This question is a simplified version of the positioning problem in Robocup 2D (https://en.wikipedia.org/wiki/RoboCup_2D_Soccer_Simulation_League).
The goal is to determine the own position and body angle of an agent on a two dimensional playing field out of some noisy information pieces. While in the game, the task is to compute this very fast, in this question I don't care for the fast calculation, but for the most accurate way to calculate it.
Given:
- the correct 2D positions (x,y) of some fixed objects
- the distance and angle (relative to the body direction) to three of those fixed objects. Both, the distance and and angle are given within an error margin, so the distance could be 21m +/- 0.5m and the angle could be 5.7 degrees +/- 0.2 degrees. Within those margins, all distances and angles are equally distributed (they were calculated after rounding / cutting off digits after some other calculations)
- the distance and angle to the agents old position, also within error margins
How can I combine those pieces of information to get my most probable position, or even better a distribution over the position space?