We proposed an adaptive H-infinity Cubature Kalman Filter (AH∞CKF) to improve the navigation accuracy of a highly manoeuvrable unmanned aerial vehicle (UAV). AH∞CKF fuses the Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) measurements. Traditional state estimation filters like extended Kalman filters (EKF) and cubature Kalman filters (CKF) assume Gaussian noises. However, their performance degrades for non-Gaussian noises and system uncertainties encountered in real-world applications. Thus, designing filters robust to noise and distribution is crucial. AH∞CKF combines H∞CKF design with an added adaptive factor to adjust the state estimation covariance matrix according to measurements by exploiting the square root method to yield more numerically stable results (SrAH∞CKF). We conducted multiple dynamically rich flight tests to validate our claims using a UAV equipped with a commercially well-known GNSS solution. Results show that the SrAH∞CKF state estimation outperforms EKF and CKF methods on average by 90% in various statistical measures.

Due to the exceptional complexity of the propulsion system (sails), square-riggers form a special group of sailing vessels. In modern pleasure and sport sailing, simple Bermuda (triangular) sailing rigging prevails, which is widely discussed in the literature, both in terms of theory and numerous experiments. The literature on the theory on square-riggers is, in turn, limited mainly to the description of good sailing practice developed over the centuries. Its important element was maximising vessel speed, but this discussion has not been documented by scientific research. This paper presents the significant parameters influencing the speed of a square-rigged sailing vessel and selects those which are the most important from the point of view of its maximisation. The paper also proposes methods and measurement systems which optimise selected parameters affecting the achievement of higher speeds. The paper describes the types of speeds of typical sailing vessels, provides a historical synthesis of sailing ships with respect to their speed, and presents a selection and description of the parameters affecting the speed of modern square-rigged vessels. The paper ends with a proposed method and measurement system for experimental research aiming at rigging optimisation in a square-rigged sailing vessel from the point of view of maximising its speed.

A relatively novel approach of autonomous navigation employing platform dynamics as the primary process model raises new implementational challenges. These are related to: (i) potential numerical instabilities during longer flights; (ii) the quality of model self-calibration and its applicability to different flights; (iii) the establishment of a global estimation methodology when handling different initialisation flight phases; and (iv) the possibility of reducing computational load through model simplification. We propose a unified strategy for handling different flight phases with a combination of factorisation and a partial Schmidt–Kalman approach. We then investigate the stability of the in-air initialisation and the suitability of reusing pre-calibrated model parameters with their correlations. Without GNSS updates, we suggest setting a subset of the state vector as ‘considered’ states within the filter to remove their estimation from the remaining observations. We support all propositions with new empirical evidence: first in model-parameter self-calibration via optimal smoothing and second through applying our methods on three test flights with dissimilar durations and geometries. Our experiments demonstrate a significant improvement in autonomous navigation quality for twelve different scenarios.

Complex domestic airspace requires collision risk models and monitoring tools suitable for arbitrary aircraft trajectories. This paper presents a new mathematically based collision risk approach that extends the International Civil Aviation Organisation (ICAO) models to full aircraft encounters based on real trajectory data. A new continuous time intervention model is presented, along with a position uncertainty propagation model that better reflects aircraft behaviour and allows generalisation to all trajectories to eliminate degenerate cases. The proposed risk model is computationally efficient compared to the models it is based on and can be applied to large-scale trajectory data. The utility of the model is demonstrated through a series of case studies using real aircraft trajectories.

This paper proposes a proper compass adjustment method using only a GPS (or any other GNSS receiver) and a single visual reference to enhance the efficiency of compass adjustment. During compass adjustment, the ship proceeds on magnetic courses using a gyroscopic or satellite compass and considering magnetic declination. However, non-magnetic compasses are only compulsory for ships of 500 gross tonnage or upwards (SOLAS V/19.2.5.1). Many ships of less than 500 gross tonnage have only a magnetic compass to indicate heading. In these cases, a minimum of five leading lines or a minimum of five bearings of conspicuous and distant points or sun azimuths are necessary to adjust the compass. This makes compass adjustment more laborious and time consuming. To expedite this process, a reliable and practical method was developed to use the courses over ground given by a GNSS receiver and a single visual reference instead of the headings provided by a gyroscopic or satellite compass. The method is valid for all ships, but is primarily intended for those equipped with only a magnetic compass to indicate heading.

