arXiv subjects

Marcus Baum

Publications and source records attributed to Marcus Baum.

13 recordsLinked to original sources

arXiv2025

Decoupled Quadratic Kalman Filter for Elliptical Extended Object Tracking with Log-normal Axis Modeling

Extended object tracking involves estimating both the physical extent and kinematic parameters of a target object, where typically multiple measurements are observed per time step. In this article, we propose a deterministic closed-form elliptical extended object tracker, based on decoupling of the kinematics, orientation, and axis lengths. By disregarding potential correlations between these state components, fewer approximations are required for the individual estimators than for an overall joint solution. This also enables a log-normal representation of the semi-axis lengths, i.e., opposed to related approaches, only positive axis lengths have support. The resulting algorithm outperforms existing algorithms, reaching the accuracy of sampling-based procedures. Additionally, a batch-based variant is introduced, yielding highly efficient computation while outperforming all comparable state-of-the-art algorithms. This is validated both by a simulation study using common models from literature, as well as an extensive quantitative evaluation on real automotive radar data.

eess.SP↗

arXiv2025

Odyssey: An Automotive Lidar-Inertial Odometry Dataset with GNSS-denied situations

The development and evaluation of Lidar-Inertial Odometry (LIO) and Simultaneous Localization and Mapping (SLAM) systems requires a precise ground truth. The Global Navigation Satellite System (GNSS) is often used as a foundation for this, but its signals can be unreliable in obstructed environments due to multi-path effects or loss-of-signal. While existing datasets compensate for sporadic GNSS loss by incorporating Inertial Measurement Unit (IMU) measurements, the commonly used systems do not permit prolonged study of GNSS-denied environments due to accumulated drift. Therefore, the diversity of such datasets is limited. To close this gap, we present Odyssey, an automotive LIO dataset featuring: (1) a ground truth derived from a navigation-grade Ring Laser Gyroscope (RLG)-based RTK/INS, offering bias stability one to four orders of magnitude better than existing automotive datasets; (2) a comprehensive collection of 36 sequences across diverse environments, enabling robust and comprehensive evaluation and (3) prolonged GNSS-denied environments, including tunnels and, previously unseen in the context of automotive benchmarks, indoor parking garages. Here, our RLG-based system enables accurate evaluation in scenarios where commonly employed systems would drift excessively. Besides providing data for LIO, Odyssey also supports place recognition tasks through threefold trajectory repetition and integration of external mapping data via precise geodetic coordinates. All data, dataloader and supplementary material are available online at https://odyssey.uni-goettingen.de/ .

cs.RO↗

arXiv2025

Track-to-Track Association for Collective Perception based on Stochastic Optimization

Collective perception is a key aspect for autonomous driving in smart cities as it aims to combine the local environment models of multiple intelligent vehicles in order to overcome sensor limitations. A crucial part of multi-sensor fusion is track-to-track association. Previous works often suffer from high computational complexity or are based on heuristics. We propose an association algorithms based on stochastic optimization, which leverages a multidimensional likelihood incorporating the number of tracks and their spatial distribution and furthermore computes several association hypotheses. We demonstrate the effectiveness of our approach in Monte Carlo simulations and a realistic collective perception scenario computing high-likelihood associations in ambiguous settings.

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arXiv2025

Online Lidar-Only Odometry with Retrospective Refinement of Overlapping Submaps

Lidar odometry aims to estimate the ego-motion of a mobile platform from a stream of lidar scans. Traditional scan-to-map approaches register each scan against a single, evolving map, which propagates registration errors over time. To mitigate this, we propose a multi-submap approach where the current scan is registered against multiple overlapping submaps instead of a single static map. By optimizing the resulting constraints in a pose graph, our method enables not only precise estimation of the current pose, but also retrospective refinement of the submaps' anchor points, which improves short-term consistency and long-term accuracy. We demonstrate that our approach achieves significant accuracy gains over several state-of-the art lidar odometry methods on a variety of automotive datasets while simultaneously maintaining real-time performance. Ablation studies confirm the critical role of multiple registrations and retrospective refinement of the map as core factors for our accuracy gains. Code and raw results are available on our public GitHub at https://github.com/Fusion-Goettingen/RAL_2026_Kurda_Online.

cs.RO↗

arXiv2021

Continuous Herded Gibbs Sampling

Herding is a technique to sequentially generate deterministic samples from a probability distribution. In this work, we propose a continuous herded Gibbs sampler that combines kernel herding on continuous densities with the Gibbs sampling idea. Our algorithm allows for deterministically sampling from high-dimensional multivariate probability densities, without directly sampling from the joint density. Experiments with Gaussian mixture densities indicate that the L2 error decreases similarly to kernel herding, while the computation time is significantly lower, i.e., linear in the number of dimensions.

