In a previous article in this Journal mention was made of an unexamined manuscript by Hariot belonging to the Petworth Collection entitled The Doctrine of Nauticall Triangles Compendious, which promised to be of interest to navigators. When Lord Leconfield, the owner of the Collection, heard of this he very kindly himself brought this manuscript to the British Museum for study there, and meanwhile Dr. Shirley of the United States, who is at work on other aspects of Hariot's life, sent over from America a transcript from a microfilm copy which was in his possession. The contents of the manuscript more than fulfilled expectation, for it appeared that the main theme was the computation of meridional parts for drawing a Mercator chart and, as Mr. Sadler, the Superintendent of H.M. Nautical Almanac Office, shows in the second part of this paper, Hariot was remarkably in advance of his time in his mathematical treatment of this problem, which continued to be a favourite one for discussion until the discovery of the calculus. As is well known, the first table of meridional parts to be published was that compiled (by simple addition of secants) by Edward Wright (1558–1615) of Caius College, Cambridge, a mathematician who had been nautical adviser to the Earl of Cumberland, and on occasion to the Lord High Admiral himself.

Since the large-scale development of offshore oil installations started in the 1970s the requirements for navigating men and machines around structures and on the sea bed have increased dramatically.

The earliest forms of navigation were by tracking with fish-finding sonar, either directly or with the aid of an acoustic transponder. The sonar would usually be fitted to a surface craft, whose position was found by using one of the commercial navigation systems such as HIFIX. The range and bearing of the object being tracked was then applied to this position. Most of this work was done by hand and the position up-date rate was of the order of minutes. The error of position was the sum of the surface system and tracking system errors and was of the order of at least 10 m.

In this paper, which is a revised and up-dated version of an article which appeared on the back of the United States Pilot Chart of the North Pacific Ocean for May 1964, Mr. Fricker, a member of the Maritime Safety Division of the United States Naval Oceanographic Office, first of all analyses world-wide statistics of collision at sea on a geographical basis. He highlights the results of an investigation conducted by the U.S. Coast Guard into the conditions surrounding marine collisions; taking into account the results of this enquiry the author then goes into the common causes of collision. The paper then reviews the whole subject of radar and collision and the interpretation of the Collision Regulations in relation to the use of that aid. Certain collision counter-measures such as particular radar displays, improved lights and sound signals, bridge to bridge communication, &c. are then discussed.

As Professor Taylor has described, the Hariot ms. is largely concerned with the calculation of meridional parts. These calculations are of great interest not only as regards the question of priority, but also because they are based on a method which was more than fifty years in advance of contemporary mathematical knowledge. Although the ms. is paged and cross-referenced, the calculations are incomplete and inadequately explained; arithmetical errors (remarkably few when all calculations had to be done by long multiplication!) make absolute interpretation of all figures almost impossible. Considerable detail is thus unavoidable if the essential parts of the ms. are to be put on record and explained; though the most important point must be left unexplained. There can be little doubt that Hariot's calculations are original and independent.

The shipping industry is faced with unilateral legislation proposed by the United States of America covering navigational equipment and, in the interests of harmonization, IMCO is compiling performance specifications and carriage requirements for navigational equipment including collision avoidance systems; the establishment of type approval procedures can be anticipated. The shipowner has reservations, in respect of the need for adequate training in the use of advanced systems and the risk of navigators placing reliance on such devices as collision avoidance systems when their constant availability cannot be guaranteed.

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.

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.

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.

A weather routing tool is presented based on forecasted weather data along the route and considering safety aspects. The tool aims to determine the optimal path for the minimisation of the fuel oil consumption, ensuring a safe passage. It is developed in MATLAB and considers detailed ship characteristics. Specifically, ship's motions and fuel oil consumption of the main engine during a potential path are estimated. For the latter, a physics-based model for a specific vessel is developed where tools of different level of detail are utilised to calculate the various resistance components. A speed management strategy along the route is specified as well as safety criteria representing acceptable limits of ship's responses. When the set criteria and constraints have been set, a genetic algorithm is used to find the optimal route by means of ship's heading or by considering both heading and ship's power settings as variables to minimise the fuel oil consumption. The search space of the algorithm lies within a predefined envelop, but still the evolutionary optimisation approach used has no pre-assigned values to any possible candidate waypoint.

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.

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.

During pulsar navigation, the high-frequency noise carried by the pulsar profile signal reduces the accuracy of the pulse TOA (Time of Arrival) estimation. At present, the main method to remove signal noise by using wavelet transform is to redesign the function of the threshold and level of wavelet transform. However, the signal-to-noise ratio and other indicators of the filtered signal need to be further optimised, so a more appropriate wavelet basis needs to be designed. This paper proposes a wavelet basis design method based on frequency domain analysis to improve the denoising effect of pulsar signals. This method first analyses the pulsar contour signal in the frequency domain and then designs a Crab pulsar wavelet basis (CPn, where n represents the wavelet basis length) based on its frequency domain characteristics. In order to improve the real-time performance of the algorithm, a wavelet lifting scheme is implemented. Through simulation, this method analyses the pulsar contour signal data at home and abroad. Results show the signal-to-noise ratio can be increased by 4 dB, the mean square error is reduced by 61% and the peak error is reduced by 45%. Therefore, this method has better filtering effect.

The accuracy of the Global Positioning System (GPS) observable, especially for the code observable, has improved with the development of Global Navigation Satellite System (GNSS) receiver technology. An evaluation of the GPS code observable is presented in this paper, together with a stochastic model for the code and phase observables in Precise Point Positioning (PPP), established using the evaluated results. The results show that the code observables of Leica GNSS receivers are generally better than those of some other brand receivers and the Root Mean Square (RMS) for the code observables of the Leica GRX1200PRO, which includes the multipath effect, reaches 0·71 m, although Coarse/Acquisition (C/A) code observables are tracked. The static positioning of the code observable can reach centimetre level and the convergence time for the JPLM station is just 2·5 hours. The positioning results show that it is difficult to converge the Up direction to the centimetre level, compared with the North and East directions. The results show that static positioning can be correlated with the accumulation characteristic of the error for the code observable, while that that of the kinematic mode can be correlated to the error value. The shortened PPP convergence times verify that the presented stochastic models are effective.

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.

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.

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.

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.

This paper is concerned primarily with an investigation of the loxodromic distance between two points on the spheroid. This is derived by a modification of the meridional parts method in terms of the track angle and the difference of latitude reduced by a correction which is a function of the latitudes concerned.

Since the method is unsuitable when the track angle is near to 90°, the known formula for the mid-latitude correction is examined and an alternative method suggested for use in this case.

The results obtained are compared in a practical example with those found by the usual methods, and finally means are proposed by which the refinement described above can be incorporated into current plotting practice on aeronautical Mercator charts.

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 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.