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.

Electronic navigational charts (ENCs) are specialised geospatial datasets, issued by or on the authority of a government or hydrographic office, in accordance with the International Hydrographic Organisation's (IHO) standards, specifications and symbol sets. The datasets generally comprise encoded information collected from hydrographic surveys, aimed primarily at the safety of navigation. Most ENCs are not openly available, since the encrypted datasets can be acquired through various license schemes via a centralised distribution network coordinated by two organisations operating on behalf of the coastal states that produce them. This paper describes a methodology and an integrated system developed at the National Technical University of Athens Cartography Laboratory for the generation of web-based nautical charts utilising open data and free software. The system compiles nautical charts compliant with IHO's S-101 latest standard; using open hydrospatial data retrieved from marine spatial data infrastructures (MSDI) and other qualified volunteered geographic information (VGI) sources. Open-source geospatial libraries and web-map vector technologies are used to build the system components and software scripts developed to enable automated compilation. The study also discusses how the system can be improved further by leveraging web services for end-to-end process automation and satellite-derived bathymetry for accurate depiction of seabed topography in low-depth areas.

Standards IEC 62288:2014 and MSC.191(79) require information on the displays of shipboard navigation systems to be logically grouped, but only provide limited specification for this ‘logical’ criterion. Meanwhile, complex interfaces and information overload remain as major design issues, being connected to several maritime accidents. To address this matter, a three-phase study was conducted to develop a pattern to organise essential information on Radar and Electronic Chart Display and Information System (ECDIS) displays and their equivalent modules on integrated navigation systems and integrated bridge systems. The first phase involved identifying the information most essential for safe navigation using cognitive task analyses, equipment performance standards and frequency of use. The second phase involved a card-sorting experiment with seafarers (n = 63) to develop an initial grouping pattern for the identified essential information. The third phase involved validating the initial grouping pattern with a new sample of seafarers (n = 35). The result is a pattern to group 48 types of information on shipboard navigation displays into 13 groups. The paper details the selected methods and the findings, and provides implications for future research.

In 1915 while the Imperial Trans-Antarctic Expedition's vessel Endurance was icebound in the Weddell Sea, lunar occultation timings were carried out in order to rate the chronometers and thereby find longitude. The original observations have been re-analysed using modern lunar ephemerides and catalogues of star positions. The times derived in this way are found to differ by an average of 20 s from those obtained during the expedition using positions given from the Nautical Almanac and introduces an additional offset of the true positions to the east of those recorded in the log.

We investigated the contribution of visual imagination to the cognitive mapping of a building when initial exploration was simulated either visually by using a passive video walk-through, or mentally by using verbal guidance. Building layout had repeating elements with either rotational or mirror symmetry. Cognitive mapping of the virtual building, determined using questionnaires and map drawings, was present following verbal guidance but inferior to that following video guidance. Mapping was not affected by the building's structural symmetry. However, notably, it correlated with small-scale mental rotation scores for both video and verbal guidance conditions. There was no difference between males and females. A common factor that may have influenced cognitive mapping was the availability of visual information about the relationships of the building elements, either directly perceived (during the video walk-through) or imagined (during the verbal walk-through and/or during recall). Differences in visual imagination, particularly mental rotation, may thus account for some of the individual variance in cognitive mapping of complex built environments, which is relevant to how designers provide navigation-relevant information.

Travel demand models (TDMs) with freight forecasts estimate performance metrics for competing infrastructure investments and potential policy changes. Unfortunately, freight TDMs fail to represent non-truck modes with levels of detail adequate for multi-modal infrastructure and policy evaluation. Recent expansions in the availability of maritime movement data, i.e. Automatic Identification System (AIS), make it possible to expand and improve representation of maritime modes within freight TDMs. AIS may be used to track vessel locations as timestamped latitude–longitude points. For estimation, calibration and validation of freight TDMs, this work identifies vessel trips by applying network mapping (map-matching) heuristics to AIS data. The automated methods are evaluated on a 747-mile inland waterway network, with AIS data representing 88% of vessel activity. Inspection of 3820 AIS trajectories was used to train the heuristic parameters including stop time, duration and location. Validation shows 84⋅0% accuracy in detecting stops at ports and 83⋅5% accuracy in identifying trips crossing locks. The resulting map-matched vessel trips may be applied to generate origin–destination matrices, calculate time impedances, etc. The proposed methods are transferable to waterways or maritime port systems, as AIS continues to grow.

A local positional system (LPS) is proposed, in which particles are launched at given velocities, and a sensor system measures the trajectory of the particles in the platform frame. These measurements allow us to restore the position and orientation of the platform in the frame of the rotating Earth, without solving navigation equations. When the platform velocity is known and if the platform orientation stays the same, the LPS technique allows a navigational accuracy of 100 $\mu$m per one hour to be achieved. In this case, the LPS technique is insensitive to the type of platform trajectory. If there are also velocimeters installed on the platform, then one can restore the platform velocity and angular rate of the platform rotation with respect to the Earth. Instead of navigational equations, it is necessary to obtain the classical trajectory of a particle in the field of a rotating gravity source. Taking into account the gravity-gradient, Coriolis, and centrifugal forces, the exact expression for this trajectory is derived, which can be widely used in atomic interferometry. A new iterative method for restoring the orientation of the platform without using gyroscopes is developed. The simulation allows us to determine the conditions under which the LPS navigation error per hour is approximately $10$ m.

