In the integrated navigation system using extended Kalman filter (EKF), the state error conventionally uses linear approximation to tackle the commonly nonlinear problem. However, this error definition can diverge the filter in some adverse situations due to significant distortion of the linear approximation. By contrast, the nonlinear state error defined in the Lie group satisfies the autonomous equation, which thus has distinctively better convergence property. This work proposes a novel strapdown inertial navigation system (SINS) nonlinear state error defined in the Lie group and derives the SINS equations of the Lie group EKF (LG-EKF) for the MIMU/GNSS/magnetometer integrated navigation system. The corresponding measurement equations are also derived. A land vehicle field test has been conducted to evaluate the performance of EKF, ST-EKF (state transformation extended Kalman filter) and LG-EKF, which verifies LG-EKF's superior estimation accuracy of the heading angle as well as the other two horizontal angles (pitch and roll). The LG-EKF proposed in this paper is unlimited in the choice of sensors, which means it can be applied with both high-end and low-end inertial sensors.

In this paper, by T. Degré and X. Lefèvre of the Organisme de Recherches Informatiques et Opérationnelles appliqués à la Navigation (ORION), the authors outline the principles of a proposed collision avoidance aid based on the concept of a ship's ‘room to manoeuvre’ in the presence of the vessels' or hazards to navigation and a corresponding bridge display.

The paper introduces a new approach to displaying information on targets. The proposed display visualises three types of information: targets' motion parameters (typical for target tracking), combinations of own course and speed which collide with those targets (typical for Collision Threat Parameters Area display by Lenart (1983)) and combinations of own course and speed which are not compliant with COLREGS in this case (based on ships' motion parameters and visibility conditions). A superposition of the last two types of data enables a navigator to quickly choose a collision avoidance manoeuvre which is both sufficient and COLREGS-compliant. Additionally, the displayed data may be filtered based on the remaining Time To Collision (TTC) so that navigators can concentrate on direct threats. The paper includes a description of the proposed visualisation technique as well as examples of visualised data for some encounter situations.

Domain analysis has a well-documented history in peer reviewed academic literature; however there are few instances of its application to facilitate the assessment of system specific navigation risk. This paper details one example of a practical approach to domain analysis for a busy section of the River Thames in Central London. The results correlate well to known high risk collision areas on the river and help to quantify and corroborate expert opinion and local knowledge. However a number of conditions must be accounted for in undertaking a robust study such as the geography of the study site, the purpose and audience of the research, and the availability of data and its limitations.

A dynamic collision avoidance algorithm via layered artificial potential field with collision cone (LAPF-CC) is proposed to overcome the shortcomings of the traditional artificial potential field method in dynamic collision avoidance. In order to reduce invalid actions for collision avoidance, the potential field is divided into four layers, and a collision cone with risk detection function is introduced. Relative distance and relative velocity are used as variables to establish the risk of collision, and a torque named ‘speed torque’ is constructed. Speed torque, attractive force and repulsive force work together to change the speed and heading of the unmanned surface vehicle (USV). Driving force and torque are controlled separately, which makes it possible for the LAPF-CC algorithm to be used for real-time collision avoidance control of underactuated USVs. Simulation results show that the LAPF-CC algorithm performs well in dynamic collision avoidance.

A robust state estimation technique based on the Huber-based Cubature Kalman Filter (HCKF) is proposed for Global Positioning System (GPS) navigation processing. The Cubature Kalman Filter (CKF) employs a third-degree spherical-radial cubature rule to compute the Gaussian weighted integration, such that the numerical instability induced by round-off errors can be avoided. In GPS navigation, the filter-based estimation of the position and velocity states can be severely degraded due to contaminated measurements caused by outliers or deviation from a Gaussian distribution assumption. For the signals contaminated with non-Gaussian noise or outliers, a robust scheme combining the Huber M-estimation methodology and the CKF framework is beneficial where the Huber M-estimation methodology is used to reformulate the measurement information of the CKF. GPS navigation processing using the HCKF algorithm has been carried out and the performance has been compared to those based on the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and CKF approaches. Simulation and experimental results presented in this paper confirm the effectiveness of the method.

Ionospheric plasma irregularities or bubbles, that are regions with depleted density, are generated at the magnetic equator after sunset due to plasma instabilities, and as they move upward they map along the magnetic field lines to low latitudes. To analyse the temporal and spatial evolution of the bubbles over Brazilian territory, the mapping of ionospheric plasma bubbles for the night of 17/18 March 2002 was generated using data collected from one GPS receiver array, and applying interpolation techniques. The impact on the performance of Global Navigation Satellites System (GNSS) and on the Space Based Augmentation System (SBAS) in the tropical regions of the GPS signal losses of lock and of the signal amplitude fades during ionospheric irregularities is presented.

