An X-ray pulsar/starlight Doppler deeply-integrated navigation method is proposed in this paper. A starlight Doppler measurement-aided phase propagation model, which can remove the orbital effect within the recorded photon Time Of Arrivals (TOAs), is derived, and guarantees that the pulse phase can be extracted from the converted photon TOAs using computationally efficient methods. Some simulations are performed by a hardware-in-loop system to verify the performance of the integrated pulse phase estimation method as well as of the integrated navigation method. The integrated pulse phase estimation method could achieve an estimation performance similar to the existing method for orbiting vehicles at the cost of much less computational complexity, is capable of handling the signals of millisecond pulsars, and is applicable to various vehicles. In addition, the proposed integrated navigation method could provide reliable positioning results for various vehicles.

This study examines maritime routes between ports along the Atlantic coast of the US, utilising Automated Identification System (AIS) data for the years 2010 through 2012. The delineation of vessel routes conducted in this study was motivated by development planned for offshore Wind Energy Areas (WEAs) along the Atlantic coast of the US and the need to evaluate the effect of these development areas on commercial shipping. To this end, available AIS data were processed to generate commercial vessel tracks for individual vessels, though cargo vessels are the focus in this study. The individual vessel tracks were sampled at transects placed along the Atlantic coast. The transect samples were analysed and partitioned by voyages between Atlantic ports to facilitate computation of vessel routes between ports. The route boundary analysis utilised a definition from UK guidance in which routes' boundaries encompassed 95% of the vessel traffic between ports. In addition to delineating route boundaries, we found multi-modal transverse distributions of vessels for well-travelled routes, which indicated preference for lanes of travel within the delineated routes.

Ship collision risk is an important aspect of ship navigation safety. A systematic method to assess collision risk by monitoring parameter states continually is necessary and has proven effective. Another important factor in risk assessment is ship size, but the effect of the size of ship pairs has not been considered properly in many previous studies. This research utilises a systematic perspective to study collision risk of near-misses in ship-ship encounters. This fills a secondary research gap where previous risk assessments only investigated near-misses from the perspective of a single vessel. Following this proposed approach, ship pair encounter states can be continually tracked. Ultimately, a method of improved Vessel Collision Risk Operator (VCRO) to merge risk assessments of both ships is proposed through integration of near-miss collision risks in a systematic way, which overcomes the disadvantages of prior VCROs that only consider the maximum value, from which it is difficult to track and judge the risk trend. Utilising a case study, the effectiveness of the proposed method is validated through analysis of ship encounters, with ships of different sizes in the Baltic Sea.

This paper presents a framework for a strapdown Inertial Navigation System (INS) algorithm design by using Lie group and Lie algebra. The general way to solve Lie group differential equations is introduced. Investigations reveal that this general Lie group method provides a simpler unified way to solve differential equations involving direction cosine matrix, quaternion and dual quaternion, which are widely used in INS algorithm design. Furthermore, we also present a new INS algorithm based on the Special Euclidean group se(3) under the guidelines of Lie group method. Analyses show that se(3) algorithm has the same accuracy as a dual quaternion algorithm, this is also justified by numerical simulations. Though the se(3) algorithm has no improvements in accuracy, the general Lie group method used in the design process shows its brevity and uniformity.

In-motion alignment plays an important role in improving the manoeuvring capability of a vehicle, and allows the initialisation of a Strapdown Inertial Navigation System (SINS) while moving. Odometer (OD) aided in-motion alignment is widely adopted owing to its fully self-contained characteristic. This paper proposes a complete in-motion alignment algorithm for a vehicle-carried SINS based on odometer aiding, in which an in-motion coarse alignment method using the integration form of the velocity update equation in the body frame to give a rough initial angle is introduced and a new measurement equation in the body frame with a Kalman filter (KF) for the in-motion fine alignment is established. The advantages of the proposed method are verified by simulation and measured data.

Mapping points on the Riemann sphere to points on the plane of complex numbers by stereographic projection has been shown to offer a number of advantages when applied to problems in navigation traditionally handled using spherical trigonometry. Here it is shown that the same approach can be used for problems involving great circles and/or rhumb lines and it results in simple, compact expressions suitable for efficient computer evaluation. Worked numerical examples are given and the values obtained are compared to standard references.

A region tracking fault tolerant control approach based on backstepping technique is proposed for Autonomous Underwater Vehicles (AUV). The proposed approach aims at driving tracking error to reach into the desired region in presence of ocean current disturbance, modelling uncertainty, unknown thruster faults and thruster amplitude and rate saturation constraints. At first, a type of piecewise and differential Lyapunov function is constructed to achieve region tracking control in the frame of backstepping technique. Then, the paper analyses and acquires the bound structures of the lumped uncertainty (including ocean current disturbance and model uncertainty) and the variation of thruster distribution matrix caused by unknown thruster faults, respectively. An adaptive technique is used to estimate the unknown coefficients in the above bound structures. In addition, an adaptive adjustment scheme for the desired trajectory is developed to achieve region tracking control with thruster amplitude and rate saturation constraints. The stability of the closed-loop system is analysed based on Barbalat's lemma. Finally, simulations and pool-experiments are presented to illustrate the effectiveness of the proposed method.

