Columbus's first voyage to America has been widely regarded as a considerable feat of navigation. Feat it certainly was, but the great advances in navigation during the fifteenth century were in fact made by the Portuguese, whose adaptation and development of Mediterranean methods to the more demanding requirements of the ocean made the European voyages of discovery possible. It was in Portugal too, probably during the years 1478–85, that Columbus acquired his knowledge of navigation. This paper, which was presented to a meeting at Brown University, USA on 26 September 1989, where the author was Gulbenkian Research Fellow at the John Carter Brown Library, examines navigational practice in the Mediterranean during the late middle ages and its subsequent development during the Great Age of Discovery.

We proposed an adaptive H-infinity Cubature Kalman Filter (AH∞CKF) to improve the navigation accuracy of a highly manoeuvrable unmanned aerial vehicle (UAV). AH∞CKF fuses the Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) measurements. Traditional state estimation filters like extended Kalman filters (EKF) and cubature Kalman filters (CKF) assume Gaussian noises. However, their performance degrades for non-Gaussian noises and system uncertainties encountered in real-world applications. Thus, designing filters robust to noise and distribution is crucial. AH∞CKF combines H∞CKF design with an added adaptive factor to adjust the state estimation covariance matrix according to measurements by exploiting the square root method to yield more numerically stable results (SrAH∞CKF). We conducted multiple dynamically rich flight tests to validate our claims using a UAV equipped with a commercially well-known GNSS solution. Results show that the SrAH∞CKF state estimation outperforms EKF and CKF methods on average by 90% in various statistical measures.

Many ingenious mechanical methods were used by hydrographic surveyors for measuring the depth of water in the early part of the 20th Century. These were superseded by echo-sounding and sonar techniques in the later decades. Relatively few of the mechanical methods were used by merchant ships but, in the years before radar and satellite navigation, they, and the increasingly popular echo sounder, had a useful place in the navigator's armoury of navigation aids. This paper is not intended to provide a detailed description of the development of sounding devices. Sections 1 to 5 simply outline the principles of the sounding devices with which the authors were familiar during their time at sea. In Sections 6 to 9 the authors recount their anecdotal experiences of the way in which they, personally, used depth measuring devices during the middle years of the 20th century.

CAPTAIN JAMES COOK is deservedly esteemed as a great seaman, and he must be acclaimed also in the more particular role of a great navigator. For although he made no specific contribution to the art of navigation as such, he advanced it by sheer force of character. It was, indeed, a task for the mathematicians and astronomers, not for the sailors, to lay down new principles and new observations or calculations by which a ship's position could be found and her course directed when at sea. And it was for the mathematical and optical instrument-makers to design and perfect the instruments by which such observations could be made. But, in the last resort, everything depended upon the ships' captains, the masters and the pilots. They alone could decide whether some novel principle should be mastered, some new instrument actually used. ‘We have piped unto you and ye have not danced’ is a cry which echoes through the ages. For the sailor was not alone in turning a deaf ear to the advice of public men, scientists and his own professional instructors. He was hostile to change, he preferred some old rule of thumb. And this is to be expected from all such men as learn the actual practice of their trade or craft by working beside an experienced master who in turn is passing on the traditions of an earlier generation.

Navigation is a human activity with the aim being to arrive at a predetermined destination. In order to find the way to the destination, the use of current input from the actual environment while travelling is needed as well as stored and organized knowledge of the local geography. Although the knowledge requirement has been studied extensively in the form of cognitive maps or other spatial representation, few studies deal with how the knowledge is used together with the input from the actual environment while navigating.

Aiming at improving the poor real-time performance of existing nonlinear filtering algorithms applied to spacecraft autonomous navigation based on Global Positioning System (GPS) measurements and simplifying the algorithm design of navigation algorithms, a spacecraft autonomous navigation algorithm based on polytopic linear differential inclusion is proposed in this paper. Firstly, it is demonstrated that the nonlinear estimation error system of spacecraft autonomous navigation can be modelled as a polytopic linear differential inclusion system model according to the idea of global linearization. Thus, the filtering of a nonlinear system simplified to a filtering of a polytopic linear system with coefficients. Secondly, Tensor-Product (TP) model transformation is applied to determine the polytopic linear differential inclusion system model. The model error introduced by global linearization is reduced and the compromise between computational complexity and modelling accuracy is realised. Finally, a spacecraft autonomous navigation algorithm based on polytopic linear differential inclusion is designed by combining multi-model Kalman filtering with data fusion. Compared with an Extended Kalman Filter (EKF), the proposed algorithm is simpler and easier to implement since it need not update the Jacobian matrices online. Simulation results demonstrate the same estimation accuracy of the proposed algorithm to that of EKF.

