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.

Unlike industrial-grade Inertial Navigation Sensors (INSs) that can provide credible tracking performance, more affordable consumer-grade low-cost INSs produce drifts in heading angles and positions that result in a poor tracking accuracy. Researchers have proposed drift correction methods that attempt to attenuate the drifts when walking straight along the dominant directions is detected. While determining the type of a pedestrian's walk is essential before the heading corrections are made, the current detection techniques heavily rely on thresholding. This paper proposes a novel threshold-less method to detect turns in walking by using pelvic rotation and correct the heading angle based on consumer-grade INSs. The experiments indicate the proposed turn detector and heading correction methods produce very good results which can be applied for future pedestrian tracking, activity recognition or rehabilitation.

This paper addresses two aspects of high accuracy GPS positioning : single point positioning and real-time kinematic positioning. In both cases, it is shown that use of the correct models significantly improves the quality of the resulting positions. In the first case, emphasis is placed on physical models, especially the satellite orbit, and in the second case, emphasis is placed on the stochastic model, i.e. understanding the statistics of the GPS observables.

This paper was first presented at the RIN97 Conference held in Oxford under the auspices of the Animal Navigation Special Interest Group, April 1997.

Migrating species may utilise hydrostatic pressure. In the aquatic environment, hydrostatic pressure changes much more rapidly than in air. In shallow water, tidal changes will impose larger percentage changes on organisms than those experienced in deep water. Small changes in pressure often cause locomotion (barokinesis) accompanied by orientation to light or gravity, often partially compensating for the equivalent depth change. Until recently, identification of hydrostatic pressure receptors without a gas phase has proved elusive, but it is now known that thread hair receptors in the statocyst of the shore crab Carcinus maenas respond to small changes in hydrostatic pressure. Using a tide machine, the responses of thread hairs to sinusoidally changing pressure cycles have been examined, and this paper reports progress monitoring this receptor and making long-term recordings from hydrostatic pressure sensitive pathways in the crab's nervous system.

This paper outlines the results of a project to develop and test an augmented reality smart phone application (‘app’) to aid the safety of navigation of leisure sailors with limited navigational skills. The app works in two modes: in the ‘turned off mode’ the app gives an alarm 30 seconds before the boat is predicted to ground. The navigator then immediately stops the boat, picks up the phone and, uses the app to view the surrounding water where NoGo areas less than 3 metres in depth are outlined in red. By panning the smart phone around, safe escape routes with deep water are visible. The prototype app was tested on a group of boat owners in western Norway with very good results, both from technical and usability perspectives. This report outlines the concept of operation of the app, details some of the difficulties encountered in its development and testing, specifies the issues that remain to be resolved to turn the concept into an effective system, and outlines future development plans.

Clod Shannon's fundamental works in the field of Theory of Information are well known and used in many different fields of science and practice. The Theory provides good criteria to evaluate equipment, systems, different effects and situations from the point of view of the necessary information. This article uses the Theory to attempt to create an information model for a “Ship-Danger to Navigation” system, which can evaluate an Integrated Bridge System in critical situations.

As the technology of global navigation satellite system (GNSS) and augmentation systems are evolving rapidly, compatibility becomes a critical issue for system providers. By April 2011, China had successfully launched eight satellites of the Compass phase II (CP II) navigation system, which will provide positioning, navigation, timing and communication services to the Asia-Pacific region by the year 2012. Due to the limitations of available radio frequency bandwidths, it is important to assess the compatibility and to design signals based on the compatibility within these limited radio frequency bandwidths. This paper presents a modified compatibility assessment methodology, derived from the traditional methodologies that are based on the spectral separation coefficient (SSC) and the effective carrier-power-to-noise density ratio. The modified methodology takes into account additional factors including the Doppler offset, code tracking loop, and band-limiting, sampling and quantisation (BSQ) of the GNSS receiver. In the simulation section, the comprehensive compatibility assessment between CP II and other GNSSs, such as GPS, Galileo, Wide Area Augmentation System (WAAS) and European Geostationary Navigation Overlay Service (EGNOS) on L1 Band are carried out and presented with some new results. Simulation results reveal that CP II does not cause serious interference on GPS, Galileo, WAAS and EGNOS as the interference level is below the 0·25 dB threshold recommended by ITU.

