Given a map of the environment, the algorithm estimates the position and orientation of a robot as it moves and senses the environment. The algorithm uses a particle filter to represent the distribution of likely states, with each particle representing a possible state, i.e., a hypothesis of where the robot is. The algorithm typically starts with a uniform random distribution of particles over the configuration space, meaning the robot has no information about where it is and assumes it is equally likely to be at any point in space.
Given an environment map, the algorithm estimates the robot's location and orientation as it navigates. It uses a particle filter to model the possible locations of the robot, with each particle representing a potential position. The algorithm begins by assuming equal probability for the robot's location, meaning it has no prior knowledge about its position.