In this paper, equations are established to solve problems of Rhumb Line Sailing (RLS) on an oblate spheroid. Solutions are provided for both the inverse problem and the direct problem, thereby providing a complete solution to RLS. Development of these solutions was achieved in part by means of computer based symbolic algebra. The inverse solution described attains a high degree of accuracy for distance and azimuth. The direct solution has been obtained from a solution for latitude in terms of distance derived with the introduction of an inverse series expansion of meridian arc-length via the rectifying latitude. Also, a series to determine latitude at any longitude has been derived via the conformal latitude. This was achieved through application of Hermite's Interpolation Scheme or the Lagrange Inversion Theorem. Numerical examples show that the algorithms are very accurate and that the differences between original data and recovered data after applying the inverse or direct solution of RLS to recover the data calculated by the direct or inverse solution are very small. It reveals that the algorithms provided here are suitable for programming implementation and can be applied in the areas of maritime routing and cartographical computation in Graphical Information System (GIS) and Electronic Chart Display and Information System (ECDIS) environments.

This paper proposes a Radio Frequency Identification (RFID)/ in-vehicle sensors fusion strategy for vehicle positioning in completely Global Positioning System (GPS)-denied environments such as tunnels. The strategy employs a two-step approach, namely, the calculation of the distances between the RFID tags and the reader, and then the global fusion estimation of vehicle position. First, a Least Square Support Vector Machine (LSSVM) algorithm is developed to obtain distance. Next a novel Federated Unscented Kalman Filter (FUKF) is designed to realise the global fusion. The decentralised federated filter is adopted to combine the data from RFID and in-vehicle sensors, and the UKF is employed to design a local filter since it has better ability to deal with a nonlinear problem than an Extended Kalman Filter (EKF). Due to the optimised layout of RFID tags and the application of the decentralised filter, the number of tags is reduced. Finally, the feasibility and effectiveness of the proposed strategy are evaluated through experiments.

This study describes the estimation of spherical wave parameters that appears in Synthetic Aperture Radar (SAR) images acquired over the coast of Chukk, Micronesia. The main causes for the interaction of SAR signals with ocean waves can be retrieved through the Bragg scattering mechanism. Dominant wavelengths were retrieved by means of Fast Fourier Transform (FFT) analysis in terms of peak frequency responses. Sea surface slopes were then obtained from the dispersion relation with consideration of different water wave conditions for each subset area, and wave heights were estimated with the use of dominant wavelengths and sea surface slopes. The work presented in this paper may be useful to retrieve the various wave parameters over different regions. The method used is a novel technique to correlate the relationship between SAR image parameters and dispersion relation.

Air traffic controllers use a radar separation minimum when keeping aircraft safely apart. The choice of minimum needs to ensure, to a very high degree of confidence, that radar inaccuracies are not putting the aircraft into a risk of collision – controllers can of course be required to use larger minima for operational reasons. A particular separation minimum necessarily feeds back into requirements on radar design criteria, data processing and performance. The estimation of the radar separation minimum is significantly improved by the use of a new methodology. Previous derivations were a major step forward, but were ‘static’, in that they did not attempt to take properly into account how controllers use separation minima dynamically. An analysis on the use of separation minima in en route airspace by controllers concludes that they are generally likely to use the radar minimum to pass aircraft, rather than to use the minimum in a ‘strategic’ sense (e.g. ‘in trail’ separation). The new ‘Event Model’ methodology recognises that collisions cannot happen instantly: the aircraft pair concerned must move from a safe configuration to a hazardous one. Collisions are therefore events caused by flawed flight paths, dependent on both the initial positions of aircraft and their subsequent movements and velocities.

Dr. David Lewis has contributed two earlier papers to the Journal on Polynesian navigation: ‘Ara Moana’ in 1964, a theoretical examination of navigation methods, and ‘An experiment in Polynesian navigation’ in 1966, an account of his own voyage in the catamaran Rehu-Moana from Tahiti to New Zealand. The present paper presents the result of further research which included voyages between the islands with Polynesian navigators. A version of this paper, which was presented at the Annual General Meeting of the Australian Institute of Navigation in Sydney on 10 and 11 October 1969, has been published in Navigation (Sydney).

