UTONOMOUS vehicles are poised to revolutionize transportation by improving road safety, reducing traffic congestion, and increasing mobility convenience [1]. To perceive and interact with their environment accurately, these vehicles rely on a combination of complementary sensors, including LiDAR, RADAR, and cameras. Each sensor offers unique advantages: cameras capture rich visual detail, LiDAR provides precise 3D spatial measurements, and RADAR performs robustly under adverse weather conditions [2]. Sensor fusion leverages the strengths of these modalities to ensure redundancy and resilience, allowing the vehicle to maintain accurate perception in diverse and dynamic environments [3]. A critical component of sensor fusion is extrinsic calibration, which involves the determination of the relative positions and orientations of sensors in a common coordinate frame. However, maintaining precise calibration over time is a persistent challenge. Factors such as mechanical vibrations, temperature changes, and minor collisions can lead to sensor drift, where even small misalignments in sensor orientation or position can result in substantial perception errors, potentially compromising vehicle safety.

In online (sequential) calibration, a forecaster predicts probability distributions over a finite outcome space $[d]$ over a sequence of $T$ days, with the goal of being calibrated. While asymptotically calibrated strategies are known to exist, they suffer from the curse of dimensionality: the best known algorithms require $\exp(d)$ days to achieve non-trivial calibration. In this work, we present the first asymptotically calibrated strategy that guarantees non-trivial calibration after a polynomial number of rounds. Specifically, for any desired accuracy $\epsilon > 0$, our forecaster becomes $\epsilon$-calibrated after $T = d^{O(1/\epsilon^2)}$ days. We complement this result with a lower bound, proving that at least $T = d^{\Omega(\log(1/\epsilon))}$ rounds are necessary to achieve $\epsilon$-calibration. Our results resolve the open questions posed by [Abernethy-Mannor'11, Hazan-Kakade'12]. Our algorithm is inspired by recent breakthroughs in swap regret minimization [Peng-Rubinstein'24, Dagan et al.'24]. Despite its strong theoretical guarantees, the approach is remarkably simple and intuitive: it randomly selects among a set of sub-forecasters, each of which predicts the empirical outcome frequency over recent time windows.

The goal of extrinsic calibration is the alignment of sensor data to ensure an accurate representation of the surroundings and enable sensor fusion applications. From a safety perspective, sensor calibration is a key enabler of autonomous driving. In the current state of the art, a trend from target-based offline calibration towards targetless online calibration can be observed. However, online calibration is subject to strict real-time and resource constraints which are not met by state-of-the-art methods. This is mainly due to the high number of parameters to estimate, the reliance on geometric features, or the dependence on specific vehicle maneuvers. To meet these requirements and ensure the vehicle's safety at any time, we propose a miscalibration detection framework that shifts the focus from the direct regression of calibration parameters to a binary classification of the calibration state, i.e., calibrated or miscalibrated. Therefore, we propose a contrastive learning approach that compares embedded features in a latent space to classify the calibration state of two different sensor modalities. Moreover, we provide a comprehensive analysis of the feature embeddings and challenging calibration errors that highlight the performance of our approach. As a result, our method outperforms the current state-of-the-art in terms of detection performance, inference time, and resource demand. The code is open source and available on https://github.com/TUMFTM/MiscalibrationDetection.

Online conformal prediction enables the runtime calibration of a pre-trained artificial intelligence model using feedback on its performance. Calibration is achieved through set predictions that are updated via online rules so as to ensure long-term coverage guarantees. While recent research has demonstrated the benefits of incorporating prior knowledge into the calibration process, this has come at the cost of replacing coverage guarantees with less tangible regret guarantees based on the quantile loss. This work introduces intermittent mirror online conformal prediction (IM-OCP), a novel runtime calibration framework that integrates prior knowledge, while maintaining long-term coverage and achieving sub-linear regret. IM-OCP features closed-form updates with minimal memory complexity, and is designed to operate under potentially intermittent feedback.

Tunnels and long corridors are challenging environments for mobile robots because a LiDAR point cloud should degenerate in these environments. To tackle point cloud degeneration, this study presents a tightly-coupled LiDAR-IMU-wheel odometry algorithm with an online calibration for skid-steering robots. We propose a full linear wheel odometry factor, which not only serves as a motion constraint but also performs the online calibration of kinematic models for skid-steering robots. Despite the dynamically changing kinematic model (e.g., wheel radii changes caused by tire pressures) and terrain conditions, our method can address the model error via online calibration. Moreover, our method enables an accurate localization in cases of degenerated environments, such as long and straight corridors, by calibration while the LiDAR-IMU fusion sufficiently operates. Furthermore, we estimate the uncertainty (i.e., covariance matrix) of the wheel odometry online for creating a reasonable constraint. The proposed method is validated through three experiments. The first indoor experiment shows that the proposed method is robust in severe degeneracy cases (long corridors) and changes in the wheel radii. The second outdoor experiment demonstrates that our method accurately estimates the sensor trajectory despite being in rough outdoor terrain owing to online uncertainty estimation of wheel odometry. The third experiment shows the proposed online calibration enables robust odometry estimation in changing terrains.

