Two Receiver Autonomous Integrity Monitoring (RAIM) architectures, Advanced RAIM (A-RAIM) and Relative RAIM (R-RAIM), are compared with two different RAIM algorithms, the Classic method and the Multiple Hypothesis Solution Separation (MHSS) method. The difference between A-RAIM and R-RAIM is in the positioning methods that produce different error models and projection matrices for integrity monitoring. The difference between RAIM algorithms lies in the methods of risk distribution. The influences of different positioning methods on integrity results are analysed in this paper via a generalized RAIM framework. Simulation results for the LPV-200 service with worldwide coverage show that the R-RAIM position domain method has the best results, while the differences between these methods decrease with application of the optimization method.

An approach formulated by vector algebra is proposed to deal with great circle sailing problems. Using the technique of the fixed coordinates system and relative longitude concept, derivations of formulae for this approach are simpler than those of the conventional methods. Due to fixing the initial great circle course, the great circle track (GCT) is determined. Since the course is fixed (known as “COFI” in this paper), the proposed approach, which we have named the “COFI method”, can directly calculate the waypoints along the GCT. It is considered that the COFI method is a more understandable and straightforward method to solve waypoint problems than older approaches in the literature. Based on the COFI method, a program has been developed for the navigator. In addition, the spherical triangle method with respect to the equator crossing point (STM-E) is developed by supplemental theorem. Several examples are demonstrated to validate the proposed COFI method and STM-E.

AIS was primarily developed to exchange vessel-related data among vessels or AIS stations by using very-high frequency (VHF) technology to increase safety at sea. This study evaluates the formal integrity, availability, and the reporting intervals of AIS data with a focus on vessel movement prediction. In contrast to former studies, this study is based on a large data collection of over 85 million AIS messages, which were continuously received within a time period of two months. Thus, the evaluated data represent a comprehensive and up-to-date view of the current usage of AIS systems installed on vessels. Results of previous studies concerning the availability of AIS data are confirmed and extended. New aspects such as reporting intervals are additionally evaluated. Received messages are stored in a database, which allows for performing database queries to evaluate the obtained data in an automatic way. This study shows that almost ten years after becoming mandatory for professional operating vessels, AIS still lacks availability for both static and dynamic data and that the reporting intervals are not as reliable as specified within the technical AIS standard.

A guide star catalogue characterised by fewer guide stars, uniform distribution and high completeness is conducive to the improvement of star pattern identification and star tracking efficiency, and it has become an important study objective. A screening method, which takes “quasi-uniform distribution” of space solid angles as the principle and the size of the space solid angle corresponding to 4°×4° on the equator as the reference and divided the whole celestial sphere into 2,664 sub-blocks in sequence, is proposed in this paper. Based on this method, a “quasi-uniform” guide star catalogue with 2,937 guide stars was obtained. According to our ergodic statistical analysis of the whole celestial sphere, in a 12°×12° field of view, after the space solid angle method was used to divide the celestial sphere, the probability of emergence of three guide stars was 99·9% or above, while the number of guide stars decreased by 12·6% compared to the inscribed cube method. It can be concluded that when the completeness is equal, the space solid angle method is superior to the inscribed cube method in both capacity and distribution uniformity.

A loosely coupled Inertial Navigation System (INS) and Global Positioning System (GPS) are studied, particularly considering the constant lever arm effect. A five-element vector, comprising a craft's horizontal velocities in the navigation frame and its position in the earth-centred and earth-fixed frame, is observed by GPS, and in the presence of lever arm effect, the nonlinear observation equation from the state vector to the observation vector is established and addressed by the correction stage of an unscented Kalman filter (UKF). The conditionally linear substructure in the nonlinear observation equation is exploited, and a computationally efficient refinement of the UKF called marginalized UKF (MUKF) is investigated to incorporate this substructure where fewer sigma points are needed, and the computational expense is cut down while the high accuracy and good applicability of the UKF are retained. A performance comparison between UKF and MUKF demonstrates that the MUKF can achieve, if not better, at least a comparable performance to the UKF, but at a lower computational expense.

This paper reviews currently existing electronic magnetic sensor technologies for navigation applications. Magnetic compasses have been used in navigation for centuries. The Earth's geomagnetic field is considered to provide accurate, reliable and economically available information for orientation. Meanwhile, modern magnetometers and compass calibration technologies have allowed the electronic compass to become a crucial navigation tool, even in times of modern satellite navigation using Global Navigation Satellite Systems (GNSS). Magnetic sensor technologies, error modelling and compensating approaches have been reviewed in this paper. Current trends and the outlook for future development of the electronic compass are analysed.

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.

NextGen and SESAR have now been under development for several years, but have increasingly complex engineering and operational specifications. A variant Air Traffic Management (ATM) concept is sketched for generating fuel-efficient, very accurate and air-ground synchronized 4D-trajectories by using flight segment groundspeed profiles and linking Global Navigation Satellite Systems (GNSS) data to the aircraft Flight Management Systems (FMS) with feedback control. Is this a flawed concept or a feasible and operationally practical proposition?