The voyage data recorder (VDR) is a data recording system that aims to provide all navigational, positional, communicational, sensor, control and command information for data-driven investigation of accidents onboard ships. Due to the increasing dependence on interconnected networks, cybersecurity threats are one of the most severe issues and critical problems when it comes to safeguarding sensitive information and assets. Cybersecurity issues are extremely important for the VDR, considering that modern VDRs may have internet connections for data transfer, network links to the ship's critical systems and the capacity to record potentially sensitive data. Thus, this research adopted failure modes and effects analysis (FMEA) to perform a cybersecurity risk assessment of a VDR in order to identify cyber vulnerabilities and specific cyberattacks that might be launched against the VDR. The findings of the study indicate certain cyberattacks (false information, command injection, viruses) as well as specific VDR components (data acquisition unit (DAU), remote access, playback software) that required special attention. Accordingly, preventative and control measures to improve VDR cybersecurity have been discussed in detail. This research makes a contribution significantly to the improvement of ship safety management systems, particularly in terms of cybersecurity.

Several studies have been conducted on collision avoidance (CA) and path planning for maritime autonomous surface ships (MASS) based on artificial potential field (APF) and electronic navigation chart (ENC) data. However, to date, accurate, highly efficient, and automatic modelling of complicated geometry environment potential fields (EPFs) has not been realised. In this study, an accurate EPF model is established using ENC data to describe different types of obstacles, navigable areas, and non-navigable areas. The implicit equations of complex polygons are constructed based on the R-function theory, and the discrete-convex hull method is introduced to realise the automatic modelling of EPF. Moreover, collaborative CA and obstacle avoidance (OA) experiments are designed and conducted in a simulated environment and based on the ENC data. The results show that the proposed EPF modelling method is accurate, reliable, and time-efficient even with numerous ENC data and complex shapes owing to the R-function representation for geometric objects and discrete-convex hull method. The combination of improved APF and EPF models is proven to be effective for CA and OA. This paper presents a practical EPF modelling approach for APF-based ship path planning.

Ship collision avoidance has always been one of the classic topics in the field of marine research. In traditional encounter situations, officers on watch (OOWs) usually use a very high frequency (VHF) radio to coordinate each other. In recent years, with the continuous development of autonomous ships, there will be a mixed situation where ships of different levels of autonomy coexist at the same time. Under such a scenario, different decision makers have different perceptions of the current scene and different decision-making logic, so conventional collision avoidance methods may not be applicable. Therefore, this paper proposes a collaborative collision avoidance strategy for multi-ship collision avoidance under mixed scenarios. It builds a multi-ship cooperative network to determine cooperative objects and timing, at the same time. Based on a cooperative game model, a global collision avoidance responsibility distribution that satisfies group rationality and individual rationality is realised, and finally achieves a collaborative strategy according to the generalised reciprocal velocity obstacle (GRVO) algorithm. Case studies show that the strategy proposed in this paper can make all ships pass each other clearly and safely.

Maritime cybersecurity has attracted increasing attention in industrial and academic scope, which may be relevant to the increasing cyber-incidents in the maritime shipping industry. This paper presents a critical review of publications related to cybersecurity in the maritime transportation industry, to explore the current research status and gaps, as wells as to guide new probe avenues by employing bibliometric approaches. With the advantage of bibliometric methods, the research focus and evolution are conformed and visualised. Representative papers are reviewed together to demonstrate maritime cyber-threats recognition and categories, as well as potential consequence assessment and risk mitigation actions recommendation. This paper also created a detailed database that is comprised of attack form, occurring time, targets, purpose, as well as potential results and cost, which has been included in the Appendix and is fully portable and extendible.

In missile test ranges, complex missions demand precise trajectory generated by radar. Both the radar and Global Navigation Satellite System (GNSS) signals are affected by atmospheric effects, degrading their accuracy and performance. The Indian Regional Navigation Satellite System/Navigation with Indian Constellation (IRNSS/NavIC) transmits signals in the S-band together with the L-band. This paper presents a novel experimental technique to improve the tracking accuracy of S-band radars using the concurrent NavIC S-band signal. The ionospheric delay using the NavIC S-band signal is calculated first, and the results are used to improve the trajectory data of simultaneously operating S-band radars. This is a unique application of the NavIC S-band signals apart from its conventional usage. During a launch mission, for low elevation angles, the ionospheric error is found to be ~130 m while at higher elevation angles the error values are found to be ~1–3 m. The concept is validated using data from a missile test mission. This report on the use of S-band GNSS signals for the correction of S-band radar range data offers a clear advantage of simplicity and accuracy.

