As long as man has ventured to go to sea, sailing directions have existed. Man's survival depended upon knowing the best fishing and hunting places and how to find these were secrets, told only to family or friends.

Later, sailing directions covered areas in the world where trade or new settlements had begun and, as early as 500 years B.C., some of these sailing directions were written down. They covered the Mediterranean Sea and part of western Europe and they were called PERIPLUS meaning ‘sailing around’. They contained almost the same information as sailing directions today, namely: harbours, anchorages, currents, possibilities for fresh water, provisions and other supplies.

Distance and course to steer along part of a great ellipse can be readily determined with the use of vector analysis and differential geometry. Although the resulting integral for distance is not amenable to direct solution, it can nevertheless be handled efficiently and quickly by available commercial mathematical software. In this paper, a method of computing distance along with course to steer is presented and is one that has been prepared with the syntax of a particular commercial mathematics package in mind. This approach was intended to appeal to the navigator who is interested in the mathematics of navigation, and who nowadays solves his problems with a portable computer.

Large container ships can only be berthed in hub ports with deep water, which requires a feeder ship service to transit and transport containers from the hub ports. This paper presents a feeder routing optimisation method for container ships through an intelligent Electronic Chart Display and Information System (ECDIS). ECDIS has been adopted to design routes and calculate the estimated time of arrival in two ports, and a mixed integer programming model is established for container vessel regional transportation where the shortest ship sailing time is designated as the objective function. In this paper, through using heuristic tour-route coding, the solution of the model based on genetic algorithms is presented to select ship capacities and routes simultaneously. Taking the Pearl River in China as an example, for different types of vessel capacity, vessel costs and fuel costs, 100 TEU and 150 TEU ship capacities with six optimal routes are selected to minimise sailing time and operating costs.

Marine accident frequencies reported in 20 different sources have been studied and compared. Further than this, comparisons were made with an analysis done by the present authors. There seems to be consistency within the sources in the use of the terms total loss, casualty and accident/incident. The rates were observed to decrease by an order of magnitude going from accident/incident to casualty and likewise from casualty to total loss. The overall frequencies were found to be in the range of 0·0009 to 0·07 total losses per 106 ship miles, 0·03 to 1 casualties per 106 ship miles, and 0·5 to 13 accidents/incidents per 106 ship miles. It was found that the frequency depends on visibility, brightness, geographical environment, age of vessel and size of vessel. Collision and grounding frequencies were found to increase with decreasing visibility, brightness and more restricted waters. Collision frequencies were found to increase with increasing size of vessel. Fire/explosion and structural damage frequencies were found to increase with increasing age, and collisions to decrease with increasing age. No firm trend was found from the effect of flag state or type of vessel.

In order to solve the problem of a strapdown Inertial Navigation System (INS) under a vibrating base, a ground fine alignment method is proposed in this paper, and it is about reconstructing the error equations of a strapdown INS. In this method, the effects aroused by the linear and angular vibration are considered as system and measurement noise; in addition, they are also regarded as the components of a system matrix. This setting avoids the effects of linear and angular vibration under a vibrating base. The results of simulation and experiment show that our method is suitable for a ground fine alignment of a strapdown INS under a vibrating base.