In this paper, the author analyses piracy at sea in Somalia, to provide a general up-to-date vision of the problem which threatens the security of ships sailing in the Gulf of Aden. The pirates' modus operandi, the existing factors behind these punishable acts and the prevailing international response are analysed. Finally the paper reviews how the international community could act in order to tackle the problem with a view to its possible eradication.

A new acoustic positioning method for Autonomous Underwater Vehicles (AUV) that uses a single underwater hydrophone is proposed in this paper to solve problems of Long Baseline (LBL) array laying and communication synchronisation problems among all hydrophones in the traditional method. The proposed system comprises a Strapdown Inertial Navigation System (SINS), a single hydrophone installed at the bottom of the AUV and a single underwater sound source that emits signals periodically. A matrix of several virtual hydrophones is formed with the movement of the AUV. In every virtual LBL window, the time difference from the transmitted sound source to each virtual hydrophone is obtained by means of a Smooth Coherent Transformation (SCOT) weighting cross-correlation in the frequency domain. Then, the recent location of the AUV can be calculated. Simulation results indicate that the proposed method can effectively compensate for the position error of SINS. Thus, the positioning accuracy can be confined to 2 m, and the method achieves good applicability. Compared with traditional underwater acoustic positioning systems, the proposed method can provide great convenience in engineering implementation and can reduce costs.

In this paper, the ship manoeuvring problems particular to maritime search and rescue are investigated. A solution to such problems is necessary for successful ship handling to save human life. A fuzzy gain scheduling Proportional Derivative (PD) controller, using a back-propagation algorithm, is developed to solve these maritime search and rescue problems. The parameters of the proposed PD controller are determined on-line by fuzzy rules and adjustable fuzzy reasons. The proposed controller is self-adaptive and can accommodate the effects caused by wave or wind disturbance. Some computer simulations are provided to illustrate the use of the main ideas.

The new Global Positioning System (GPS) Civil Navigation Message (CNAV) has been transmitted by Block IIR-M and Block IIF satellites since April 2014, both on the L2C and L5 signals. Compared to the Legacy Navigation Message (LNAV), the CNAV message provides six additional parameters (two orbit parameters and four Inter-Signal Correction (ISC) parameters) for prospective civil users. Using the precise products of the International Global Navigation Satellite System Service (IGS), we evaluate the precision of satellite orbit, clock and ISCs of the CNAV. Additionally, the contribution of the six new parameters to GPS Single Point Positioning (SPP) is analysed using data from 22 selected Multi-Global Navigation Satellite System Experiment (MGEX) stations from a 30-day period. The results indicate that the CNAV/LNAV Signal-In-Space Range Error (SISRE) and orbit-only SISRE from January 2016 to March 2018 is of 0·5 m and 0·3 m respectively, which is improved in comparison with the results from an earlier period. The ISC precision of L1 Coarse/Acquisition (C/A) is better than 0·1 ns, and those of L2C and L5Q5 are about 0·4 ns. Remarkably, ISC correction has little effect on the single-frequency SPP for GPS users using civil signals (for example, L1C, L2C), whereas dual-frequency SPP with the consideration of ISCs results have an accuracy improvement of 18·6%, which is comparable with positioning accuracy based on an ionosphere-free combination of the L1P (Y) and L2P (Y) signals.

Statistics and information from the maritime industry show that the continuous advances in the safety of navigation do not reduce the occurrence of shipping casualties. This controversial fact leads the authors to analyse the applicability of the risk homeostasis theory to maritime transportation. With the aim of investigating this matter 2,584 ship incidents, which took place during the years 2005 and 2006, have been recorded and examined. The same variables which the Paris MOU usually employs to identify substandard ships (flag, classification society, age, type and size) have been used in this research to establish their level of safety in an effort to determine the relationship between that level and the occurrence of maritime incidents in the world cargo carrying fleet with appropriate statistical methods.

