This paper considers a practical solution to the stopping distance of ships, with particular reference to modern giant tankers. One solution to the problem has already been evolved by Captain H. Topley of the Honourable Company of Master Mariners. The present paper tackles the same subject from quite a different viewpoint.

The basic assumptions on which the mathematical treatment has been based is presented in Section 1, which also includes the calculation formulae of the speed and distance run at any time in a manœuvre, without proofs. Section 2 deals with clarifying the essential differences between Captain Topley's theory and the author's. The validity of the theories is examined in Section 3 by comparison with the results of actual ship tests. Section 4 presents calculation diagrams prepared by the author.

The only reliable data available by means of which captains can predict the stopping behaviour of their ships after ordering STOP ENGINES are the results of inertia tests conducted at the sea trials when the ships were built.

The inertia tests, however, are usually performed for only one case in which the approach speed is assigned to HALF AHEAD or the so-called manœuvring full ahead speed. Therefore most masters are glad of any knowledge of how to predict the movements of ships from any reduced speed.

A significant feature of the modernised Global Navigation Satellite System (GNSS) signals is that there are multiple signal components needing to be transmitted on a carrier frequency. How to combine these signal components into a constant envelope composite signal is a challenge. Existing constant envelope modulation techniques have some limitations, and are not effective enough. To solve this problem, we propose a quasi-constant-envelope multiplexing technique in this paper. The proposed method is based on numerical optimisation, and can work in two ways. The corresponding objective functions are provided. To verify the performance of the proposed method, we present three application examples. Results show that the first variation of our method can reach the same combining performance as Phase-Optimised Constant-Envelope Transmission (POCET). In the second variation, the combining efficiency can be pre-set. We can reach higher combining efficiency than POCET, and the envelope of the composite signal becomes quasi-constant. Furthermore, the inter-modulation signals in the final composite signal are adjustable. With the help of the proposed method, we can learn more details of the combining scheme than with POCET.

This paper concerns the derivation of a formula to follow geographically fixed turns in a homogeneous current or tidal stream. Until now, various well-founded but limited approximations have been used. In principle, all these approximations are based on the formula v = ω × R. One result of this research is the development and use of a fast-time simulation program. The initial aim was to illustrate to trainees the consequences and, in particular, the possible dangers of these approximations. The fast-time simulation program can be used in support of real-time simulation. Comparisons with real-time simulations carried out by the Dutch Pilots' Corporation (STODEL) indicate that the fast-time simulations generate turning-circle diameters that differ by a maximum 4 percent. The relationship with path-prediction is also dealt with. The possibility of applying the developed formulae in practice and for passage planning is currently under investigation. The fast-time simulation program has not been developed for one specific ship: apart from the use of an assumed position of the pivoting point at 1/3 of the ship's length from the bow, it does not take hydrodynamic effects into account.

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.

A high-precision line-of-sight extraction technique is essential for autonomous optical navigation during the Mars approach phase. To support future Mars exploration missions, an optical image simulation system is a necessary ground verification facility for Mars image generation and line-of-sight extraction algorithm tests. In this paper, an optical image generation procedure is first developed according to projection relationships, reference flight profiles and camera parameters. Next, a hybrid image processing and subpixel-level line-of-sight extraction algorithm is proposed through modification of moment-based sub-pixel edge detection and improvement of direct least-square fitting approaches. Finally, an optical image simulation system is established, and the experimental results show that the proposed procedure can effectively simulate the optical image in the field-of-view of a Mars spacecraft, and the hybrid extraction algorithm can obtain high-precision Mars centroid information.

Navigational information is of great significance to the safety of maritime navigation. To better guarantee navigator safety and improve navigation efficiency, an applied model of geographic information services (GI services) that consists of an operational architecture, several subsystems and multiple GI services is presented. This work is an e-navigation testbed that follows e-navigation technical architecture and integrates a large amount of navigation-related resources. Real-time, location-based and on-demand digital navigational information can be exchanged and applied in a standardised way. An experiment conducted in the Pearl River Estuary area of the South China Sea showed that application of GI services in e-navigation can supplement the existing methods of exchanging navigational information and better assist navigators in decision making. Furthermore, the proposed model is adaptable and could be easily applied in other areas.

