We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and differ when they are small. Our study relies on thermodynamic formalism where, for dominated and irreducible matrices, we completely characterise the behaviour of the pressures.

The Automatic Identification System (AIS) is extensively used in monitoring vessel traffic, and ship navigation related information can be obtained from the AIS data. However, AIS data contain extensive redundant information, which leads to the general need to compress the data when applying it in practice or conducting research. In this paper, a three-dimensional compression of ship trajectories using the Dynamic Programming algorithm has been proposed. The AIS data near the ports of Long Beach and San Francisco in the United States were used to test and compare the Dynamic Programming algorithm with the Top-down Time-ratio algorithms. The experimental results show that the proposed algorithm can better retain the position and time information at low compression ratio such as 1%, 20% and 40%. Moreover, the algorithm is applicable to ship trajectories with different motion modes such as steering, mooring and straight ahead. The results show that the proposed algorithm can reasonably solve the problem of AIS data redundancy and ensure the quality of data, which is of practical significance for water transport, transport planning and other related research.

Safe and effective navigation of the world's oceans and waterways relies on maritime education and training. This involves the learning of motor, procedural and verbal components of complex skills. Motor learning theory evaluates training variables, such as instructions, feedback and scheduling, to determine best practices for long-term retention of such skills. Motor learning theory has come a long way from focusing primarily on underlying cognitive processes to now including individual and contextual characteristics in making predictions about instructional strategies and their role in performance and learning. A remaining challenge in applying recent motor learning theory to maritime education and training is a lack of empirical testing of complex vocational skills, such as simulation scenarios, with delayed retention and transfer tests. Incorporating theory-based understanding of beneficial instructional practices, through both cognitive approaches and those considering context and environment, task complexity and learner characteristics is a fruitful way forward in advancing maritime education and training.

Information is provided to navigators through advanced onboard navigation equipment, such as the electronic chart display and information system (ECDIS), radar and the automatic identification system (AIS). However, maritime accidents still occur, especially in coastal and inland water where many navigational dangers exist. The recent artificial intelligence (AI) technology is actively applied in navigation fields, such as collision avoidance and ship detection. However, utilising the aids to navigation (AtoN) system requires more engagement and further exploration. The AtoN system provides critical navigation information by marking the navigation hazards, such as shallow water areas and wrecks, and visually marking narrow passageways. The prime function of the AtoN can be enhanced by applying AI technology, particularly deep learning technology. With the help of this technology, an algorithm could be constructed to detect AtoN in coastal and inland waters and utilise the detected AtoN to create a safety function to supplement watchkeepers using recent navigation equipment.

Ship trajectory prediction plays a critical role in collision detection and risk assessment. To enhance prediction accuracy and efficiency, a novel hybrid particle swarm optimisation (PSO) and grey wolf optimisation (GWO) long, short-term memory (LSTM) network model is proposed (PGL model). The hybrid PSO-GWO optimisation method combines the algorithm's strengths and offers improved stability and performance. The hybrid algorithm is employed to optimise the hyperparameters of the LSTM neural networks to enhance prediction accuracy and efficiency. To demonstrate the superiority of the PGL model, the LSTM, PSO-LSTM and PGL are applied to the same dataset, and then prediction performance and processing time are compared. Experimental results indicate that the proposed PGL algorithm outperforms prediction accuracy and optimisation time.

To realise the overall calibration of the error model coefficients of accelerometers in an inertial combination and to improve the navigation accuracy of the inertial navigation system, a norm-observation method is applied to the calibration, especially for the quadratic coefficient of the accelerometer. The Taylor formula is used to expand the solution of the acceleration model, and the intermediate variables with error model coefficients are obtained using the least square method. The formulas for calculating the quadratic term coefficient, scale factor and bias of the accelerometer are given. A 20-position method is designed to calibrate the accelerometer combination, the effectiveness of the method is verified by simulation, and the effects of installation misalignment and rod-arm error on calibration accuracy are analysed. The results show that the installation misalignments and rod-arm errors have little influence on the coefficient calibration, less than 10−8, and can be neglected in a practical calibration process.

Navigational safety is one of the important focuses of Maritime Education and Training (MET), and the quality of MET is the key to cultivating competent officers at sea. This study aims to understand better the effects of a rapid training method on ship handling and navigation in restricted waters, as well as decision-making skills under stressful situations. Tests were carried out in a simulator-based maritime training environment to explore the decision-making skills of maritime students in stressful situations under different training levels and methods. This study compares routine maritime training and task-aimed rapid training in improving manoeuvring and navigational and decision-making skills, and examines the training outcomes. The data used in this study is based on comparing the task performance and stress levels of the two groups of students using simulator-based training results from a designed scenario. The results analyse the training outcomes of decision-making skills and maritime operation performance by applying a specific decision-making model. In addition, the impact of students' stress levels was examined, both subjectively and objectively. The paper concludes with a set of recommendations for the design of future MET. The research helps enhance decision-making skills in maritime training programmes and understanding how learning in simulator-based maritime training environments can be improved.

In Global Navigation Satellite Systems (GNSS)-denied environments, aiding a vehicle's inertial navigation system (INS) is crucial to reducing the accumulated navigation drift caused by sensor errors (e.g. bias and noise). One potential solution is to use measurements of gravity as an aiding source. The measurements are matched to a geo-referenced map of Earth's gravity to estimate the vehicle's position. In this paper, we propose a novel formulation of the map matching problem using a hidden Markov model (HMM). Specifically, we treat the spatial cells of the map as the hidden states of the HMM and present a Viterbi style algorithm to estimate the most likely sequence of states, i.e. most likely sequence of vehicle positions, that results in the sequence of observed gravity measurements. Using a realistic gravity map, we demonstrate the accuracy of our Viterbi map matching algorithm in a navigation scenario and illustrate its robustness compared with existing methods.

The identification of fishing vessel operations holds significant importance in addressing fishing industry issues, such as overfishing and illegal, unreported and unregulated fishing (IUUF). Many countries utilise data from vessel monitoring systems (VMSs) or automatic identification systems (AISs) to monitor fishing activities. These data include vessel trajectories, headings and speeds, among others. We aimed to analyse the fishing behaviours of three types of fishing gear used by vessels (trawl, purse seine and gill net) and identify the types of gear employed by the vessels. Therefore, a 1D CNN-LSTM fishing vessel operational behaviour prediction model was proposed by combining a one-dimensional convolutional (1D CNN) neural network and a long short-term memory (LSTM) neural network. The model utilises 1D CNN to extract local features from fishing vessel trajectories and employs LSTM to capture the time series information in the data, eventually classifying fishing gears. The results show that the proposed model achieves a classification accuracy of 92% in categorising fishing vessel operational trajectories. This study significantly contributes to preventing IUUF, curtailing overfishing, and enhancing fisheries management strategies.