An aircraft wing is the carrier of imaging payload (interferometric synthetic aperture radar (SAR) or array SAR) of a high-resolution aerial remote sensing system, and high-precision estimation of wing deformation is the key. There are two main traditional modelling methods for wing deformation, namely stochastic theory modelling and material mechanics modelling only dealing with single disturbance, of which the model parameters are derived from empirical values. Aiming at the complex multi-source disturbance of an aircraft wing, this paper separately probes the influence of external disturbance (air disturbance) and internal disturbance (engine vibration) based on the real-time observation of sensors and classifies the wing deformation on the basis of auto-regressive (AR) modelling for parameter identification. With the authentic flight data of a certain types of aircraft, the experimental analysis shows that the wing deformation under the influence of engine vibration is the 14th-order AR model, and the wing deformation under the influence of turbulence is the fifth-order AR model. Meanwhile, this paper also provides an experimental verification idea for the wing deflection modelling built on the second- or third-order Markov model.

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.

Wayfinding skills decay in old age, more so for wayfinding in an allocentric than an egocentric reference frame. This study investigates whether wayfinding deficits of schoolchildren mimic those of older adults. Schoolchildren were tested on two wayfinding tasks: one could only be mastered in an allocentric, and the other only in an egocentric reference frame. The results were compared with those from a previous study of young and older adults who had been tested on the same two wayfinding tasks. It was found that wayfinding performance improved somewhat from school age to young adulthood and that this improvement proceeded more or less in parallel for the allocentric and the egocentric tasks. It was further found that wayfinding performance decayed from young to older adulthood and that this decay was more dramatic for the allocentric than for the egocentric task. This pattern of findings does not support the hypothesis that the wayfinding performance of schoolchildren mimics that of older adults.

Despite the crucial role played by nautical cartography during the 16th-century Iberian Expansion, surviving examples of charts used at sea are extremely rare, leaving gaps in our knowledge of how they were used in practice during this pivotal period. The present paper sheds light on this matter by introducing one of earliest extant Portuguese charts presenting positional fixes, which have so far gone unnoticed by researchers: the anonymous chart of about 1524 kept at the James Ford Bell Library. It is demonstrated that a second chart, kept at the Harry Ransom Center, was made by the same author from the same pattern. The production context of the charts is evidenced through a description of the manuscript copying technique most likely employed, and the rules governing chart manufacture in 16th-century Portugal. Exceptional aspects of the charts’ placenames are discussed, and a possible source for their geographical design is identified.

Spatial boundaries play an important role in defining spaces, structuring memory and supporting planning during navigation. Recent models of hierarchical route planning use boundaries to plan efficiently first across regions and then within regions. However, it remains unclear which structures (e.g. parks, rivers, major streets, etc.) will form salient boundaries in real-world cities. This study tested licensed London taxi drivers, who are unique in their ability to navigate London flexibly without physical navigation aids. They were asked to indicate streets they considered as boundaries for London districts or dividing areas. It was found that agreement on boundary streets varied considerably, from some boundaries providing almost no consensus to some boundaries consistently noted as boundaries. Examining the properties of the streets revealed that a key factor in the consistent boundaries was the near rectilinear nature of the designated region (e.g. Mayfair and Soho) and the distinctiveness of parks (e.g. Regent's Park). Surprisingly, the River Thames was not consistently considered as a boundary. These findings provide insight into types of environmental features that lead to the perception of explicit boundaries in large-scale urban space. Because route planning models assume that boundaries are used to segregate the space for efficient planning, these results help make predictions of the likely planning demands of different routes in such complex large-scale street networks. Such predictions could be used to highlight information used for navigation guidance applications to enable more efficient hierarchical planning and learning of large-scale environments.

What are the major factors contributing to ship accidents, and how do these factors evolve in the long term? This study addresses these two questions by leveraging an unsupervised machine learning method named structural topic modelling to identify the causes of ship accidents. The study analysed 2,341 task errors manually collected from 441 reports issued by four government agencies covering a 45-year time span. The results show that the structure of causes of ship accidents remained essentially the same during this period. This highlights the social-material aspect of navigation technology, indicating that the use of advanced technology may not necessarily lead to safer navigation practices, and the interaction between the technology and human agency must be focused on in the bridge management context. Additionally, the computer-assisted textual data analysis highlights pilot-related factors, which might be rooted in the unsupervised and difficult-to-verify handover procedures between pilots and captains, thereby underlining the importance of appropriate piloting regulations.