In the conventional integrated navigation system, the statistical information of the process and measurement noises is considered constant. However, due to the changing dynamic environment and imperfect knowledge of the filter statistical information, the process and measurement covariance matrices are unknown and time-varying. In this paper, a multirate adaptive Kalman filter is proposed to improve the performance of the Error State Kalman Filter (ESKF) for a marine navigation system. The designed navigation system is composed of a strapdown inertial navigation system along with Doppler velocity log and inclinometer with different sampling rates. In the proposed filter, the conventional adaptive Kalman filter is modified by adaptively tuning the measurement covariance matrix of the auxiliary sensors that have varying sampling grates based on the innovation sequence. The performance of the proposed filter is evaluated using real measurements. Experimental results show that the average root mean square error of the position estimated by the proposed filter can be decreased by approximately 60% when compared to that of the ESKF.

The maritime domain is the most utilised environment for bulk transportation, making maritime safety and security an important concern. A major aspect of maritime safety and security is maritime situational awareness. To achieve effective maritime situational awareness, recently many efforts have been made in automatic anomalous maritime vessel movement behaviour detection based on movement data provided by the Automatic Identification System (AIS). In this paper we present a review of state-of-the-art automatic anomalous maritime vessel behaviour detection techniques based on AIS movement data. First, we categorise some approaches proposed in the period 2011 to 2016 to automatically detect anomalous maritime vessel behaviour into distinct categories including statistical, machine learning and data mining, and provide an overview of them. Then we discuss some issues related to the proposed approaches and identify the trend in automatic detection of anomalous maritime vessel behaviour.

Vision navigation using environmental features has been widely applied when satellite signals are not available. However, the matching performance of traditional environmental features such as keypoints degrades significantly in weakly textured areas, deteriorating navigation performance. Further, the user needs to evaluate and assure feature matching quality. In this paper, a new feature, named Line Segment Intersection Feature (LSIF), is proposed to solve the availability problem in weakly textured regions. Then a combined descriptor involving global structure and local gradient is designed for similarity comparison. To achieve reliable point-to-point matching, a coarse-to-fine matching algorithm is developed, which improves the performance of the point set matching algorithm. Finally, a framework of matching quality evaluation is proposed to assure matching performance. Through the comparison, it is demonstrated that the proposed new feature has superior overall performance especially on correctly matched numbers of keypoints and matching correctness. Also, using real image sets with weak texture, it is shown that the proposed LSIF can achieve improved navigation solutions with high continuity and accuracy.

The Strait of Istanbul is one of the most congested and risky waterways in the world. Navigation patterns have been investigated using Automatic Indentification System (AIS) data collected over a long period. 1·5 billion AIS messages, gathered over a year from 309,000 moving vessels in the Strait were stored in a Structured Query Language (SQL) database. Grid-based analysis is used to track the time, number, position, type, dimension, heading, speed and course over ground of ships. Local traffic, whose effect on maritime risk has often been neglected, is found to dominate transit traffic by a ratio of eight to one. Vessel distributions indicate that the most common lengths of vessels are 100 m and 170 m. Draught analysis shows a net transfer of goods from north to south. Southbound vessels are more likely to exceed the enforced speed limit due to predominant currents. Courses indicate that the local traffic strongly affects navigation patterns, especially at sectors with sharp turns. All these results help to understand the navigation patterns of ships and give the necessary input to assist in predicting maritime risk.

Container shipping is one of the most important transport modes in international trade. For a large-scale container shipping network, an optimisation model is proposed to minimise the total shipping cost of container flow. Considering the directional property of the container shipping process, a steering vector search pattern is incorporated in a Max-Min Ant System (MMAS) solving algorithm, and an orthogonal array method is adopted in parameter settings. In numerical experiments, a traditional ant colony algorithm and an MMAS algorithm based on a steering vector search pattern are used respectively to optimise the network of five node scales. The results show that a steering vector search pattern can speed up the computation process and improve the optimisation effect.

The purpose of this study is to determine the navigation efficiency for transiting from various ports in Asia and Rotterdam in Europe via the Northern Sea Route. Navigation efficiency was derived from fuel consumption ratios. Preliminary research results showed that fuel consumption and the amount of carbon dioxide emissions was reduced by transiting from various ports through the European Sea Route, and the navigation efficiencies of the various ports ranked in the following descending order: Yokohama - Busan - Shanghai - Kaohsiung - Hong Kong - Singapore. The higher the ratio was, the lower the navigation efficiency of using the Northern Sea Route, i.e. more fuel was consumed and travel costs were higher. In contrast, the lower the ratio was, the higher the navigation efficiency, i.e. less fuel was consumed and travel costs were lower. Recommendations were discussed in the study.

