Shape Estimation and Tracking using Spherical Double Fourier Series for Three-Dimensional Range Sensors

In this paper, a novel measurement model based on spherical double Fourier series (DFS) for estimating the 3D shape of a target concurrently with its kinematic state is introduced. Here, the shape is represented as a star-convex radial function, decomposed as spherical DFS. In comparison to ordinary DFS, spherical DFS do not suffer from ambiguities at the poles. Details will be given in the paper. The shape representation is integrated into a Bayesian state estimator framework via a measurement equation. As range sensors only generate measurements from the target side facing the sensor, the shape representation is modified to enable application of shape symmetries during the estimation process. The model is analyzed in simulations and compared to a shape estimation procedure using spherical harmonics. Finally, shape estimation using spherical and ordinary DFS is compared to analyze the effect of the pole problem in extended object tracking (EOT) scenarios.