Distribution in a particle filter

Particle filters are the state-of-the-art solution to difficult tracking problems. The crucial step in the efficient application of particle filters to specific problems is the design of the proposal distribution. This proposal distribution defines how the particles are propagated from one time step to the next. If the proposal is not well designed, then one typically needs a huge number of particles to achieve good performance. The paper focuses on the design of a proposal distribution that is well suited to the specific problem being considered; the work is motivated by the need to use particle filters to track using multiple radars observing multiple closely spaced targets at high range. The targets can be resolved in radar co-ordinates, but not easily tracked in Cartesian co-ordinates. In the general case, it often happens that the proposal needs to interpolate between both the information derived using the dynamic model for the target behaviour and the information inherent in the measurement. Schemes to conduct this interpolation are often based on extended or unscented Kalman filters. When using such filters in non-linear environments, such as when tracking using radars, a pertinent choice of co-ordinate frame can improve performance. Based on this idea, a proposal distribution is described that uses an extended Kalman filter in radar co-ordinates. This results in a skewed proposal in Cartesian co-ordinates that, in this specific problem, improves on the performance possible using a particle filter with other choices of proposal distribution.