Precise GPS simulated data requires accurate simulation of the two major sources of error in GPS measurements, namely the ionospheric and tropospheric delays. The ionospheric delay modelling has been handled in a previous work (Farah, 2002). In this paper the simulation of the tropospheric delay is discussed. The suggested model should be accurate in estimating the tropospheric delay as well as capable of simulating high spatial variations of the troposphere resulting in more realistic simulated GPS data. In this paper, the EGNOS tropospheric correction model is considered as a possible tool for simulating the tropospheric delay in order to obtain more realistic simulated GPS data. Comparing the total tropospheric zenith delays from the EGNOS model with the CODE-tropospheric product has allowed the quality of the EGNOS model to be assessed. Four IGS-tracking stations have been selected for this study. Data from four non-consecutive weeks in different seasons over a period of one year were tested to assess the seasonal variation of the weather conditions. It is shown that the EGNOS model agrees well with the CODE-estimations with a mean zenith delay difference of approximately 2 cm. The maximum zenith delay difference between the EGNOS model and the CODE-estimations was in the range of 5 cm to 16 cm, which agrees well with previous studies. A second study has investigated the behaviour of the EGNOS model with other established tropospheric models such as the Saastamoinen, the Hopfield, the Marini and the Magnet model for three IGS-stations. It can be concluded from this study that the EGNOS model shows better agreement with the IGS estimations than the Magnet model and compares well with other models. The major shortcoming in the EGNOS model is its inability to simulate the variations in the troposphere over small regions. This shortcoming could be overcome by using the theory of Gaussian Random Fields, which has been previously used to model real life phenomena such as surface roughness (Chan, 1999). This paper was first presented at ION GPS 2003, the 16th Technical Meeting of the Satellite Division of the Institute of Navigation held at Portland Oregon, USA.

In nature, science and engineering, we often come across helicoidal surfaces. A curve on a helicoidal surface in Euclidean 3-space is called a loxodrome if the curve intersects all meridians at a constant azimuth angle. Thus loxodromes are important in navigation. In this paper, we find the differential equation of the loxodrome on a helicoidal surface in Euclidean 3-space. Also we give some examples and draw the corresponding pictures via the Mathematica computer program to aid understanding of the mathematics of navigation.

This is the second of two papers on Quantitative Safety Assessment – vital to the successful introduction of future Air Traffic Management systems. The focus is en route European controlled commercial traffic, particularly the mid-air collision risk. Part 2 develops soundly based and practical methods for safety assessment. The objective is to determine the key questions and the best ways to answer them. Aspects covered include lessons from Hazard Analysis and Airproxes together with ‘realistic’ risk budgeting. Two abstract concepts are introduced: Position Integrity and Reasonable Intent (essentially the need to be on the ‘right’ flight path), and their implications for risk calculations are discussed.

As the geographical meridians converge rapidly, traditional inertial navigation methods fail in the polar regions. Classic transversal navigation methods can address the problem by transversal rotation of the original north and south poles, but this can introduce errors based on the spherical Earth model. To reduce the principle errors, some fruitful research work using an ellipsoidal Earth model has been done. Under the ellipsoid Earth model, transversal navigation for polar region becomes a complex coupling problem. Considering the coupling of the three-dimensional motion, a more rigorous mechanism for transversal navigation using an ellipsoidal Earth model is proposed. Starting from the relationship between Euclidean coordinates and spherical coordinates, the main equations of transversal polar navigation based on an ellipsoidal Earth model are derived in detail. Complete mechanical arrangements of attitude, position and velocity calculation are presented. The new derivation in this paper completely avoids solving the ellipsoidal radius. Numerical results indicate that the proposed transversal navigation mechanism can outperform the traditional method, especially in the condition of vertical motion.

Many issues related to incorporating real-time spatial information within Geographic Information Systems (GIS) need to be investigated. It can be established that the concept of real-time in relation to the input, analysis, display, and output of complex spatial information depends directly on specific user applications. This dependency has been evident throughout the Naval Research Laboratory's development of a real-time GIS for hydrographic surveys. This paper contrasts the issues and requirements observed for this application with those of vector moving-map displays for high-speed aeronautical applications. It also attempts to quantify the influence of various factors and impacts affecting real-time response to specialised applications like vector moving-map displays.

Licensed mariners carried out two simulated navigation studies testing electronic chart and information display systems (ECDIS) against paper chart navigation. In the first study, six mariners each completed approaches to Halifax, Nova Scotia, harbour with good and bad visibility and a range of wind and currents. Conditions included chart with radar, ECDIS with radar overlay and ECDIS with separate radar. ECDIS produced better performance and a smaller workload than paper charts and the radar overlay was slightly better than the separate radar display. In the second study, six new mariners completed exercises with low visibility and heavy or light radar traffic using ECDIS with radar overlay, ECDIS without overlay and ECDIS with optional overlay. Mariners preferred the optional overlay but all three conditions produced about equal performance. Based on mariners' performance and expressed preference, we recommend that ECDIS systems provide optional radar overlays.

