Geometric Dilution Of Precision (GDOP) is a factor that describes the effect of geometry on the relationship between measurement error and position determination error. It is used to provide an indication of the quality of the solution. Conventional closed-form GDOP calculation formula applied to all possible combinations of visible satellites is rather time consuming, especially as the number of satellites grows. Approximations, such as the maximum volume method, are faster but optimum selection is not guaranteed. In this paper, a more concise but efficient solution for the calculation of GDOP value in the case of four Global Positioning System (GPS) satellites is firstly reviewed and then extended to cover the other forms of dilution of precision (DOP) values, including vertical DOP (VDOP) and horizontal DOP (HDOP). Secondly, a review and extension of the conventional solution is performed in the case of three GPS satellites aided by an altimeter. Based on the ideas gained from these two approaches, a simpler closed-form DOP formula for three GPS satellites aided by an altimeter is derived. The advantage of the proposed formulation is that it is simpler and thus reduces the computational load in comparison to the conventional one.

One of the most important factors for the safety of navigation is to ensure proper collision avoidance manoeuvres in a congested traffic area. There are many aids for this purpose; for example, an ARPA, which is mandatory for certain ships and which is expected to be effective.

As tugboats interact very closely with ships in restricted waters, the possibility of accidents increases in these operations. Despite the high accident possibility, there is a gap in studies on tugboat accidents. This study aims to analyse accidents involving tugboats using data mining. For this purpose, a tugboat accidents dataset consisting of a total of 496 accident records for the period from 2008 to 2019 was collected. Logistic regression and decision tree algorithms were implemented to the dataset. The results revealed that tugboat propulsion type is the most important and influential factor in the severity of tugboat accidents. The inferences drawn from these results could be beneficial for tugboat operators and port authorities in enhancing their awareness of the factors affecting tugboat accidents. In addition, the outputs of this study can be a reference for management units in developing strategies for preventing tugboat accidents and can also be used in effective planning for practicable prevention programmes and practices.

This paper introduces a scheme for waypoint-based path-following control for an Unmanned Robot Sailboat (URS) in the presence of actuator gain uncertainty and unknown environment disturbances. The proposed scheme has two components: intelligent guidance and an adaptive neural controller. Considering upwind and downwind navigation, an improved version of the integral Line-Of-Sight (LOS) guidance principle is developed to generate the appropriate heading reference for a URS. Associated with the integral LOS guidance law, a robust adaptive algorithm is proposed for a URS using Radial Basic Function Neural Networks (RBF-NNs) and a robust neural damping technique. In order to achieve a robust neural damping technique, one single adaptive parameter must be updated online to stabilise the effect of the gain uncertainty and the external disturbance. To ensure Semi-Global Uniform Ultimate Bounded (SGUUB) stability, the Lyapunov theory has been employed. Two simulated experiments have been conducted to illustrate that the control effects can achieve a satisfactory performance.

Real-time and accurate fault detection and isolation is very important to ensure the reliability and precision of integrated inertial navigation and global navigation satellite systems. In this paper, the detection performance of a residual chi-square method is analysed, and on this basis an improved method of fault detection is proposed. The local test based on a standardised residual is introduced to detect and identify faulty measurements directly. Differing from the traditional method, two appropriate thresholds are selected to calculate the weight factor of each measurement, and the gain matrix is adjusted adaptively to reduce the influence of the undetected faulty measurement. The sliding window test, which uses past measurements, is also added to further improve the fault detection performance for small faults when the local test based on current measurements cannot judge whether a fault has occurred or not. Several simulations are conducted to evaluate the proposed method. The results show that the improved method has better fault detection performance than the traditional detection method, especially for small faults, and can improve the reliability and precision of the navigation system effectively.

This paper presents the results of distance measurements performed with an AT86RF233 chip. It uses a combination of time of flight and phase shift measurements to perform ranging. The statistical parameters describing the ranging results are presented and an algorithm to process raw measurement data is proposed. The results show significant improvement in ranging accuracy.

The basic concepts safety at sea and the maritime safety system have remained almost unchanged for a comparatively long time. However, the components and elements of these concepts are now subject to many changes created by the ‘information age’. This paper presents thoughts on today's concept of the maritime safety system, its main components and their elements. Although the thoughts and ideas presented are those of the authors, they take account of the legal instruments in force and recent developments in technology, especially developments in radio-communications. The paper provides an overall review of the institutions, regulations and procedures concerned with safety at sea.

