Autonomous navigation capabilities are mandatory in places where Global Navigation Satellite Systems (GNSS) are either denied (e.g. jamming or spoofing) or not available yet (Moon, Mars). However, such navigation systems, that usually rely on an inertial measurement unit (IMU) are limited by the noise and bias of the inertial sensors (gyroscopes and accelerometers) which turns, at navigation system level, into drifts and random walks. The resulting position error provided by the inertial navigation system thus increases over time, limiting the carrier mission duration. Sodern is addressing the challenge to improve autonomous navigation through the development of star trackers, whose absolute attitude measurement based on star observation can be used to compensate the errors induced by the inertial sensors. Once hybridized with an IMU, the resulting celestial navigation system (CNS) aims at providing a cost-effective position evaluation with a 100 meters class precision, independent of the mission duration in a GNSS denied environment.
In recent communications, Sodern has presented celestial navigation solutions for Moon-based and Earth-based carriers, including our Astradia product, first commercial daytime star tracker able to detect stars during both day and night time. In this paper, we present the results of operational tests performed with a celestial navigation system, composed by a star tracker hybridized with a tactical class IMU and embedded on a moving vehicle in different operational scenarios. We show its capability to provide a reliable position evaluation in operational conditions (notably during daytime) without any GNSS contribution and demonstrate the benefits of the stellar measurement hybridization compared to the use of the IMU alone. In addition, we demonstrate the consistency of our simulation models with observed performances, which validates them and allows for extensive simulations to be carried out.

A fundamental requirement for full autonomy for mobile robots is accurate navigation even in situations where satellite navigation (outdoors) or cameras (indoors) are unavailable. The inherent noise and error terms of inertial sensors in such practical situations will cause the navigation solution to drift. To circumvent drift in situations of pure inertial navigation several approaches were suggested in the literature including information aiding [1], multiple inertial sensors [2], and maneuvering the robot in a snake-like slithering motion [3]. In the latter, such motion has already proven to increase the inertial signal-to-noise ratio, allowing regression of the mobile robot’s position using both model-based and deep-learning approaches.

The conventional deep-learning models are black-box in nature, which limits their reliability for critical navigation tasks. Furthermore, they rely on large labelled sensor datasets, which are often difficult to obtain or not publicly available. Purely data-driven models also exhibit poor generalization across devices, users, and motion patterns, and violate the known physical constraints of inertial navigation.

To address these challenges, we propose a physics-informed inertial dead-reckoning framework for mobile robots. The framework embeds the strapdown inertial navigation equations of motion directly into the learning process through the physics-informed residual component. In parallel, a data-driven component ensures that predicted and observed navigation states are in agreement. During training, a composite objective function combining these two components is minimized to obtain optimized model parameters.

To evaluate our approach, field experiments were conducted using a ROSbot XL wheeled robot equipped with low-cost inertial sensors. The real-world experiments demonstrate that our approach achieves more than 70% improvement in performance compared to baseline model-based and deep learning approaches. In addition, the proposed model significantly reduces accumulated drift relative to the traversed path length, achieving a total distance error of 8%. With a lightweight yet effective architecture, our approach can be deployed on embedded platforms, enabling real-time navigation in challenging environments. Therefore, our approach effectively overcomes the limitations of pure inertial navigation. It enables seamless navigation using inertial sensor data for short periods.

References:
[1] Engelsman, D., and Klein, I., Information-aided inertial navigation: A review, IEEE Transactions on Instrumentation and Measurement, vol. 72, pp. 1-18, 2023.
[2] Nilsson, J.O. and Skog, I., Inertial sensor arrays—A literature review, 2016 European Navigation Conference (ENC), pp. 1-10, 2016.
[3] Etzion, A., Cohen, N., Levi, O., Yampolsky, Z. and Klein, I., Snake-inspired mobile robot positioning with hybrid learning, Scientific Reports, vol. 15(1), pp. 15602, 2025.

Keywords:
GNSS-Denied Navigation; Inertial Dead Reckoning; Physics-Informed Learning; Inertial Navigation System (INS); Inertial Sensors; Mobile Robots.

Magnetometer calibration remains a challenge for reliable heading estimation in GNSS-denied environments. In such settings, magnetic disturbances, soft-iron and hard-iron effects, and slowly timevarying sensor biases can significantly degrade attitude solutions if not estimated accurately and continuously. Although several online calibration methods exist, their performance is limited by poor observability of magnetic bias parameters, especially when the platform undergoes constrained or low dynamic motion.

In this work, we present a polarised-light-aided Rao–Blackwellised Particle Filter (RBPF) for online magnetometer calibration. The method augments traditional magnetometer-based estimation with orientation cues derived from simulated sky polarisation patterns. These patterns are generated using PySkyLumos, a physics-based sky polarisation simulation framework that models Rayleigh scattering andhigher-order atmospheric effects to produce realistic polarisation fields. The key motivation is that the polarisation pattern provides absolute orientation information with respect to the Sun vector and the scattering plane, improving the identifiability of magnetometer biases.

Our RBPF formulation treats the magnetic bias parameters as part of the Rao–Blackwellised component, estimated using an Unscented Kalman Filter, while particle filtering is used to represent nonlinear attitude dynamics and to fuse the polarisation-derived orientation likelihood.