This paper describes the application of navigational ideas during a late stage of the Yorkshire Ripper investigation. The conclusions reached were irrevocably recorded before the ultimate facts were established by the arrest and conviction of the killer. The reader is invited to assess the degree of success of the method and to rework the data supplied according to his own navigational ideas. The suggestion is made that navigational concepts may become a valuable weapon in the field of crime investigation.

An electronic navigational chart is a major source of information for the navigator. The component that contributes most significantly to the safety of navigation on water is the information on the depth of an area. For the purposes of this article, the authors use data obtained by the interferometric sonar GeoSwath Plus. The data were collected in the area of the Port of Szczecin. The samples constitute large sets of data. Data reduction is a procedure to reduce the size of a data set to make it easier and more effective to analyse. The main objective of the authors is the compilation of a new reduction algorithm for bathymetric data. The clustering of data is the first part of the search algorithm. The next step consists of generalisation of bathymetric data. This article presents a comparison and analysis of results of clustering bathymetric data using the following selected methods: K-means clustering algorithm, traditional hierarchical clustering algorithms and self-organising map (using artificial neural networks).

The use of radar information for collision avoidance is common, however it is effective only for constant values of ship motion parameters. As information delays or information errors occur, it is reasonable to supplement the information derived from radar with another information system. An ideal system should operate automatically and continuously. A system that appears to be suitable to provide this kind of information is the Automatic Identification System (AIS), which may be classified as a radio communication system that uses radio waves to transmit data with regard to ship motion parameters. In this paper the topic of integrity and completeness of AIS information is discussed and the research results for the completeness and integrity of dynamic information are presented. In addition, the outcomes of AIS information correctness from the Gulf of Gdańsk were compared with studies carried out in the Baltic Sea, east of Bornholm, between Trelleborg and Arkona. The results of research for AIS dynamic information with the highest completeness (Position, Course over Ground and Speed over Ground) are presented. The research outcomes presented in the paper lead to the conclusion that AIS could deliver useful supplementary information in the process of collision avoidance.

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.

Recently new location technologies have emerged that can be employed in modern advanced navigation systems. They can be employed to augment Global Navigation Satellite System (GNSS) positioning techniques and dead reckoning as they offer different levels of positioning accuracies and performance. An integration of other technologies is especially required in indoor and outdoor-to-indoor environments. The paper gives an overview of the newly developed ubiquitous positioning technologies and their integration in navigation systems. Furthermore two case studies are presented, i.e., the improvement of land vehicle safety using Augmented Reality (AR) technologies and pedestrian navigation services for the guidance of users to certain University offices. In the first case study the integration of map matching into a Kalman filter approach is performed (referred to as “Intelligent Vehicle Navigation”) and its principle is briefly described. This approach can also be adapted for the pedestrian navigation service described in the second case study.

Inertial Navigation Systems (INS) were large, heavy and expensive until the development of cost-effective inertial sensors constructed with Micro-electro-mechanical systems (MEMS). However, the large errors and poor error repeatability of MEMS sensors make them inadequate for application in many situations even with frequent calibration. To solve this problem, a systematic error auto-compensation method, Rotation Modulation (RM) is introduced and detailed. RM does no damage to autonomy, which is one of the most important characteristics of an INS. In this paper, the RM effects on navigation performance are analysed and different forms of rotation schemes are discussed. A MEMS-based INS with the RM technique applied is developed and specific calibrations related to rotation are investigated. Experiments on the developed system are conducted and results verify that RM can significantly improve navigation performance of MEMS-based INS. The attitude accuracy is improved by a factor of 5, and velocity/position accuracy by a factor of 10.

With the European Commission (EC) and European Space Agency's (ESA) plans to develop a new satellite navigation system, Galileo and the modernisation of GPS well underway the integrity of such systems is as much, if not more, of a concern as ever. Receiver Autonomous Integrity Monitoring (RAIM) refers to the integrity monitoring of the GPS/Galileo navigation signals autonomously performed by the receiver independent of any external reference systems, apart from the navigation signals themselves. Quality measures need to be used to evaluate the RAIM performance at different locations and under various navigation modes, such as GPS only and GPS/Galileo integration, etc. The quality measures should include both the reliability and localizability measures. Reliability is used to assess the capability of GPS/Galileo receivers to detect the outliers while localizability is used to determine the capability of GPS/Galileo receivers to correctly identify the detected outlier from the measurements processed.

Within this paper, the fundamental equations required for effective outlier detection and identification algorithms are described together with the measures of reliability and localizability. Detailed simulations and analyses have been performed to assess the performances of GPS only and integrated GPS/Galileo navigation solutions with respect to reliability and localizability. Simulation results show that, in comparison with the GPS-only solution, the localizability of the integrated GPS/Galileo solution can be improved by up to 270%. The results also indicate an expectation of a considerable increase in the sensitivity to outliers and accuracy of their estimation with the augmentation of the Galileo system with the existing GPS system.