The problem of analysing a single vessel's behaviour from real but incomplete Automatic Identification System (AIS) data received by satellite has been investigated. The main objective was to infer the route of any single vessel of interest, utilising the dynamic information decoded from AIS messages. A complete process of route inference using position, speed, course over ground and time stamp information is proposed in this paper. Due to the incompleteness of satellite AIS messages, an algorithm incorporating random deviations is also presented to account for the missing sections of obtained vessel routes. Analysis results from a set of real AIS data have demonstrated the applicability of the proposed algorithms in various scenarios.

Albatrosses are known for their extreme navigation performance enabling them to locate isolated breeding islands after long-distance migrations across open seas. Little is known about the migration of young albatrosses and how they reach the adults' navigation and foraging skills during the period of immaturity lasting several years and spent permanently flying across the open ocean. We tracked by satellite telemetry the dispersal and migration of 13 juvenile wandering albatrosses from the Crozet Islands during their first year at sea. The young albatrosses covered an average distance of 184,000 km during the first year, restricting their dispersal movement to the unproductive and low wind subtropical Indian Ocean and Tasman Sea. The juveniles initiated the migration by an innate phase of rapid dispersal encoded as a fixed flight direction assisted by southerly winds towards north and northeast. Thereafter each individual restricted its movement to a particular zone of the ocean that will possibly be used until they start breeding 7–10 years later and return in contact with breeding adults. This dispersal in young birds corresponds well with movements observed for adult non-breeding wandering albatrosses. The results show clearly an inherited ability to navigate back to already visited areas in young wandering albatrosses. The juvenile dispersal behaviour and migration at sea suggest a genetically based migration program, encoding navigation to a destination area used throughout the life.

In this paper, adaptive noise estimation is used along with a previously proposed Huber-based robust algorithm for cooperative localisation of Autonomous Underwater Vehicles (AUVs). The Huber-based robust cooperative localisation algorithm named Huber-based Iterative Divided Difference Filtering (HIDDF), proposed in our previous work, effectively achieved a robust result against abnormal measurement noise, enhanced the stability of the filtering algorithm and improved the performance of cooperative localisation state estimation. However, its performance could be significantly further improved if it could estimate the system's noise statistical properties online in real time and then adaptively adjust the filtering gain matrix accordingly. In this paper, a novel adaptive noise estimation algorithm is proposed based on a covariance matching method. The proposed algorithm is suitable for adaptively estimating Gaussian and non-Gaussian measurement as well as process noise. The efficacy of the proposed algorithm has been verified through simulation results. In order to further verify the effectiveness of the proposed algorithm in practical systems, lake tests were conducted. Then, based on offline test data, the performance of the cooperative positioning algorithm under dual-pilot and single-pilot schemes was simulated. The advantages and feasibility of the algorithm are analysed and compared through performance comparison. Cooperative localisation accuracy of the previously proposed Huber-based robust algorithm has been enhanced significantly when used with the proposed adaptive noise estimation algorithm.

Navigational error accounts for half of the accidents and serious incidents in close to shore maritime transport in Norway predominantly due to the rapidly changing weather conditions and the dangerous nature of the narrow inshore waters found along the Norwegian coast. This creates a dependence on Differential Global Positioning System (DGPS) use and any disruption to this service can lead to an increased accident rate. The aim of this paper is to research the jamming vulnerability of existing maritime receivers and to understand if an upgrade to a multi-constellation or multi-frequency receiver would improve system resilience. The novelty of this work is a comparison of jamming resilience between different combinations of multiple constellations (GPS and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS)) and multi-frequency Global Navigation Satellite System (GNSS) signals. This paper presents results from GNSS jamming trials conducted in the northern part of Norway, confirming previous research and indicating that typical maritime GPS receivers are easy to jam and may produce erroneous positional information. Results demonstrate that the single frequency multi-constellation receivers offer better jamming resilience than multi-frequency (L1 + L2) GPS receivers. Further, the GLONASS constellation demonstrated a better resilience than GPS. Results demonstrate a known correlation between GPS L1 and L2 frequencies, as well as a probable over-dependence on GPS for signal acquisition, meaning that no signal can be received without GPS L1 present. With these limitations in mind, the authors suggest that the most economic update to the single frequency GPS receivers, currently used for maritime applications, should be multi-constellation GPS + GLONASS receivers. This solution is cheaper and it also offer better jamming resistance for close to shore navigation than dual frequency receivers.