Artificial intelligence and deep learning are currently reshaping numerical simulation frameworks by introducing new modeling capabilities. These frameworks are extensively investigated in the context of model correction and parameterization where they demonstrate great potential and often outperform traditional physical models. Most of these efforts in defining hybrid dynamical systems follow {offline} learning strategies in which the neural parameterization (called here sub-model) is trained to output an ideal correction. Yet, these hybrid models can face hard limitations when defining what should be a relevant sub-model response that would translate into a good forecasting performance. End-to-end learning schemes, also referred to as online learning, could address such a shortcoming by allowing the deep learning sub-models to train on historical data. However, defining end-to-end training schemes for the calibration of neural sub-models in hybrid systems requires working with an optimization problem that involves the solver of the physical equations. Online learning methodologies thus require the numerical model to be differentiable, which is not the case for most modeling systems. To overcome this difficulty and bypass the differentiability challenge of physical models, we present an efficient and practical online learning approach for hybrid systems. The method, called EGA for Euler Gradient Approximation, assumes an additive neural correction to the physical model, and an explicit Euler approximation of the gradients. We demonstrate that the EGA converges to the exact gradients in the limit of infinitely small time steps. Numerical experiments are performed on various case studies, including prototypical ocean-atmosphere dynamics. Results show significant improvements over offline learning, highlighting the potential of end-to-end online learning for hybrid modeling.

Wheeled mobile robots need the ability to estimate their motion and the effect of their control actions for navigation planning. In this paper, we present ST-VIO, a novel approach which tightly fuses a single-track dynamics model for wheeled ground vehicles with visual inertial odometry. Our method calibrates and adapts the dynamics model online and facilitates accurate forward prediction conditioned on future control inputs. The single-track dynamics model approximates wheeled vehicle motion under specific control inputs on flat ground using ordinary differential equations. We use a singularity-free and differentiable variant of the single-track model to enable seamless integration as dynamics factor into VIO and to optimize the model parameters online together with the VIO state variables. We validate our method with real-world data in both indoor and outdoor environments with different terrain types and wheels. In our experiments, we demonstrate that our ST-VIO can not only adapt to the change of the environments and achieve accurate prediction under new control inputs, but even improves the tracking accuracy. Supplementary video: https://youtu.be/BuGY1L1FRa4.

Accurately estimating uncertainty is an essential component of decision-making and forecasting in machine learning. However, existing uncertainty estimation methods may fail when data no longer follows the distribution seen during training. Here, we introduce online uncertainty estimation algorithms that are guaranteed to be reliable on arbitrary streams of data points, including data chosen by an adversary. Specifically, our algorithms perform post-hoc recalibration of a black-box regression model and produce outputs that are provably calibrated -- i.e., an 80% confidence interval will contain the true outcome 80% of the time -- and that have low regret relative to the learning objective of the base model. We apply our algorithms in the context of Bayesian optimization, an online model-based decision-making task in which the data distribution shifts over time, and observe accelerated convergence to improved optima. Our results suggest that robust uncertainty quantification has the potential to improve online decision-making.

We describe the current content moderation strategy employed by Meta to remove policy-violating content from its platforms. Meta relies on both handcrafted and learned risk models to flag potentially violating content for human review. Our approach aggregates these risk models into a single ranking score, calibrating them to prioritize more reliable risk models. A key challenge is that violation trends change over time, affecting which risk models are most reliable. Our system additionally handles production challenges such as changing risk models and novel risk models. We use a contextual bandit to update the calibration in response to such trends. Our approach increases Meta's top-line metric for measuring the effectiveness of its content moderation strategy by 13%.

Recently, multi-sensors fusion has achieved significant progress in the field of automobility to improve navigation and position performance. As the prerequisite of the fusion algorithm, the demand for the extrinsic calibration of multi-sensors is growing. To calculate the extrinsic parameter, many researches have been dedicated to the two-step method, which integrates the respective calibration in pairs. It is inefficient and incompact because of losing sight of the constrain of all sensors. With regard to remove this burden, an optimization-based IMU/Lidar/Camera co-calibration method is proposed in the paper. Firstly, the IMU/camera and IMU/lidar online calibrations are conducted, respectively. Then, the corner and surface feature points in the chessboard are associated with the coarse result and the camera/lidar constraint is constructed. Finally, construct the co-calibration optimization to refine all extrinsic parameters. We evaluate the performance of the proposed scheme in simulation and the result demonstrates that our proposed method outperforms the two-step method.