Map-matching is widely used in automotive navigation systems to locate vehicle positions on a given digital road map. Various map-matching algorithms have been developed focusing on different application needs. Within the Ghosthunter project, a weighting-function-based map-matching algorithm has been developed for detecting wrong-way driving in order to improve road safety, particularly in Autobahn entrance and exit areas. This paper aims at exploring the potential use of lane-level attributes and height data in improving the success rate of the previously presented algorithm. This algorithm performs well in entrance and exit areas to the Autobahn, with a high success rate of 99.5% in identifying the road on which the vehicle is actually travelling. In the enhanced algorithm presented in this paper the weight coefficients used for computing the total weighting score of candidate roads are adjusted with the aid of one or both kinds of these precise data. The results confirmed that the usage of these precise data can effectively help to detect and correct mismatches at junctions and overpasses.

The High-degree Cubature Kalman Filter (HCKF) is proposed as a novel methodology based on the arbitrary degree spherical rule, which can achieve better performance than the traditional Kalman filter. However, it also has a large calculation burden when used in a high-dimension and high-degree of accuracy estimation system. The number of sampling points of an HCKF increases polynomially with increasing state-space dimensions, which further increases the calculation burden. The reduction of the number of the state-space dimensions is the main contribution of this study. A strategy for HCKF based on the partitioning of the state-space and orthogonal principle is introduced, referred to as the Multiple Robust HCKF (MRHCKF). It is shown that this technique can effectively reduce the calculation burden for the high-dimension system with robust performance. Numerical simulations are performed for the example of high-dimension relative position and attitude estimation to show that the proposed method can obtain nearly the same performance as the HCKF, while drastically reducing computational complexity.

Of immense importance to nautical astronomers are tables of trigonometrical functions. The history of these begins with the table of chords first suggested by Hipparchus two centuries before the beginning of the Christian Era. The earliest table of chords extant is that computed by Ptolemy (fl. c. 150 a.d.) whose table, true to the sexagesimal tradition, is based on the division of the radius of a circle into sixty parts. The first table of half-chords, or sines, is supposed to be of Indian origin and to date from the sixth century; but credit for being first to use a table of half-chords for solving spherical triangles belongs to the Arab mathematician Albategnius who flourished during the tenth century. The first printed table of sines, according to De Morgan, is a small work giving sines to each minute of arc from 0° to 90°, undated and unsigned but evidently published before 1500.

The dynamic precise orbit determination of a Low Earth Orbit satellite using triple differenced GPS phases is presented in this study. The atmospheric drag parameters are estimated to compensate the incomplete atmosphere model for better precision of the orbit solution. In addition, the empirical force parameters, especially once- and twice-per-revolution components, along with the new IERS Conventions and models to compute the perturbing forces are introduced to absorb the remaining unmodelled forces. The optimal arc length for the parameterization and the data processing strategy are also tested and analyzed for the best orbit solutions. The triple differencing technique enables fast and efficient orbit estimation, because no ambiguity resolution and cycle slip detection are required. With the triple differenced ion-free GPS phase observables, the orbit and the velocity solutions for 24 hours of CHAMP are calculated; they compare with the published Rapid Science Orbit with the accuracy of 8 cm and 0·12 mm/s in 3D RMS for the orbit and the velocity, respectively, and are statistically consistent with the RSO when it is not better than 4 cm in terms of an absolute accuracy. The approach presented here provides an efficient and simple, but robust, alternative approach, while the solution's accuracy is still comparable to the double-difference results.

This paper introduces a novel approach for extracting vessel navigation patterns from very large automatic identification system (AIS) trajectory big data. AIS trajectory data records are first converted to a series of code documents using vector quantisation, such as k-means and PQk-means algorithms, whose performance is evaluated in terms of precision and computational time. Therefore, a topic model is applied to these code documents from which vessels’ navigation patterns are extracted and identified. The potential of the proposed approach is illustrated by several experiments conducted with a practical AIS dataset in a region of North West France. These experimental results show that the proposed approach is highly appropriate for mining AIS trajectory big data and outperforms common DBSCAN algorithms and Gaussian mixture models.