We show that polarised-light cues improve the calibration and accelerate the convergence of magnetic bias estimates compared to magnetometer-only approaches.

Cold-atom interferometry (CAI) based inertial sensors present strong potential for future space applications, attributed to their stable long-term and precise measurements independent of external signals. This makes them beneficial for deep space missions where the Global Navigation Satellite System (GNSS) space service volume is either inaccessible or where GNSS signals suffer significant attenuation. However, the limitations of CAI quantum sensors, such as low measurement rates and ambiguities due to the measurement principle, necessitate the hybridization of quantum sensors with classical inertial sensors with higher bandwidth. The hybridization approach (Tennstedt et al., 2023) in this study follows two main objectives: First, data from high-rate sensors is used to solve the fringe ambiguity inherent to the sinusoidal nature of the raw CAI quantum sensor signal. Second, the superior long-term stability of the CAI quantum sensor principally enables real-time calibration of the classical inertial sensors. Previous research has shown that performance in terrestrial applications can be significantly enhanced depending on sensor parameters and trajectory dynamics (Gersemann et al., 2025), while future satellite gravity missions may also benefit from similar improvements. The CAI sensor hybridisation increases performance by one to two orders of magnitude in both applications. Currently, missions such as LuGRE and Artemis are pioneering a new paradigm for lunar navigation by using weak Global Navigation Satellite System (GNSS) signals. While these approaches provide a foundational framework, they achieve a moderate level of precision. Internal analysis conducted at IfE, consistent with the LuGRE mission’s concept confirms that geometric dilution of precision (GDOP), receiver sensitivity, and antenna gain are critical determinants of navigation accuracy in weak GNSS environments. The simulation results of hybrid classic quantum inertial navigation will be used to quantify potential performance gains relative to the navigation accuracy achieved by lunar missions like LuGRE and Artemis, offering an assessment of the proposed approach for lunar navigation.
To exploit the advantages of hybridization, the angular rates and specific forces recorded by the IMU are employed to predict the CAI phase shift. This data is subsequently integrated with the CAI observation through the application of an Extended Kalman Filter. The final phase shift is determined by resolving the fringe ambiguity of the CAI sensor, from which bias estimates intrinsic to classical inertial sensors are derived. These bias-corrected IMU data values are then utilized to compute the rover’s navigation states (position, velocity, and orientation). The potentials, fundamental limitations, and optimal interrogation durations of the CAI sensor will be analysed through typical trajectories for lunar rover navigation.
This work is funded by the Federal Ministry for Economic Affairs and Climate Action (BMWK), Projects 50NA2310A and 50NA2106.

Key words: Cold-atom interferometry (CAI), GNSS, Lunar Rover, Lunar navigation, Hybridisation

Mobile autonomous systems such as UAVs, robotic swarms, and distributed sensing platforms rely on precise and continuous timing for navigation, sensor fusion, and cooperative behaviour. These systems often require sub-millisecond timestamp alignment across sensors and microsecond-level synchronisation between mobile agents. While GNSS provides high timing accuracy in favourable conditions, its vulnerability to blockage, multipath, jamming, and spoofing poses a significant limitation for mobile platforms operating in challenging or contested environments. Local oscillators provide short-term stability but drift rapidly during GNSS outages, and network-based timing methods such as NTP/PTP are difficult to maintain in mobile, infrastructure-free scenarios. This creates a clear gap for mobile systems that require timing that is accurate, robust, and secure.

This work investigates a novel multi-source time integration framework that combines GNSS, Quantum Time Transfer (QTT), and local clocks to enhance continuity and robustness for mobile platforms. QTT offers a stable and spoof-resistant timing reference via free-space optical links, while GNSS provides high accuracy when signals are available. The onboard Real-Time Clock (RTC) supports holdover during loss of external timing. The objective of the framework is to utilise these complementary sources to provide more resilient and accurate timing for mobile applications.

The framework integrates multiple timing inputs by comparing periodic timestamps from each source against the system clock to compute offset measurements (Δt). These measurements are evaluated using simple quality indicators, including jitter, continuity, and signal validity, to assess the reliability of each source. A rule-based switching mechanism selects the most trustworthy timing input at any given time, prioritising QTT when available, followed by GNSS and the RTC during holdover. The selected measurements are processed by a Kalman filter that estimates system clock offset and drift while smoothing noise and maintaining continuity during short outages. The resulting estimate is used by a software clock-disciplining module (such as chrony) to maintain a stable and monotonic system time suitable for mobile sensing and navigation.

The framework is prototyped using Linux embedded platform. Evaluation is performed on timing continuity, offset stability, drift during outages, and how quickly the system recovers when external timing becomes available again. Key metrics include Δt variance, drift rate, holdover performance, and switching behaviour. It is demonstrated that incorporating QTT improves stability during GNSS outages and provides a more reliable basis for timing in mobility scenarios characterised by the temporary unavailability of timing information from GNSS. The results provide an initial indication of system behaviour and help guide future designs of end user solutions. Overall, the work demonstrates benefits from multi-source time integration that can support more resilient timing for mobile autonomous users as well as accuracy improvements via integration of the quantum time transfer technologies.

This research has been undertaken with support from TimeLink project led by Xairos, funded by Innovate UK [10164956].