Possible point location algorithm

I need to calculate possible point location based on its speed and some other factors. For example, there is a man in the middle of the forest and I need to calculate his possible location at some time periods. There are few facts about his movement:

1. His speed differs at certain periods of time - it can be raining, or it can be super hot - speed lowers / increases;


2. Some objects in space - swamps, rocks - can lower his speed as well;


3. At some time periods the man does not move at all.

So, here is the question - is there any algorithm that can calculate possible location of the man based on following parameters? The output should be a polygon for every given time_period.

{
  time_periods: [{
    from: 2012-12-12T20:00:00,
    to: 2012-12-12T22:00:00,

    speed: 5
  }, {}],
  objects: [{
    geodata: POLYGON(...),
    speed_modifier: 0.5
  }, {}]
}

Generated polygons will be visualized on the map afterwards.

Answer

I’ve taken land use layer (included hiking tracks and roads) and reclassified it into speed pattern:

the outcome for “possible” locations /no breaks for sleep, fine weather conditions/ looked like this:

However, when I considered true topography of the area:

And applied hiking function , the pattern of possible locations has become profoundly different:

My point here that topography is a major factor for hikers, thus it has to be taken into account before dealing with weather and darkness.

I used vector approach, i.e. directed graphs, because it was much easier to implement hiking function.

Note: the terrain in above example is extremely rugged, changes will be less dramatic for flat country. Of course this is the situation for very experienced traveller, who knows where the tracks are. Most of the time person can be found somewhere inside isochrones, unless swept by river.