The volume of air traffic has increased considerably in the United Kingdom in recent decades and with further predicted increases, there is concern that safety is not compromised. In the UK, the number of occurrences is a key safety performance indicator. An occurrence can be thought of as a failure in the chain of operations in the air traffic system. Some of these occurrences result in a loss of separation between aircraft, varying from a slight loss of separation posing no danger of collision to a very serious loss with a significant risk of collision, known as an airprox. However, in the UK this definition is extended to include controller overload that does not necessarily involve a loss of separation. This paper analyses recent occurrence trends in the UK airspace attributed to air traffic control during the period 1998 to 2000 using data from the Civil Aviation Authority and the United Kingdom Airprox Board. The results indicate a decline in the rate of occurrences over the period 1990–1999 due to safety aids on board aircraft and in control rooms. Furthermore, the different conditions under which airproxes occur have been explored and observations made on duration and causes of controller overloads.

There are three aspects of collision avoidance in the air which require mathematical investigation:

• (a) discovery and evaluation of the risk;

• (b) the remedial manœuvre;

• (c) the probabilities associated with (a) and (b).

A description is given of the basic principles and method of operation of a single-channel automatic blind landing system developed by the Blind Landing Experimental Unit. The system uses the internationally accepted radio aid ILS for approach guidance to the point where more accurate information is required and then two new guidance elements, magnetic leader cable and radio altimeter, are introduced for the final landing. One of the great advantages of the system is its flexibility and if new guidance elements are developed the system will be easily adapted.

Extensive flight tests have been made in all weathers and the performance achieved is much better than that obtained in manual landings in good visibility.

In considering the application of the system to civil aviation the outstanding problem Is that of safety and reliability. Various suggestions are discussed briefly and the possible requirement for an independent pictorial monitor is mentioned. Early thoughts on a monitoring system are described.

In the last number of the Journal (14, 243) Hollingdale showed mathematically that anticollision manoeuvres for the case of two craft moving in a plane can be formulated on a rigorous logical basis; and that a simple set of manoeuvres could be devised to meet all the geometrical requirements for anti-collision. The convention adopted was that each craft should manoeuvre so that if the other craft stood-on, the sight-line (the line joining the two craft) would always rotate in an anti-clockwise direction. The analysis showed that, mathematically, this was the complete and only answer to the basic problem.

The author of the present paper compares systems, such as that represented by the Collision Regulations and the Rules of the Air, based on onus to avoid, with a system based on a convention as to the direction of rotation of the sight-line. The first type of system, he holds, is defective for visual sightings and almost useless for radar sightings. The system put forward in the paper can be applied to both visual and radar sightings whether unilateral or bilateral by orientating a simple diagram with own course. A means of inter-communication is desirable but even without it such a system can, the author believes, safely be employed in the greater proportion of encounters.

The collision problem as a whole is beset by operational factors which are entirely distinct from the geometry of the situation, and for that reason no purely mathematical approach can, in isolation, be entirely valid. Nevertheless, there can be no doubt that studies such as the present one, based on a proper understanding of the geometry, can contribute greatly to the solution of this most pressing problem of navigation.

In this paper, a novel method for autonomous navigation for an extra-terrestrial body landing mission is proposed. Based on state-of-the-art crater detection and matching algorithms, a crater edge-based navigation method is formulated, in which solar illumination direction is adopted as a complementary optical cue to aid crater edge-based navigation when only one crater is available. To improve the pose estimation accuracy, a distributed Extended Kalman Filter (EKF) is developed to encapsulate the crater edge-based estimation approach. Finally, the effectiveness of proposed approach is validated by Monte Carlo simulations using a specifically designed planetary landing simulation toolbox.

Marine traffic survey is a fundamental part of marine traffic engineering. In the assessment of the safety or effectiveness in particular water areas, the distribution of ship tracks is always included as one of the most significant results of a marine traffic survey. In this paper, methods of marine traffic survey are discussed and an appropriate method is selected to obtain the traffic data considering the available research circumstances in China. A semi-automatic artificial way of plotting a distribution diagram of ship tracks is presented with illustrations. Details of the diagram plotted by using the collected traffic data are described for reference.