In waist-worn pedestrian navigation systems, the periodic vertical acceleration peak signal at body centre of gravity is widely used for detecting steps. Due to vibration and waist shaking interference, accelerometer output signals contain false peaks and thus reduce step detection accuracy. This paper analyses the relationship between periodic acceleration at pedestrian centre of gravity and walking stance during walking. An adaptive dual-window step detection method is proposed based on this analysis. The peak signal is detected by a dual-window and the window length is adjusted according to the change in step frequency. The adaptive dual window approach is shown to successfully suppress the effects of vibration and waist shaking, thereby improving the step detection accuracy. The effectiveness of this method is demonstrated through step detection experiments and pedestrian navigation positioning experiments respectively. The step detection error rate was found to be less than 0·15% in repeated experiments consisting of 345 steps, while the longer (about 1·3 km) pedestrian navigation experiments demonstrated typical positioning error was around 0·67% of the distance travelled.

This paper presents a binocular vision-IMU (Inertial Measurement Unit) tightly-coupled structure based on a Minimum sigma set Square-Root Unscented Kalman Filter (M-SRUKF) for real time navigation applications. Though the M-SRUKF has only half the sigma points of the SRUKF, it has the same accuracy as the SRUKF when applied to the binocular vision-IMU tightly-coupled system. As the Kalman filter flow is a kind of square-root system, the stability of the system can be guaranteed. The measurement model and the outlier rejection model of this tightly-coupled system not only utilises the epipolar constraint and the trifocal tensor geometry constraint between the consecutive two image pairs, but also uses the quadrifocal tensor geometry among four views. The structure of the binocular vision-IMU tightly-coupled system is in the form of an error state, and the time updates of the state and the state covariance are directly estimated without using Unscented Transformation (UT). Experiments are carried out based on an outdoor land vehicle open source dataset and an indoor Micro Aerial Vehicle (MAV) open source dataset. Results clearly show the effectiveness of the proposed new mechanisation.

A version of this paper was first presented at the Royal Institute of Navigation NAV 08 Conference held at Church House, Westminster, London in October 2008.

There exist various applications for indoor positioning, amongst which indoor positioning and tracking in urban environments has gained significant attention. Some user communities, like fire fighters, ideally require indoor accuracy of less than one metre, with accuracies of less than six metres acceptable by some other user communities. Achieving this level of accuracy requires a detailed profiling of error sources so that they can be better understood so that, in turn, indoor positioning accuracy in the presence of these errors can be further improved. Some well known error sources like multipath, NLOS (non line of sight), oscillator drift, dilution of precision and others have been studied and can be found in the literature. A less well known error source that can substantially affect indoor positioning accuracy are the effects of the dielectric properties of building materials on propagation delay.

Various RF and non-RF based prototypes that claim to be suitable for indoor positioning can be found in the literature. Most of the existing literature discusses algorithms and summarizes the positioning results that were achieved during field tests using a prototype system or, more commonly, simulations. Little of this existing literature provides a breakdown of the total navigation system errors observed with the objective of analyzing the contribution of each error source independently.

The paper will first provide a brief overview of the precision personnel locator system developed at the Worcester Polytechnic Institute. The field tests and observed indoor positioning results using this RF prototype will then be summarized and used to provide a baseline to establish a system error budget. The total observed error will be broken down and a detailed analysis of each of the error sources will be presented based on actual measured data in a variety of indoor environments. This leads to a better understanding of how each error source affects indoor positioning accuracy. Each of the error sources can then be independently optimized to minimize the observed errors. Specifically, the interplay between the dielectric properties and multipath profiles will be highlighted. This paper will conclude by presenting an error budget which can be used as a practical lower bound when designing precise indoor positioning systems.

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.

Three distinct mechanisms of interference of JTIDS transmissions to DME are investigated: false interrogator triggering, transponder overloading and desensitization of either transponder or interrogator receivers. The effect of transponder overloading due to JTIDS transmissions is found the most serious. An analytical method is provided which relates the transponder reply efficiency to the load of the interrogations received in the presence of JTIDS transmissions.

Bathymetric simultaneous localisation and mapping (SLAM) methods yield accurate navigation results for autonomous underwater vehicles (AUVs) and can construct consistent seabed terrain maps. Multiple independently working vehicles can complete tasks like surveying and mapping efficiently, which means cooperative bathymetric SLAM using multiple AUVs is suitable for large-scale seabed mapping. However, the transmission of bathymetric measurements collected using a multi-beam echo sounder over a low bandwidth, noisy, and unreliable acoustic channel is difficult, making cooperative bathymetric SLAM very challenging. This paper develops a graph-based cooperative bathymetric SLAM system that can compress many bathymetric measurements into small-scale acoustic packets and yield accurate navigation results with a 10% loss of acoustic packets caused by unreliable acoustic communication. According to the simulation conducted using the field data, the new algorithm is shown to be robust and capable of providing accurate location and mapping results over a low bandwidth, noisy, and unreliable acoustic channel.

