Magnetic sensors have been used in navigation for many centuries. During this time the effects of magnetic interference from ferromagnetic materials used in vehicle construction have become an increasing problem, and correction techniques have evolved progressively to allow the continued use of magnetic heading detection. The advent of the microprocessor has made it possible to take a fresh look at the problems of compass operation in vehicles and to devise more accurate processes for the correction of the indicated heading. The compass system described in this paper uses a mathematical representation of the magnetic environment based on fundamental physical principles to supply accurate heading information even in the most magnetically hostile land vehicles.

This paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

The authors of this paper are the three General Lighthouse Authorities (GLAs) of the United Kingdom and the Republic of Ireland. It was presented on their behalf at the RIN-96 conference by Captain Turner. The paper gives a brief overview of the policy of the GLAs (i.e. the Corporation of Trinity House, the Northern Lighthouse Board and the Commissioners of Irish Lights) regarding the provision of an aids to navigation service with emphasis on the future prospects of traditional aids to navigation over the next 25 years. The three GLAs have recently carried out a consultation exercise on marine aids to navigation into the 21st century. The results of this consultation exercise are discussed. It should be noted that, for clarity, the General Lighthouse Authorities (GLAs) refer to the systems that they provide as ‘aids to navigation’ (AtoN), to differentiate their provision from the equipment carried on board ships for navigational purposes which are referred to by the GLAs as ‘navigational aids’. This paper therefore in the main deals with AtoN.

The coastlines within the GLAs' areas of responsibility rank with the most heavily trafficked and dangerous in the world. The coastlines vary from isolated rocks and the steep, Atlantic coastline, to the low-lying relatively featureless coastline of south-east England, off which are shifting sandbanks and channels. The tidal range in GLA waters is significant and tidal streams can reach 10 knots or more in a number of places.

It seems probable that the magnetic compass, the mariner's compass as it is often called, first made its appearance at some time between the tenth and twelfth centuries A.D. Attempts have been made to prove that the compass was in existence earlier, and that some of the early voyages could not possibly have been performed without its help; but there is no evidence to support this contention and a certain amount to show that other methods were used.

Again, it has been suggested that some obscure remarks by certain classical writers could be explained if the author were assumed to be describing the use of a compass, whilst having only the haziest notion of what it was. Among such is the legend of Abaris, the Hyperborean priest, who visited Greece, some say from Britain, many centuries B.C., and had with him a mysterious arrow which showed him the way. If we cut out the fancies of some writers who credited him with the possession of a kind of aircraft (capable of supersonic speeds), it is not difficult to imagine that the arrow may have been a magnetized needle. The difficulty is in understanding how no one down the centuries which followed came to write of the compass. There is, of course, little doubt that much scientific knowledge was possessed by the ancient priestly cults and the knowledge of the compass may have been kept secret for their own ends. If the great library of Alexandria had not been destroyed we might have had the answer to the riddle; but perhaps there is none and the whole tale of Abaris is a fabrication.

No account of the observations described in this paper has previously been published, though they were made nearly eighteen years ago. The author has kindly presented the Institute with all the data he obtained from them and with a detailed description of the investigation. We print here a short account of the observations and of the principal results obtained, which it is felt should go on record.—Ed.

Largely as a result of discussions with Dr. Per Collinder of the Swedish Hydrographic Service and Dr. Knut Lundmark, Professor of Astronomy at Lund, the author undertook, between June and August 1934, a series of sextant observations to determine the degree of refraction at low altitudes, the normal accuracy of sights at sea, the accuracy of twilight and night observations and possible elevations of the horizon at noon. 1908 observations were taken during the period.

The twelfth Duke of Edinburgh Lecture was presented in London on 15 October 1986 at the Royal Geographical Society to the thirty-ninth Annual General Meeting of the Institute, the President in the Chair. The lecturer, the President said in his introductory remarks, was a geographical scholar who had devoted much of his time to the verification of early voyages by following the paths described in the often legendary accounts:the travels of Marco Polo in 1961 and later the voyages on which the present paper is based, of St Brendan, Sindbad and Jason. In 1976–7 in the medieval leather boat Brendan he followed a route from Ireland across the Atlantic described in the 8/9th century Navigatio. In 1980–81 in the Arabian boom Sohar he sailed over 6000 miles from Oman to Canton in a reconstruction of Sindbad's seven voyages described in One Thousand and One Nights, and finally in 1984 in Argo, a reconstructed Greek vessel of the 13th century B.C., his voyage took him from Greece through the Bosphorus to Georgia in the USSR, following the legendary path of Jason in search of the Golden Fleece. No-one could be better fitted to reflect on the human factor in early navigation.

‘There are no charts of any part of the world so accurate and no directions so perfect as not to furnish frequent occasion for revision and amendment.’ (From the title page of the Nautical Magazine, 1832.)

