections, which probably means the road is empty and journey time would be good, although it could indicate the road is closed, and the journey time would be terrible. Or there could be lots of detections showing traffic not moving, and it could be queueing to turn off the road, but other vehicles are travelling at normal speeds.

The plots look like random noise.

EDIT:

At the moment I am looking at two methods:

  1. Use the interquartile range to discard outliers
  2. Use a Kalman filter.

I think the filter is the wrong way to go as I don't have a model for the journey time other than from moment to moment I don't expect it to change much.

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    $\begingroup$ This looks like a piece of work that requires a methodological paper in Annals of Applied Statistics and a substantive paper in Journal of Transportation Research. You should not expect the community to write both papers for you in neither the answers nor comments, and would rather want to seek the collaboration of a transportation statistician or economist. Or throw this at a grad student in statistics or economics as a dissertation topic. $\endgroup$
    – StasK
    Commented Nov 6, 2012 at 14:52
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    $\begingroup$ @StasK I wasn't expecting the community to write papers for me, I asked for pointers in the right direction. Thank you for letting me know that this is a substantial undertaking, though. $\endgroup$ Commented Nov 7, 2012 at 0:52
  • $\begingroup$ I think it is, that's all I wanted to say. If you have uneven time intervals, you may want to consider using variogram modeling and kriging, which generally are considered to be a spatial statistics tools. $\endgroup$
    – StasK
    Commented Nov 7, 2012 at 18:55
  • $\begingroup$ @StasK I don't think kriging and variograms are what I need. The geometry of the route between two points is relatively unknown, and unimportant in the kind of results we're looking for. We have two points with detections at each point, and a lot of bogus journey detections. We want to filter out the noise and get a good estimate of current and historical road conditions. Many thanks for your interest. $\endgroup$ Commented Nov 19, 2012 at 8:48

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I don't know if can give you an expected answer, but I think some Bayesian approach would be good in this case.

You may want to take a look in particle filters instead of Kalman as I susspect it may be a problem to set up correct model for Kalman filter in this case. If you want to go for Kalman, there are different types of the filter and some of them require good knowledge about error covariance, which may cause troubles, but some can compute it with Mante Carlo. Take a look on unscented Kalman Filter.

You may also like http://www.udacity.com/overview/Course/cs373/CourseRev/apr2012 as it explain some basic about estimation for moving vehicle and google's self-driving car. (and it is in python).

Maybe some more details in your question would be more helpful and you can get more precise answers.

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