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.

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.

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.

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.

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.

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.

We investigate a strategy to address the problem of low aircraft detection probability of space-based Automatic Dependent Surveillance-Broadcast (ADS-B). A nineteen-element hexagonal array and adaptive multi-beamforming method is proposed. This method aims to adjust the beam pattern dynamically to reduce signal collision and enlarge coverage. With the focus on the mission requirement of global aircraft detection by 2020, the appropriate gain and direction of beams are studied and designed in detail. Theoretical analysis and simulations show that this adaptive multi-beam antenna can greatly improve flight detection probability at an average reporting interval from 10 seconds to 5 seconds when compared with the traditional fixed multi-beam antenna. The results of this work show that the design of a 19-element antenna along with the adaptive multi-beamforming method can be considered as a building block of future space-based ADS-B.

The performance of Global Navigation Satellite System (GNSS) and Micro-Electro-Mechanical System (MEMS)-based Inertial Navigation System (INS) integrated navigation is reduced during GNSS outages. To bridge the period during GNSS outages, a novel hybrid intelligent algorithm incorporating a Discrete Grey Predictor (DGP) and a Multilayer Perceptron (MLP) neural network (DGP-MLP) is proposed. The DGP-MLP is used to provide a pseudo-GNSS position to correct the INS errors during GNSS outages; the DGP uses the GNSS position information of the latest few moments to predict the position of future moments; in the process of DGP-MLP, the MLP is used to modify the prediction errors of DGP, and the MLP is improved by adding momentum terms and adaptively adjusting the learning rate and momentum factor. To evaluate the effectiveness of the proposed methodology, four GNSS outages in different cases over a real field test data were employed. The experimental results demonstrate that the proposed methodology can significantly improve positioning accuracy during GNSS outages.

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.

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.

Due to the limitations of the existing methods (for example, the route binary tree method) that can only automatically generate routes based on a single chart, a method for automatically generating the shortest distance route based on an obstacle spatial database is proposed. Using this proposed method, the route between two arbitrary points at sea can be automatically generated. First, the differences in accuracy and updating time of charts are quantitatively analysed. Next, the mechanism for updating obstacles is designed, an obstacle spatial database is constructed, and the obstacle data extracted from multiple charts are fused. Finally, considering the effect of efficiency on the amount of obstacle data, a route window and an improved R-tree index are designed for quickly extracting and querying the obstacle database. The experimental results demonstrate that compared with existing methods, the proposed method can generate the shortest distance between two arbitrary points at sea and eliminates the limitation of the area of the chart. In addition, with data from multiple charts, the route generated by the proposed method is more reliable than that of the existing methods, and it is more efficient.

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 paper, we propose a novel dynamic fuzzy ship domain that considers factors associated with both one's own ship and other ships. This is in contrast to existing ship domain models that operate from the perspective of one's own ship, considering only the factors relevant to that ship. First, the domain was determined by considering the distance of the ships around one's own ship in different directions, which sufficiently accounts for factors associated with one's own ship and with the other ships. At the same time, the factors were chosen based on an analysis of their importance. Second, the domain was dynamic and modelled by establishing the relationship between the domain size and the chosen factors in different directions from one's own ship, obtained by using neural networking and wavelet decomposition. Third, the domain was developed using fuzzy sets related to different safety levels and this related the model to the practical applications of estimating spatial collision risk. The model was calibrated using Automatic Identification System (AIS) data of vessel movements in the Bohai Sea and the northern Yellow Sea. The reasonableness and the superiority of establishing a ship domain model considering the factors affecting both one's own ship and other ships were analysed, and the results show that the new model can determine the spatial collision risk of the navigational situation and is thus suitable for use as part of a ship collision avoidance system.

A priori attitude information can improve the success rate and reliability of Global Navigation Satellite System (GNSS) multi-antennae attitude determination. However, a priori attitude information is nonlinear, and integrating a priori information into the objective function rigorously will increase the complexity of an ambiguity domain search, such as the Multivariate Constrained-Least-squares Ambiguity Decorrelation Adjustment (MC-LAMBDA) method. In this paper, a new method based on attitude domain search is presented to make use of the a priori attitude angle information with high efficiency. First, the a priori information of pitch and roll is integrated into the search process to derive the analytic search step for attitude angle, and the integer candidates are determined by traversal search in the three-dimensional attitude domain. Then, the objective function is parameterised with Euler angles, and a non-iterative approximate method is utilised to simplify the iterative computation in calculating objective function values. Experimental results reveal that compared to the MC-LAMBDA method, our new method has the same success rate and reliability, but higher efficiency in making use of a priori attitude information.

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.