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.
