Michael Botsch

Lakshman Balasubramanian, Jonas Wurst, Robin Egolf et al.

Representation learning in recent years has been addressed with self-supervised learning methods. The input data is augmented into two distorted views and an encoder learns the representations that are invariant to distortions -- cross-view prediction. Augmentation is one of the key components in cross-view self-supervised learning frameworks to learn visual representations. This paper presents ExAgt, a novel method to include expert knowledge for augmenting traffic scenarios, to improve the learnt representations without any human annotation. The expert-guided augmentations are generated in an automated fashion based on the infrastructure, the interactions between the EGO and the traffic participants and an ideal sensor model. The ExAgt method is applied in two state-of-the-art cross-view prediction methods and the representations learnt are tested in downstream tasks like classification and clustering. Results show that the ExAgt method improves representation learning compared to using only standard augmentations and it provides a better representation space stability. The code is available at https://github.com/lab176344/ExAgt.

Jonas Wurst, Lakshman Balasubramanian, Michael Botsch et al.

Clustering traffic scenarios and detecting novel scenario types are required for scenario-based testing of autonomous vehicles. These tasks benefit from either good similarity measures or good representations for the traffic scenarios. In this work, an expert-knowledge aided representation learning for traffic scenarios is presented. The latent space so formed is used for successful clustering and novel scenario type detection. Expert-knowledge is used to define objectives that the latent representations of traffic scenarios shall fulfill. It is presented, how the network architecture and loss is designed from these objectives, thereby incorporating expert-knowledge. An automatic mining strategy for traffic scenarios is presented, such that no manual labeling is required. Results show the performance advantage compared to baseline methods. Additionally, extensive analysis of the latent space is performed.

Marion Neumeier, Andreas Tollkühn, Sebastian Dorn et al.

This work provides a comprehensive derivation of the parameter gradients for GATv2 [4], a widely used implementation of Graph Attention Networks (GATs). GATs have proven to be powerful frameworks for processing graph-structured data and, hence, have been used in a range of applications. However, the achieved performance by these attempts has been found to be inconsistent across different datasets and the reasons for this remains an open research question. As the gradient flow provides valuable insights into the training dynamics of statistically learning models, this work obtains the gradients for the trainable model parameters of GATv2. The gradient derivations supplement the efforts of [2], where potential pitfalls of GATv2 are investigated.

Niklas Roßberg, Sinan Hasirlioglu, Mohamed Essayed Bouzouraa et al.

Approval of ADS depends on evaluating its behavior within representative real-world traffic scenarios. A common way to obtain such scenarios is to extract them from real-world data recordings. These can then be grouped and serve as basis on which the ADS is subsequently tested. This poses two central challenges: how scenarios are extracted and how they are grouped. Existing extraction methods rely on heterogeneous definitions, hindering scenario comparability. For the grouping of scenarios, rule-based or ML-based methods can be utilized. However, while modern ML-based approaches can handle the complexity of traffic scenarios, unlike rule-based approaches, they lack interpretability and may not align with domain-knowledge. This work contributes to a standardized scenario extraction based on the Scenario-as-Specification concept, as well as a domain-knowledge-guided scenario clustering process. Experiments on the highD dataset demonstrate that scenarios can be extracted reliably and that domain-knowledge can be effectively integrated into the clustering process. As a result, the proposed methodology supports a more standardized process for deriving scenario categories from highway data recordings and thus enables a more efficient validation process of automated vehicles.

Parthasarathy Nadarajan, Michael Botsch, Sebastian Sardina

In this paper, a probabilistic space-time representation of complex traffic scenarios is predicted using machine learning algorithms. Such a representation is significant for all active vehicle safety applications especially when performing dynamic maneuvers in a complex traffic scenario. As a first step, a hierarchical situation classifier is used to distinguish the different types of traffic scenarios. This classifier is responsible for identifying the type of the road infrastructure and the safety-relevant traffic participants of the driving environment. With each class representing similar traffic scenarios, a set of Random Forests (RFs) is individually trained to predict the probabilistic space-time representation, which depicts the future behavior of traffic participants. This representation is termed as a Predicted-Occupancy Grid (POG). The input to the RFs is an Augmented Occupancy Grid (AOG). In order to increase the learning accuracy of the RFs and to perform better predictions, the AOG is reduced to low-dimensional features using a Stacked Denoising Autoencoder (SDA). The excellent performance of the proposed machine learning approach consisting of SDAs and RFs is demonstrated in simulations and in experiments with real vehicles. An application of POGs to estimate the criticality of traffic scenarios and to determine safe trajectories is also presented.

