This paper proposes a bi-level model from the perspective of game theory to describe the effect of the rise of Arctic shipping routes on traditional routes and their response. The upper-level model demonstrates the competition between shipping companies that maximise their own profits via speed adjustment, which can be presented as a generalised Nash equilibrium problem and is solved by the generalised reduced-gradient method. The lower-level model illustrates the response of customers who reassign their demands with an elastic total demand, which is presented as a logit-type multi-path assignment problem and is solved by the iterative balancing method. A case study is used to examine the rationality of the proposed model and algorithm.

Spherical trigonometry formulae are widely adopted to solve various navigation problems. However, these formulae only express the relationships between the sides and angles of a single spherical triangle. In fact, many problems may involve different types of spherical shapes. If we can develop the different formulae for specific spherical shapes, it will help us solve these problems directly. Thus, we propose two types of formulae for combined spherical triangles. The first set are the formulae of the divided spherical triangle, and the second set are the formulae of the spherical quadrilateral. By applying the formulae of the divided spherical triangle, waypoints on a great circle track can be obtained directly without finding the initial great circle course angle in advance. By applying the formulae of the spherical quadrilateral, the astronomical vessel position can be yielded directly from two celestial bodies, and the calculation process concept is easier to comprehend. The formulae we propose can not only be directly used to solve corresponding problems, but also expand the spherical trigonometry research field.

Global Navigation Satellite System (GNSS) safety issues of have been of concern for some time. Spoofing attacks have received much attention as they can be difficult to detect and have the potential to cause disruption at best and major damage in extremis. To mitigate such threats, a spoofing detection method based on the consistency check of Doppler positioning fixes and pseudorange positioning fixes is proposed. The primary contributions of this paper include establishing a Generalised Likelihood Ratio Test (GLRT)-based statistical detection model for the introduced spoofing detection method and efficiently improving the accuracy of the Doppler positioning method as well as the performance of the detection approach by a modified α-filter-based Doppler smoothing technique. Theoretical performance of the proposed detection model is analysed. Monte Carlo simulations were also conducted to verify the theoretical analysis. Moreover, grounded on the developed test statistic and the optimised threshold, a consistency check module was specifically realised in both software defined and real-time GNSS receivers. Additionally, a Doppler smoothing technique was applied to the receivers. Spoofing attack experiments on both software defined and real-time platforms validated the effectiveness of the statistical spoofing detection model.

In this study, possible ionospheric precursors of the Mw7·1 Van earthquake are investigated with temporal, spatial and spectral analyses. For this purpose, Global Navigation Satellite System (GNSS) data of 11 International GNSS Service (IGS) stations and 17 Turkish National Permanent Real-Time Kinematic (RTK) Network (TNPGN-Active) stations were utilised. In addition, Global Ionosphere Map (GIM) data produced by the Center for Orbit Determination in Europe (CODE) was used to obtain GIM-vertical Total Electron Content (vTEC) values for the epicentre. The results of the temporal and spectral analysis indicate an increase (2–8 Total Electron Content Units (TECU)) before the Van earthquake occurred on 9 October, 15–16 October and 21–23 October within 15 days, 8–9 days and 1–3 days prior to the earthquake. The Cross-Wavelet Transform (CWT) method was used to examine the presence of correlation between noticeable variations and space-weather. It is deduced from the CWT analysis that the anomalies should originate from either solar effects or the Van earthquake due to coupling between the F10·7 solar activity index and TEC variations on the anomaly days. The results demonstrate that interdisciplinary approaches and various methods including frequency domain could be used to determine the presence of an earthquake-related anomaly in the ionosphere accurately.

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.

Clustering methods that use a similarity measurement for evaluating vessel trajectories are important for mining spatial distribution information in water transportation. To better measure the similarity of vessel trajectories, a novel similarity measure is proposed based on the dynamic time warping distance, which considers the course change of track points and the meaning at the route level. Parallel experiments were conducted based on a month of Automatic Identification System (AIS) data collected from the Zhoushan Islands area, China. After evaluation of the accuracy and the cluster degree, the novel measure demonstrated its capabilities for distinguishing different vessel trajectories and detecting similar vessel trajectories with high accuracy and has a better performance compared to some existing methods.

