A New Formulation of the Rao-Blackwellized Particle Filter

For performance gain and efficiency it is important to utilize model structure in particle filtering. Applying Bayes' rule, present linear Gaussian substructure can be efficiently handled by a bank of Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF), by some authors denoted the marginalized particle filter (MPF), and usually presented in a way that makes it hard to implement in an object oriented fashion. This paper discusses how the solution can be rewritten in order to increase the understanding as well as simplify the implementation and reuse of standard filtering components, such as Kalman filter banks and particle filters. Calculations show that the new algorithm is equivalent to the classical formulation, and the new algorithm is exemplified in a target tracking simulation study.