Automatic Dependent Surveillance Broadcast (ADS-B) is envisioned to support seamless aircraft surveillance and enhanced air-to-air and air-to-ground applications. ADS-B is an integrated system, dependent on on board navigation systems to obtain aircraft state information as well as a communication data link to broadcast this information to Air Traffic Control (ATC) on the ground and other ADS-B equipped aircraft. To quantify system safety, a good understanding of the potential failure modes of the system is vital. ADS-B system failure modes include those from the communication and navigation systems and human and environmental factors, as well as ADS-B-specific components. In this paper, potential failure modes of the ADS-B system are identified using an approach developed in this paper. The end output of the approach is an ADS-B failure mode register. However, the approach is transferable to other ATC surveillance systems. The paper further provides the failure classification and modelling, and also analyses the failure modes' impact on ATC operations and finally proposes potential mitigations. It is important to note that the work carried out in this paper is based on the assumption that the ADS-B operates as the primary surveillance source for the ATC.

With the availability of Galileo signals from four in-orbit validation (IOV) satellites, positioning with Galileo-only observations has become possible, which allows us to assess its positioning performance. The performance of the Galileo system is evaluated in respect of carrier-to-noise density ratio (C/N0), pseudorange multipath (including noise), Galileo broadcast satellite orbit and satellite clock errors, and single point positioning (SPP) accuracy in Galileo-only mode as well as in GPS/Galileo combined mode. The precision of the broadcast ephemeris data is assessed using the precise satellite orbit and clock products from the Institute of Astronomical and Physical Geodesy of the Technische Universität München (IAPG/TUM) as references. The GPS-Galileo time offset (GGTO) is estimated using datasets from different types of GNSS receivers and the results indicate that a systematic bias exists between different receiver types. Positioning solutions indicate that Galileo-only SPP can achieve a three-dimensional position accuracy of about six metres. The integration of Galileo and GPS data can improve the positioning accuracies by about 10% in the vertical components compared with GPS-only solutions.

For multi-Global Navigation Satellite System (GNSS) constellations, the Geometric Dilution of Precision (GDOP) is an important parameter utilised for the selection of satellites. This paper has derived new formulae to describe the change of GDOP. The result shows that, for GNSS single point positioning solutions, if one more satellite belonging to the existing tracked multi-GNSS constellation used in the single point positioning solution is added, the GDOP always decreases with the number of the added satellites. On the other hand, when the constellation of the added satellite is not from the tracked existing constellations, the different numbers of the added satellites have different influences on the change of GDOP. Generally, adding one satellite from another constellation into the existing multi-GNSS constellations will increase the GDOP, but adding two satellites will decrease the GDOP compared with adding one from another constellation. Additionally, the GDOP also increases in the cases of adding two satellites from two different constellations into the tracked existing constellations.

Celestial navigation is an important type of autonomous navigation technology which could be used as an alternative to Global Navigation Satellite Systems (GNSS) when a vessel is at sea. After several centuries of development, a variety of astronomical vessel position (AVP) determination methods have been invented, but the basic concepts of these methods are all based on angular observations with a device such as a sextant, which has disadvantages including low accuracy, manual operation, and a limited period of observation. This paper proposes a new method that utilises a fisheye camera to image the celestial bodies and horizon simultaneously. Then, we calculate the obliquity of the fisheye camera's principal optical axis according to the image coordinates of the horizon. Next, we calculate the altitude of the celestial bodies according to the image coordinates of the celestial bodies and the obliquity. Finally, the AVP is determined by the altitudes according to the robust estimation method. Experimental results indicate that this method not only could realize automation and miniaturization of the AVP determination system, but could also greatly improve the efficiency of celestial navigation.

Collective detection is a promising approach to positioning in a weak signal environment, in which the navigation solution is directly obtained by acquisition search in a multi-dimensional position and common clock bias uncertainty space. By combining the correlation values from multiple satellites and fully utilizing the coherence between them, the detectable C/N0 of individual satellites can be lowered. However, the lack of a computationally efficient optimization algorithm due to high dimensionality and complexity has hindered its application. A multi-resolution collective detection is therefore proposed to be a coarse-to-fine searching approach to solve for the position and common clock bias estimation. Although it reduces the computation time of collective detection, there is a gap in the efficiency study, which is the contribution of this research. The features of different levels of search in a multi-resolution algorithm are investigated. For a coarse search with large horizontal position step size, a smaller common clock bias step size is proposed instead of an averaging correlogram to reduce computation complexity as well as to obtain high time resolution. For the fine search with small horizontal space step size, a 3-D Dichotomous searching scheme is designed and applied to reduce the number of searching grids. Computer simulation results using experimental raw data are provided, to demonstrate the performance improvement against the conventional methods.

