8. Markov Localization Discrete, finite number of possible poses (grid, topological map) p(A) : probability that A is true p(A|B) : probability that A is true knowing B p(A^B)=p(A|B)p(B)
9. Bayes rule p(A|B)=p(B|A)p(A)/p(B) p(loc|sensing)=p(sensing|loc)p(loc)/p(sensing) Example: I believe to be at location X and think that I see a door. What’s the likelihood to be at X? The higher the likelihood to see a door at X, the higher the likelihood that I am at X.
10. Markov Localization But: I know more than that! I have an estimate on how much I moved and where I were Before! 0.33 0.33 0.33 p(l’t-1) ot 0.1 0.7 0.2 (example depends on error-model for ot)
11. Markov Localization Two step process Action update based on proprioception Perception update based on exterioception p(loc|sensing)=p(sensing|loc)p(loc)/p(sensing)
14. Example 2: Grid map 3D (x,y, theta) leads to 3D grid Same approach for updating belief using perception and action
15. Reducing the complexity of Markov Localization Instead of maintaining a high-granularity belief state, perform random sampling. Problem: Completeness “Particle filter”
