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.

Global Navigation Satellite Systems (GNSS) are central to modern navigation, yet their performance degrades significantly in dense urban environments where satellite signals are obstructed or weakened by urban canyons. To ensure robust and safe navigation, complementary technologies or fallback systems are required. Pseudolites have emerged as a promising solution, with several systems proposed in recent years. However, existing implementations often rely on dedicated receivers, costly synchronization hardware, or zone-based positioning methods. This paper presents the development of a compact pseudolite system capable of transmitting an OFDM-based signal that integrates both communication and navigation functionalities.

The proposed pseudolite synchronizes to GNSS and employs a dual-component signal structure. The communication (COM) component adheres to the 3GPP 5G NR Release 16 standard, transmitting synchronization sequences including PSS, SSS, and TRS, and supporting 20 MHz and 40 MHz bandwidth configurations with numerologies 0 and 1. The navigation (NAV) component overlays two BPSK subcarriers onto the unused guard bands of the OFDM spectrum. This NAV signal carries a PRN code and a dedicated navigation message that broadcasts the pseudolite’s position and clock correction parameters.

The transmitter incorporates a transceiver unit equipped with an RF front-end that samples the GNSS bands and delivers digital IQ data to an onboard computer running a software-defined GNSS receiver. This receiver extracts GNSS-derived time and provides clock drift estimates to a clock control module, enabling physical clock steering to maintain alignment with GNSS time. The SDR additionally configures the OFDM 5G pseudolite signal and issues generation triggers within the transmitter chain. To mitigate internal processing latency, a loop-back mechanism is implemented that feeds a pulse-mode version of the generated signal into the receiver chain for real-time timing calibration. The pseudolite signal generator is realized on an FPGA-based platform with user-selectable parameters including carrier frequency, transmit power, PRN code, pulse shaping, and duty cycle. The SDR determines the pseudolite position, constructs the navigation message, and communicates with the signal generator via UDP to configure parameters, initiate transmission, and upload the encoded message.

This paper details the architectural design of the pseudolite system and its implementation across both the transceiver hardware and software receiver components, including the RF front-end, FPGA-based signal generator, GNSS timing subsystem, and the SDR processing modules responsible for signal configuration, synchronization, and navigation message generation.

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.

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].

With the increase of jamming and spoofing attacks targeting global navigation satellite systems (GNSS) in the Baltic Sea region, the demand is growing, to establish an alternative navigation system which can provide a reliable source of position, navigation and timing (PNT) information. The most promising alternative PNT system for the Baltic Sea region is known as R-Mode. R-Mode makes use of very high frequency (VHF) and medium frequency (MF) signals transmitted from maritime ground infrastructure to provide positioning and timing services in their overlapping coverage areas. Currently supported by several countries of the Baltic Sea region and under the umbrella of the project ORMOBASS (pre-Operational R-Mode Baltic Sea System), the number of available transmitters is rapidly increasing, with the system foreseen to be declared pre-operational by the end of 2026.

Several measurement campaigns have shown that MF R-Mode can provide horizontal positioning accuracies approaching 10 m (95%) under optimal propagation conditions. Less favorable conditions occur in case one or several transmitters provide unstable signals with jumps within a range of several meters or the propagation of the groundwave from the MF R-Mode transmitter to the receiver is affected by changes in the environmental conditions in between. These effects can cause significantly increased positioning errors.

This work presents how the authors tackled this challenge with a differential R-Mode approach. The R-Mode reference station is placed at a known location. It receives MF R-Mode signals from different transmitters. The role of the reference station is to assess the quality of the received signals and compute corrections which can then be transmitted to the users to increase the R-Mode ranging accuracy. The approach is explained in details and results from real measurement campaign are presented to demonstrate the validity of the developed technique.

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.

This paper addresses observer design for inertial navigation systems (INS) operating in GPS-limited or GPS-denied environments, with a focus on airborne platforms. The INS dynamics driven by inertial measurement unit (IMU) data are first cast into a port-Hamiltonian (pH) representation, where the Hamiltonian encodes the kinetic and potential energy of the system and the interconnection structure captures the underlying physics. Based on this representation, a structure-preserving observer is developed by shaping the energy function through a matching equation inspired by interconnection and damping assignment passivity-based control (IDA-PBC).

A desired pH system with appropriately selected interconnection, damping, and Hamiltonian terms is constructed such that the INS dynamics and the observer error dynamics coincide on the unobservable subspace defined by the available position and attitude measurements. A contraction-based analysis is then employed to establish exponential convergence of the estimation error with respect to a constant metric under mild convexity assumptions on the shaped Hamiltonian. In particular, sufficient conditions are derived that guarantee that the resulting closed-loop error system is contractive on a suitable domain.

The proposed design is subsequently extended to a distributed setting in which a network of INS-equipped agents communicates over a directed graph, and only one agent has access to absolute GPS measurements. Relative output information is integrated via a consensus-type potential in the pH framework, yielding a distributed observer that preserves the port-Hamiltonian structure at the network level. It is shown that, under standard connectivity assumptions and the same contraction conditions, all local estimates converge exponentially to the true state of the GPS-equipped agent, and hence to the global navigation state. The resulting methodology provides a systematic and physically interpretable framework for INS observer design and distributed state estimation in GPS-limited airborne networks.