# Bayesian filter for 2-D grid localizaton

I have some data obtained from an experiment in terms of movements and observations with odometry and sensor data. My task is to find the probability mass on each of the grid cells after each set of motion and observation. I'm a bit lost in figuring out how to compute probability mass for each of the grid cell. My odometry information is in terms of rotation, translation and rotation and my sensor information is in terms of range and bearing angle. How do I calculate the probability of robot present in each of the grid cell?

I have the formula for belief after motion as summation(P(x|u, x')xBel(x')) How do I compute the motion model with noise? which is a variant of Markov localization: The Grid Localization algorithm precisely calculates at each time step the probability of each cell to correspond to the actual robot's state. If you only care about estimating the position (x,y), your grid is in 2D. If you also want to estimate the orientation (x,y,theta), your grid is in 3D, and each plane of the grid corresponds to an orientation: