To meet the requirements of different applications, the International Global Navigation Satellite System (GNSS) Service (IGS) has provided Global Positioning System (GPS) satellite ephemerides and clock products with different accuracy levels (final, rapid and ultra-rapid products). Comparison of Precise Point Positioning/Inertial Navigation System/Ultra Wideband (PPP/INS/UWB) tightly coupled positioning with different precise satellite ephemeris and clock products is made and corresponding data analysis is provided. Final, rapid and ultra-rapid products are applied in a PPP/INS/UWB integrated system. The field trajectories, position and velocity errors of the integrated system with different products are compared. The results indicate that PPP/INS/UWB tightly coupled positioning with final and rapid products achieves an accurate performance. Compared with the position resolution using final products, the position accuracy with the ultra-rapid products (observed half) is slightly reduced and the position accuracy with the ultra-rapid products (predicted half) has a 0·1–0·2 m reduction. The influence of precise satellite ephemeris and clock products is very minor for non-real-time positioning, relative to the accuracy of PPP/INS/UWB tightly coupled positioning.

The current positioning accuracy of the BeiDou Navigation Satellite System (BDS) Single Point Positioning (SPP) with code measurement is in the order of several metres due to systematic errors. To further reduce the systematic errors in SPP, this contribution develops a new strategy to BDS SPP with a sparse reference network, named Augmented SPP (A-SPP). In this method, the Combined Residual Errors (CRE) products of BDS B1I measurement are integrated with three optional base stations that are close to the rover station. Based on the Satellite Elevation Angle Weighted (SEAW) average technique, the code residual errors of each BDS satellite observed by the rover station can be acquired epoch-by-epoch. Finally, the corrected code observations for the rover station can be utilised to achieve an A-SPP solution. The validation of this method is confirmed by both static and kinematic tests. Results clearly show that the accuracies of the A-SPP solution for horizontal and vertical directions are better than 0·5 m and 1·0 m. This study suggests that the proposed A-SPP solution is a good option for single-frequency GNSS users to improve their positioning performance.

Positioning and Navigation (PN) of Martian rovers still faces challenges due to limited observations. In this paper, the PN feasibilities of Mars rovers based on a Gravity-aided Odometry (GO) system are proposed and investigated in terms of numeric simulations and a case study. Statistical features of the Mars gravity field are studied to evaluate the feature diversity of the background map. The Iterative Closest Point (ICP) algorithm is introduced to match gravity measurements with the gravitational map. The trajectories of Mars Exploration Rovers (MER) and Mars Gravity Map 2011 (MGM2011) are used to complete the experiments. Several key factors of GO including odometry errors, measurement uncertainties, and grid resolution of the map are investigated to evaluate their influences on the positioning ability of the system. Simulated experiments indicate that the GO method could provide an alternative positioning solution for Martian surface rovers.

The planning of vessel navigation along a tidal river is a complex task that can affect the efficiency of inland ports and intermodal chains. The availability of water may represent a significant restriction to port accessibility, having an impact on waiting times, cost and even safety. This paper presents a heuristic procedure to schedule vessels on a tidal waterway, which seeks to optimise navigation according to a multi-criteria objective function combining the number of vessels serviced, the total waiting time, the waterway occupation time and the number of crossing operations, where the term “crossing” implies inbound and outbound vessels passing each other. The procedure requires a previous step of estimation of real-time water depth, which identifies the critical points or navigation bottlenecks along the waterway, and contemplates the possibility of vessels having to anchor in the middle of their journey and wait for next tide rise. We validate the procedure through its application to a set of real and test problems and show that its results are reliable in terms of performance and solution quality.

We present a method of teaching the basics of celestial navigation, using the Javascript programming interface to Google Maps. This offers the teacher of celestial navigation many highly visual and flexible investigative and presentation options, all using the familiar Google Map system. In this paper, we discuss the programming route to Google Maps, and demonstrate an exercise of correcting the assumed position of a hypothetical lost ship, using sights of the Sun, suitable for classroom use. We also present an analysis of the relationship between the proximity of the assumed to the actual position of the ship, and the outcome of a sight-reduction procedure.

The safety of maritime transportation has become increasingly important in recent decades. In this paper, a decision model (a multi-objective and multi-layer fuzzy optimisation model) for navigation risk in different sea areas is established. This is done according to the evaluation index system based on relative data extracted and analysed from Automatic Identification Systems (AIS) information and the multi-objective and multi-layer fuzzy optimisation theory. Then, sorted by an optimal relative membership degree vector and calculated from lower layer to higher layer, the sea areas which have higher navigation risk are selected. Finally, the decision model is shown to be scientific and practical since the results from it are basically consistent with real traffic in Chengshantou waters and the results from the fuzzy comprehensive evaluation model. With the decision model, navigation risk judgments in different sea areas can be offered. It can also provide decision making references to the design of ship routing systems, the layout of search and rescue sites, the configuration of rescue forces and the administration of navigation safety.

For multi-Autonomous Underwater Vehicle (multi-AUV) system task assignment and path planning, a novel Glasius Bio-inspired Self-Organising Map (GBSOM) neural networks algorithm is proposed to solve relevant problems in a Three-Dimensional (3D) grid map. Firstly, a 3D Glasius Bio-inspired Neural Network (GBNN) model is established to represent the 3D underwater working environment. Using this model, the strength of neural activity is calculated at each node within the GBNN. Secondly, a Self-Organising Map (SOM) neural network is used to assign the targets to a set of AUVs and determine the order of the AUVs to access the target point. Finally, according to the magnitude of the neuron activity in the GBNN, the next AUV target point can be autonomously planned when the task assignment is completed. By repeating the above three steps, access to all target points is completed. Simulation and comparison studies are presented to demonstrate that the proposed algorithm can overcome the speed jump problem of SOM algorithms and path planning in the 3D underwater environments with static or dynamic obstacles.

The basis of all recommended methods for obtaining position by using celestial bodies is the known altitude of the celestial body being observed. Accordingly, it is necessary to have a sextant, classic or with an artificial horizon, or some other device that can measure altitude. However, there is a way to obtain position using astronomical navigation without determining the altitude of a celestial body, and this method will be analysed in this paper. The introduced method requires only precise measurement of the azimuth, and is based on determining two positions close to the dead reckoning position and lying on the isoazimuthal curve, i.e. a curve of the same great circle azimuths of a celestial body. Furthermore, the model assumes that a part of this curve, between the selected positions, can be replaced by a straight line. Special attention will be given to the analysis of errors of the line of position for various azimuth errors and various dead reckoning (assumed) positions. It will also be shown how a modern Electronic Chart Display and Information System (ECDIS) can help in approximate position determination, knowing only the azimuths of celestial bodies.

This paper optimises two-ship collision-avoidance manoeuvres accounting for both collision risk and fuel use. A collision-avoidance manoeuvring optimisation model is developed to minimise fuel consumption while assuring ships' operational safety. The model can optimally determine when to begin collision-avoidance actions, how to change courses, and what rudder angles are needed. A quantitative scenario simulation is developed to illustrate the model application. The methodology can be further developed to guide practical ship collision-avoidance manoeuvring decisions made under more operational scenarios. In particular, this research can contribute to the development of computer-aided collision-avoidance operations to improve the safety and energy efficiency of maritime transportation.

With the improvement of the bias instability of Micro-Electromechanical Systems (MEMS) gyroscopes, the g-sensitivity error is gradually becoming one of the more important factors that affects the dynamic accuracy of a MEMS gyroscope. Hence there is a need for correcting the g-sensitivity error. However, the traditional calibration of g-sensitivity error uses a centrifuge. The calibration conditions are harsh, the process is complex and the cost is relatively high. In this paper, a fast and simple method of g-sensitivity error calibration for MEMS gyroscopes is proposed. With respect to the bias and random noise of a MEMS gyroscope, the g-sensitivity error magnitude is relatively small and it is simultaneously coupled with the Earth's rotation rate. Therefore, in order to correct the g-sensitivity error, this work models the calibration for g-sensitivity error coefficients, designs an (8+N)-position calibration scheme, and then proposes a fitting method for g-sensitivity error coefficients based on the Newton iteration and least squares methods. Multi-group calibration experiments designed on a MEMS Inertial Measurement Unit (MEMS IMU) product demonstrate that the proposed method can calibrate g-sensitivity error coefficients and correct the g-sensitivity error effectively and simply.

The demand for accurate indoor positioning continues to grow but the predominant positioning technologies such as Global Navigation Satellite Systems (GNSS) are not suitable for indoor environments due to multipath effects and Non-Line-Of-Sight (NLOS) conditions. This paper presents a new indoor positioning system using artificial encoded magnetic fields, which has good properties for NLOS conditions and fewer multipath effects. The encoded magnetic fields are generated by multiple beacons; each beacon periodically generates unique magnetic field sequences, which consist of a gold code sequence and a beacon location sequence. The position of an object can be determined with measurements from a tri-axial magnetometer using a three-step method: performing time synchronisation between sensor and beacons, identifying the beacon field and the beacon location, and estimating the position of the object. The results of the simulation and experiment show that the proposed system is capable of achieving Two-Dimensional (2D) and Three-Dimensional (3D) accuracy at sub-decimetre and decimetre levels, respectively.

A better understanding of passenger movement in multi-modal transit situations is the major aim of this study. By using a novel Cooperative Positioning (CP) approach, algorithms can be generated which considerably increase the accuracy of person tracking. Smooth transit at stations is enabled, thus the total waiting time for routing at the traffic interchange is reduced. A Location-Based Services (LBS) user is guided by the service and located with the assistance of the whole user group. In addition to the technological developments, the acceptance and end-user needs are considered. End-users of such a service have the right to withdraw their consent for transferring location-based and other personal data at any time. They also receive clear and comprehensive information about when and why they reveal their personal data and location and its further use. In this paper, the concept is introduced followed by a comprehensive discussion of the suitable CP localisation techniques as well as an implementation strategy. Furthermore, ethical and usability aspects are discussed to ensure user-friendly results.

The adoption of a robust collision avoidance module is required to realise fully autonomous Unmanned Surface Vehicles (USVs). In this work, collision detection and path planning methods for USVs are presented. Attention is focused on the difference between local and global path planners, describing the most common techniques derived from classical graph search theory. In addition, a dedicated section is reserved for intelligent methods, such as artificial neural networks and evolutionary algorithms. Born as optimisation methods, they can learn a close-to-optimal solution without requiring large computation effort under certain constraints. Finally, the deficiencies of the existing methods are highlighted and discussed. It has been concluded that almost all the existing method do not address sea or weather conditions, or do not involve the dynamics of the vessel while defining the path. Therefore, this research area is still far from being considered fully explored.

The objective of this paper is to accurately determine mobile robots' position and orientation by integrating information received from odometry and an inertial sensor. The position and orientation provided by odometry are subject to different types of errors. To improve the odometry, an inertial measurement unit is exploited to give more reliable attitude information. However, the nonlinear dynamic of these systems and their complexities such as different sources of errors make navigation difficult. Since the dynamic models of navigation systems are nonlinear in practice, in this study, a Cubature Kalman Filter (CKF) has been proposed to estimate and correct the errors of these systems. The information from odometry and a gyroscope are integrated using a CKF. Simulation results are provided to illustrate the superiority and the higher reliability of the proposed approach in comparison with conventional nonlinear filtering algorithms such as an Extended Kalman Filter (EKF).

The current Korean national geodetic reference frame, KGD2002, refers to the fixed epoch at 2002·0 under the assumption that there is no crustal movement of the Korean peninsula. A discontinuity in the coordinates of the reference stations may occur due to the relocation of the stations, antenna replacement, or earthquakes. The static reference frame has difficulty in covering continuous and/or discontinuous crustal movements at the same time. A new dynamic local geodetic reference frame has been calculated based on eight years (2007–2014) of Global Navigation Satellite System (GNSS) data. The final geodetic coordinates and velocities were calculated on the basis of the IGb08 reference frame. The discontinuity caused by the 2011 Tohoku earthquake can be addressed using the newly proposed model in this study, which ensures the consistency and continuity of the local geodetic datum.

Increasing the stability and reliability of navigation for mobile objects of different classes is becoming increasingly significant. Satellite navigation systems have a fundamental defect: a vulnerability to hacking and spoofing. Observation of the horizon line is significant for two applications. The first is stellar inertial navigation systems. In this case, the horizon line can be used for local vertical estimation. Errors in local vertical estimation directly affect coordinate errors. The second is correlation-extremal navigation based on the observed horizon line shape (when islands or continents are observed from aerial vehicles). In both cases, instability of the horizon line produces navigation errors. A measurement procedure for horizon line position estimation was proposed and realised. Around-the-clock horizon line shooting was undertaken in 2013. Processing of the results shows a horizon line direction instability of about 5–7 angular minutes during the day time.

This paper discusses the estimation algorithms for Three-Dimensional (3D) displacement and 3D rotation using Two-Dimensional (2D) laser scanners. An efficient outlier detection method is proposed for both algorithms to help protect the integrity of navigation. The algorithms have been evaluated using both simulation and field test results. They are able to produce a robust odometry solution for an autonomous aircraft in an indoor environment.

The integration of multi-constellation Global Navigation Satellite System (GNSS) measurements can effectively improve the accuracy and reliability of navigation and positioning solutions, while the Inter-System Bias (ISB) is a key issue for compatibility. The ISB is traditionally estimated as an unknown parameter along with three-dimensional position coordinates and a receiver clock offset with respect to Global Positioning System (GPS) time. ISB estimation of this sort will sacrifice a satellite observation for each integrated GNSS system. These sacrificed observations could be vital in situations of limited satellite visibility. In this study, an enhanced multi-GNSS navigation algorithm is developed to avoid sacrificing observations under poor visibility conditions. The main idea of this algorithm is to employ a moving average filter to smooth the ISBs estimated at previous epochs. The filtered value is utilised as a priori information at the current epoch. Experimental tests were conducted to evaluate the enhanced algorithm under open and blocked sky conditions. The results show that the enhanced algorithm effectively improves the accuracy and availability of navigation solutions under the blocked sky condition, with performance being comparable to traditional ISB estimation algorithms in open sky conditions. The improvement rates of the three-dimensional position accuracy and availability reach up to 63% and 21% in the blocked sky environment. Even in the case of only four different GNSS satellites, a position solution can still be obtained using the enhanced algorithm.