The name of John Dee (1527–1608) is one which every navigator, whether seaman or airman, has good cause to respect. For he was the first to try to teach unscholarly English sailors the use of the spherical triangle to find the distance and direction of some desired haven on the globe. Nor was that his only contribution to nautical science. Yet historians have treated him slightingly, dubbing him astrologer and alchemist, by which words they understand ‘charlatan’. Consequently the popular picture of him is of a servile, ignoble figure, eager to dupe the first Elizabeth and her courtiers. The acclaimed mathematician, and the ever-ready instructor are forgotten. It is true, of course, that Dee cast horoscopes, and that he hoped to find the formula for transmuting the baser metals into gold. It is true, besides, that in middle age he took to crystal-gazing, believing that he conversed with angelic spirits. Hence when in 1583 he went abroad at the invitation of the Polish Prince Lasky, a mob broke into his house at Mortlake and wrecked his library, which contained over 4000 books and manuscripts, besides scientific instruments. But by this date his work on navigation had come to an end. Yet his simple account of his meeting with the medium Edward Kelly (who was indeed a cheat) reveals him as a sincere man. Kelly at once asked to see what feats he could perform, but, says Dee, ‘I truly excused myself therein, as not in ye vulgarly accounted magic either studied or exercised. But… I brought forth to him my stone in ye frame … and said to. him that I was credibly informed that to it, after a sort, were answerable aliqui boni Angeli—certain good Angels.’ We should perhaps echo, therefore, the judgment of Disraeli—Dee's imagination often predominated over his science—but science he had.

The Executive Secretary has referred to me two notes on this subject, one by M. S. Dixon and the other by Bruno Ortlepp. Although submitted independently, and at different times, they clearly relate not only to the. same technique, but also to the same set of observations.

Now much has been recently written on the determination of time, and thus of longitude, from observations of the Moon's altitude (for example, in this Journal, reference can be made to the notes by Francis Chichester, 19, 106, 1966; D. H. Sadler, 19, 107, 1966; J. J. Evans, 19, 392, 1966; and to the comments in the article by H.M. Nautical Almanac Office in 19, 133 and 1 $2, 1966) and it should be unnecessary toNrestate either the principle or the practical disadvantages of this method.

In mid-1985 the 20 metre outrigger canoe Sarimanok, built in the Southern Philippines from tropical forest materials, sailed out of Bali, Indonesia, to follow the direct east-west Indian Ocean track which the first Austronesian settlers of Madagascar may have taken.

This paper surveys the present methods of pilotage and berthing, discusses some of the statistics of collision and grounding in confined waters, and suggests the development of shipborne automatic control devices to be used for the pilotage and berthing of large vessels. The proposed system, with its associated shore-based equipment, would carry out a similar function to the automatic landing devices fitted in aircraft, and would be part of an overall marine traffic control system. This system would enable large ships to be berthed automatically in reduced visibility and improve the safety of the movement of large ships in congested waters. The author lectures in the Department of Marine Electronics at Southampton College of Technology.

Some lessons and observations experienced during a series of radar simulator courses in the period of one year are listed below:

1. The practice of plotting is generally favoured by the students and they learn quickly how to determine which targets are of concern and should be plotted and which targets may be rejected. It has to be pointed out fairly often that recordings should be taken down in an orderly manner and that—besides the time, bearing and range of a target—the heading and speed (or log reading) of the observing vessel should be written down with each set of observations.

Maritime traffic has significantly increased in recent decades due to its advantageous costs, delivery rate and environmental compatibility. With the advent of the new generation of marine radars, based on the solid-state transmitter technology that calls for much longer transmitted pulses, the interference problem can become critical. Knowing the positions and the heights of the ships, the mean number of the vessels in radar range can be estimated to evaluate the effects of their mutual radar interferences. This paper aims to estimate the probability density function of the mutual distances. The truncation of the density function within a limited area related to horizon visibility leads to a simple single-parameter expression, useful to classify the ships as either randomly distributed or following a defined route. Practical results have been obtained using Automatic Identification System (AIS) data provided by the Italian Coast Guard in the Mediterranean Sea.

This paper covers the wide area and short range locational technologies that are available for vehicle tracking in particular and mobile user security in general. It also summarises the radio communications services that can deliver information to the user. It considers the use that can be made of these technologies, when combined with procedures for delivering a response, in the security field, notably in relation to personal security, high-value load protection and the after-theft tracking markets.

There are endless regulations concerning the speed and size of vehicles on our roads, but none that apply to vessels using our maritime routes, even though there is a regular increase, in step with technical advances, in both the size and speed of ships. For reasons of economy roads are narrow, and the necessity to avoid obstacles means that they have to be winding. No such considerations apply at sea; changes of direction are slight and widely spaced out, nor are there any ditches or hedges to limit the width of the routes that are used. Nevertheless, studies of maritime traffic have shown that overcrowding is becoming more and more pronounced on the busiest routes, and the present tendency to develop oneway routes is an implicit recognition of the fact that the remedies for such overcrowding on the roads and at sea have something in common. One-way traffic, for example, is derived from the Collision Regulations (Rule 25). It is worth examining what help the Regulations can give in solving problems raised by the size and speed of ships.

The History of Air Navigation Group commissioned the author to provide a brief account of airborne DR development by discussing both the methods and the equipment used in the air. This first part covers the period before 1940. The split is arbitrary, although it is obvious from a British perspective that military events around that date had a major impact on the pace of navigation development. However, it is equally obvious that airborne DR developed alongside a worldwide technical and intellectual revolution. This aspect of the story is abstract and involves some conjecture, so the paper takes it for granted and concentrates instead on practical matters. Accounts of air navigators' experiences as well as material on DR theory and descriptions of DR equipment in navigation manuals, journals and various surviving research documents have been used as the source material.