A ship's perception of risk is an important basis for collision avoidance. To improve such perception, several risk measurement parameters on the ship domain are determined, including the approach factor, the time to domain violation (TDV) and the possible collision domain. Then, a risk hierarchy prewarning (RHP) model based on the violation detection of a ship domain is proposed, in which a two-level alarm scheme is adopted accordingly. A low-intensity alarm will be activated by reaching the minimum approach factor and the TDV threshold, and a high-intensity alarm will be activated by the factor of the possible collision domain and the TDV threshold. Subsequently, a novel guard zone in ARPA radar utilising the RHP model has been developed to establish a ship's risk perception system for officers on watch at sea. The model proposed in this paper can not only enhance the veracity of risk assessment around our own ship, but also be used as a decision support system for collision avoidance.

The layout of seafloor datum points is the key to constructing the seafloor geodetic datum network, and a reliable underwater positioning model is the prerequisite for achieving precise deployment of the datum points. The traditional average sound speed positioning model is generally adopted in underwater positioning due to its simple and efficient algorithm, but it is sensitive to incident angle related errors, which lead to unreliable positioning results. Based on the relationship between incident angle and sound speed, the sound speed function model considering the incident angle has been established. Results show that the accuracy of positioning is easily affected by errors related to the incident angle; the new average sound speed correction model based on the incident angle proposed in this paper is used to significantly improve the underwater positioning accuracy.

This paper presents accurate orbit determination (OD) of the Iran University of Science and Technology Satellite (IUSTSAT) from Global Positioning System (GPS) data. The GPS position data are treated as pseudo-measurements within an onboard orbit determination process that is based on the numerical integration of the equations of motion using an earth gravity model and applying an Extended Kalman Filter for the data processing. In this paper, through accurate tuning of GPS duty cycle and on/off time intervals, a solution is suggested to achieve the desired OD accuracy despite power constraints. Moreover, a new scheme for automatic fault management in the orbit determination system is derived that provides fault detection and accommodation features.

Integer ambiguity validation is pivotal in precise positioning with Global Navigation Satellite Systems (GNSS). Recent research has shown traditionally used ambiguity validation methods can be classified as members of the Integer Aperture (IA) estimators, and by the virtue of the IA estimation, a user controllable IA fail-rate is preferred. However, an appropriately chosen fail-rate is essential for ambiguity validation. In this paper, the upper bound and the lower bound for the IA fail-rate, which are extremely useful even at the designing stage of a GNSS positioning system, have been analysed, and numerical results imply that a meaningful IA fail-rate should be within this range.

This paper briefly reviews some of the research findings with respect to factors which affect the efficiency of radar operation. One of the most important factors in determining whether or not a radar target will be visually detected is the brightness of the radar scope. A simple method is described for setting optimum scope brightness. Visual search habits are discussed and the implications of such habits for the design of radar displays are pointed out. Reference is made to some of the design factors which determine the accuracy with which target range and bearing are reported. It is shown that human monitors perform less efficiently as a watch progresses and factors which impair or aid their vigilance are described. Finally, a brief account is given of illusions on radar displays.

The Royal Institute of Navigation, with its counterparts in France and Germany, played a fundamental role in the introduction of traffic separation at sea, a role that is freely acknowledged in Imco's publications on the subject. J. H. Beattie, who was a member of the successive international working groups whose reports led to the introduction of routing, first of all in the Dover Strait and later throughout North West Europe, recounts the history of routing at sea, whose origins lay perhaps in the Great Lakes. A condensed version of this paper was presented at an Ordinary Meeting of the Institute on 14 December 1977, followed by Captain Emden's paper which is printed at page 203 with the ensuing discussion. Captain Maybourn was in the chair.

Air traffic control (ATC) makes extensive use of computer technology in subordinate roles for processing flight-plan and radar data and for message switching. It is usual to stress that such computers are aids to human controllers who take the decisions. It can, however, be argued that computers are, in fact, already encroaching on the decision-taking processes. The SSR plot extractor, for example, produces a censored summary which amounts to only a few per cent of the torrent of radar data from which it is derived. This summary is then subjected to code conversion and coordinate transformation before it reaches the controllers who cannot refer back to the data sources. Once computer-processing has been introduced, the issue is no longer whether a computer may take some of the decisions involved in ATC, but merely the extent of the authority it can exercise.

This paper first presents some of the results of my recent work on error distributions in navigation which may be worth summarizing for navigation practitioners. Some further explanations and insights in the second part may be useful for future studies on the subject.

Discussion on this subject was initiated by E. W. Anderson who questioned the adequacy of the gaussian distribution as the probability model for navigational position errors. He observed that empirical position error distributions are usually long-tailed (i.e. with raised skirts) compared to the gaussian and have a strong tendency to form an exponential function of error magnitude, especially in the far tail-region. Attempts to explain this phenomenon have been made by Abbott, Crossley, Lloyd, Parker, Lord, O. D. Anderson, etc., based on various aspects of navigation performance. To provide a general structure for characterizing the error distributions, Anderson and Ellis made a significant step forward in suggesting ‘Student's t’ distributions as error models. As pointed out by Parker, however, this suggestion has to be taken with reservation and requires further verification based upon empirical data. My own recent work has indeed taken the direction advocated by Parker and has attempted to fill a theoretical deficiency in Anderson and Ellis's work, to provide examples of empirical model fitting and to discuss the merits of Student's t distributions relative to the double exponential model. The main findings are summarized below.

