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.

The problem of differences between the sea mile and the international nautical mile has been analysed. Algorithms for the calculation of sea miles with applications in different sailing methods on the ellipsoid that can be easily incorporated in modern microprocessor controlled navigational devices are proposed. These algorithms can also be employed on an outfit of large-scale nautical charts with a double scale in sea miles and international nautical miles.

The paper introduces a new method of solving multi-ship encounter situations for both open waters and restricted water regions. The method, called evolutionary sets of safe trajectories, combines some of the assumptions of game theory with evolutionary programming and aims to find optimal sets of safe trajectories of all ships involved in an encounter situation. In a two-ship encounter situation it enables the operator of an onboard collision-avoidance system to predict the most probable behaviour of a target and to plan the own manoeuvres in advance. In a multi-ship encounter the method may be used to help an operator of a VTS system to coordinate the manoeuvres of all ships. The paper contains a detailed description of collision-avoidance operators used by the evolutionary method and simulation examples of the method's results for digital maps.

Many researchers have studied vessel systems to enhance navigation safety at sea, or analysed the statistics of marine casualties of different flagged vessels as well as the fatalities and injuries in ferry accidents. However, little research has been devoted to port safety and especially navigation safety within Taiwanese territorial waters where over a 10-year period there have been 3428 marine accidents with 548 deaths and 524 vessels sunk. In this paper, we use the Grey Relational Analysis (GRA) to analyse the marine accident records of each of Taiwan's commercial ports from 1992–2003. Then, after interviewing the port authority managers and marine specialists, we discover the concerns felt by these professionals about Taiwanese commercial ports. We provide suggestions to strengthen port navigation safety.

Errors of different positioning algorithms for tracked targets used in the ARPA systems and their influence on estimated speed of targets is analysed. Examples show their significance in tracking targets at low ranges.

The issues in this paper are a continuation of those presented previously by the authors in The Journal. In this paper we discuss the changes in maritime navigation and their consequences. We show the changes taking place in the ship's navigation process and in development of Maritime Navigation Safety and Efficiency System (MNSES). The relations between these two processes are examined. As the result, a probable scope of the competencies required by future navigators is proposed.

This paper discusses the ship's navigation function, navigation processes, and navigational information. The relationship between these concepts and their substance are analysed in depth. However, the primary aim of this paper is to consider how the various types of navigational information and their content might be brought together in a logically defined structure as a Ship's Information System.

A new navigation method, called a Line of Sight Counteraction Navigation (LOSCAN) algorithm has been introduced to aid manoeuvre decision making for collision avoidance based on a two-ship encounter. The LOSCAN algorithm is derived from an extension of the basic principle of traditional missile proportional navigation, recognising that the objective of the latter is target capture rather than target avoidance. The basic concept is to derive an acceleration command so as to increase the misalignment between the ships' relative velocity and the line-of-sight. The algorithm includes a risk assessment and the generation of appropriate navigation commands to manoeuvre own ship free of collision if a risk of collision exists. Numerical examples have been used to demonstrate the effectiveness of the algorithm. The relationship between the distance at the closest point of approach with respect to early warning distance, and with the norm of the acceleration, has also been analysed. In operation, the collision avoidance decision making process is a complicated problem, with its solution subject to ship states, practical dynamic constraints, Collision Avoidance Regulations (COLREGS), encountering ship manoeuvre coordination and human decision making factors. The proposed algorithm provides a consistent manoeuvre signal to aid decision-making.

In the May 1997 issue of the Journal, a paper on this subject was presented by Captain Turner on behalf of the General Lighthouse Authorities. I read the paper with interest, and in general concur with their assessment of the situation. However, I think that the situation regarding visual Aids to Navigation (AtoN) needs further consideration.

This paper looks at the stimulus given by the practice and theory of navigation to certain problems in mathematical astronomy. The need for more accurate techniques of finding latitude and longitude, brought about largely by the great voyages of discovery and exploration as well as an increase in sea trade, gave rise to navigational instrument makers who produced devices of increasing accuracy. These craftsmen also made better measuring devices for the new observatories. Improvements in measurements led not only to new discoveries, but also made greater demands of theories underlying the practice of navigation. This gave impetus to the search for solutions to related problems in mathematical astronomy. Methods and special functions developed in this context were eventually to find application in a much wider range of problems in theoretical physics and engineering.