The Earth Gravity Model 2008 (EGM2008) is now some years old, and yet information on how to use it to calculate Earth's gravity remains obscure outside the field of geodesy. We describe the mathematics necessary to implement EGM2008, and use this to discuss several points of the model: its sensitivity to the number of spherical harmonics being summed, nuances and a trap for physicists and mathematicians in the normalisation it uses, and a comparison with other work. We conclude that one must not overestimate the precision shown by a global-fit model such as EGM2008.

Maritime navigation is a complex task involving the acquisition, analysis, and interpretation of information using seamanship, professional knowledge, and technology. As the maritime industry transitions towards maritime autonomous surface ships (MASS), there is an increasing gap between the operator and the technology. This paper explores a collision avoidance decision support system for navigation from the navigator's perspective. The system, developed by Wärtsilä, is called Advanced Intelligent Manoeuvring (AIM) and can generate suggestions for course or speed alterations based on data from surrounding traffic. Nineteen Swedish navigators completed three ship traffic scenarios with and without decision support. Qualitative data were collected using interviews and analysed with thematic analysis. The results show that the participants perceive the decision support system as an advisory tool to visualise how traffic situations could unfold, a task currently difficult for most navigators. This paper discusses the present and near future of maritime navigation, highlighting the benefits of automation, while remaining vigilant about the potential dangers.

A new method is proposed for determining a ship's position at sea using naturally occurring pulsar signals to provide an alternative to the sextant. Use is made of four distinct pulsar radio signals whose timing stabilities are comparable to atomic clocks and whose characteristic signatures can be used as natural radio navigation beacons. Pulse peak time difference measurements, accurate to within 10−5 and 10−6 s, were generated for a key reference observatory which provides long-term pulsar timing observations and for the unknown ship location. These time differences when multiplied by the velocity of light provide a distance value that is fundamental in calculating the ship's position. Resultant simulations provided a position accuracy to ≈1⋅1 km (≈0⋅6 nm) for the higher timing difference measurement. A single-pulsar-based approach, which gave a position accuracy to ≈2⋅8 km (≈1⋅5 nm), was also investigated for affordable equipment solutions and comparison with NASA space-based navigation experiments.

Adverse effects of intoxicated driving have been well documented over the years, with clear conclusions. In addition, it is evident that the cognitive and neurological functions and reaction times deteriorate with the consumption of alcohol. Addressing the lack of literature on the subject, this paper focuses on studying the effects of alcohol on manoeuvring, navigational and decision-making ability in ship navigation. Ten participants – five cadets and five experienced navigation officers – volunteered and carried out a standard manoeuvre using a computer-controlled vessel simulator, under three different blood alcohol concentrations (0⋅00%, 0⋅05% and 0⋅08% BAC). Results from the simulations were used to assess the performance and the decision-making ability of participants under the influence of alcohol. In addition, the responses and behaviour of the simulated vessel when the navigators were intoxicated were analysed. Workload experienced by participants during the simulations were also assessed using the NASA Task Load Index. Findings of this preliminary study proved that the ability to make the correct decisions at the right time was drastically deteriorated when the blood alcohol concentration was increased.

This study summarises the scenario of maritime traffic anomalies, like the increased congestion and U-turn of ships caused by the ship grounding in the Suez Canal in March 2021. Here, satellite automatic identification system based ship trajectories, and Sentinel-1 and Sentinel-2 images based ship positions are analysed after subdividing the study area into seas, lakes and canals. The results show that the blockage affected the maritime traffic for more than three weeks, waiting ship numbers increased from 5 to 122, and daily one to three ships made a U-turn between 23 and 31 March in the Gulf of Suez. Ship density also increased to more than double in Bitter Lakes with a minimum waiting time of 7 days. Hence, to avoid such prolonged waiting of ships, we propose a warning method based on the sharp speed decrease rate, U-turn and congestion.