In this paper, the spacecraft close-range safe proximity problem is investigated. In the presence of a “chief” spacecraft, a Multi-Equal-Collision-Probability-Curve (MECPC) method is developed. The influence of the chief spacecraft with a convex polygon shape is considered and the chief spacecraft is divided into several small components. Each component generates a corresponding separate repulsive force and the superposition of these forces is regarded as the ultimate avoidance force. As a result, the proposed MECPC method not only improves the system robustness against control and navigation uncertainties but is also analytically validated in collision avoidance. The MECPC method solves the safe proximity problem in the presence of a convex polygon shape. In addition, an Improved Linear Quadratic Regulator (ILQR) is designed to track the expected trajectory. Numerical simulations are performed in a close-range operation environment to verify the effectiveness of the proposed MECPC method.

Two pre-processes for Automatic Identification System (AIS) trajectories commonly reported in the maritime knowledge discovery literature are trajectory simplification and event identification. Both pre-processes reduce storage and computational expenses by reducing the number of data points to be used in an analysis. This paper presents an event identification and trajectory simplification method based on behaviour identification and translation. Trajectory segments deemed to correspond to coastal or ocean navigation are translated into equivalent passage plan segments; a succinct description of the movements and behaviour of the ship. As a trajectory simplification method, it provides two main advantages over commonly used trajectory simplification methods: more meaningful simplified trajectories with better encoding of basic behaviours and the possibility to retain interesting behaviours in full resolution. As an event identification method, it is capable of differentiating between normal ocean or coastal navigating behaviour and complex or interesting behaviour, such as pilotage, reaction to a traffic conflict, or an involuntary deviation from the passage plan.

A conventional Differential GPS (DGPS) techniques-based velocity and acceleration method (named here as ‘DVA’) may be difficult to implement in the Antarctic as there is a sparse distribution of reference stations over Antarctica. Thus, in order to overcome the baseline limitations and to obtain highly accurate and reliable velocity and acceleration estimates for airborne gravimetry, a network-based velocity and acceleration determination approach (named here as ‘NVA’), which introduces a wide network of stations and is independent of precise clock information, is applied. Here its performance for velocity and acceleration determination is fully exploited by using Global Positioning System (GPS), GLONASS, Galileo and BeiDou observations. Additionally, a standalone receiver-based method named ‘SVA’, which requires precise clock information, is also implemented for comparison. During static tests and a flight experiment over Antarctica, it was found that the NVA method yields more robust results than the SVA and DVA methods when applied to a wide area network. Moreover, the addition of GLONASS, Galileo and BeiDou systems can increase the accuracy of velocity and acceleration estimates by 39% and 43% with NVA compared to a GPS-only solution.

Precise Point Positioning/Inertial Navigation System (PPP/INS) integrated navigation based on PPP and low-accuracy INS is often used to provide position and attitude information for vehicle-mounted or airborne mobile mapping systems. With proper processing, the position accuracy of PPP/INS is comparable to that of Differential Global Navigation Satellite System (DGNSS)/INS, but the accuracy of the attitude, especially the yaw angle, cannot be guaranteed. However, the yaw angle is crucial for mobile mapping systems. To compensate for the insufficiency of PPP/INS, we have designed a Multi-Antenna GNSS (MAGNSS)/INS integrated navigation system. First, the attitude determination method using MAGNSS is presented in detail. Then, the MAGNSS attitude is combined with the PPP position and velocity as measurements for integration with the INS. Thus, PPP/INS integrated navigation was improved to MAGNSS/INS integrated navigation. Finally, a three-hour car-borne test was conducted to evaluate the performance of the proposed method. The results indicate that the attitude determined from MAGNSS is accurate and stable over time. Compared to PPP/INS, MAGNSS/INS integrated navigation can improve the attitude accuracy significantly because of the inclusion of MAGNSS attitude.

The trajectory tracking of Autonomous Underwater Vehicles (AUV) is an important research topic. However, in the traditional research into AUV trajectory tracking control, the AUV often follows human-set trajectories without obstacles, and trajectory planning and tracking are separated. Focusing on this separation, a trajectory re-planning controller based on Model Predictive Control (MPC) is designed and added into the trajectory tracking controller to form a new control system. Firstly, an obstacle avoidance function is set up for the design of an MPC trajectory re-planning controller, so that the re-planned trajectory produced by the re-planning controller can avoid obstacles. Then, the tracking controller in the MPC receives the re-planned trajectory and obtains the optimal tracking control law after calculating the object function with a Sequential Quadratic Programming (SQP) optimisation algorithm. Lastly, in a backstepping algorithm, the speed jump can be sharp while the MPC tracking controller can solve the speed jump problem. Simulation results of different obstacles and trajectories demonstrate the efficiency of the proposed MPC trajectory re-planning tracking control algorithm for AUVs.

