Update Equations (9) and (16) form the core of the Markov localization algorithm. The full algorithm is shown in Table 1. Following [Basye et al. 1992] and [Russell & Norvig1995], we denote as the robot's motion model, since it models how motion effect the robot's position. The conditional probability is called perceptual model, because it models the outcome of the robot's sensors.
In the Markov localization algorithm , which initializes the belief , reflects the prior knowledge about the starting position of the robot. This distribution can be initialized arbitrarily, but in practice two cases prevail: If the position of the robot relative to its map is entirely unknown, is usually uniformly distributed. If the initial position of the robot is approximately known, then is typically a narrow Gaussian distribution centered at the robot's position.