The Kalman filter (KF) is a form of optimal estimator characterized by recursive evaluation, which has been widely applied to the navigation sensor fusion. Utilizing the KF requires that all the plant dynamics and noise processes are completely known, and the noise process is zero mean white noise. If the theoretical behaviour of the filter and its actual behaviour do not agree, divergence problems tend to occur. The adaptive algorithm has been one of the approaches to prevent divergence problems in the Kalman filter when precise knowledge on the system models is not available. Two popular types of adaptive Kalman filter are the innovation-based adaptive estimation (IAE) approach and the adaptive fading Kalman filter (AFKF) approach. In this paper, an approach involving the concept of the two methods is presented. The proposed method is a synergy of the IAE and AFKF approaches. The ratio of the actual innovation covariance based on the sampled sequence to the theoretical innovation covariance will be employed for dynamically tuning two filter parameters – fading factors and measurement noise scaling factors. The method has the merits of good computational efficiency and numerical stability. The matrices in the KF loop are able to remain positive definitive. Navigation sensor fusion using the proposed scheme will be demonstrated. Performance of the proposed scheme on the loosely coupled GPS/INS navigation applications will be discussed.

Modern attitude and heading reference systems (AHRS) generally use Kalman filters to integrate gyros with some other augmenting sensors, such as accelerometers and magnetometers, to provide a long term stable orientation solution. The construction of the Kalman filter for the AHRS is flexible, while the general options are the methods based on quaternion, Euler angles, or Euler angle errors. But the quaternion and Euler angle based methods need to model system angular motions, and, meanwhile, all these three methods suffer from nonlinear problems which will increase the system complexities and the computational difficulties. This paper proposes a novel implementation method for the AHRS integrating IMU and magnetometer sensors. In the proposed method, the Kalman filtering is implemented to use the Euler angle errors to express the local level frame (l frame) errors, rather than express the body frame (b frame) errors as the customary methods do. A linear system error model based on the Euler angles errors expressing the l frame errors for the AHRS has been developed and the corresponding system observation model has been derived. This proposed method for AHRS does not need to model system angular motions and also avoids the nonlinear problem which is inherent in the commonly used methods. The experimental results show that the proposed method is a promising alternative for the AHRS.

A type of fixed integral interval sliding method for optimization-based alignment is proposed in this paper. The method is more reasonable and suitable than those in the references due to the appropriate treatment of the noise in the outputs of the Inertial Measurement Unit (IMU). The undesired sensor noise of sensors includes both random noise and bias. Our optimal alignment is based on an integrated form where the bias will be integrated during the process of alignment. In this respect, the length of the integrated data is a key factor in determining current attitude due to the ambivalent effect of integrating the sensor noise. If the length is too great the precision deteriorates due to the integration of bias. If the length is too small the precision also deteriorates because of the randomness of the noise. The validity of the method is verified by simulation and measured data.

Shoe mounted Inertial Measurement Units (IMU) are often used for indoor pedestrian navigation systems. The presence of a zero velocity condition during the stance phase enables Zero Velocity Updates (ZUPT) to be applied regularly every time the user takes a step. Most of the velocity and attitude errors can be estimated using ZUPTs. However, good heading estimation for such a system remains a challenge. This is due to the poor observability of heading error for a low cost Micro-Electro-Mechanical (MEMS) IMU, even with the use of ZUPTs in a Kalman filter. In this paper, the same approach is adopted where a MEMS IMU is mounted on a shoe, but with additional constraints applied. The three constraints proposed herein are used to generate measurement updates for a Kalman filter, known as ‘Heading Update’, ‘Zero Integrated Heading Rate Update’ and ‘Height Update’.

The first constraint involves restricting heading drift in a typical building where the user is walking. Due to the fact that typical buildings are rectangular in shape, an assumption is made that most walking in this environment is constrained to only follow one of the four main headings of the building. A second constraint is further used to restrict heading drift during a non-walking situation. This is carried out because the first constraint cannot be applied when the user is stationary. Finally, the third constraint is applied to limit the error growth in height. An assumption is made that the height changes in indoor buildings are only caused when the user walks up and down a staircase. Several trials were shown to demonstrate the effectiveness of integrating these constraints for indoor pedestrian navigation. The results show that an average return position error of 4·62 meters is obtained for an average distance of 1557 meters using only a low cost MEMS IMU.

