Methods to Handle Interior and Boundary Measurements for the Gaussian Process Model

In many applications of extended object tracking, 2-dimensional models are used due to the simplicity of the parametrization of the extent compared to a 3-dimensional model. However, many high-resolution sensors today provide a 3D point cloud which represents a challenge for how to relate these measurements with a 2D model. This is particularly relevant when modeling the extent using a parametrization of its contour, as with the random hypersurface model, since the measurements need to be related to the boundary of the object, whereas the measurements may also be generated from the interior of the object. The random hypersurface model uses a scaling factor to account for measurements being generated across the surface defined by the contour. In this article, we use the Gaussian process model and explore different ways to handle interior measurements either by using a boundary model, a surface model, or a combination of the two and we present a study on both simulated and real maritime data of these different approaches. The results show that using the boundary model results in a more precise extent estimate but one which could be underestimated, whereas incorporating the surface model results in a more conservative, overestimated extent. We also show that estimating the scaling factor for the surface model generally results in improved performance.