When conducting accident analysis, the assessment of risk is one of the important links. Moreover, with regards to crew training, risk cognition is also an important training subject. However, most of the existing researches only rely on a single or a few data sources. It is necessary to fuse the collected multi-source data to obtain a more comprehensive risk evaluation model. There are few studies on the three-dimensional (3D) multi-modal data-fusion-based trajectory risk cognition. In this paper, a fuzzy logic-based trajectory risk cognition method is proposed based on multi-model spatial data fusion and accident data mining. First, the necessity of multi-model spatial data fusion is analysed and a data-fusion-based scene map is constructed. Second, a risk cognition model fused by multiple factors, multi-dimensional spatial calculations as well as data mining results is proposed, including a novel ship boundary calculation approach and newly constructed factors. Finally, a radar chart is used to illustrate the risk, and a risk cognition system is developed. Experiment results confirm the effectiveness of the method. It can be applied to train human operators of unmanned ship systems.

The use of multiple observations near noon with a traditional sextant to determine a fix is common among celestial navigators. A recent invention is the fixed-angle ‘Bris sextant’ that comes with advantages, but imposes constraints due to its invariant nature. We propose a method by which both longitude and latitude can be fixed using only two sightings with such a device, each equidistant from the meridian. By modelling the solution space for the method, we explore some of the potential utility across geography and seasonal variation. Although this method was developed for use with a Bris fixed-angle sextant, it can also be conveniently used with a more traditional marine or level-bubble sextant. Because this method is computationally cumbersome, it is most convenient when used in a computer or tablet application, or with tables.

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.

Almost all robust stereo visual odometry work uses the random sample consensus (RANSAC) algorithm for model estimation with the existence of noise and outliers. To date, there have been few comparative studies to evaluate the performance of RANSAC algorithms based on different hypothesis generators. In this work, we analyse and compare three popular and efficient RANSAC schemes. They mainly differ in using the two-dimensional (2-D) data points measured directly and the three-dimensional (3-D) data points inferred through triangulation. This comparison presents several quantitative experiments intended for comparing the accuracy, robustness and efficiency of each scheme under varying levels of noise and different percentages of outlier conditions. The results suggest that in the presence of noise and outliers, the perspective-three-point RANSAC provides more accurate and robust pose estimates. However, in the absence of noise, the iterative closest point RANSAC obtains better results regardless of the percentage of outliers. Efficiency, in terms of the number of RANSAC iterations, is found in that the relative speed of the perspective-three-point RANSAC becomes superior under low noise levels and low percentages of outlier conditions. Otherwise, the iterative closest-point RANSAC may be computationally more efficient.

Recent progress in using real-time kinematic (RTK) positioning has motivated the exploration of its application due to its high accuracy and efficiency. However, poorly-observed satellite data will cause unfixed ambiguities and markedly biased solutions. A novel partial ambiguity resolution method, named the irrespective of integer ambiguity resolution (IIAR) model, is proposed and applied to improve the reliability of ambiguity resolution. The proposed method contains initial ambiguity resolution and irrespective of integer ambiguity processes. The initial ambiguity resolution process applies an iterative partial ambiguity resolution method to obtain an approximate solution. The irrespective of integer ambiguity process transforms the approximate solution to a high-precision solution. Experiments show that the approximate solution is unreliable when the initial ambiguity resolution process has small redundancy, and the proposed method can obtain better results for those cases. The IIAR method showed about a 40% improvement of multi-GNSS ambiguity success rate and about a 25% improvement of standard deviation. Therefore, these results show that the proposed IIAR method can improve the results of multi-GNSS RTK positioning significantly.

Cadets training to become licensed mariners based on the International Convention on Standards of Training, Certification and Watchkeeping for Seafarers (STCW) Code have been under pressure to keep up with the countermeasures against COVID-19 from the Spring of 2020. For several reasons, sea training voyages were restricted or cancelled, and the schooling style was drastically changed from face-to-face to remote. Since the research vessel owned by Tokai University is not a training vessel exclusively for cadets, the decision was inevitably made to make more effective use of the shiphandling simulator. Because training in the simulator also had to be done remotely, new ideas were put into practice to explore the possibility of building new educational methods. Numerous open-ended evaluation comments were submitted by the cadets who received remote training on the simulator. The results suggested that the remote use of the simulator is likely to be an effective method for training in bridge resource management (BRM).

Inadequate human actions are still the main cause of all reported accidents and incidents on board ships. The aim of this study is to explore the influence of safety resource activities and other exploratory variables on seafarers’ safety behaviour. For this study, a series of open-ended interviews were conducted to gain insight into how shipping organisations struggle with this issue. Following the interviews, a questionnaire was prepared and distributed to professional seafarers. Two exploratory factor analyses were conducted to identify the underlying factor structure and five factors emerged. Furthermore, three hierarchical multiple regression analyses were conducted to examine the influence of the factors obtained, namely, Company safety orientation and Additional safety incentives on seafarers’ perceived Safety awareness, Job satisfaction, Risk acceptance and other exploratory variables. The study shows that the perceived resource-related activities of the organisation and the demographic characteristics of the respondents can influence the safety behaviour of seafarers.