There is increasing demand for navigation capability for space vehicles. The idea to extend the application of Global Navigation Satellite Systems (GNSS) from terrestrial to space applications by the use of main beam and side lobe signals has been shown to be feasible. In order to understand the performance and the potential space applications GNSS can support, this paper characterises the Space Service Volume (SSV) in terms of the four parameters of minimum received power, satellite visibility, pseudorange accuracy and Geometric Dilution of Precision (GDOP). This new definition enables the position errors to be estimated. An analytical methodology is proposed to characterise minimum received power for the worst location. Satellite visibility and GDOP are assessed based on grid points at different height layers (to capture the relationship between height and visibility) for single and multiple GNSS constellations, the former represented by BeiDou III (BDS III) and the latter, BDS III in various combinations with GPS, GLONASS and GALILEO. Additional simulation shows that GNSS can potentially support lunar exploration spacecraft at the Earth phasing orbit. This initial assessment of SSV shows the potential of GNSS for space vehicle navigation.

This paper analyses two different methods of estimating ship collision candidates. The first one is an analytical approach; accordingly, an overview of various analytical expressions for estimating the number of collision candidates for three main situations (encounter, overtaking, and crossing) will be presented. The second is a simulation approach: the paper will present how to simulate ship movements by replacing them with circles in order to obtain a graphical presentation of ship movements in the zone of danger, including the calculation of collision candidates. The applied simulation model will also feature three main situations, i.e. encounter, overtaking, and crossing, and the results of simulations will be compared with the results of analytical models. The results and conclusions should improve the existing models for obtaining the potential number of ship collisions and encourage new advanced simulation methods.

The autonomous navigation of navigation and positioning systems such as the Global Positioning System (GPS) and other Global Navigation Satellite Systems (GNSS) was motivated to improve accuracy and survivability of the navigation function for 180 days without ground contact. These improvements are accomplished by establishing inter-satellite links in the constellation for pseudo-range observations and communications between satellites. But observability issues arise for both ephemeris and clock since the pseudo-range describes only the relative distance between satellites. A differential measurement method is proposed to measure the rotation of the constellation as a whole for the first time. The feasibility of the proposed method is verified by simulations.

A novel relative spacecraft attitude and position estimation approach based on an Unscented Kalman Filter (UKF) is derived. The integrated sensor suite comprises the gyro sensors on each spacecraft and a vision-based navigation system on the slave spacecraft. In the traditional algorithm, an assumption that the master's body frame coincides with its Local Vertical Local Horizontal (LVLH) frame is made to construct the line-of-sight observations for convenience. To solve this problem, two relative quaternions that map the master's LVLH frame to the slave and master body frames are involved. The general relative equations of motion for eccentric orbits are used to describe the positional dynamics. The implementation equations for the UKF are derived. A modified version of the UKF is presented based on the averaging-quaternion algorithm. Simulation results indicate that the proposed filters provide more accurate estimates of relative attitude and position than the Extended Kalman Filter (EKF).

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.

To solve the problem of attitude determination using magnetometers independently and uniquely, which is important for underwater vehicles, a type of full attitude determination method based on geomagnetic gradient tensor is proposed in this paper. In this method, a group of non-linear equations concerning geomagnetic gradient tensors is established, where a quaternion is selected to calculate three attitude angles of an underwater vehicle. The optimal quaternion is estimated using Newton Down-hill to optimise the object function. The detailed steps of the full attitude determination based on geomagnetic gradient tensor are given, and the effects of the initial angle error and the sensor noise on the attitude determination are investigated. Simulations show that the algorithm can identify precisely and quickly the attitudes even in the presence of larger initial angle error and sensor noise, which proves the attitude determination algorithm.

This paper proposes the novel use of a weighted Interval Kalman Filter (wIKF) in a robust navigational approach for integration with the guidance and control systems of an uninhabited surface vehicle named Springer. The waypoint tracking capability of this technique is compared with that of one that uses a conventional Kalman Filter (KF) navigational design, when the model of the sensing equipment used by the filter is incorrect. In this case, the KF fails to predict correctly the vehicle's heading, which consequently impacts negatively on the performance of its integrated navigation, guidance and control (NGC). However, the use of a wIKF technique that is immune to this kind of erroneous modelling endows the integrated NGC system with better accuracy and efficiency in completing a mission.