Positioning in the urban environment using GNSS is hampered by poor satellite availability due to signal obstruction created by both man-made and natural features of the urban environment. In addition, range measurement to satellites for positioning and for navigation is severely degraded by the multipath effect. The arrival and continuous enhancement of computerised geometric city models makes it possible to tackle these problems through modelling. In this paper description is given of a method for determining the local multipath environment, defined by the surfaces within a city model that will cause disruptive signal reflections to be presented to a receiver. An example simulation is performed, and graphical and numerical results are produced.

The paper presents a weather routing algorithm utilising a multi-objective optimisation with constraints, namely the Multi-objective Evolutionary Weather Routing Algorithm (MEWRA). In the proposed approach weather route recommendations can be made simultaneously e.g. for passage time, fuel consumption and safety of passage by means of Pareto optimisation. The sets of criteria and constraints in the optimisation process are fully customisable. The algorithm handles static (time-independent) and dynamic (time-dependent) constraints e.g. forecasted high wind speed regions or customisable areas to be excluded from routing (e.g. due to piracy). The paper includes a description of MEWRA as well as examples of its usage for finding Pareto-optimal transoceanic ship routes.

This paper proposes a novel sensor fusion approach using Ultra Wide Band (UWB) wireless radio and an Inertial Navigation System (INS), which aims to reduce the accumulated error of low-cost Micro-Electromechanical Systems (MEMS) Inertial Navigation Systems used for real-time navigation and tracking of mobile robots in a closed environment. A tightly-coupled model of INS/UWB is established within the integrated positioning system. A two-dimensional kinematic model of the mobile robot based on kinematics analysis is then established, and an Auto-Regressive (AR) algorithm is used to establish third-order error equations of the gyroscope and the accelerometer. An Improved Adaptive Kalman Filter (IAKF) algorithm is proposed. The orthogonality judgment method of innovation is used to identify the “outliers”, and a covariance matching technique is introduced to judge the filter state. The simulation results show that the IAKF algorithm has a higher positioning accuracy than the KF algorithm and the UWB system. Finally, static and dynamic experiments are performed using an indoor experimental platform. The results show that the INS/UWB integrated navigation system can achieve a positioning accuracy of within 0·24 m, which meets the requirements for practical conditions and is superior to other independent subsystems.

In view that most Global Navigation Satellite System (GNSS) users are still using single-frequency receivers due to the low costs, single-frequency Precise Point Positioning (PPP) has been attracting increasing attention in the GNSS community. For a long period, single-frequency PPP technology has mainly relied on the Global Positioning System (GPS). With the recent revitalisation of the Russian GLONASS constellation and two newly emerging constellations, BeiDou and Galileo, it is now feasible to investigate the performance of Four-Constellation integrated Single-Frequency PPP (FCSF-PPP) with GPS, GLONASS, BeiDou and Galileo measurements. In this study, a FCSF-PPP model is presented to simultaneously process observations from all four GNSS constellations. Datasets collected at 47 globally distributed four-system Multi-GNSS Experiment (MGEX) stations on seven consecutive days and a kinematic experimental dataset are employed to fully assess the performance of FCSF-PPP. The FCSF-PPP solutions are compared to GPS-only and combined GPS/GLONASS single-frequency PPP solutions. The results indicate that the positioning performance is significantly improved by integrating multi-constellation signals.

Nowadays GPS is widely used to monitor the ionosphere. However, the current results from ground-based GPS observations only provide some information on the horizontal structure of the ionosphere, and are extremely restricted in mapping its vertical structure. In this paper, tomography reconstruction technique was used to image 3D ionospheric structure with ground-based GPS. The first result of the 3D images of the ionospheric electron density distribution in South Korea has been generated from the permanent Korean GPS Network (KGN) data. Compared with the profiles obtained by independent ionosondes at or near the GPS receiver stations, the electron density profiles obtained by the GPS tomographic construction method are in better agreement, showing the validity of the GPS ionospheric tomographic reconstruction. It has also indicated that GPS-based 3D ionospheric mapping has the potential to complement other expensive observing techniques in ionospheric mapping, such as ionosondes and radar.