Marion Neumeier, Sebastian Dorn, Michael Botsch et al.

This work provides a comprehensive analysis and interpretation of the graph spectral representation of traffic scenarios. Based on a spatio-temporal vehicle interaction graph, an observed traffic scenario can be transformed into the graph spectral domain by means of the multidimensional Graph Fourier Transformation. Since these spectral scenario representations have shown to successfully incorporate the complex and interactive nature of traffic scenarios, the beneficial feature representation is employed for the purpose of predicting vehicle trajectories. This work introduces GFTNNv2, a deep learning network predicting vehicle trajectories in the graph spectral domain. Evaluation of the GFTNNv2 on the publicly available datasets highD and NGSIM shows a performance gain of up to 25% in comparison to state-of-the-art prediction approaches.

Marion Neumeier, Niklas Roßberg, Michael Botsch et al.

Accurate and uncertainty-aware trajectory prediction remains a core challenge for autonomous driving, driven by complex multi-agent interactions, diverse scene contexts and the inherently stochastic nature of future motion. Diffusion-based generative models have recently shown strong potential for capturing multimodal futures, yet existing approaches such as cVMD suffer from slow sampling, limited exploitation of generative diversity and brittle scenario encodings. This work introduces cVMDx, an enhanced diffusion-based trajectory prediction framework that improves efficiency, robustness and multimodal predictive capability. Through DDIM sampling, cVMDx achieves up to a 100x reduction in inference time, enabling practical multi-sample generation for uncertainty estimation. A fitted Gaussian Mixture Model further provides tractable multimodal predictions from the generated trajectories. In addition, a CVQ-VAE variant is evaluated for scenario encoding. Experiments on the publicly available highD dataset show that cVMDx achieves higher accuracy and significantly improved efficiency over cVMD, enabling fully stochastic, multimodal trajectory prediction.

Alexander Fertig, Karthikeyan Chandra Sekaran, Lakshman Balasubramanian et al.

As autonomous vehicles are rolled out, measures must be taken to ensure their safe operation. In order to supervise a system that is already in operation, monitoring frameworks are frequently employed. These run continuously online in the background, supervising the system status and recording anomalies. This work proposes an online monitoring framework to detect anomalies in object state representations. Thereby, a key challenge is creating a framework for anomaly detection without anomaly labels, which are usually unavailable for unknown anomalies. To address this issue, this work applies a self-supervised embedding method to translate object data into a latent representation space. For this, a JEPA-based self-supervised prediction task is constructed, allowing training without anomaly labels and the creation of rich object embeddings. The resulting expressive JEPA embeddings serve as input for established anomaly detection methods, in order to identify anomalies within object state representations. This framework is particularly useful for applications in real-world environments, where new or unknown anomalies may occur during operation for which there are no labels available. Experiments performed on the publicly available, real-world nuScenes dataset illustrate the framework's capabilities.

Abinav Kalyanasundaram, Karthikeyan Chandra Sekaran, Wolfgang Utschick et al.

Accurate and robust localization is essential for autonomous mobility systems in real-world environments. While fusing Inertial Measurement Unit (IMU) data with satellite-based correction signals provides precise vehicle pose estimates, performance degrades substantially during outages. Recent studies indicate that Machine Learning (ML) can improve IMU-based proprioceptive localization, highlighting untapped potential for onboard sensors readily available in production vehicles. This paper introduces Physics-Regularized Machine Learning for Localization (PRML2), a hybrid framework that combines the complementary strengths of Kalman filtering and data-driven learning to estimate vehicle pose directly from onboard sensors. A key aspect of PRML2 is its physics-regularized learning, enabled by end-to-end training of an ML model through a differentiable Kalman filter. This improves consistency with vehicle motion models, thereby enhancing both localization accuracy and generalization across driving conditions. We evaluate the performance limits of ML-enhanced onboard odometry on a publicly available dataset and show that PRML2 achieves superior localization accuracy and demonstrates real-time capability. This work also introduces a novel dataset to support vehicle localization research under low-friction conditions. The proposed framework provides a robust and cost-effective solution for vehicle localization under degraded sensing conditions by integrating learning with physics-based priors.

