In extended object tracking, basic parametric shapes such as ellipses and rectangles or non-parametric shape representations such as Fourier series or Gaussian processes can be utilized as shape priors. However, flexible non-parametric shape representations can be disproportionately detailed and computationally intensive for many applications. Therefore, we propose to adopt deformable superellipses for a low-dimensional and flexible representation of basic parametric shapes in this paper. We present a measurement model in 2D space that can cope with boundary and interior measurements simultaneously by recursively estimating an artificial noise variance for interior measurements. We investigate and compare the model in a simulated and real-world maritime scenario with the result that the combination of deformable superellipses and artificial measurement noise estimation performs better than state-of-the-art methods.

In extended object tracking, random matrices are commonly used to filter the mean and covariance matrix from measurement data. However, the relation from mean and covariance matrix to the extension parameters can become challenging when a lidar sensor is used. To address this, we propose virtual measurement models to estimate those parameters iteratively by adapting them, until the statistical moments of the measurements they would cause, match the random matrix result. While previous work has focused on 2D shapes, this paper extends the methodology to encompass 3D shapes such as cones, ellipsoids and rectangular cuboids. Additionally, we introduce a classification method based on Chamfer distances for identifying the best-fitting shape when the object’s shape is unknown. Our approach is evaluated through simulation studies and with real lidar data from maritime scenarios. The results indicate that a cone is the best representation for sailing boats, while ellipsoids are optimal for motorboats.

In the past years, algorithms for 3D shape tracking using radial functions in spherical coordinates represented with different methods have been proposed. However, we have seen that mainly measurements from the lateral surface of the target can be expected in a lot of dynamic scenarios and only few measurements from the top and bottom parts leading to an error-prone shape estimate in the top and bottom regions when using a representation in spherical coordinates. We, therefore, propose to represent the shape of the target using a radial function in cylindrical coordinates, as these only represent regions of the lateral surface, and no information from the top or bottom parts is needed. In this paper, we use a Fourier-Chebyshev double series for 3D shape representation since a mixture of Fourier and Chebyshev series is a suitable basis for expanding a radial function in cylindrical coordinates. We investigate the method in a simulated and real-world maritime scenario with a CAD model of the target boat as a reference. We have found that shape representation in cylindrical coordinates has decisive advantages compared to a shape representation in spherical coordinates and should preferably be used if no prior knowledge of the measurement distribution on the surface of the target is available.

Modeling a suitable birth density is a challenge when using Bernoulli filters such as the Labeled Multi-Bernoulli (LMB) filter. The birth density of newborn targets is unknown in most applications, but must be given as a prior to the filter. Usually the birth density stays unchanged or is designed based on the measurements from previous time steps. In this paper, we assume that the true initial state of new objects is normally distributed. The expected value and covariance of the underlying density are unknown parameters. Using the estimated multi-object state of the LMB and the Rauch-Tung-Striebel (RTS) recursion, these parameters are recursively estimated and adapted after a target is detected. The main contribution of this paper is an algorithm to estimate the parameters of the birth density and its integration into the LMB framework. Monte Carlo simulations are used to evaluate the detection driven adaptive birth density in two scenarios. The approach can also be applied to filters that are able to estimate trajectories.