Recent studies show that basic satellite positioning is reaching its limits in terms of performance improvements. Further enhancements in positioning performance can be based almost entirely on augmentation and procedures supported by other systems. Considering the complexity of the interrelationship with additional systems, intrinsically different solutions are being developed to solve the positioning performance improvement problem. Here we present a new concept in positioning. Dubbed distributed positioning, it merges basic satellite positioning with advanced and assisted positioning procedures. The resulting complex synergy unavoidably includes the use of additional technologies in mobile communications, wireless Internet, and advanced computer systems. The real advantage from the introduction of distributed positioning lies in its capability to provide a significant improvement in overall positioning performance. Latest navigation status and up-to-date local environment models are much easier to apply on rover positioning, compared with classical assisted-GPS positioning procedures. Distributed positioning presents a completely different approach in positioning performance improvement, opening new prospects in research and development not only in the field of the satellite positioning, but also in telecommunications and computer engineering.

There can be little doubt that the overall standards of safety at sea are high, particularly with the traditional maritime nations. Cockcroft states that of a total of 22600 ships over 1000 g.r.t trading in 1979, 9400 were from the traditional maritime nations. He goes on to say that during the period 1977–9 these countries lost 16 ships out of a total of 189 worldwide losses. Thus the traditional maritime nations ran 41·59 per cent of the ships and incurred only 8·4 per cent of the losses. This does suggest that high standards are not universal and there may be considerable resentment among operators of high standard ships when casualties to sub-standard vessels result in the implementation of measures, such as marine traffic management systems, which give rise to increased operating costs.

In order to achieve high accuracy of autonomous navigation for Mars probes, an integrated navigation method using X-ray pulsar measurement and optical data of viewing Martian moons is proposed. For single X-ray pulsar measurement on board a Mars probe, navigation accuracy is low due to its poor observability. On the other hand, Phobos and Deimos, two natural moons of Mars, are important optical navigation information sources available for Mars missions. However, the Martian moons ephemeris bias and the differences between barycentre and centre of brightness of Martian moons will result in low navigation accuracy. The method of integrated navigation using X-ray pulsar measurement and optical data of viewing Martian moons can overcome the defect and achieve accurate navigation. Two sequential orbit determination algorithms, Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), are compared. The simulation results show this method can obtain high autonomous navigation accuracy during the phase of a probe orbiting Mars.

E-navigation poses significant challenges for shipping. The analysis of the legal norms in the International Regulations for Preventing Collisions at Sea (COLREGS) and court decisions supports the use of information technology on the bridge for the purpose of improving navigational safety. However, the current regulatory and standardisation requirements hamper the introduction of new information streams in navigational systems and remove the incentives for investment in navigation technology. The liability arising from navigational failures will remain on the employer of the crew irrespective of how the additional navigational information is provided to the navigational systems. The shipowner's liability may depend on the way information streams are provided to the ship only within the context of the Civil Liability Convention (CLC) 1992 and other similar pollution conventions where the characterisation of the navigational system as a navigational aid or an aid to navigation may decide the issue of liability. Research on the legal background of these terms underlines the need for a clear distinction between the two terms to be made. An interpretation is proposed which ensures that the CLC liability exception operates in accordance with the underlying legal requirements.

Visual navigation is comparatively advanced without a Global Positioning System (GPS). It obtains environmental information via real-time processing of the data gained through visual sensors. Compared with other methods, visual navigation is a passive method that does not launch light or other radiation applications, thus making it easier to hide. The novel navigation system described in this paper uses stereo-matching combined with Inertial Measurement Units (IMU). This system applies photogrammetric theory and a matching algorithm to identify the matching points of two images of the same scene taken from different views and obtains their 3D coordinates. Integrated with the orientation information output by the IMU, the system reduces model-accumulated errors and improves the point accuracy.