The navigational feats of the Vikings and Norse in the Middle Ages have excited much interest and admiration, and we are fortunate that actual sailing directions for their various North Atlantic routes have been passed down to us in the Icelandic sagas. Using statistical data of modern wind conditions, this paper examines the sailing directions to determine whether the sailing times quoted are reasonable for a type of ship that was making these voyages in the Middle Ages. The findings show very good correlation between the calculated times and those of the sagas. The paper goes on to study an apparent anomaly for a particular route quoted in the sagas and concludes that the departure and destination points have probably been misinterpreted in the past.

Several studies have been conducted on collision avoidance (CA) and path planning for maritime autonomous surface ships (MASS) based on artificial potential field (APF) and electronic navigation chart (ENC) data. However, to date, accurate, highly efficient, and automatic modelling of complicated geometry environment potential fields (EPFs) has not been realised. In this study, an accurate EPF model is established using ENC data to describe different types of obstacles, navigable areas, and non-navigable areas. The implicit equations of complex polygons are constructed based on the R-function theory, and the discrete-convex hull method is introduced to realise the automatic modelling of EPF. Moreover, collaborative CA and obstacle avoidance (OA) experiments are designed and conducted in a simulated environment and based on the ENC data. The results show that the proposed EPF modelling method is accurate, reliable, and time-efficient even with numerous ENC data and complex shapes owing to the R-function representation for geometric objects and discrete-convex hull method. The combination of improved APF and EPF models is proven to be effective for CA and OA. This paper presents a practical EPF modelling approach for APF-based ship path planning.

Investigating the underlying predictors of speeding behaviour deserves the full attention of research. This study aims to examine the effects of demographic variables on the perceived deterrent mechanisms and to predict speeding behaviour to target appropriate prevention programmes. In this study, 212 randomly selected drivers having a valid car driving licence participated in an online survey. The results revealed that demographic variables influenced drivers’ perceptions towards social and legal sanctions as well as material loss. The model revealed that two sanction-related constructs, that is, legal sanction (b = −0⋅227, P = 0⋅007) and material loss (b = −0⋅218, P = 0⋅005), as well as lax perception towards traffic accident (b = −0⋅176, P = 0⋅025), were the significant predictors of speeding behaviour. These findings suggested that prevention programmes should prioritise young and single drivers. The most effective targeted prevention programmes are highlighted accordingly based on the study results.

In some cases, navigation of aircraft or spacecraft may need to be conducted in a Global Navigation Satellite System (GNSS)-denied environment. So, additional sources of navigation information may need to be used to increase navigation precision and resilience. Such sources can include visual navigation systems such as visual shoreline navigation. The main feature of visual shoreline navigation is the severe variability of navigation errors depending on the shape of the observed shoreline, the distance and the view angle of the observation. Such variations are so great that it is not possible to use average values of errors. So, each measurement of an aircraft or spacecraft position should be accompanied with an estimation of the error covariance matrix in real time. It is proposed to use the Cramer-Rao lower bound of visual shoreline navigation errors as such a matrix. The method for constructing the Cramer-Rao lower bound is described in this paper.

Around 1992 Navstar/GPS will become fully operational. Public access is then provided in the Standard Precision Service, SPS, at a reduced accuracy of 100 metres for 95 per cent of the fixes. The exclusively US military-operated system and the deliberately introduced degradation (SA, selective availability) of the attainable accuracy have some drawbacks for European navigation. Neither the probability density function of the error amplitude, nor its power spectral density function is known. So, using Navstar/GPS as a sole-means precise and reliable navigational aid for high-risk transports is not possible.

Modern ship simulators enable simulations of reality using available environment and ship models. When choosing a specific vessel from a catalogue, however, it is not always immediately apparent as to how true a simulation is to the original vessel. Its makers are required only to have software certificates, which does not ensure the exact modelling of a ship in the simulation. This paper presents research in continuation of previous work presenting a general methodology for the evaluation of the degree of accuracy of a simulated ship model compared to its real-world counterpart. In this paper, the results are shown of a comparative analysis based on actual measurements with the use of one of the methods of multi-criteria analysis. Furthermore, the methodology for the construction of ship models is presented. The paper concludes with a test verifying the accuracy of the assumptions.

Recent articles in this Journal will have suggested that there is a conflict between certain mathematicians and certain mariners on the subject of the efficacy of the Collision Regulations. The controversy is really philosophic rather than mathematical and, although it would never be suggested that the mathematical system we have seen is anything but flawless in isolation, there are grave doubts that it would work, even on a planet composed solely of deep water and supporting ships staffed only with mathematicians, having collision avoidance as their single preoccupation.