An innovative algorithm to determine the inverse solution of a geodesic with the vertex or Clairaut constant located between two points on a spheroid is presented. This solution to the inverse problem will be useful for solving problems in navigation as well as geodesy. The algorithm to be described derives from a series expansion that replaces integrals for distance and longitude, while avoiding reliance on trigonometric functions. In addition, these series expansions are economical in terms of computational cost. For end points located at each side of a vertex, certain numerical difficulties arise. A finite difference method together with an innovative method of iteration that approximates Newton's method is presented which overcomes these shortcomings encountered for nearly antipodal regions. The method provided here, which does not involve an auxiliary sphere, was aided by the Computer Algebra System (CAS) that can yield arbitrarily truncated series suitable to the users accuracy objectives and which are limited only by machine precisions.

Location and navigation services based on global navigation satellite systems (GNSS) are needed for real-time high-precision positioning applications in relevant economic sectors, such as precision agriculture, transport, civil engineering or mapping. Real-time navigation users of GNSS networks have significantly increased all around the world, since the 1990s, and usage has exceeded initial expectations. Therefore, if the evolution of GNSS network users is monitored, the dynamics of market segments can be studied. The implementation of this hypothesis requires the treatment of big volumes of navigation data over several years and the continuous monitoring of customers. This paper is focused on the management of massive connection of GNSS users in an efficient way, in order to obtain analysis and statistics. Big data architecture and data analyses based on data mining algorithms have been implemented as the best way to approach the hypothesis. Results demonstrate the dynamic of users of different market segments, the increasing demand over the years and, specifically, conclusions are obtained about the trends, year-on-year correlation and business volume recovering after economic crisis periods.

In this paper, a novel algorithm of weighted k-means clustering with geodesic criteria is presented to generate a uniform database for a star sensor. For this purpose, selecting the appropriate star catalogue and desirable minimum magnitude and eliminating double stars are among the steps of the uniformity process. Further, Delaunay triangulation and determining the scattered data density by using a Voronoi diagram were used to solve the problems of the proposed clustering method. Thus, by running a Monte Carlo simulation to count the number of stars observed in different fields of view, it was found that the uniformity leads to a significant reduction of the probability of observing a large number of stars in all fields of view. In contrast, the uniformity slightly increased the field of view needed to observe the minimum number of required stars for an identification algorithm.

I am very pleased to be with you on this occasion which gathers annually the friends and admirers of Professor Eva G. R. Taylor to honour her memory. My presence here reflects the globe-circling impact her work continues to have, as more and more people from many disciplines rely on her varied contributions. As for the distance of the echo to her work, I qualify, coming from close to half way around the globe, or from Long. 110° 58′ 08″ west of Greenwich. I have elected to talk about Felipe Bauzá who, on an autumn day of 1823, presented himself to the Royal Geographical Society here in London, some way north and east from his birthplace, Palma de Mallorca, and his port of departure, Gibraltar. For he was one of the Spanish liberals with a price on his head under orders of that treacherous puppet of the Holy Alliance, Ferdinand VII.

The standard height rules applied in off-route airspace are examined to assess the degree of intrinsic safety they provide, i.e. the reduction of conflicts without action being taken by pilots or ATC. The yardstick used is the conflict rate which would obtain if the aircraft were uniformly randomly distributed in the height dimension and flying straight and level on uniformly randomly distributed tracks. It is shown that the application of the standard rules can lead to a reduction in intrinsic safety unless significant height-keeping errors are present. An alternative height rule apparently having more desirable characteristics is examined on the same basis.

The problem of navigation in high latitudes is becoming increasingly important as the range of modern aircraft increases and the consequent inevitability of the extension of possible operational theatres to include polar regions becomes apparent. The provision of suitable maps of such areas is therefore a matter requiring attention in the near future, and the adoption of a standard projection together with uniformity of presentation of topographical detail must be regarded as a desirable objective in this connection. The aim of this paper is briefly to review and compare the various projections available and so assess which one is most suitable for the purpose.

The dip of the horizon resulting from the observer's height of eye can be calculated from the formula Dip = 1′·06√H, where H is the height of eye in feet, or by Dip = 1′·93√h, where h is the height in metres. In this paper the latter form will be used so that comparison can be made with studies in international publications.