Abinav Kalyanasundaram, Karthikeyan Chandra Sekaran, Wolfgang Utschick et al.

Reliable localization in GNSS-denied environments remains a fundamental challenge for intelligent vehicles, as inertial navigation systems accumulate unbounded drift without external correction. Existing approaches provide drift correction through dedicated infrastructure, expensive external sensors, or complex multi-sensor fusion, each introducing practical deployment barriers. We propose Evidential Velocity Correction using Mamba (EVC-Mamba), a learning-based architecture that transforms onboard vehicle sensor data into a virtual velocity sensor for IMU drift correction without additional hardware. A Mamba-based selective state space model captures the temporal dynamics of vehicle motion, while evidential deep learning with a Normal-Inverse-Gamma distribution provides principled uncertainty quantification. The resulting uncertainty-aware velocity estimate is incorporated as a virtual correction measurement into an Error-State Extended Kalman Filter to reduce position drift. Evaluation on real-world vehicle data demonstrates that inertial navigation using the proposed velocity correction achieves localization accuracy within 10% of a dedicated external velocity sensor across different outage durations. The proposed architecture supports real-time onboard deployment at 40 Hz on edge hardware, enabling reliable localization during prolonged GNSS outages.

Marion Neumeier, Sebastian Dorn, Michael Botsch et al.

This work introduces the conditioned Vehicle Motion Diffusion (cVMD) model, a novel network architecture for highway trajectory prediction using diffusion models. The proposed model ensures the drivability of the predicted trajectory by integrating non-holonomic motion constraints and physical constraints into the generative prediction module. Central to the architecture of cVMD is its capacity to perform uncertainty quantification, a feature that is crucial in safety-critical applications. By integrating the quantified uncertainty into the prediction process, the cVMD's trajectory prediction performance is improved considerably. The model's performance was evaluated using the publicly available highD dataset. Experiments show that the proposed architecture achieves competitive trajectory prediction accuracy compared to state-of-the-art models, while providing guaranteed drivable trajectories and uncertainty quantification.

Alexander Fertig, Lakshman Balasubramanian, Michael Botsch

Trajectory prediction is crucial to advance autonomous driving, improving safety, and efficiency. Although end-to-end models based on deep learning have great potential, they often do not consider vehicle dynamic limitations, leading to unrealistic predictions. To address this problem, this work introduces a novel hybrid model that combines deep learning with a kinematic motion model. It is able to predict object attributes such as acceleration and yaw rate and generate trajectories based on them. A key contribution is the incorporation of expert knowledge into the learning objective of the deep learning model. This results in the constraint of the available action space, thus enabling the prediction of physically feasible object attributes and trajectories, thereby increasing safety and robustness. The proposed hybrid model facilitates enhanced interpretability, thereby reinforcing the trustworthiness of deep learning methods and promoting the development of safe planning solutions. Experiments conducted on the publicly available real-world Argoverse dataset demonstrate realistic driving behaviour, with benchmark comparisons and ablation studies showing promising results.

Niklas Roßberg, Marion Neumeier, Sinan Hasirlioglu et al.

The ability to operate safely in increasingly complex traffic scenarios is a fundamental requirement for Automated Driving Systems (ADS). Ensuring the safe release of ADS functions necessitates a precise understanding of the occurring traffic scenarios. To support this objective, this work introduces a pipeline for traffic scenario clustering and the analysis of scenario category completeness. The Clustering Vector Quantized - Variational Autoencoder (CVQ-VAE) is employed for the clustering of highway traffic scenarios and utilized to create various catalogs with differing numbers of traffic scenario categories. Subsequently, the impact of the number of categories on the completeness considerations of the traffic scenario categories is analyzed. The results show an outperforming clustering performance compared to previous work. The trade-off between cluster quality and the amount of required data to maintain completeness is discussed based on the publicly available highD dataset.