As technology continues to develop, information and communication technology and operational technology on board ships are increasingly being networked, and more frequently connected to the Internet. The introduction of cyber systems changes the work environment with the aim of decreasing the workload for the navigator, but at the same time introduces more complexity and vulnerabilities that in turn may alter the competencies needed to perform safe and efficient navigation. Contemporary examples of how cyber-attacks can distort situational awareness and interfere with operations are needed to enhance the navigator's competence through increased system awareness. This paper demonstrates some of the possible attack vectors that a cyber-attack can present to a ship, as well as discussing the plausibility and consequences of such attacks. In this study we provide a practical example to better understand how one can demystify cyber threats in order to enhance the navigators' competence.

In dense urban areas, conventional Global Navigation Satellite Systems (GNSS) positioning can exhibit errors of tens of metres due to the obstruction and reflection of the signals by the surrounding buildings. By using Three-Dimensional (3D) mapping of the buildings, the accuracy can be significantly improved. This paper demonstrates the first integration of GNSS shadow matching with 3D-mapping-aided GNSS ranging. The integration is performed in the position domain, whereby separate ranging and shadow matching position solutions are computed, then combined using direction-dependent weighting. Two weighting strategies are compared, one based on the computation of ranging-based and shadow matching position error covariance matrices, and a deterministic approach based on the street azimuth. Using experimental data collected from a u-blox GNSS receiver, it is shown that both integrated position solutions are significantly more accurate than either shadow matching or 3D-mapping-aided ranging on their own. The overall Root Mean Square (RMS) horizontal accuracy obtained using covariance-based weighting was 6·1 m, a factor of four improvement on the 25·9 m obtained using conventional GNSS positioning. Results are also presented using smartphone data, where shadow matching is integrated with conventional GNSS positioning.

In this paper, a novel method of sensor based pedestrian dead reckoning is presented using sensors mounted on a shoe. Sensor based systems are a practical alternative to global navigation satellite systems when positioning accuracy is degraded such as in thick forest, urban areas with tall buildings and indoors. Using miniature, inexpensive sensors it is possible to create self-contained systems using sensor-only navigation techniques optimised for pedestrian motion. The systems developed extend existing foot based stride measurement technology by adding the capability to sense direction, making it possible to determine the path and displacement of the user. The proposed dead-reckoning navigation system applies an array of accelerometers and magneto-resistive sensors worn on the subject's shoe. Measurement of the foot's acceleration allows the precise identification of separate stride segments, thus providing improved stride length estimation. The system relies on identifying the stance phase to resolve the sensor attitude and determine the step heading. Field trials were carried out in forested conditions. Performance metrics include position, stride length estimation and heading with respect to a high accuracy reference trajectory.

The Hatch filter is a code-smoothing technique using integrated carrier phase observations. It is an easy technique that non-experts can use to reduce receiver noise on the pseudorange. This paper suggests a new algorithm for the optimal Hatch filter whose smoothing window width varies adaptively depending on the regional, diurnal and seasonal ionospheric variation and satellite elevation angle. We consider both quiet and storm conditions of the ionosphere. Using the well-known quiet ionospheric model, a conservative boundary value for ionospheric storm and the receiver noise statistics function of the satellite elevation angle, this algorithm can mathematically solve the optimal averaging constant for each satellite in every epoch. From a 24 hr data process result and real-time experiment, we found that the position accuracy of the optimal Hatch filter is better and more robust than that of the traditional Hatch filter. The optimal Hatch filter algorithm and its results are expected to provide a new solution for a single-frequency DGPS receiver and a thorough understanding of the relationship between the position error and the averaging constant. Furthermore, a DGPS user who applies this algorithm to a low-cost single-frequency receiver can obtain a more accurate and robust position result than via the classical Hatch filter.

The performance of Global Positioning System and Inertial Navigation System (GPS/INS) integrated navigation is reduced when GPS is blocked. This paper proposes an algorithm to overcome the condition where GPS is unavailable. Together with a parameter-optimised Genetic Algorithm (GA), a Support Vector Regression (SVR) algorithm is used to construct the mapping function between the specific force, angular rate increments of INS measurements and the increments of the GPS position. During GPS outages, the real-time pseudo-GPS position is predicted with the mapping function, and the corresponding covariance matrix is estimated by an improved adaptive filtering algorithm. A GPS/INS integration scheme is demonstrated where the vehicle travels along a straight line and around a curve, with respect to both low-speed-stable and high-speed-unstable navigation platforms. The results show that the proposed algorithm provides a better performance when GPS is unavailable.

In this paper collision threat parameters such as the distance at closest point of approach and time to the closest point of approach are derived and analysed for special cases and features; collision criteria are analysed for limitations. A new collision threat parameter - time to safe distance - is proposed and its different applications to collision avoidance are presented. Time to safe distance can replace time to the closest point of approach, as it gives a safer time in a dangerous situation. It can be applied in Automatic Radar Plotting Aids (ARPAs) to detect dangerous objects and to display possible evasive manoeuvres.