stat.ML↗

arXiv2020

Simulation-based Analysis of Multipath Delay Distributions in Urban Canyons

Global navigation satellite systems provide accurate positioning nearly worldwide. However, in the urban canyons of dense cities, buildings block and reflect the signals, causing multipath errors. To mitigate multipath errors, knowledge of the distribution of the reflection delays is important. Measurements of this distribution have been done in several dense cities, but it is unknown how the delay distribution depends on the depth of the urban canyon. To fill this gap, we simulated reflection scenarios in 12 different environments: from suburban to deep urban canyon. Subsequently, we analyzed the resulting delay distributions. This paper presents these distributions, and a method to estimate them using the number of received satellites. According to our simulation, the multipath delays follow gamma distributions, whose shape parameters decrease when the urban canyon depth increases. A quadratic model can estimate the shape parameter using the number of received satellites. Consequently, depending on the number of received satellites, the distribution of the reflection delays can be estimated. This information can be combined with prior knowledge from other methods for improved multipath delay estimation. In the future, for more realistic results, the effects on signals that are reflected multiple times and environments other than urban canyons should be simulated.

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arXiv2019

A Hybrid Approach To Hierarchical Density-based Cluster Selection

HDBSCAN is a density-based clustering algorithm that constructs a cluster hierarchy tree and then uses a specific stability measure to extract flat clusters from the tree. We show how the application of an additional threshold value can result in a combination of DBSCAN* and HDBSCAN clusters, and demonstrate potential benefits of this hybrid approach when clustering data of variable densities. In particular, our approach is useful in scenarios where we require a low minimum cluster size but want to avoid an abundance of micro-clusters in high-density regions. The method can directly be applied to HDBSCAN's tree of cluster candidates and does not require any modifications to the hierarchy itself. It can easily be integrated as an addition to existing HDBSCAN implementations.

cs.DB↗

arXiv2019

Optimal Fusion of Elliptic Extended Target Estimates based on the Wasserstein Distance

This paper considers the fusion of multiple estimates of a spatially extended object, where the object extent is modeled as an ellipse parameterized by the orientation and semiaxes lengths. For this purpose, we propose a novel systematic approach that employs a distance measure for ellipses, i.e., the Gaussian Wasserstein distance, as a cost function. We derive an explicit approximate expression for the Minimum Mean Gaussian Wasserstein distance (MMGW) estimate. Based on the concept of a MMGW estimator, we develop efficient methods for the fusion of extended target estimates. The proposed fusion methods are evaluated in a simulated experiment and the benefits of the novel methods are discussed.

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arXiv2018

Tracking the Orientation and Axes Lengths of an Elliptical Extended Object

Extended object tracking considers the simultaneous estimation of the kinematic state and the shape parameters of a moving object based on a varying number of noisy detections. A main challenge in extended object tracking is the nonlinearity and high-dimensionality of the estimation problem. This work presents compact closed-form expressions for a recursive Kalman filter that explicitly estimates the orientation and axes lengths of an extended object based on detections that are scattered over the object surface (according to a Gaussian distribution). Existing approaches are either based on Monte Carlo approximations or do not allow for explicitly maintaining all ellipse parameters. The performance of the novel approach is demonstrated with respect to the state-of-the-art by means of simulations.

eess.SY↗

arXiv2016

Second-Order Extended Kalman Filter for Extended Object and Group Tracking

In this paper, we propose a novel method for estimating an elliptic shape approximation of a moving extended object that gives rise to multiple scattered measurements per frame. For this purpose, we parameterize the elliptic shape with its orientation and the lengths of the semi-axes. We relate an individual measurement with the ellipse parameters by means of a multiplicative noise model and derive a second-order extended Kalman filter for a closed-form recursive measurement update. The benefits of the new method are discussed by means of Monte Carlo simulations for both static and dynamic scenarios.

eess.SY↗

arXiv2016

Extended Object Tracking: Introduction, Overview and Applications

This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.

cs.CV↗

arXiv2013

Extended Object Tracking with Random Hypersurface Models

The Random Hypersurface Model (RHM) is introduced that allows for estimating a shape approximation of an extended object in addition to its kinematic state. An RHM represents the spatial extent by means of randomly scaled versions of the shape boundary. In doing so, the shape parameters and the measurements are related via a measurement equation that serves as the basis for a Gaussian state estimator. Specific estimators are derived for elliptic and star-convex shapes.

eess.SY↗

arXiv2012

The Kernel-SME Filter for Multiple Target Tracking

We present a novel method called Kernel-SME filter for tracking multiple targets when the association of the measurements to the targets is unknown. The method is a further development of the Symmetric Measurement Equation (SME) filter, which removes the data association uncertainty of the original measurement equation with the help of a symmetric transformation. The underlying idea of the Kernel-SME filter is to construct a symmetric transformation by means of mapping the measurements to a Gaussian mixture. This transformation is scalable to a large number of targets and allows for deriving a Gaussian state estimator that has a cubic time complexity in the number of targets.

eess.SY↗