Benefiting from video surveillance systems that provide real-time traffic conditions, automatic vessel detection has become an indispensable part of the maritime surveillance system. However, high-level vision tasks generally rely on high-quality images. Affected by the imaging environment, maritime images taken under poor lighting conditions easily suffer from heavy noise and colour distortion. Such degraded images may interfere with the analysis of maritime video by regulatory agencies, such as vessel detection, recognition and tracking. To improve the accuracy and robustness of detection accuracy, we propose a lightweight generative adversarial network (LGAN) to enhance maritime images under low-light conditions. The LGAN uses an attention mechanism to locally enhance low-light images and prevent overexposure. Both mixed loss functions and local discriminator are then adopted to reduce loss of detail and improve image quality. Meanwhile, to satisfy the demand for real-time enhancement of low-light maritime images, model compression strategy is exploited to enhance images efficiently while reducing the network parameters. Experiments on synthetic and realistic images indicate that the proposed LGAN can effectively enhance low-light images with better preservation of detail and visual quality than other competing methods.

If the Earth's oblateness is neglected in marine navigation, then the sphere gives a relatively simple solution for course and distance between any two points. The navigation sphere where a span of one minute of arc is equal to nautical mile is used. The primary deficiency of this approach is the lack of a closed-form formula that takes the Earth's eccentricity into account. Considering the Earth as an oblate spheroid, i.e., a rotational ellipsoid with a small flattening, the problem of computing the length of the meridian arc leads to the understanding of elliptic integrals. In this paper, incomplete elliptic integrals of the first, second and third kind are used to find an arbitrary elliptical arc. The results prove an advantage of using geocentric latitude compared to geodetic and reduced latitude.

Because of the high photon flux, the Crab nebula pulsar is widely used as the observation target for X-ray pulsar-based navigation. The built profile of the Crab pulsar will change over time, however, which means that the pre-calibrated template cannot be used for the long term. In this paper, a novel pulsar-based template-independent navigation method is proposed. The detected phase propagation model is given as a term of position of the vehicle, taking the orbital motion into account. A different method of time-of-arrival process between the recovered profiles is introduced. With the aid of orbital transition matrix, a measurement model is derived to be a term of velocity error of the vehicle varying with time. The state errors of the vehicle are transformed into velocity errors by performing multi-segment observations to achieve the navigation system observability. The navigation equations of the system are then established and can be solved directly. Some simulations are performed to verify the method and suggest that the proposed method is feasible, effective and easy to implement. The precise orbit information of the vehicle can be determined. The state estimation accuracy is basically consistent with the traditional filtering algorithms, and the computational cost is still very low.

Integrated navigation systems made up of a strap-down inertial navigation system (SINS) and global positioning system (GPS) are increasingly being used to improve the position, speed, and attitude information of unmanned surface vessels (USV). However, a GPS outage could occur due to the dependence of GPS performance on the external environment and the number of available satellites. This study uses an innovative combination of Dempster–Shafer (DS) theory and broad learning (BL) method to design a SINS/GPS integrated navigation system. First, the velocity and position information derived from the SINS and their corresponding GPS were fused using DS fusion rules, while the SINS error was modelled using the BL method. A ‘virtual’ GPS was then designed using the proposed DS–BL approach to provide the speed and position information when the GPS signal was interrupted, thereby ensuring the continuous navigation of the USV. The results of both simulation and sea trial demonstrate that the proposed virtual GPS estimation approach is effective, and the navigational accuracy of the proposed method is superior to other methods.

To verify whether a graph is suitable for describing driver behaviour performance under the effects of navigation information, this study applies two types of prompt messages: simple and detailed. The simple messages contain only direction instructions, while the detailed messages contain distance, direction, road and lane instructions. A driving simulation experiment was designed to collect the empirical data. Two vehicle operating indicators (velocity and lateral offset), and two driver manoeuvre indicators (accelerator power and steering wheel angle) were selected, and T-test was used to compare the differences of behavioural performance. Driving behaviour graphs were constructed for the two message conditions; their characteristics and similarities were further analysed. Finally, the results of T-test of behavioural performance and similarity results of the driving behaviour graphs were compared. Results indicated that the two different types of prompt messages were associated with significant differences in driving behaviours, which implies that it is feasible to describe the characteristics of driving behaviours guided by navigation information using such graphs. This study provides a new method for systematically exploring the mechanisms affecting drivers’ response to navigation information, and presents a new perspective for the optimisation of navigation information.