Autonomous navigation has become a key technology for deep space exploration missions. Phobos and Deimos, the two natural moons of Mars, are important optical navigation information sources available for Mars missions. However, during the phase of the probe orbiting close to Mars, the ephemeris bias and the difference between the barycentre and the centre of brightness of a Martian moon will result in low navigation accuracy. On the other hand, Satellite-to-Satellite Tracking (SST) can achieve convenient and high accuracy observation for autonomous navigation. However, this cannot apply for a Mars mission during the Mars orbit phase only by SST data because of a rank defect problem of the Jacobian matrix. To improve the autonomous navigation accuracy of Mars probes, this paper presents a new autonomous navigation method that combines SST radio data provided by two probes and optical measurement by viewing the natural Martian moons. Two sequential orbit determination algorithms, an Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are compared. Simulation results show this method can obtain high autonomous navigation accuracy during the probe's Mars Orbit phase.

In precise relative positioning applications, an effective approach to improve the interoperability of GNSS systems is the tightly combining or inter-system double-differencing of observations from the common frequencies that are shared by different constellations. As the BeiDou satellites are currently transmitting a B2 signal at 1207.14 MHz that is identical to the Galileo E5b signal, the inter-system double-differenced observations can also be created between observations from both systems at that particular frequency. In this paper, we will focus on the instantaneous ambiguity resolution performance analysis of tightly combining BeiDou B2 and Galileo E5b observations. The size and stability of phase and code Differential Inter-System Biases (DISBs) between BeiDou B2 and Galileo E5b signals are first investigated, in which the new BeiDou and Galileo satellites launched recently will also be included. Then, first results of the Tightly Combined Model (TCM) with a priori corrected DISBs (TCM_C) are evaluated in comparison to the Loosely Combined Model (LCM) and tightly combined model with unknown DISBs (TCM_F) in an instantaneous approach. It is demonstrated that the instantaneous integer ambiguity resolution performance can be improved using the TCM_C with respect to LCM and TCM_F.

The three research topics, ship collision risk assessment, ship traffic hotspot detection and prediction, and collision-avoidance based ship path planning, are vital for next-generation vessel traffic management and monitoring systems. The system development is closely related to big data analytics and artificial intelligence for restricted waters. This study, therefore, aims to analyse the state-of-the art of these three topics over the latest decade, identify research gaps, and shed light on future research avenues. To achieve these three objectives, we critically and systematically review related articles that were published during the period between 2011 and 2021. We believe that this comprehensive and critical literature review would have a significant and profound impact on the formal safety assessment and vessel traffic management, and monitoring studies because it is not only an extension but also an essential continuity work of the literature review on maritime waterway risk assessment and prediction, as well as ship path guidance for ship collision risk mitigation in accordance with current automation vessels development and modern intelligent port construction.

Measurement bias and lack of terrain features often cause false peaks during underwater terrain matching positioning, that is, there is more than one peak near the real position. Previous methods to address this problem have increased the number of measurement beams, but this also increases the data processing time and energy consumption. At the same time, the ratio of measured information that is used does not increase. In other words, we should increase the ratio of measured information that is used, not simply increase the amount of information that is measured. Conventional matching algorithms only use the height of nodes without considering surface information, which is composed of height and the position of multiple nodes in three-dimensional space. Multi-beam sonar can obtain the three-dimensional distribution of terrain nodes. This node information is not just a height sequence, as it is used in previous methods. If we consider the nodes as a three-dimensional distribution of points with height and position information, this increases the matching position information and more of the terrain features can be extracted from the same measured data. Hence, in this paper, a terrain positioning method called the Node Multi-information Fusion (NMIF) is presented. This method focuses on improving the stability and accuracy degraded by bias in the Digital Elevation Map (DEM), terrain repeatability, and other factors. First, the concept of a Single Node Data Packet (SNDP) is introduced. The SNDP includes elevation and surface information surrounding the node, such as roughness, gradient, and slope. This additional topographic feature information improves the robustness and accuracy of the system. A computer simulation using actual ocean bottom topography verifies the advantages of the proposed NMIF algorithm.