Abinav Kalyanasundaram, Karthikeyan Chandra Sekaran, Philipp Stauber et al.

Precise vehicle state estimation is crucial for safe and reliable autonomous driving. The number of measurable states and their precision offered by the onboard vehicle sensor system are often constrained by cost. For instance, measuring critical quantities such as the Vehicle Sideslip Angle (VSA) poses significant commercial challenges using current optical sensors. This paper addresses these limitations by focusing on the development of high-performance virtual sensors to enhance vehicle state estimation for active safety. The proposed Uncertainty-Aware Hybrid Learning (UAHL) architecture integrates a machine learning model with vehicle motion models to estimate VSA directly from onboard sensor data. A key aspect of the UAHL architecture is its focus on uncertainty quantification for individual model estimates and hybrid fusion. These mechanisms enable the dynamic weighting of uncertainty-aware predictions from machine learning and vehicle motion models to produce accurate and reliable hybrid VSA estimates. This work also presents a novel dataset named Real-world Vehicle State Estimation Dataset (ReV-StED), comprising synchronized measurements from advanced vehicle dynamic sensors. The experimental results demonstrate the superior performance of the proposed method for VSA estimation, highlighting UAHL as a promising architecture for advancing virtual sensors and enhancing active safety in autonomous vehicles.

Marion Neumeier, Andreas Tollkühn, Sebastian Dorn et al.

For automotive applications, the Graph Attention Network (GAT) is a prominently used architecture to include relational information of a traffic scenario during feature embedding. As shown in this work, however, one of the most popular GAT realizations, namely GATv2, has potential pitfalls that hinder an optimal parameter learning. Especially for small and sparse graph structures a proper optimization is problematic. To surpass limitations, this work proposes architectural modifications of GATv2. In controlled experiments, it is shown that the proposed model adaptions improve prediction performance in a node-level regression task and make it more robust to parameter initialization. This work aims for a better understanding of the attention mechanism and analyzes its interpretability of identifying causal importance.

Marion Neumeier, Andreas Tollkühn, Michael Botsch et al.

This work introduces the multidimensional Graph Fourier Transformation Neural Network (GFTNN) for long-term trajectory predictions on highways. Similar to Graph Neural Networks (GNNs), the GFTNN is a novel network architecture that operates on graph structures. While several GNNs lack discriminative power due to suboptimal aggregation schemes, the proposed model aggregates scenario properties through a powerful operation: the multidimensional Graph Fourier Transformation (GFT). The spatio-temporal vehicle interaction graph of a scenario is converted into a spectral scenario representation using the GFT. This beneficial representation is input to the prediction framework composed of a neural network and a descriptive decoder. Even though the proposed GFTNN does not include any recurrent element, it outperforms state-of-the-art models in the task of highway trajectory prediction. For experiments and evaluation, the publicly available datasets highD and NGSIM are used

Lakshman Balasubramanian, Jonas Wurst, Michael Botsch et al.

Traffic scenario categorisation is an essential component of automated driving, for e.\,g., in motion planning algorithms and their validation. Finding new relevant scenarios without handcrafted steps reduce the required resources for the development of autonomous driving dramatically. In this work, a method is proposed to address this challenge by introducing a clustering technique based on a novel data-adaptive similarity measure, called Random Forest Activation Pattern (RFAP) similarity. The RFAP similarity is generated using a tree encoding scheme in a Random Forest algorithm. The clustering method proposed in this work takes into account that there are labelled scenarios available and the information from the labelled scenarios can help to guide the clustering of unlabelled scenarios. It consists of three steps. First, a self-supervised Convolutional Neural Network~(CNN) is trained on all available traffic scenarios using a defined self-supervised objective. Second, the CNN is fine-tuned for classification of the labelled scenarios. Third, using the labelled and unlabelled scenarios an iterative optimisation procedure is performed for clustering. In the third step at each epoch of the iterative optimisation, the CNN is used as a feature generator for an unsupervised Random Forest. The trained forest, in turn, provides the RFAP similarity to adapt iteratively the feature generation process implemented by the CNN. Extensive experiments and ablation studies have been done on the highD dataset. The proposed method shows superior performance compared to baseline clustering techniques.

