                    Title    Particle Filter Tracking a Biker in a City   Author    Jonas Sjöberg
 Organization: Chalmers University of Technology   Revision date    2008-08-14   Description    This demonstration illustrates the use of a particle filter for tracking a biker using only noise measurements of the position.

Briefly, a particle filter is a probabilistic filter where the probability density is represented by a number of samples, i.e., the particles. This makes it possible to handle problems where no standard distribution (typically a Gaussian) describes the distributions well. An example is when you have two branches in a tracking and both branches are probable, but the probability is zero between the branches. Each particle in the particle filter corresponds to on realization of the possible outcome, and it is the weightening of all particles which makes up the estimate. Measurements are used to indicate the probability of each individual particle.

The underlying model used in this example is a constant velocity model, i.e., the biker is assumed to move in a straight line. The velocity and direction are changed by the process noise which is added to each particle at each sampling time. In this way the particles spread with time, and they spread faster if you set the process noise higher.

The filter also makes use of the map of the city, and particles which are not longer on the road are given the probability zero and they are not longer contributing to the estimate. Sometimes the filter performs a re-sampling of the particles (you can influence this with the parameter "re-sampling", 1 corresponds to a re-sampling each sampling instant). At the re-sampling all the particles with zero probability are removed and replaced by new one at the more probable places. If you set "re-sampling" slightly smaller than 1 you should be able to see when a res-sampling takes place, and the spread of the new particles after a re-sampling.

If you play around with the filter you should be able to see that most of the information about the true position is given in connection to that the biker makes turns in crossings. Hence, if you generate trajectories with many turns,the filter should be able to obtain better estimates.

More about particle filters can be found, e.g., in Branko, R., Arulampalam, S., Gordon, N., (2004). "Beyond the Kalman Filter" Artech House, Boston, Mass; London.   Subjects     Mathematics > Probability and Statistics Science > Physics > Nuclear and Particle Physics   Keywords    particle filter, constant velocity model, Jonas Sjöberg, probability, noise measurements, physics, fun   Downloads     Particle Filter Tracking a Biker in a City.nb (30.5 KB) - Mathematica Notebook [for Mathematica 6.0]       