Parametric Representation of the Environment of a Mobile Robot for Measurement Update in a Particle Filter

A mobile robot must know its position and heading, all the time during navigation. This is called localization. Recently particle filters [1] have become extremely popular for position estimation. These are simple to program, can process raw sensor data and can handle any probability distributions. A good tutorial on particle filters is [2]. Particle filters update the pose of the robot by using a motion model and a measurement model alternatively and recursively. The motion model predicts a few possible positions of the robot (also called particles) based on onboard sensors when a control action is taken and assigns weight to each of these poses. The measurement model describes the relationship between sensor measurements and the physical world and is used to update the weights of particles. This measurement model is usually represented as a conditional probability or likelihood. The two important issues in using a distribution for measurement update are making use of maximum information available and the computational efficiency. The particle filters require a large number of particles in order to accurately estimate the state. This negates their advantage in real-time applications. Further discussion on computational complexity can be found in [3]. The likelihood updates are the major cause of computational inefficiency.