Lakshman Balasubramanian, Friedrich Kruber, Michael Botsch et al.

An understanding and classification of driving scenarios are important for testing and development of autonomous driving functionalities. Machine learning models are useful for scenario classification but most of them assume that data received during the testing are from one of the classes used in the training. This assumption is not true always because of the open environment where vehicles operate. This is addressed by a new machine learning paradigm called open-set recognition. Open-set recognition is the problem of assigning test samples to one of the classes used in training or to an unknown class. This work proposes a combination of Convolutional Neural Networks (CNN) and Random Forest (RF) for open set recognition of traffic scenarios. CNNs are used for the feature generation and the RF algorithm along with extreme value theory for the detection of known and unknown classes. The proposed solution is featured by exploring the vote patterns of trees in RF instead of just majority voting. By inheriting the ensemble nature of RF, the vote pattern of all trees combined with extreme value theory is shown to be well suited for detecting unknown classes. The proposed method has been tested on the highD and OpenTraffic datasets and has demonstrated superior performance in various aspects compared to existing solutions.

Marion Neumeier, Andreas Tollkühn, Thomas Berberich et al.

This paper introduces the Descriptive Variational Autoencoder (DVAE), an unsupervised and end-to-end trainable neural network for predicting vehicle trajectories that provides partial interpretability. The novel approach is based on the architecture and objective of common variational autoencoders. By introducing expert knowledge within the decoder part of the autoencoder, the encoder learns to extract latent parameters that provide a graspable meaning in human terms. Such an interpretable latent space enables the validation by expert defined rule sets. The evaluation of the DVAE is performed using the publicly available highD dataset for highway traffic scenarios. In comparison to a conventional variational autoencoder with equivalent complexity, the proposed model provides a similar prediction accuracy but with the great advantage of having an interpretable latent space. For crucial decision making and assessing trustworthiness of a prediction this property is highly desirable.

Jonas Wurst, Alberto Flores Fernández, Michael Botsch et al.

A novel unsupervised outlier score, which can be embedded into graph based dimensionality reduction techniques, is presented in this work. The score uses the directed nearest neighbor graphs of those techniques. Hence, the same measure of similarity that is used to project the data into lower dimensions, is also utilized to determine the outlier score. The outlier score is realized through a weighted normalized entropy of the similarities. This score is applied to road infrastructure images. The aim is to identify newly observed infrastructures given a pre-collected base dataset. Detecting unknown scenarios is a key for accelerated validation of autonomous vehicles. The results show the high potential of the proposed technique. To validate the generalization capabilities of the outlier score, it is additionally applied to various real world datasets. The overall average performance in identifying outliers using the proposed methods is higher compared to state-of-the-art methods. In order to generate the infrastructure images, an openDRIVE parsing and plotting tool for Matlab is developed as part of this work. This tool and the implementation of the entropy based outlier score in combination with Uniform Manifold Approximation and Projection are made publicly available.

Eduardo Sánchez Morales, Michael Botsch, Bertold Huber et al.

The trend towards autonomous driving and the continuous research in the automotive area, like Advanced Driver Assistance Systems (ADAS), requires an accurate localization under all circumstances. An accurate estimation of the vehicle state is a basic requirement for any trajectory-planning algorithm. Still, even when the introduction of the GPS L5 band promises lane-accuracy, coverage limitations in roofed areas still have to be addressed. In this work, a method for high precision indoor positioning using a LiDAR is presented. The method is based on the combination of motion models with LiDAR measurements, and uses infrastructural elements as positioning references. This allows to estimate the orientation, velocity over ground and position of a vehicle in a Local Tangent Plane (LTP) reference frame. When the outputs of the proposed method are compared to those of an Automotive Dynamic Motion Analyzer (ADMA), mean errors of 1 degree, 0.1 m/s and of 4.7 cm respectively are obtained. The method can be implemented by using a LiDAR sensor as a stand-alone unit. A median runtime of 40.77 us on an Intel i7-6820HQ CPU signals the possibility of real-time processing.