1. Introduction. Active MTC (Marine Traffic Control), in its various forms, is at present mainly confined to port areas and canals and their approaches, whereas all other areas are mainly subject to passive MTC measures; that is, the Collision Regulations, including traffic separation schemes, areas to be avoided by certain classes of vessels, deep water routes, etc. The Collision Regulations, however, despite many attempts to improve them, are fundamentally flawed by specious logic sanctioned, unfortunately, by legislation which is supported in turn by the well-meaning connivance of the courts. This paper highlights some of the insoluble problems of the Collision Regulations and looks at the planning of ocean passages, weather routeing, search and rescue, and fishery protection; and shows that there is already a measure of active MTC in these areas of activity. The future possibility of a comprehensive global active MTC system to deal with avoidance of collisions and strandings, in addition to those other activities, is considered with respect to technical feasibility and to social and political impediments.

Over the last two decades, my colleagues and I have sailed a modern reconstruction of a Polynesian voyaging canoe some 40 000 nautical miles through Polynesian waters. This programme has been driven by two intertwined goals: one experimental – to test the sailing technology and navigational methods of the ancient Polynesians in order to resolve issues in Polynesian prehistory; and the other cultural – to enable contemporary Polynesians to relearn the means by which their ancestors found and settled their islands, and thereby gain a better sense of their uniquely maritime heritage and, ultimately, themselves. This paper focuses on the effort to rediscover how to navigate without instruments, and how that rediscovery is helping both to change scientific thinking about the colonization of Polynesia and to transform the selfimage of contemporary Polynesians.

This paper presents a novel estimation method for coarse alignment of a marine strapdown inertial navigation system (SINS) under mooring conditions. The properties of gravitational motion are used to improve the accuracy of coarse alignment. The parametric motion of gravitational apparent is a circle that is on the surface of a sphere. The location of this parametric circle is dependent on the definition of the reference frames and the initial angles of SINS. In the method proposed here the initial direct cosine matrix is calculated only from the location of the gravity motion parametric circle. The novelty of this paper is to provide a new method for estimating the gravity motion trajectory in inertial frame, as well as direct extraction of the initial direct cosine matrix from this estimated trajectory. Simulation and testing show that the proposed method is suitable for coarse alignment in mooring conditions.

The advantages of being able to process marine radar imagery in an on-line computer system have been illustrated by study of some navigational problems. The experiments suggest that accuracies of the order of 100 metres may be obtained in navigation in coastal regions using map overlays with marine radar data. A similar technique using different radar imagery of the same location suggests that the pattern-recognition technique may well yield a position-keeping ability of better than 10 metres.

Of the great oceans of the world, the Atlantic, because of its violence, was the last to be mastered by man. The task in its entirety had to wait for the Portuguese sailors of the Renaissance. Isidore of Seville (c. 570–636), a Christian writer of the late Roman Empire, had written of the Atlantic that it was ‘incommensurable and uncrossable’. Although Pliny (a.d. 23–79) refers vaguely to the Canary Islands, all knowledge of them disappears in the Middle Ages until a Portuguese expedition under the command of the Italian Lanzarotto Malocello ‘re- discovered’ them in 1336. Italian charts of the XIVth century begin progressively to show the Canaries, Madeira, Porto Santo and the Azores, but all aligned along a N/S axis without any appreciation of the relative distances between them or how far they lay from the European shore. The first written evidence of the Portuguese ‘discovery’ of the islands of Madeira and Porto Santo appears in 1419–20 and of the Azores in 1427, about the same time as they began to be colonised under the aegis of Prince Henry of Portugal, called the ‘Navigator’. The difficulties of returning to them on regular voyages was to motivate the Portuguese to develop methods of measurement using the Pole Star as a navigational aid and this led, not only to a greater accuracy in placing the islands on the charts, but also to a greater precision in the charting of the west African coastline which they were progressively exploring during the second half of the XVth century.

Claims that Portuguese nautical astronomy originated in Aragon and was transmitted from there to Portugal or was introduced into Portugal from Germany by Regiomontanus and Martin Behaim have long ago been shown to be baseless.

In this paper, the accuracy of astronomical (astro) navigation will be considered against the wide variety of factors that affect it. A series of practical observations will be analysed and astro positions compared with GPS positions and the reasons for the differences discussed. The paper will reach the conclusion that only by understanding the processes of astro navigation can its accuracy be fully understood and properly used by a practical navigator.