Autonomous vehicles rely on a combination of sensors for safe navigation around the world. For precise localisation, high-definition (HD) maps are used. These maps are a representation of the world containing information about objects on the road infrastructure. Currently, there are tens of HD map makers, however, no rigorous description of the requirements for the accuracy of HD maps has been published yet. This study fills the gap and offers a mathematical description of the minimum required accuracy for HD maps. In the first part, we identify factors that influence the quality of a map. Based on that, we proceed to present our solution for determining the minimum required accuracy for HD maps, both for static and dynamic models, and present a new formula for the minimum necessary accuracy for HD maps.

This paper summarizes the current situation on maritime navigation transponders, including those used in the Global Maritime Distress and Safety System (GMDSS) and those installed in Rescue Co-ordination Centres (RCCs) and on board Search and Rescue boats, and discusses the possible future trends. The paper then describes the methods used and conclusions reached during a variety of tests carried out in Tenerife Roads, RCC Tenerife and on board Sociedad Estatal de Salvamento vessels, in order to determine the accuracy and efficiency of various ships' identification, positioning, location, tracking and homing systems in normal and distress situations. The systems tested included Radar/Automatic Radar Plotting Aids (ARPAs), Search and Rescue Transponders (SARTs), Target Enhancers and Radar Reflectors.

The whole question of Polynesian navigation is highly controversial. Dr. David Lewis's paper ‘Ara Moana: Stars of the Sea Road’, in the July issue of this journal, prompts me relate the story of Kau Moala in somewhat greater detail and to assess his achievements and motives, largely from his own account of his voyages.

Kau Moala was a Tongan Chief renowned for his epic feat of navigation which probably took place in the years just before 1800. The details come to us from a young English castaway named William Mariner, who spent several years in Tonga and knew Kau Moala personally. When Mariner got back to England his experiences were compiled by J. Martin and published by John Murray, London, in 1817. The work is generally known as ‘Mariner's Tonga’, the full title being An Account of the Natives of the Tonga Islands. The story of Kau Moala's famous Odyssey is given on pages 307–322 of volume I of the second edition, published in 1818. Mariner gives the Chief's name as Cow Mooaly.

The story starts with Kau Moala going from Tonga to Fiji to engage in some warlike adventures to enhance his prestige, as many another Tongan Chief had done before, and as several did later. After two years of fun and mischief he decided to return home, and set out in his large double canoe.

It may be interesting to report some measurements of refraction which Professor A. N. Black and I made this winter. These were made on the setting Sun, and as the altitude of the observing station was 480.0 ft. it was possible to carry the observations down to the horizontal and, in fact, under clear conditions, to −20′.

Introducing the notion of a pseudoloxodrome, we generalise a single-heading navigation to conformally flat Riemannian manifolds, under the action of a perturbing vector field (wind, current) of arbitrary force. The findings are applied to time-optimal navigation with the use of the Euler–Lagrange equations. We refer to the Zermelo navigation problem admitting space and time dependence of both a perturbation and a ship's speed. The necessary conditions for single-heading time-optimal navigation are obtained and the pseudoloxodromes of minimum and maximum time are discussed. Furthermore, we describe winds which yield the pseudoloxodromic and loxodromic time extremals. Our research is also illustrated with the examples in dimension two emphasising the single-heading solutions among the time-optimal trajectories in the presence of some space-dependent winds.

A paper by Captain J. F. Kemp under this title was published in the April number of this Journal together with some comments on these proposals. Further contributions to the discussion and a reply from Captain Kemp are printed below.

In the April issue of this Journal Captain Kemp has put forward a carefully considered proposal for making the Rule of the Road more effective. His proposal is well considered because he is aware of the audacity which its careful presentation conceals; he is also careful to suggest a change in the Rules only as a basis for discussion. His suggestion is precise, for it is simply to extend Rule 18 to all encounters, or in other words to require both vessels, when crossing or overtaking, to rotate the line of sight in the normal direction as required in Rule 18.

This paper proposes a novel speed optimisation scheme for unmanned sailboats by sliding mode extremum seeking control (SMESC) without steady-state oscillation. In the sailing speed optimisation scheme, an initial sail angle of attack is first computed by a piecewise constant function in the feed forward block, which ensures a small deviation between sailing speed and the maximum speed. Second, the sailing speed approaches to maximum gradually by extremum search control (ESC) in the feedback block. In SMESC without steady-state oscillation, a switching law is designed to carry out the control transformation, so that the speed optimisation system carries out SMESC in the first convergence phase and ESC without steady-state oscillation in the second stability phase. This scheme combines the advantages of both control algorithms to maintain a faster convergence rate and to eliminate steady-state oscillation. Furthermore, the strict stability of the speed optimisation system is proved in this paper. Finally, we test a 12-m mathematical model of an unmanned sailboat in the simulation to demonstrate the effectiveness and robustness of this speed optimisation scheme.

Binary Offset Carrier (BOC) modulation signals have been applied in Global Navigation Satellite Systems (GNSS) because they offer a higher positioning accuracy and higher multipath rejection. However, there is a drawback in that the autocorrelation functions have multiple side peaks, meaning that this technique also leads to the large main peak estimation error problem and a low correlation decision efficiency problem. In this paper, we propose a new Main Peak Extraction (MPE) method for high-order BOC signals to solve these problems. In the new method, the synthesis cross-correlation function is established, and the geometry graph is formatted to calculate the estimation main peak. We eliminate all side peaks and improve the main peak phase estimation precision under the condition that the sub-carrier phase is offset. The results of the simulation demonstrate that the new method can achieve better main peak decision efficiency, side peak cancellation ability and phase estimation performance than traditional methods.