Eduardo Sánchez Morales, Michael Botsch, Bertold Huber et al.

Autonomous driving is an important trend of the automotive industry. The continuous research towards this goal requires a precise reference vehicle state estimation under all circumstances in order to develop and test autonomous vehicle functions. However, even when lane-accurate positioning is expected from oncoming technologies, like the L5 GPS band, the question of accurate positioning in roofed areas, e.\,g., tunnels or park houses, still has to be addressed. In this paper, a novel procedure for a reference vehicle state estimation is presented. The procedure includes three main components. First, a robust standstill detection based purely on signals from an Inertial Measurement Unit. Second, a vehicle state estimation by means of statistical filtering. Third, a high accuracy LiDAR-based positioning method that delivers velocity, position and orientation correction data with a mean error of 0.1 m/s, 4.7 cm and 1$^\circ$ respectively. Runtime tests on a CPU indicates the possibility of real-time implementation.

Eduardo Sánchez Morales, Richard Membarth, Andreas Gaull et al.

Due to the current developments towards autonomous driving and vehicle active safety, there is an increasing necessity for algorithms that are able to perform complex criticality predictions in real-time. Being able to process multi-object traffic scenarios aids the implementation of a variety of automotive applications such as driver assistance systems for collision prevention and mitigation as well as fall-back systems for autonomous vehicles. We present a fully model-based algorithm with a parallelizable architecture. The proposed algorithm can evaluate the criticality of complex, multi-modal (vehicles and pedestrians) traffic scenarios by simulating millions of trajectory combinations and detecting collisions between objects. The algorithm is able to estimate upcoming criticality at very early stages, demonstrating its potential for vehicle safety-systems and autonomous driving applications. An implementation on an embedded system in a test vehicle proves in a prototypical manner the compatibility of the algorithm with the hardware possibilities of modern cars. For a complex traffic scenario with 11 dynamic objects, more than 86 million pose combinations are evaluated in 21 ms on the GPU of a Drive PX~2.

Friedrich Kruber, Eduardo Sánchez Morales, Samarjit Chakraborty et al.

The availability of real-world data is a key element for novel developments in the fields of automotive and traffic research. Aerial imagery has the major advantage of recording multiple objects simultaneously and overcomes limitations such as occlusions. However, there are only few data sets available. This work describes a process to estimate a precise vehicle position from aerial imagery. A robust object detection is crucial for reliable results, hence the state-of-the-art deep neural network Mask-RCNN is applied for that purpose. Two training data sets are employed: The first one is optimized for detecting the test vehicle, while the second one consists of randomly selected images recorded on public roads. To reduce errors, several aspects are accounted for, such as the drone movement and the perspective projection from a photograph. The estimated position is comapared with a reference system installed in the test vehicle. It is shown, that a mean accuracy of 20 cm can be achieved with flight altitudes up to 100 m, Full-HD resolution and a frame-by-frame detection. A reliable position estimation is the basis for further data processing, such as obtaining additional vehicle state variables. The source code, training weights, labeled data and example videos are made publicly available. This supports researchers to create new traffic data sets with specific local conditions.

Friedrich Kruber, Jonas Wurst, Eduardo Sánchez Morales et al.

The goal of this paper is to provide a method, which is able to find categories of traffic scenarios automatically. The architecture consists of three main components: A microscopic traffic simulation, a clustering technique and a classification technique for the operational phase. The developed simulation tool models each vehicle separately, while maintaining the dependencies between each other. The clustering approach consists of a modified unsupervised Random Forest algorithm to find a data adaptive similarity measure between all scenarios. As part of this, the path proximity, a novel technique to determine a similarity based on the Random Forest algorithm is presented. In the second part of the clustering, the similarities are used to define a set of clusters. In the third part, a Random Forest classifier is trained using the defined clusters for the operational phase. A thresholding technique is described to ensure a certain confidence level for the class assignment. The method is applied for highway scenarios. The results show that the proposed method is an excellent approach to automatically categorize traffic scenarios, which is particularly relevant for testing autonomous vehicle functionality.