Real-time Precise Point Positioning (PPP) has been evolved as a cost-effective technique for highly precise maritime positioning. For a long period, maritime PPP technology has mainly relied on the Global Positioning System (GPS). With the revitalisation of GLONASS and the emerging BeiDou navigation satellite system (BDS), it is now feasible to investigate real-time navigation performance of multi-constellation maritime PPP with GPS, BDS and GLONASS. In this contribution, we focus on maritime PPP performance using real world maritime kinematic data and real-time satellite correction products. The results show that BDS has lower position accuracy and slower convergence time than GPS. The BDS and GPS combination has the best performance among the dual-constellation configurations. Meanwhile, the integration of BDS, GLONASS and GPS significantly improves the position accuracy and the convergence time. Some outliers in the single constellation configuration can be mitigated when multi-constellation observations are utilised.

Conventional visual ship tracking methods employ single and shallow features for the ship tracking task, which may fail when a ship presents a different appearance and shape in maritime surveillance videos. To overcome this difficulty, we propose to employ a multi-view learning algorithm to extract a highly coupled and robust ship descriptor from multiple distinct ship feature sets. First, we explore multiple distinct ship feature sets consisting of a Laplacian-of-Gaussian (LoG) descriptor, a Local Binary Patterns (LBP) descriptor, a Gabor filter, a Histogram of Oriented Gradients (HOG) descriptor and a Canny descriptor, which present geometry structure, texture and contour information, and more. Then, we propose a framework for integrating a multi-view learning algorithm and a sparse representation method to track ships efficiently and effectively. Finally, our framework is evaluated in four typical maritime surveillance scenarios. The experimental results show that the proposed framework outperforms the conventional and typical ship tracking methods.

The location of the wreck of Shackleton's ship the Steam Yacht Endurance is recorded in the expedition log books as 68°39′30′′S 52°26′30′′W. The methods and assumptions that went into obtaining this fix are examined in detail by consulting the original log entries with a view to understanding the size of the errors and uncertainties it may be subject to and providing guidance to possible future searches. It is found that a dearth of navigational sights around the time of the sinking, the inevitable growth of uncertainties in the chronometer time since rating and other factors, introduce the possibility of errors in the position of several nautical miles in both latitude and longitude.

The accuracy and fault tolerance of filters are directly affected by the filter architecture and algorithm, thus influencing navigation performance. The chi square detection used in the conventional reset federated filter is not sensitive to soft faults, and it is easy to cause the health subsystem to be polluted through information sharing. It is a challenge to design an adaptive reset federated filter to improve the performance of the navigation system. Therefore, taking the Strapdown Inertial Navigation System/Global Positioning System/Celestial Navigation System/Synthetic Aperture Radar (SINS/GPS/CNS/SAR) integrated navigation system as an example, an adaptive federated filter architecture for vector-formed information sharing without a fault isolation module is designed in this paper. The proposed method uses the two-state chi square detection algorithm to calculate the parameters corresponding to each state, making the state with higher accuracy obtain a greater information distribution coefficient. In addition, according to the value of vector-formed information sharing, an adaptive coefficient of measurement noise is designed. This improves the adaptability of the navigation system to soft faults. Simulation results show that the accuracy of the proposed algorithm has the same performance compared with the conventional method under normal circumstances. When the sensor has a soft fault, the adaptive federated filter algorithm proposed in this paper can adaptively adjust the distribution coefficients, eliminate the influence of the fault information and improve the precision of the navigation system. The approach described in this paper can be used in multi-sensor integrated navigation. It will have better performance in engineering applications.

An H∞ controller combined with an Artificial Potential Field Method (APFM) was applied to seabed navigation for Autonomous Underwater Vehicles (AUVs), aimed particularly at obstacle avoidance and bottom-following operations in the vertical plane. Depth control and altitude control prevented the AUV from colliding with the sea bottom or with obstacles and prevented the AUV from diving beyond its maximum depth limit when bottom following. Simulation and laboratory trials with various seabed contours indicated that with the H∞ controller, the AUV was able to safely reach appointed destinations without collisions. Tests also showed that the H∞ controller was robust and suppressed interference, hence ensuring the precision of its navigation control. The proposed H∞ controller combined with the APFM has thus been proved to be both feasible and effective.