Satellite based navigation system integrity monitoring is essential both for liability and safety critical services. The threats to system integrity are the potential failure modes that could occur at system, operational and user sensor levels. Research on identification, characterisation and modelling of such failure modes, suggests that failures that grow slowly over time (e.g. ramp error less than 2 m/s), also referred to as slowly growing errors (SGE) are the most difficult to detect early. Conventional snapshot algorithms detect SGEs when the test statistic crosses the threshold usually after relatively long periods of time. A recent concept based on the average of residuals over time has been found to have a significant weakness. This paper proposes a “difference test” algorithm capable of detecting SGEs early. In this method, the test statistic is the difference between the norm of current residuals and the norm of the residuals at a previous epoch. The distribution of the test statistic is over-bounded by a normal distribution whose parameters are derived from two Chi-distributions. Results show that the new algorithm results in a significant reduction in detection time compared to conventional methods.

Besides offset biases (such as range, the gain of range, azimuth, and elevation biases), for mobile radars, platform attitude biases (such as yaw, pitch, and roll biases) induced by the accumulated errors of the Inertial Measurement Units (IMU) of the Inertial Navigation System (INS) can also influence radar measurements. Both kinds of biases are coupled. Based on the analyses of the coupling influences and the observability of 3-D radars’ error registration model, in the article, an Attitude Bias Conversion Model (ABCM) based on Square Root Unscented Kalman Filter (SRUKF) is proposed. ABCM can estimate 3-D radars’ absolute offset biases under the influences of platform attitude biases. It converts platform attitude biases into radar measurement errors, by which the target East-North-Up (ENU) coordinates can be obtained from radar measurements directly without using the rotation transformation, which was usually used in the transition from platform frame to ENU considering attitude biases. In addition, SRUKF can avoid the inaccurate estimations caused by linearization, and it can weaken the adverse influences of the poor attitude bias estimation results in the application of ABCM. Theoretical derivations and simulation results show that 1) ABCM-SRUKF can improve elevation bias estimate accuracy to about 0·8 degree in the mean square error sense; 2) linearization is not the main reason for poor estimation of attitude biases; and 3) unobservability is the main reason.

X-ray Pulsar Navigation (XPNAV) uses the Time Difference of Arrival (TDOA) of the pulsar signal between the spacecraft and Solar System Barycentre (SSB) to determine position. In this paper, a novel method to improve the performance of XPNAV via exploiting the pulsar position vector is proposed. First, the field of view of the collimator is utilised to find the pulsar orientation direction. Then, a searching strategy based on the modified Powell method under given coordinate frames is proposed. We also mathematically prove the existence of the extreme value of the searching strategy. Subsequently, an observation model based on the pulsar radiation vector is presented and applied to formulate the observation function together with pulsar time transfer function. Finally, an Adaptive Divided Difference Filter (ADDF) algorithm is introduced to iteratively estimate the position and velocity of the spacecraft. Numerical simulations show that the vector searching method is feasible and the pulsar radiation direction can improve the navigation performance by 75%. The simulation results also show that the ADDF performs better than Unscented Kalman Filtering (UKF) and DDF in position estimation.

Cooperative Localisation (CL) technology is required in some situations for Multiple Unmanned Underwater Vehicle (MUUVs) missions. During the CL process, the Relative Localisation Information (RLI) of the master UUV is transmitted to slave UUVs via acoustic communication. In the underwater environment, the RLI is subject to a random time delay. Considering the time delay characteristic of the RLI during the acoustic communication, a Moving Horizon Estimation (MHE) method with a Delayed Extended Kalman Filter (DEKF)-based arrival cost update law is presented in this paper to obtain an accurate and reliable estimation of present location. Additionally, an effective computation method for the MHE method is employed, in which the “Lower Upper” (LU) factorization is used to compute the solution of the Karush-Kuhn-Tucker (KKT) system. At the end of this paper, simulation results are presented to prove the superiority and practicality of the proposed MHE algorithm.