There is no starting location. Let's say that we have:
- a rectangular room of any size,
- assuming that you don't know the original facing direction
- a set of observations with distance to the concrete wall and angles of turning available to you
My job is to then populate possible solutions for the locations. For example, at the example below, the room size 5x7 dekameter(= 10 meters) I chose point (1, 2) with the set of observations as (distance in dekameter, angle in degree) to it as:
I = [(sqrt(5), 0), (1, 60), (6, 150), (4, 240)]
The person diagonally facing the corner A or the origin (0,0) with sqrt(5) meters from it but we don't know that, the person could have been just perpendicularly facing the wall AB with sqrt(5) meter away from it as well.
To understand the observations, the angle means the angle in relation to the first original facing direction, so the second record in I is (1, 60) means that the location is 1 unit of distance from the wall and 60 degrees away from the original facing direction.
How would I go about approaching this problem? Like visually I can see that point (1, 5), (4, 5) and (4, 2) have matching solutions as well but I think there could be more than just those extra 3 but they should be finite in my opinions. Any helps, leads, or advice is definitely appreciated!
I posted the same question at mathoverflow as well because I think this could have been overlapped but if it needs to be taken down in either one I can do that too.