In March 1832 a new monthly was published, the Nautical Magazine. Subsidized at first by the Admiralty and the Mercantile Marine Fund, it was edited by Beecher who was the right-hand man to Admiral Beaufort in the Hydrographic Department. Part of the introduction to this first volume read as follows: ‘The principal feature of the work will consist of the particulars of those hidden maritime dangers which are too often fatal to ships. … Much information, of a nature highly valuable to mariners, is scattered about, destitute of any systematic arrangement by which it can be made available to them; but the pages of the Nautical Magazine will hereafter become the receptacle, in which it will be preserved for their reference.’

For the efficient use of doppler techniques it is necessary that the beam of short radio waves, emitted from the aircraft shall be reflected from the roughness of the surface or from a plane surface at right angles to the incident beam. Over land there are plenty of roughnesses from which the beam is always thrown back, but over smooth sea there would seem to be no surface feature which can reflect the beam. It therefore is of interest to know the effect of surface winds in producing waves and ripples with various slopes and secondly the frequency with which light winds occur in various parts of the world.

The orbits of navigation satellites have to be determined very precisely. The Transit broadcast (predicted) ephemeris, which is computed by the US Navy Astronautics Group, has an estimated orbital positional accuracy of the order of 25 m in each direction. By contrast, the precise (post-mission) ephemeris, which is determined by the US Defense Mapping Agency, from tracking data collected by the global TRANET network, reaches accuracies of the order of 10 m. These orbital precisions affect the navigation and (static) positioning accuracies which can be achieved by users of the system. The same is true of the GPS system which will become fully operational some time during 1988—89. However, unlike Transit, GPS will allow quasi-instantaneous absolute positioning (i.e. real-time navigation) as well as very high relative positioning accuracies. The latter will be obtained by using special operational and processing techniques (e.g. ‘differential GPS’ and ‘GPS interferometry’).

During the first years of the last war the navigational problem was how to get to the target at all. In such conditions solutions to the navigation problem are priceless. Towards the end of the war it came to be accepted that, in transport operations at least, guidance to destination was almost a matter of course. Navigational performance ceased to be regarded as a question of success or failure and became a question of efficiency. This development in air transport we owed most of all to the radio compass.

As the volume of civil traffic grew, it rapidly became clear that the major limitation on navigational efficiency of air transportation was (and it still is) air traffic control. Although there has been considerable interest in the optimum trajectory particularly in connection with turbine aircraft, the development of refined operating techniques has been damped by restrictions on their application by A.T.C. The flat assertion by some would-be supersonic aircraft manufacturers that the supersonic (unlike the subsonic) jet will not take NO for an answer from A.T.C. once it is committed to a flight programme has recently been a most valuable stimulus.

The A.T.C. problem is well known. It is generally accepted that the capacity of an air space depends on the quality of navigational data, of the data link between aircraft and control centre and of the data correlation capabilities of the centre.

On 26 November 1954 The Mathematical Practitioners of Tudor and Stuart England by E. G. R. Taylor was published for the Institute by Cambridge University Press. Dr. Derek Price, of the Whipple Museum of the History of Science at Cambridge, here describes the book for the Journal.

During the last twenty-five years there has been a revolution in writings on the history of science. Now, just as the profits are beginning to materialize, a second great change has occurred.

There are now radar installations which track ships automatically, and these radars can provide the researcher with statistics on collision-avoidance manoeuvres. The extraction, by hand, is laborious and time consuming. This paper describes a mathematical model which automatically detects collision-avoidance manoeuvres. The model operates on an adaption of the Range to Domain Over Range Rate (RDRR) principle, which enables ships to be identified for analysis shortly before they are expected to initiate a collision-avoidance manoeuvre. The model has been computerized and results presented.

The use of VLF radio transmissions as the basis of a navigation system has been under consideration for many years, and has been the subject of extensive theoretical work and field trials. Although a system of this kind has yet to reach operational status, the subject is of considerable interest in relation to marine and to air navigation. This paper indicates the main features that might be expected to characterize a practical VLF navigational aid, and outlines some of the work that has been carried out in this field. Brief reference is made to the question, so far largely unresolved, of the operational scope for VLF systems.

A mainly theoretical study has been undertaken to demonstrate how the extent of cover from a hyperbolic navigation system chain can be evaluated. The impetus for the study was the need to assess how Loran-C could be extended over Western Europe, particularly in the South western Approaches, North Sea, English Channel and Bay of Biscay sea areas.

The technique described in this article leads to an accurate determination of the electric field strength at a distance from each transmitting site and takes into account the complexities of the ground-wave propagation path. This field-strength contour is combined with the geometric effects of station siting (expansion factors) to yield a constant S/N contour (–10 dB) which defines the ¼n.m. error and hence the limit of cover for the hyperbolic chain under study.