Thanks to the development of the real-time kinematic (RTK) algorithm and the emerging Global Navigation Satellite System (GNSS), especially for Galileo and BeiDou-3, reliable positioning accuracy for medium and long-baseline RTK became possible globally. Moreover, with the development of the GNSS receiver hardware, baseline length limitations due to radio-based communications are removed thanks to internet-based communication. In this work, single-baseline RTK, incorporated partial ambiguity resolution with troposphere and ionosphere weighting, using GPS (G), Galileo (E), BeiDou-3 (C3) and multi-GNSS (GE and GEC3), is conducted with real GNSS data of EUREF Permanent GNSS network under three different cutoff angles (10°, 20°, and 30°) for six different lengths of baselines (~50, ~150, ~250, ~350, ~450, and ~550 km). The results show that the multi-GNSS RTK solution significantly contributed to the positioning accuracy and convergence time of the single-system RTK solutions. Based on the results, non-available epoch-wise solutions for the high-degree cutoff angles are more obvious for the single-system RTK, whereas multi-GNSS solutions provide 100% solutions for each cutoff angle and baseline. The results indicate that instantaneous and a few epochs single-epoch ambiguity resolution is feasible for 50, 150, 250 and 350 km baseline lengths for multi-GNSS RTK. Based on the positioning results, horizontal–vertical positioning improvements of multi-GNSS RTK (GEC3) compared with the single-system GPS RTK are found as 50%–37%, 40%–35%, 55%–47%, 53%–54%, 57%–49% and 57%–49% for 50, 150, 250, 350, 450 and 550 km, respectively, under a 10° cutoff angle. For 20° and 30° cutoff angles, the accuracy improvements are much higher. The convergence time improvements (n/e/u) of multi-GNSS RTK (GEC3) compared with the single-system GPS RTK are found as 86/92/75%, 77/67/72%, 75/77/83%, 53/56/52%, 69/49/62%, and 52/45/39% for 50, 150, 250, 350, 450 and 550 km, respectively, under a 10° cutoff angle.

In this paper, the well-known multiplicative extended Kalman filter (MEKF) is re-investigated for attitude estimation using vector observations. From the Lie group theory, it is shown that the attitude estimation model is group-affine and its error state model should be trajectory-independent. Moreover, with such a trajectory-independent error state model, the linear Kalman filter is still effective for large initialisation errors. However, the measurement model of the traditional MEKF is dependent on the attitude prediction, which is therefore trajectory-dependent. This is also the main reason why the performance of traditional MEKF is degraded for large initialisation errors. Through substitution of the attitude prediction related term with vector observations in the body frame, a trajectory-independent measurement model is derived for MEKF. Meanwhile, MEKFs with reference attitude error definition and with global state formulating on special Euclidean group have also been studied, with the main focus on derivation of the trajectory-independent measurement models. Extensive Monte Carlo simulations of spacecraft attitude estimation implementations demonstrate that the performance of MEKFs can be much improved with trajectory-independent measurement models.

Autonomous vehicles rely on a combination of sensors for safe navigation around the world. For precise localisation, high-definition (HD) maps are used. These maps are a representation of the world containing information about objects on the road infrastructure. Currently, there are tens of HD map makers, however, no rigorous description of the requirements for the accuracy of HD maps has been published yet. This study fills the gap and offers a mathematical description of the minimum required accuracy for HD maps. In the first part, we identify factors that influence the quality of a map. Based on that, we proceed to present our solution for determining the minimum required accuracy for HD maps, both for static and dynamic models, and present a new formula for the minimum necessary accuracy for HD maps.

Navigation safety at sea is vital for each autonomous surface vehicle (ASV), which involves the problem of motion planning in dynamic environments and their robust tracking through feedback control. We present a practical path-planning method that generates smooth trajectories for a marine vehicle traveling in an unknown environment, where obstacles are detected in real time by millimetre wave (mmWave) radar. Our approach introduces a polynomial curve to describe the lateral and longitudinal trajectories in the Frenet frame, known as the ‘motion primitives’, whose combination ensures that the planning area is properly covered. In addition, we can select a feasible, optimal and collision-free trajectory from such a set of motion primitives that is generated by considering the vehicle dynamics and comfort. The capabilities of proposed algorithm are demonstrated in the experiment with static and dynamic obstacles.

