Marginalized Particle Filters for Nonlinear State-space Models

The recently developed particle filter offers a general numerical tool to approximate the state a posteriori density in nonlinear and non-Gaussian filtering problems with arbitrary accuracy. Because the particle filter is fairly easy to implement and tune, it has quickly become a popular tool in signal processing applications. Its main drawback is that it is quite computer intensive. For a given filtering accuracy, the computational complexity increases quickly with the state dimension. One remedy to this problem is what in statistics is called Rao-Blackwellization, where states appearing linearly in the dynamics are marginalized out. This leads to that a Kalman filter is attached to each particle. Our main contribution here is to sort out when marginalization is possible for state space models, and to point out the implications in some typical signal processing applications. The methodology and impact in practice is illustrated on terrain navigation for aircrafts. The marginalized particle filter for a state-space model with nine states is evaluated on real aircraft data, and the result is that very good accuracy is achieved with quite reasonable complexity