The acquisition of modern Global Navigation Satellite System (GNSS) signals may be difficult due to the presence of a secondary code. Indeed, short coherent integration times should be used without non-coherent integration, which implies a low sensitivity; or long coherent integration times should be used, requiring synchronisation with the secondary code and thus a full correlation, which implies a significant computational burden, especially for signals with long secondary codes such as the Galileo E5 signal. A third option that lies between the previous two is to perform a partial correlation using less than one secondary code period as input, however this is less efficient in terms of complexity than using an entire secondary code period, and the code's autocorrelation properties are completely changed. The authors recently proposed a method based on combining secondary code correlations, allowing the use of intermediate coherent integration times with the possibility to do non-coherent integrations, and the method was successfully applied to the Global Positioning System (GPS) L5 signal. This paper studies the application of the method to the Galileo E5 signal, compares it with the partial correlation method, and discusses the case where less than one secondary code period is used as an input

To solve the problem of spacecraft attitude manoeuvre planning under dynamic multiple mandatory pointing constraints and prohibited pointing constraints, a systematic attitude manoeuvre planning approach is proposed that is based on improved policy gradient reinforcement learning. This paper presents a succinct model of dynamic multiple constraints that is similar to a real situation faced by an in-orbit spacecraft. By introducing return baseline and adaptive policy exploration methods, the proposed method overcomes issues such as large variances and slow convergence rates. Concurrently, the required computation time of the proposed method is markedly reduced. Using the proposed method, the near optimal path of the attitude manoeuvre can be determined, making the method suitable for the control of micro spacecraft. Simulation results demonstrate that the planning results fully satisfy all constraints, including six prohibited pointing constraints and two mandatory pointing constraints. The spacecraft also maintains high orientation accuracy to the Earth and Sun during all attitude manoeuvres.

It has for some years now almost been folklore that the marine traffic situation in the Dover Strait is one of great potential danger. Very considerable efforts have been made to alleviate the situation. There is a complete traffic separation scheme (the first in the world), there is continuous radar surveillance both from England and France, there are routine broadcasts on v.h.f. to warn mariners of any navigational problems, and there is now a system whereby certain ships report-in. Concurrently with all this activity, the accident rate has dropped significantly over the last decade, especially in fog, and it is a reasonable inference that the reduction in the number and severity of accidents is attributable to this activity.

But patterns of navigation change, and it is necessary for marine administrators to be aware of problem areas as or before they arise so that marine management measures can be introduced when appropriate. Factors to be taken into account are the volume and characteristics of the traffic, the difficulty of navigation and the accident record. One of us has drawn attention to the traffic situation off East Anglia and suggested that a prima facie case for some remedial measures had been made. This paper examines the available evidence in more detail.

First, an account is given of the accident record in the area under consideration (Figs 1, 2) over the last 10 years. Both the numbers and severity of collisions and strandings are discussed.

Wing Commander Anderson has drawn attention to the fact that the distribution of the larger navigational errors is frequently observed to be non-gaussian in character. He raises the point whether this can be accounted for by the generation of such errors in succession, rather than simultaneously. The successive generation of navigation errors arises through the error incurred on a particular leg being distributed about a mean which is dependent on the error up to the end of the previous leg.

In June 1955, Canadian Pacific Airlines inaugurated a regular scheduled service between Vancouver and Amsterdam via the polar route. The Company had a wealth of northern experience which was of immense operational value on the polar route. In addition to its overseas services, C.P.A. has operated regular flights for many years to far northern parts of Canada and some of the group of companies which amalgamated to form C.P.A. in 1942 had arctic experience dating from the days when commercial aviation was in its infancy. One aspect of navigational experience which has helped its navigators on many occasions has been the map reading talents of the former bush pilots who show an astonishing ability to locate themselves visually over country which is mostly water, and where one lake looks much like every other lake.

The problems of submarine navigation are entirely distinct from those encountered on the surface. Not only does the medium introduce a third dimension, which is not wholly analagous to that of the air since a definite limit is imposed on depth, but also a great many of the aids to surface navigation are either restricted in their use underwater, or are wholly inappropriate and will not function. The use of the principal aids to submarine navigation is briefly described in this paper, future developments being mentioned where possible. A more detailed examination is then made of the problems of underwater navigation, problems in the main that affect the accuracy of keeping a reliable dead reckoning. An account is also given of a gravity survey carried out in H.M. Submarine Talent, during which the author served as navigating officer. On this operation the requirement for position accuracy was high, and some of the methods used were of considerable interest. The survey also provided the opportunity for current and tidal-stream observations to be made at different depths and an account of these observations is given.