The main problem in bringing autonomy to any vehicle lies in the design of a suitable guidance law. For truly autonomous operation, the vehicle needs to have a reliable Navigation, Guidance and Control (NGC) system of which the guidance system is the key element that generates suitable trajectories to be followed. In this review paper, various guidance laws found in the literature and their relevance to autonomous underwater vehicles (AUVs) are discussed. Since existing guidance laws for underwater vehicles have emulated from tactical airborne missile systems, a number of approaches for the missile guidance systems are considered. Finally, potential guidance strategies for AUVs are proposed.

Since programmable electronic calculators were first employed in marine navigation, a variety of formulae has been used for calculating astronomical refraction. As the choice is wide, some formulae have been selected from commonly used reference sources and their accuracy and suitability examined. No attempt has been made to assess the validity of the selected formulae to represent astronomical refraction in practical circumstances. Accuracy comparisons have been made using the refraction algorithm proposed by Garfinkel – the standard adopted by the British and American Nautical Almanac Offices. New formulae are given that are simple and accurate, even over a wide range of temperature and pressure, and which for all practical purposes may be considered equivalent to the tables of refraction given in the Nautical Almanac.

For maritime safety and security, vessels should be able to predict the trajectories of nearby vessels to avoid collision. This research proposes three novel models based on similarity search of trajectories that predict vessels' trajectories in the short and long term. The first and second prediction models are, respectively, point-based and trajectory-based models that consider constant distances between target and sample trajectories. The third prediction model is a trajectory-based model that exploits a long short-term memory approach to measure the dynamic distance between target and sample trajectories. To evaluate the performance of the proposed models, they are applied to a real automatic identification system (AIS) vessel dataset in the Strait of Georgia, USA. The models' accuracies in terms of Haversine distance between the predicted and actual positions show relative prediction error reductions of 40·85% for the second model compared with the first model and 23% for the third model compared with the second model.

The maritime transport industry is increasingly reliant on computing and communication technologies, and the need for cyber risk management of critical systems and assets on vessels is becoming critically important. In this paper, a comprehensive cyber risk assessment of a ship is presented. An experimental process consisting of assessment preparation activities, assessment conduct and results communication has been developed. The assessment conduct relies on a survey developed and performed by interviewing a ship's crew. Computational vulnerability scanning of the ship's Electronic Chart Display and Information System (ECDIS) is introduced as a specific part of this cyber security assessment. The assessment process presented has been experimentally tested by evaluating the cyber security level of Kobe University's training ship Fukae-maru. For computational vulnerability scanning, an industry-leading software tool has been used, and a quantitative cyber risk analysis has been conducted to evaluate cyber risks on the ship.

The main routes of ships voluntarily completing meteorological observations across the North Atlantic are detected by the intensity of the geographical distribution of the voluntary ship observations. The routes are then analysed in order to assess the relative intensity of traffic, the seasonal changes and the trend over the years. This paper will provide a better understanding of the North Atlantic trades and the relationship among the different routes, allowing the identification of the busiest areas. A discussion over the impact of routing on the weather that a transoceanic ship can experience during its life is also provided.

Attitude estimation systems often use two or more different sensors to increase reliability and accuracy. Although gyroscopes do not have problems like limited range, interference, and line of sight obscuration, they suffer from slow drift. On the other hand, inclinometers are drift-free but they are sensitive to transverse accelerations and have slow dynamics. This paper presents an extended Kalman filter (EKF)-based data fusion algorithm which utilizes the complementary noise profiles of these two types of sensors to extend their limits. To avoid complexities of dynamic modelling of the platform and its interaction with the environment, gyro modelling will be used to implement indirect (error state) form of the Kalman filter. The great advantage of this approach is its independence from the structure of the platform and its applicability to any system with a similar set of sensors. Separate bias formulation of the Kalman filter will be used to reduce the computational complexity of the algorithm. In addition, a systematic approach based on wavelet decomposition will be utilized to estimate noise covariances used in the Kalman filter formulation. This approach solves many of the convergence problems encountered in the implementation of EKF due to the choice of covariance matrices. Experimental implementation of the estimator shows the excellent performance of the filter.

