A Closed-Form Likelihood for Particle Filters to Track Extended Objects with Star-Convex RHMs

Modeling 2D extended targets with star-convex Random Hypersurface Models (RHMs) allows for
accurate object pose and shape estimation. A star-convex RHM models the shape of an object with the aid of
a radial function that describes the distance from the object center to any point on its boundary. However,
up to now only linear estimators, i.e., Kalman Filters, are used due to the lack of a explicit likelihood function.
In this paper, we propose a closed-form and easy to implement likelihood function for tracking extended targets
with star-convex RHMs. This makes it possible to apply nonlinear estimators such as Particle Filters to estimate
a detailed shape of a target. We compared the proposed likelihood against the usual Kalman filter approaches
with tracking pose and shape of an airplane in 2D. The evaluations showed that the combination of the
Progressive Gaussian Filter (PGF) and the new likelihood function delivers the best estimation performance
and can outperform the usually employed Kalman Filters.