This paper is concerned with measures which may be used to reduce the effect of echoes from the sea surface and from rain (sea and rain clutter) on radar displays so that targets which give a reflected signal power greater than the reflected clutter power can be detected. It should be noted that a conventional PPI display is fully brightened by signals of amplitude about three times the level of the inherent noise background, so that once the clutter has exceeded this limit it will appear on the display as a fully bright patch in which signals can be lost, even though their amplitude at the receiver input may be many times greater than the amplitude of the clutter.

This paper describes the infrastructure and concept of two multi-site reference station differential GPS (DGPS) options being offered to land and marine users by Racal Survey. The infrastructure of the Racal SkyFix system is briefly outlined followed by descriptions of Racal's internetting and network capabilities.

The two systems are compared including infrastructure, differential data management, user coverage, datalinks and positioning performance in various parts of the world. The paper describes the design of each of the systems and the tests undertaken to assess their functionality, before going on to compare their performances under a variety of conditions. Emphasis is placed on the technical issues associated with multi-reference station DGPS including error sources, weighting observations and monitoring of the data. The fundamental approach of the systems is shown to achieve high data integrity which is necessary to develop the systems to their next phase.

Having described the two options, examples of various combinations of reference stations are used to illustrate the potential of the system and to show the increased performance over ordinary, single-station DGPS. The conclusions summarize the paper's findings and make recommendations for the future development of the system. The object of the developments so far have been to improve the quality of real-time offshore DGPS positioning. The internetting and network options are providing real-time results to illustrate the benefits and, together with SkyFix, offer significant developments in the ability of DGPS to provide accurate and reliable positioning over vast areas of the world.

Improved radar surveillance for air traffic control can be obtained by the integration of radar systems. Integration, however, might cause the delay of radar information, which would hamper the air traffic controllers in their work. To estimate the delay, a mathematical equation to assess the amount of radar information causing this delay has been deduced from the properties of the behaviour of air traffic. The mathematical equation has been tested using results obtained from operational secondary surveillance radar in the Netherlands.

One method of controlling aircraft is to assign each a given track, the distance between successive tracks being sufficiently great to ensure that the collision risk is very low. Most approaches to the problem of stipulating what this spacing should be, assume that the possible divergences of an aircraft about its preassigned path follow a Gaussian distribution with a standard deviation obtained by considering all the usual sources of navigational error (e.g. compass error and fixing error) together with meteorological errors due to inaccuracies in forecasting.

The invention of the balloon was almost a casual affair, unrelated to other contemporary inventions and unheralded by prior developments. The hot-air balloon could have been invented at any time since the mastery of thin textile manufacture, which can be dated well before the Christian era. The hydrogen balloon could not have come about until after Cavendish had isolated the gas in 1766. As it finally turned out, both types of balloon were invented in the year 1783.

Passenger and cargo liners sailing on regular routes follow tracks for a given voyage, taking account of the various seasonal conditions which may apply, and masters of these ships, with many years experience in a particular trade, can decide without great difficulty the most advantageous track for their ship when planning a voyage for a given time of year.

In the transport of oil, on the other hand, it is not common to employ ships on regular voyages, and the great majority of tankers are employed in world-wide trading, so that although a particular oil company may have a number of ships constantly voyaging on a particular route, a high degree of flexibility is maintained and ships are regularly changed from one route to another. This means that the tanker master is called upon to consider the requirements for optimum routing of his ship on any ocean voyage. Further, he is often given his orders with fairly short notice and, in some cases, he may have his destination changed either at the last moment or during the voyage, leaving him little time to consider the many factors which have to be taken into account when planning the best route for the voyage to be undertaken.

There is no doubt that visibility influences the probability of collision and stranding and even a full moon, which gives a brightness of only 0·2 lux, seems to reduce the probability compared with a dark night; there is a much greater difference in the brightness by day (several thousand lux even with cloud) and at night. However the number of accidents in a seaway is influenced by many factors, such as traffic density, average speed, encounter condition, visibility, the helmsman's skill, availability of information &c. Of these factors, traffic density has most influence on the probability and this influence must be removed in order to study the influence of brightness. The present writer has shown that the danger of collision is roughly proportional to the square of the traffic density, and therefore proportional to the square of the traffic volume. Diurnal changes in the number of accidents and in traffic volume are therefore used to estimate the ratio of the danger by day and by night.