On Covariance Matrix Degeneration in Marginalized Particle Filters with Constant Velocity Models

Marginalization enables the particle filter to be ap-plied to high-dimensional problems by invoking the Kalman filter to estimate a larger part of the state vector. The marginalized (a.k.a. Rao-Blackwellized) particle filter (MPF) has found many use cases in tracking and navigation applications. These are characterized by having position and its derivatives as states. Here, we take a closer look at the MPF for the constant velocity motion model, which well represents the basic properties of most motion models used in this context. In particular, how the Kalman filter (KF)-part depends on how the continuous time state noise is sampled in the discrete time model. We find that for many of the most common sampling approaches, the KF -part of the MPF degenerates, meaning that the covariance approaches O. Further, we show that for those same sampling approaches there is no performance increase by switching from a particle filter to an MPF in this situation.