# 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.

• Kalman filter might be what you are looking for. – bugmenot123 Feb 20 '16 at 20:41
• So is your data like this: you have a friction map that tells you how fast the man can traverse any particular location. And you have a function of time that tells you essentially how efficient his movement is, e.g., 0 for sleeping and 1 for good weather? And the spatial and temporal data are independent? – user55937 Feb 20 '16 at 21:04
• I think cost surface analysis might work for you, but stop and restart the cost surface growth every time the speed changes. – user55937 Feb 20 '16 at 21:14
• This is a cool problem. I've been thinking about it for a few hours and I think cost surfaces could be used. Are you using a particular software? I think I could give you some grass or qgis example workflows (even matlab maybe) to illustrate what I mean, but it wouldn't be useful if you're using something else. @bugmenot123 How were you thinking you would apply a Kalman filter? I'm not well-versed in Kalman filters but I'm interested. – user55937 Feb 21 '16 at 3:02
• @bugmenot123 Thanks a lot! I've looked up the Kalman filters and still can not figure it out how to use them, could you please give a hint for it? – Aleksandr Shumilov Feb 21 '16 at 5:16

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.