This study investigates whether the International Safety Management (ISM) Code remains an effective regulatory tool for the shipping industry by analysing maritime accident statistics published for the last 32 years by the Korea Maritime Safety Tribunal, 24 years by the International Maritime Organization (IMO) and seven years by the European Maritime Safety Agency. For this purpose, the data were divided into four groups: pre-ISM Code, in-transit, post-1 and post-2 periods, and tested by multilateral comparative analysis. The results show that the Korean merchant fleet has no improvement over the periods, whereas the world merchant fleet has a continual decrease in serious casualties. This study confirmed a trend of maritime accidents in recent years: fewer in number but heavier in damage. Conclusively, the results suggest that IMO and decision-makers in the maritime industry must review the ISM Code again and seek solutions to achieve the goal of continual improvement, as specified in the code.

This paper introduces a novel approach for extracting vessel navigation patterns from very large automatic identification system (AIS) trajectory big data. AIS trajectory data records are first converted to a series of code documents using vector quantisation, such as k-means and PQk-means algorithms, whose performance is evaluated in terms of precision and computational time. Therefore, a topic model is applied to these code documents from which vessels’ navigation patterns are extracted and identified. The potential of the proposed approach is illustrated by several experiments conducted with a practical AIS dataset in a region of North West France. These experimental results show that the proposed approach is highly appropriate for mining AIS trajectory big data and outperforms common DBSCAN algorithms and Gaussian mixture models.

While quantum accelerometers sense with extremely low drift and low bias, their practical sensing capabilities face at least two limitations compared with classical accelerometers: a lower sample rate due to cold atom interrogation time; and a reduced dynamic range due to signal phase wrapping. In this paper, we propose a maximum likelihood probabilistic data fusion method, under which the actual phase of the quantum accelerometer can be unwrapped by fusing it with the output of a classical accelerometer on the platform. Consequently, the recovered measurement from the quantum accelerometer is used to estimate bias and drift of the classical accelerometer which is then removed from the system output. We demonstrate the enhanced error performance achieved by the proposed fusion method using a simulated 1D accelerometer precision test scenario. We conclude with a discussion on fusion error and potential solutions.

Concentrating on a surface vessel with input saturation, model uncertainties and unknown disturbances, a path following the adaptive backstepping control method based on prescribed performance line-of-sight (PPLOS) guidance is proposed. First, a prescribed performance asymmetric modified barrier Lyapunov function (PPAMBLF) is used to design the PPLOS and the heading controller, which make the path following position and heading errors meet the prescribed performance requirements. Furthermore, the backstepping and dynamic surface technique (DSC) are used to design the path following controller and the adaptive assistant systems are constructed to compensate the influence of input saturation. In addition, neural networks are introduced to approximate model uncertainties, and the adaptive laws are designed to estimate the bounds of the neural network approximation errors and unknown disturbances. According to the Lyapunov stability theory, all signals are semi-globally uniformly ultimately bounded. Finally, a 76$\,{\cdot }\,$2 m supply surface vessel is used for simulation experiments. The experimental results show that although the control inputs are limited, the control system can still converge quickly, and both position and heading errors can be limited to the prescribed performance requirements.

Collisions are one of the major accidents in the shipping industry, causing significant losses. In this work, a framework of marine collision risk identification strategy was developed to quantitatively analyse collision risks and provide an easy and convenient way to monitor traffic flow in relevant waters to mitigate the chances of collision. The model was verified by using automatic identification system data obtained from Tianjin Port. When compared to previous research, the proposed model can identify risks earlier and give people more time to analyse and take action. The results indicate that it also can provide a visual display to alert relevant personnel. The model can be used as a reference to identify potential collision risks or as an information source for future research.

Transverse arrangement is one of the main methods used in the polar inertial navigation system (INS). In the traditional algorithm, the calculation of using the earth ellipsoid model is complex, while using the earth sphere model cannot satisfy a high-accuracy application. Therefore, an approach based on the virtual sphere model is proposed, which has been proved in simulation experiments to reduce the computational complexity and maintain the same accuracy as the ellipsoid algorithm, but its accuracy has not yet been proved in theory. Starting from the basic principles of the ellipsoid and virtual sphere model algorithm, this paper compares the key formulations of the two. Finally, it is proved that the two arrangements are actually the same.