In 1952 the Institute set up a Working Party, under the chairmanship of Mr. D. H. Sadler, to investigate the accuracy attained in the practice of astronomical navigation at sea. The report that follows was presented in summary to the Technical Committee on 15 February, 1957, and formed the subject of a discussion at the Institute's meeting on 21 June.

The following conclusions relate to a total of 424c, observations received by the Working Party from 173 observers, and are representative of navigational practice as a whole only in so far as the observations, and the observers, are so representative. Only 3319 observations from 1 r6 observers were retained as suitable for analysis, and in nearly half of these observations the ship's position is not known sufficiently accurately for them to be included in the main analysis.

The presence of any structure in the sea is a potential hazard to shipping navigating in its vicinity. It is therefore of considerable interest both to mariners and to engineers placing structures such as oil platforms in the sea to try to assess the attendant risk of collision, with such a structure.

We have over a period of time attempted several methods of assessing these risks and it was felt important to link this with our work on marine traffic flows, as experience of the traffic patterns in the southern North Sea was a useful input to the study. Hence we considered an area in the southern North Sea, to the eastwards of the outer Thames Estuary as far as the Middlebank and between the parallels of 51° 08´N and 52° 15´N, since we wished to look at the offshore situation; the area is nowhere less than 3 miles from the coast.

The aim of the Duke of Edinburgh's Lectures is ‘to extend the horizons of navigational interest’. I have been able to interpret this literally, for if you extend these horizons far enough, what do you arrive at but the subject of this lecture, the shape of the Earth? It is a subject which has been revolutionized in the past five years by analysis of the orbits of artificial satellites: the two years from 1958 to 1960 saw more progress than the previous 200 years, and since 1960 the pace of progress has shown no sign of slackening.

Six years ago, Mr. D. H. Sadler, in a memorable Presidential Address, answered the question ‘What is the Institute?’ This leads to the complementary and perhaps even more controversial question ‘What is navigation? What is its scope and its general pattern?’

If we look at the word Navigation in a dictionary, we may very well find that it is associated only with the sea. Today, of course, a much wider view is taken and the word is accepted as having to do with the land and the air and even with space. The definition: ‘the art of conducting a vessel on its ways’, may therefore be amended in words such as:

Navigation is the business of conducting a craft as it moves about its ways.

Autonomous Intelligent Cruise Control (AICC) will be marketed by a number of vehicle manufacturers before the end of the decade. This paper will describe AICC and the next generation systems currently being developed and validated within the EC Fourth Framework project, Anti-Collision Autonomous Support and Safety Intervention SysTem (AC ASSIST).

The currently available cruise control systems which maintain a fixed speed are a well-known form of longitudinal driver support. The fixed speed cruise control becomes less useful with increased traffic volumes, as the driver must disable the system when a slower preceding vehicle is encountered.

This paper presents development and application of a real-time virtual differential map-matching approach which makes use of the slow drifting property of the GPS errors and the continuous and gradual evolving characteristic of map errors to improve the accuracy and computational efficiency. A differential vector is created to approximate the real-time deviation, which is corrected continuously along with the vehicle movement during the map-matching process. Real-life application of the algorithm to the City of Hefei, a metropolis of China, shows that it corrects both GPS errors and digital map errors reasonably well with improved computational efficiency.

Global Navigation Satellite Systems (GNSS) are used widely in the provision of Intelligent Transportation System (ITS) services. Today, there is an increasing demand on GNSS to support applications at lane level. These applications required at lane level include lane control, collision avoidance and intelligent speed assistance. In lane control, detecting irregular driving behaviour within the lane is a basic requirement for safety related lane level applications. There are two major issues involved in lane level irregular driving identification: access to high accuracy positioning and vehicle dynamic parameters, and extraction of erratic driving behaviour from this and other related information. This paper proposes an integrated algorithm for lane level irregular driving identification. Access to high accuracy positioning is enabled by GNSS and its integration with an Inertial Navigation System (INS) using filtering with precise vehicle motion models and lane information. The identification of irregular driving behaviour is achieved by algorithms developed for different types of events based on the application of a Fuzzy Inference System (FIS). The results show that decimetre level accuracy can be achieved and that different types of lane level irregular driving behaviour can be identified.