In this paper, a novel Predictive Variable Structure Filter (PVSF) and its adaptive deformation (APVSF) are presented for attitude synchronisation during Satellite Formation Flying (SFF). The PVSF is proposed based on the variable structure control concept and applied to any nonlinear system with model errors. The model errors in the PVSF need not satisfy the assumption of Gaussian white noise; therefore, it has advantages in dealing with various kinds of uncertainties, parameter variations or noises. Then, the APVSF is also presented to adjust the smoothing boundary layer of PVSF by minimising the Mean-Square Error (MSE). Simulations are performed to demonstrate the accuracy, robustness, and stability of the proposed methodologies for the attitude synchronisation estimation of the SFF system.

The Unscented Kalman Filter (UKF) is a well-known nonlinear state estimation method. It shows superior performance at nonlinear estimation compared to the Extended Kalman Filter (EKF). This paper is devoted to an investigation between UKF and EKF with different feedback control modes in vehicle navigation. Theoretical formulation, simulation and field tests have been carried out to compare the performance of UKF and EKF. The simulation and test results demonstrate that the estimated state of a UKF relies on the measurements and is less sensitive to historical model information. The results also indicate that UKF has benefits for prototype model design due to avoidance of calculation of a Jacobian matrix. EKF, however, is more computationally efficient and more stable.

Maritime anomaly detection is a key technique in intelligent vessel traffic surveillance systems and implementation of maritime situational awareness. In this paper, we propose a method which combines vessel trajectory clustering and Naïve Bayes classifier to detect anomalous vessel behaviour in the maritime surveillance system. A similarity measurement between vessel trajectories is designed based on the spatial and directional characteristics of Automatic Identification System (AIS) data, then the method of hierarchical and k-medoids clustering are applied to model and learn the typical vessel sailing pattern within harbour waters. The Naïve Bayes classifier of vessel behaviour is built to classify and detect anomalous vessel behaviour. The proposed method has been tested and validated on the vessel trajectories from AIS data within the waters of Xiamen Bay and Chengsanjiao, China. The results indicate that the proposed method is effective and helpful, thus enhancing maritime situational awareness in coastal waters.

Binary Offset Carrier (BOC) modulation signals have been applied in Global Navigation Satellite Systems (GNSS) because they offer a higher positioning accuracy and higher multipath rejection. However, there is a drawback in that the autocorrelation functions have multiple side peaks, meaning that this technique also leads to the large main peak estimation error problem and a low correlation decision efficiency problem. In this paper, we propose a new Main Peak Extraction (MPE) method for high-order BOC signals to solve these problems. In the new method, the synthesis cross-correlation function is established, and the geometry graph is formatted to calculate the estimation main peak. We eliminate all side peaks and improve the main peak phase estimation precision under the condition that the sub-carrier phase is offset. The results of the simulation demonstrate that the new method can achieve better main peak decision efficiency, side peak cancellation ability and phase estimation performance than traditional methods.

Large volumes of data collected by the Automatic Identification System (AIS) provide opportunities for studying both single vessel motion behaviours and collective mobility patterns on the sea. Understanding these behaviours or patterns is of great importance to maritime situational awareness applications. In this paper, we leveraged AIS trajectories to discover vessel spatio-temporal co-occurrence patterns, which distinguish vessel behaviours simultaneously in terms of space, time and other dimensions (such as ship type, speed, width etc.). To this end, available AIS data were processed to generate spatio-temporal matrices and spatio-temporal tensors (i.e., multidimensional arrays). We then imposed a sparse bilinear decomposition on the matrices and a sparse multi-linear decomposition on the tensors. Experimental results on a real-world dataset demonstrated the effectiveness of this methodology, with which we show the existence of connection among regions, time, and vessel attributes.

Course keeping for ships is vital for automatic navigation in marine transportation. To improve the control effect and reduce the energy output of the controller, this article proposes an improved concise backstepping controller based on a Lyapunov candidate function by introducing a nonlinear function of course error to replace the course error itself in the feedback loop. The procedure of nonlinear controller design has been reduced from two steps to one step using information from controlled plant to construct the Lyapunov candidate function. Compared with the pure backstepping control, the proposed improved algorithm reserves the nonlinear item of the system, and possesses a strong disturbance rejection ability and robustness to the mathematical model uncertainty. The algorithm given here has advantages of simplified construction method, satisfactory control effect, robustness and energy saving.

Procedures based on solutions of the direct and inverse geodetic problems are presented and their application in orthodromic and loxodromic navigation is analysed. They can be used in traditional navigation during a route planning and during sailing on the planned route in real time. The optimal division of orthodromes during planning and locally predicted short loxodromes during sailing – which allow orthodromic navigation also in manual steering – are proposed.