This paper presents key models and concepts developed in psychology which help to understand the role of human factors in complex systems. It aims to explain their significance for anyone who wants to analyze the role of human factors in maritime accidents. Reason (1990, 1997, 2000) makes a crucial distinction between “active failures” that are made by first-line operators (captain, officers or members of a crew) and “latent failures” that are deeper causes and upstream factors concerning people who are at a distance from the accident. In agreement with this theoretical framework, this paper proposes examining the role of human factors in maritime accidents at three different levels: i) the level of individual – and namely cognitive – factors of first-line operators, ii) the level of social – and namely interpersonal – factors and iii) the level of systemic or organizational factors which correspond to “latent failures”. For each level, the main and recent contributions of the human and social sciences are presented and then used to analyze an emblematic accident.

Ship collision avoidance involves helping ships find routes that will best enable them to avoid a collision. When more than two ships encounter each other, the procedure becomes more complex since a slight change in course by one ship might affect the future decisions of the other ships. Two distributed algorithms have been developed in response to this problem: Distributed Local Search Algorithm (DLSA) and Distributed Tabu Search Algorithm (DTSA). Their common drawback is that it takes a relatively large number of messages for the ships to coordinate their actions. This could be fatal, especially in cases of emergency, where quick decisions should be made. In this paper, we introduce Distributed Stochastic Search Algorithm (DSSA), which allows each ship to change her intention in a stochastic manner immediately after receiving all of the intentions from the target ships. We also suggest a new cost function that considers both safety and efficiency in these distributed algorithms. We empirically show that DSSA requires many fewer messages for the benchmarks with four and 12 ships, and works properly for real data from the Automatic Identification System (AIS) in the Strait of Dover.

The Earth's magnetic field has long provided us with a directional reference of almost worldwide usable coverage. This paper examines the use of the magnetic field for ground referenced motion and position measurements

Where E is the vector representation of an electrical field, v vehicle velocity and B a magnetic field, the electromagnetic law of induction, E = v × B, indicates one possibility for measuring ground speed; the magnetic and electrical fields experienced by vehicle mounted sensors being used to solve the equation for v. This method however only gives the component of v perpendicular to the magnetic field. There are also certain difficulties associated with the measurement of B, which should be only the magnetic field of the Earth at the location of the vehicle, and E, which should be only the electrical field resulting from vehicle motion relative to the magnetic field of the Earth. The main problem appears to be the inseparability of motion dependent and non dependent electrical fields, a problem analogous to that of gravitation-acceleration inseparability for inertial navigation systems. The relative magnitudes of the vehicle-motiondependent E-field, of the order of 10−5 (volt/metre)/(metre/second), and the ever-present and very variable non-motion-dependent E-field between a highly conductive atmospheric layer at an altitude of about 50 km and the surface of the Earth, of some 102 volt/metre, are particularly unfavourable. Another potential basis for a ground-speed measurement system is the heterogeneous character of the intensity of the Earth's magnetic field.

This paper describes an ionospheric correction technique for single frequency GPS measurements from satellites in low Earth orbit. The fractional total electron content (TEC) above the receiver altitude is obtained from global TEC maps of the International GPS Service network and an altitude dependent scale factor. By choosing a suitable effective height of the residual ionosphere, the resulting path delay for positive elevations is then computed from a thin layer approximation. The scale factor can be predicted from the assumption of a Chapman profile for the altitude variation of the electron density or adjusted as a free parameter in the processing of an extended set of single frequency measurements. The suitability of the proposed model is assessed by comparison with flight data from the Champ satellite that orbits the Earth at an altitude of 450 km. For the given test case, a 90% correction of the ionospheric error is achieved in a reduced dynamic orbit determination based on single frequency C/A-code measurements.

The known navigational systems in use perform information functions and as such are helpful in the process of safe conduct of a vessel. One of the ways to assist in reducing the number of marine accidents is the development of systems which perform decision support functions, i.e. automatically generate solutions to collision situations. The use of information (and communication) technologies including knowledge engineering allows the generation of proposals for anti-collision manoeuvres taking into account the COLREGs. Demand for further enhancement of navigational safety by limiting human errors has initiated a trend to convert navigational information systems into decision support systems. The implementation of decision support systems will potentially reduce the number of human errors, which translates into a reduction of accidents at sea and their adverse consequences. This paper presents a summary of the research to date on the navigational decision support system NAVDEC. The system has been positively verified in laboratory conditions and in field tests – on a motor ferry and a sailing ship. Challenges associated with the development and implementation of such systems are outlined.