In this paper, we propose a sea current relative navigation method using an interacting multiple model (IMM) filter with adaptive fading technique that can compensate an inaccurate sea current dynamics model. Due to the marine environment, the underwater vehicles largely depend on inertial navigation. Unfortunately, since its performance deteriorates with time, it is usually aided by another sensor. An electromagnetic-log (EM-log) and a Doppler velocity log (DVL), which are mainly used in marine navigation, provide relative velocity measurements to the sea currents, and hence require an accurate sea current dynamics model to fully utilise them. However, it is difficult to reflect the actual sea current changes with just a single fixed model, resulting in degraded overall navigation performance. Therefore, this paper proposes an IMM filter that can use multiple sea current dynamics models and has sub-filters designed with adaptive fading extended Kalman filter (AFEKF) to compensate for the mismodelling of sea current dynamics. The method is verified by simulation and shows a performance improvement comparable to the optimal filter.

The integration of the inertial navigation system (INS) and global navigation satellite system (GNSS) is suited for localisation and navigation applications, such as aircrafts, land vehicles and ships. The primary challenge is for navigation system to achieve accurate and reliable navigation solution during GNSS outages. This paper presents an observation prediction methodology for INS/GNSS bridging GNSS outages, which combines partial least squares regression (PLSR) and Gaussian process regression (GPR) to model the INS/GNSS observations and enable a Kalman filter to estimate INS errors. The performance of proposed PLSR/GPR prediction methodology was validated through four GNSS outages taken on flight experiment data, including diverse manoeuvre conditions. The experiment results demonstrate that remarkable performance enhancements are achieved through applying the proposed PLSR/GPR prediction methodology into INS/GNSS integration.

E-navigation provides the opportunity to apply modern digital and other electronic enhancements to improve the safety and efficiency of maritime navigation. Under the broad banner of e-navigation, the International Hydrographic Organization's S-100 product specification framework is facilitating the establishment of a standard maritime data structure to enable a free-flowing exchange of navigation information between ships, ship-to-shore and shore-to-ship. There are currently over 30 S-100 based product specifications at various stages of development. For the data standard to be properly used, navigation software products must be capable of reading as well as comprehending the data format and content. To develop robust and stable software, the S-100 data models and product specifications must be consistent, accurate and interoperable in conveying various types of information. This paper describes the results of research on S-100 based product specifications from the viewpoint of developing maritime navigation software. In particular, issues related to software development for Electronic Chart Display Information System (ECDIS) and Vessel Traffic Service (VTS) are discussed, including appropriate data model analysis, processing of features, and symbols overlapping with other product specifications. Proposed solutions for some identified issues are presented.

Collision avoidance (COLAV) is a prerequisite for the navigation safety of unmanned surface vehicles (USVs). Since USVs have to avoid obstacles clearly and timely, i.e. the COLAV should be agile, the COLAV algorithm should have low computation complexity and make efficient COLAV decisions. However, balancing between the computation complexity and the COLAV decision optimality is still intractable at present. This paper innovatively proposes a COLAV algorithm for USVs by combining the velocity obstacle method with the predictive model method, named the collision shielded model predictive control (CS-MPC) algorithm, such that the agility of USVs COLAV is improved. The runtime of the proposed COLAV algorithm is shortened by shielding the dangerous parts of the search space of the COLAV decisions, and the COLAV decision is efficient with the aid of the accurately predicted motion trajectory by the motion mathematical model of USVs. As such, the USV can safely navigate in complex water areas where multiple vessels and obstacles exist. A series of simulations on a yacht in different kinds of encounter situations were carried out to verify the effectiveness and the agility of the proposed CS-MPC COLAV algorithm.