In Strapdown Inertial Navigation System (SINS)/Odometer (OD) integrated navigation systems, OD scale factor errors change with roadways and vehicle loads. In addition, the random noises of gyros and accelerometers tend to vary with time. These factors may cause the Kalman filter to be degraded or even diverge. To address this problem and reduce the computation load, an Adaptive Two-stage Kalman Filter (ATKF) for SINS/OD integrated navigation systems is proposed. In the Two-stage Kalman Filter (TKF), only the innovation in the bias estimator is a white noise sequence with zero-mean while the innovation in the bias-free estimator is not zero-mean. Based on this fact, a novel algorithm for computing adaptive factors is presented. The proposed ATKF is evaluated in a SINS/OD integrated navigation system, and the simulation results show that it is effective in estimating the change of the OD scale factor error and robust to the varying process noises. A real experiment is carried out to further validate the performance of the proposed algorithm.

Ocean currents impose a negative effect on Autonomous Underwater Vehicle (AUV) underwater target searches, which lengthens the search paths and consumes more energy and team effort. To solve this problem, an integrated algorithm is proposed to realise multi-AUV cooperative search in dynamic underwater environments with ocean currents. The proposed integrated algorithm combines the Biological Inspired Neurodynamics Model (BINM) and Velocity Synthesis (VS) method. Firstly, the BINM guides a team of AUVs to achieve target search in underwater environments; BINM search requires no specimen learning information and is thus easier to apply to practice, but the search path is longer because of the influence of ocean current. Next the VS algorithm offsets the effect of ocean current, and it is applied to optimise the search path for each AUV. Lastly, to demonstrate the effectiveness of the proposed integrated approach, simulation results are given in this paper. It is proved that this integrated algorithm can plan shorter search paths and thus the energy consumption is lower compared with BINM.

This paper discusses issues relating to the practical application of the collision avoidance regulations (COLREGS) from the sociological viewpoint that rules are always contingent, defeasible and that no rule can exhaustively specify the conditions of its use. It is proposed that, due to the inherent nature of rules, the only way successfully to manage collision risks at sea, is physically to separate opposing traffic flows, so as to remove the interpretative and mutually co-ordinating factors from the COLREGS.

For the path planning of autonomous underwater vehicles (AUVs) in the ocean environment, in addition to the planned path length and safe obstacle avoidance, it is also necessary to pay attention to the impact of ocean currents on the planned path. Therefore, this paper improves the original D* algorithm, and adds the obstacle cost item and the steering angle cost item as constraints on the basis of the original cost function, thus ensuring the navigation safety of the AUV. Considering that ocean currents have a greater impact on the energy consumption of AUVs, this paper establishes a cost model for the impact of ocean currents on AUV energy consumption and applies it to the D* path planning algorithm, so that AUVs can use ocean currents to reduce energy consumption, which can be seen through simulation experiments. The simulation results show that the improvement of the algorithm can plan an optimal energy consumption path.

Recently, the International Global Navigation Satellite System (GNSS) Service (IGS) has launched the Real-Time Service (IGS-RTS). The RTS products enable real-time precise positioning applications. For single-frequency Real-Time Precise Point Positioning (RT-PPP), ionospheric delay mitigation is a major challenge. To overcome this challenge, we developed a Real-Time Regional Ionospheric Model (RT-RIM) over Europe using the RTS satellite orbits and clock products. The model has spatial and temporal resolution of 1° × 1° and 15 minutes, respectively. Global Positioning System (GPS) observations from 60 IGS and EUREF reference stations are processed using the Bernese 5·2 PPP module in order to extract the Real-Time Vertical Electron Content (RT-VTEC). The PPP convergence time and positioning accuracy using the RTS products is estimated and compared with dual frequency PPP and single-frequency PPP obtained through the combined rapid IGS Global Ionospheric Maps (IGS-GIM) over three consecutive days under high solar activity and one of them under active geomagnetic activity. The results show that the proposed model improves PPP accuracy and convergence time under the mid-latitude region about 40%, 55% and 40% for the horizontal, height and three-dimensional (3D) components respectively in comparison with the IGS-GIM.