In order to exercise the analytical methods a hypothetical Loran-C chain was studied comprising a master station at Lessay (France), with secondary stations at Soustons (also in France), at Sylt (dual rated; off the North Sea coast of Germany, near the Danish border) and at a fourth station located in north-west Britain on the Hebridean island of Barra. The study indicated that such a hypothetical chain would significantly improve Loran-C cover over much of western Europe.

To address the shortcomings of existing methods for rotorcraft searching, positioning, tracking and landing on a ship at sea, a dual-channel LIDAR searching, positioning, tracking and landing system (DCLSPTLS) is proposed in this paper, which utilises the multi-pulse laser echoes accumulation method and the physical phenomenon that the laser reflectivity of the ship deck in the near-infrared band is four orders of magnitude higher than that of the sea surface. The DCLSPTLS searching and positioning model, tracking model and landing model are established, respectively. The searching and positioning model can provide estimates of the azimuth angle, the distance of the ship relative to the rotorcraft and the ship's course. With the above parameters as inputs, the total tracking time and the direction of the rotorcraft tracking speed can be obtained by using the tracking model. The landing model can calculate the pitch and the roll angles of the ship's deck relative to the rotorcraft by using the least squares method and the laser irradiation coordinates. The simulation shows that the DCLSPTLS can realise the functions of rotorcraft searching, positioning, tracking and landing by using the above parameters. To verify the effectiveness of the DCLSPTLS, a functional test is performed using a rotorcraft and a model ship on a lake. The test results are consistent with the results of the simulation.

With the development of sensor technology, sensor nodes are increasingly being used in underwater environments. The strategy presented in this paper is designed to solve the problem of using a limited number of autonomous underwater vehicles (AUVs) to complete tasks such as data collection from sensor nodes when the number of AUVs is less than the number of target sensors. A novel classified self-organising map algorithm is proposed to solve the problem. First, according to the K-means algorithm, targets are classified into groups that are determined by the number of AUVs. Second, according to the self-organising map algorithm, AUVs are matched with groups. Third, each AUV is provided with the accessible order of the targets in the group. The novel classified self-organising map algorithm can be used not only to reduce the total energy consumption in a multi-AUV system, but also to give the most efficient accessible order of targets for AUVs. Results of simulations conducted to prove the applicability of the algorithm are given.

An airport can be a stressful place for passengers. One of the reasons to get stressed might be the result of poor wayfinding. Current wayfinding signs are often static, which makes them difficult to adapt to new situations. In contrast, dynamic signs can be updated and adjusted accordingly. Light projections can be used as dynamic signs. The aim of this study is to understand if the use of animated projections onto the floor can improve the wayfinding experience. Four animations have been developed and tested within a controlled testing environment of which one animation has been tested in a real airport environment. Results indicate that animation for wayfinding purposes should show a clear vertical motion to guide towards a certain direction. Additionally, higher velocity in the animation was perceived as more positive. The observation in the airport showed that a projection in clear daylight and on the floor is not noticed by the passengers walking by.

When our Norwegian ancestors wished to navigate in the open sea they could find their bearings by the Sun or stars if the sky was not overcast. In foggy weather they used the sólaisteinn or sunstone, ‘a stone with which one could see where the sun was in the heavens’. A knife blade will do equally well as may be seen from Fig. 1. If you place the point of the knife on your thumb nail, as shown in the figure, on a sunny day you can easily see the shadow it casts; turning the blade a little one way or the other the shadow widens, but when the knife edge points towards the sun the shadow is reduced to a narrow line.

In this paper the Lucasian Professor of Applied Mathematics in the University of Cambridge studies the role of ocean science in the service of mankind, and examines the interaction between the many disciplines which make up that science. The paper, which was written in May 1972 (and a version of which was published in the Bulletin of the Institute of Mathematics and its Applications for February 1973), was presented at a conference held in Greenwich on 12–14 September 1973 to celebrate the hundredth anniversary of the Royal Naval College. (Note: the National Institute of Oceanography referred to in the text is now known as the Institute of Oceanographic Sciences.)

Dynamic trajectory prediction is an important topic in the field of navigation and positioning. Due to the drawbacks of a Global Navigation Satellite System (GNSS) receiver, the trajectory of the position always lags behind the dynamic platform's actual position, especially in highly dynamic situations. In order to solve the prediction of a dynamic trajectory, a generalised extension extrapolated model is proposed in this paper. The model utilises the current motion state and a priori position data of the platform, combines the interpolation and fitting method, adds the angle information as a constraint condition and solves the platform position prediction. In this paper, the feasibility of the generalised extended extrapolation algorithm is analysed theoretically and practically. Simulation results show that the prediction error is within 0.2 metres and experimental results show that the algorithm still has high prediction accuracy when a land vehicle platform is turned through a large angle.