Global analysis of vessel motion patterns has become possible using satellite-based Automatic Identification System (AIS). The concept of space-based AIS needs several satellites to provide complete coverage and high detection probability. However, in early development stages, often only one satellite is launched and due to its limitation of orbit and footprint, received AIS messages are discontinuous. In this paper, we have analysed real AIS data obtained by satellite to form a global maritime surveillance picture. Furthermore, we propose to take advantage of the tensor CANDECOMP/PARAFAC (CP) decomposition to analyse three mode characteristics of the data, which are location, vessel and time. For incomplete data, we exploit the link prediction technique based on tensor factorisation to recover vessel tracks in a specified area. A variant of temporal link prediction based on CP is presented. We illustrate the usefulness of exploiting the three-mode structure of AIS data by simulation, and demonstrate that the track recovery result has acceptable precision.

An innovative algorithm to determine the inverse solution of a geodesic with the vertex or Clairaut constant located between two points on a spheroid is presented. This solution to the inverse problem will be useful for solving problems in navigation as well as geodesy. The algorithm to be described derives from a series expansion that replaces integrals for distance and longitude, while avoiding reliance on trigonometric functions. In addition, these series expansions are economical in terms of computational cost. For end points located at each side of a vertex, certain numerical difficulties arise. A finite difference method together with an innovative method of iteration that approximates Newton's method is presented which overcomes these shortcomings encountered for nearly antipodal regions. The method provided here, which does not involve an auxiliary sphere, was aided by the Computer Algebra System (CAS) that can yield arbitrarily truncated series suitable to the users accuracy objectives and which are limited only by machine precisions.

An Augmented Relative Navigation System (ARNS) is proposed for autonomous satellite formation flying in low-Earth-orbit (LEO). Inter-satellite ranging systems such as those based on radio frequency transmissions can provide additional observation information, e.g. inter-satellite distance measurement, which can be used to increase the Global Positioning System (GPS) stand-alone observation dimension, or treated as a non-linear equality constraint within a smoothly-constrained Kalman filter. Both approaches are implemented in the proposed ARNS described in this paper. An innovative phase integer ambiguity fixing and feedback scheme is implemented to increase the ambiguity fix rate of the GPS carrier phase measurements. A set of Gravity Recovery and Climate Experiment (GRACE) flight data is used to test and validate the relative navigation performance of the proposed methods. Results indicate that the augmented system can improve relative positioning accuracy by an order of magnitude.

This paper presents the similarities between equations used for great circle sailing and 2D linear equations. Great circle sailing adopts spherical triangle equations and vector algebra to solve problems of distance, azimuth and waypoints on the great circle; these equations are sophisticated and deemed hard for those unfamiliar with them, whereas on the other hand, 2D linear equations can be solved easily with basic algebra and trigonometry definitions. By pointing out the similarities, readers can quickly comprehend great circle equations and grasp just how similar they are to the corresponding 2D linear equations.

Currently, the 30 nautical mile (nm) minimum longitudinal separation standard is applied on oceanic routes under the Automatic Dependent Surveillance-Contract (ADS-C) environment. However, the periodic position report should be provided at least every ten minutes in Japanese airspace based on previous safety analysis. The position report is usually sent via satellite connection, so less frequent position reports would reduce connection costs by airlines. Since the previous safety analysis estimates the risk of collision conservatively, this paper proposes a refinement of the collision risk model by considering the dependency between two closely separated aircraft. The result shows that the periodic position report interval can be extended without infringing safety.

Maintaining good positioning performance has always been a challenging task for Global Navigation Satellite Systems (GNSS) applications in partially obstructed environments. A method that can optimise positioning performance in harsh environments is proposed. Using a carrier double-difference (DD) model, the influence of the satellite-pair geometry on the correlation among different equations has been researched. This addresses the critical relationship between DD equations and its ill-posedness. From analysing the collected multi-constellation observations, a strong correlation between the condition number and the positioning standard deviation is detected as the correlation coefficient is larger than 0·92. Based on this finding, a new method for determining the reference satellites by using the minimum condition number rather than the maximum elevation is proposed. This reduces the ill-posedness of the co-factor matrix, which improves the single-epoch positioning solution with a fixed DD ambiguity. Finally, evaluation trials are carried out by masking some satellites to simulate common satellite obstruction scenarios including azimuth shielding, elevation shielding and strip shielding. Results indicate the proposed approach improves the positioning stability with multi-constellation satellites notably in harsh environments.

In urban areas, Global Positioning System (GPS) accuracy deteriorates due to signal degradation and multipath effects. To provide accurate and robust navigation in such GPS-denied environments, multi-sensor integrated navigation systems are developed. This paper introduces a 3D multi-sensor navigation system that integrates inertial sensors, odometry and GPS for land-vehicle navigation. A new error model is developed and an efficient loosely coupled closed-loop Kalman Filter (Extended KF or EKF) integration scheme is proposed. In this EKF-based integration scheme, the inertial/odometry navigation output is continuously corrected by EKF-estimated errors, which keeps the errors within acceptable linearization ranges which improves the prediction accuracy of the linearized dynamic error model. Consequently, the overall performance of the integrated system is improved. Real road experiments and comparison with earlier works have demonstrated a more reliable performance during GPS signal degradation and accurate estimation of inertial sensor errors (biases) have led to a more sustainable performance reliability during long GPS complete outages.