This paper presents a sensor fusion method for the Ultra-Tightly Coupled (UTC) Global Positioning System (GPS)/Inertial Navigation System (INS) integrated navigation. The UTC structure, also known as the deep integration, exhibits many advantages, e.g., disturbance and multipath rejection capability, improved tracking capability for dynamic scenarios and weak signals, and reduction of acquisition time. This architecture involves the integration of I (in-phase) and Q (quadrature) components from the correlator of a GPS receiver with the INS data. The Particle Filter (PF) exhibits superior performance as compared to an Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) in state estimation for the nonlinear, non-Gaussian system. To handle the problem of heavy-tailed probability distribution, one of the strategies is to incorporate the UKF into the PF as the proposal distribution, leading to the Unscented Particle Filter (UPF). The combination of an adaptive UPF and Fuzzy Logic Adaptive System (FLAS) is adopted for reducing the number of particles with sufficiently good results. The GPS tracking loops may lose lock due to the signals being weak, subjected to excessive dynamics or completely blocked. One of the principal advantages of the UTC structure is that a Doppler frequency derived from the INS is integrated with the tracking loops to improve the receiver tracking capability. The Doppler frequency shift is calculated and fed to the GPS tracking loops for elimination of the effect of stochastic errors caused by the Doppler frequency. In this paper, several nonlinear filtering approaches, including EKF, UKF, UPF and ‘FLAS assisted UPF’ (FUPF), are adopted for performance comparison for ultra-tight integration of GPS and INS. It is assumed that no outage occurs such that the inertial sensor errors can be properly corrected and accordingly the aiding information is working well. Two examples are provided for performance assessment for the various data fusion methods. The FUPF algorithm with Doppler velocity aiding demonstrates remarkable improvement, especially in the high dynamic environments, in navigation estimation accuracy with reduction of number of particles.

The Istanbul Strait is a challenging waterway for maritime traffic due to its rough topology, moderate to severe environmental conditions, and heavy local traffic. In particular, a total of 232 maritime accidents took place there between 2000 and 2011. In this study, generic fuzzy analytic hierarchy processes were used to assess the risk perception of stakeholders in the Istanbul Strait, including ship captains, maritime pilots and Vessel Traffic Services operators. These risk perceptions were then compared to the statistical maritime accident data, revealing a fundamental discrepancy between the risk perception and statistical data. Specifically, the area of the Straight with the highest number of accidents is perceived as relatively low-risk, whereas areas perceived as high-risk experience a lower number of accidents. Our results have implications for stakeholders as well as government agencies responsible for the safety of the Straight.

Strapdown inertial navigation systems (INS) often employ aiding sensors to increase accuracy. Nonlinear filtering algorithms are then needed to fuse the collected data from these aiding sensors with measurements of strapdown rate gyros. Aiding sensors usually have slower dynamics compared to gyros and therefore collect data at lower rates. Thus the system will be unobservable between aiding sensors' sampling instants, and the error covariance, which shows the uncertainty in the estimation, grows during the sampling period. This paper presents a divided difference filter (DDF)-based data fusion algorithm, which utilizes the complementary noise profile of rate gyros and gravimetric inclinometers to extend their limits and achieve more accurate attitude estimates. It is confirmed experimentally that DDF achieves better covariance estimates compared to the extended Kalman filter (EKF) because the uncertainty in the state estimate is taken care of in the DDF polynomial approximation formulation.

The Faculty of Maritime Studies, University of Rijeka, Croatia, manages the European Union (EU) project “Avoiding Collisions at Sea” (ACTs). The project is funded by the European programme “Leonardo da Vinci”. Other maritime education and training institutions participating in this project come from Great Britain, Spain, Slovenia, Bulgaria and Turkey. The purpose of this research was to identify skill gaps in knowledge and teaching of COLREGs (International Regulations for Preventing Collisions at Sea 1972 - Rules) for nautical Bachelor of Science (BSc) students and experienced deck officers. The analysis of the research on marine accidents has identified vessel collisions as one of the most frequent types of accidents. Further research showed that human error and misinterpretation of the Rules are the most frequent reasons for vessel collisions. Using a questionnaire, nautical students/navigating cadets and navigating officers' understanding of the Rules was tested. The results showed skill gaps in understanding of some parts of the COLREGs due to wrong interpretation and application of the Rules. The authors claim that it is possible to improve the professional competence of navigating officers by applying proper learning methods using real-life scenarios and e-learning.