This study attempts to offer the first ever analysis of Austrian aviation cartography from its origins in 1908 to 1938. The thematic focus is on Austria's contribution to the debate on the standardisation of aeronautical charts on an international scale, on the continuities and changes characterising the aeronautical charts produced in Austria, and on a comparison of these maps with similar ones from other countries. The paper aims to expound on the thesis that, while the theoretical basis for aeronautical charts had principally been in place internationally and in Austria during the 1910s, there had been almost no practical follow-up on this know-how in Austria between 1915 and 1922. After 1923 novel aeronautical charts were produced, but the Austrian output sometimes fell below international standards regarding both quantity and, in part, also quality. The international agreed rules were interpreted in keeping with Austria's own requirements. It appears, however, that this development was not limited to Austria, as the new rules took hold in other countries somewhat belatedly as well.

In nature, science and engineering, we often come across helicoidal surfaces. A curve on a helicoidal surface in Euclidean 3-space is called a loxodrome if the curve intersects all meridians at a constant azimuth angle. Thus loxodromes are important in navigation. In this paper, we find the differential equation of the loxodrome on a helicoidal surface in Euclidean 3-space. Also we give some examples and draw the corresponding pictures via the Mathematica computer program to aid understanding of the mathematics of navigation.

A new nonlinear robust filter is proposed in this paper to deal with the outliers of an integrated Global Positioning System/Strapdown Inertial Navigation System (GPS/SINS) navigation system. The influence of different design parameters for an H∞ cubature Kalman filter is analysed. It is found that when the design parameter is small, the robustness of the filter is stronger. However, the design parameter is easily out of step in the Riccati equation and the filter easily diverges. In this respect, a singular value decomposition algorithm is employed to replace the Cholesky decomposition in the robust cubature Kalman filter. With large conditions for the design parameter, the new filter is more robust. The test results demonstrate that the proposed filter algorithm is more reliable and effective in dealing with the outliers in the data sets produced by the integrated GPS/SINS system.

This paper presents the results of research on the fusion of tracking radar and an Automatic Identification System (AIS) in an Electronic Chart Display and Information System (ECDIS). First, the concept of these systems according to the International Maritime Organization (IMO) is described, then a set of theoretical information on radar tracking and the fusion method itself is given and finally numerical results with real data are presented. Two methods of fusion, together with their parameters, are examined. A proposal for calculating the covariance matrix for radar and AIS data is also given, and the paper ends with conclusions.

This paper presents a new type of Global Positioning System/Inertial Navigation System (GPS/INS) providing higher navigation accuracy under large initial heading error. The mechanization introduced is applicable to low cost GPS/INS systems and enhances the performance when the heading error is large. The proposed approach has the capability to decrease large heading errors very quickly and can start the strapdown navigation computations under poor heading accuracy without any special alignment procedure. Although the design is applicable to land, sea and aerial vehicles, a land vehicle is used for the performance tests. The test is conducted around a closed path and the proposed system is compared to a GPS/INS system based on small attitude error assumption. The performance of both systems is given in this paper.

This paper considers the estimation of the process state and noise parameters when the statistics of the process and measurement noise are unknown or time varying in the integration system. An adaptive Kalman Filter (AKF) with a recursive noise estimator that is based on maximum a posteriori estimation and one-step smoothing filtering is proposed, and the AKF can provide accurate noise statistical parameters for the Kalman filter in real-time. An exponentially weighted fading memory method is introduced to increase the weights of the recent innovations when the noise statistics are time varying. Also, the innovation covariances within a moving window are averaged to correct the noise statistics estimator. Experiments on the integrated Strapdown Inertial Navigation System (SINS)/ Doppler Velocity Log (DVL) system show that the proposed AKF improves the estimation accuracy effectively and the AKF is robust in the presence of vigorous-manoeuvres and rough sea conditions.

The Japanese Quasi-Zenith Satellite System (QZSS) is a regional satellite navigation system capable of transmitting navigation signals that are compatible and interoperable with other Global Navigation Satellite Systems (GNSS). In addition to navigation signals, QZSS also transmits augmentation signals, e.g. the L-band Experimental (LEX) signal. The LEX signal is unique for QZSS in delivering correction messages such as orbits and clock information that enable real-time Precise Point Positioning (PPP). This study aims to evaluate the availability of the LEX signal as well as the quality of the broadcast correction messages for real-time PPP applications. The system is tested in both static and kinematic positioning modes. The results show that the availability of the LEX signal is 60% when the QZSS satellite elevation is at 30° and above 90% when the satellite is above 40° elevation. Centimetre-level position accuracy can be obtained for static PPP processing after two hours of convergence using the current MADOCA-LEX (Multi-GNSS Advanced Demonstration of Orbit and Clock Analysis) correction messages transmitted on the LEX signal; and decimetre-level point positioning accuracy can be obtained for kinematic PPP processing.

Underwater terrain matching navigation technology is an important research area for the underwater navigation of Autonomous Underwater Vehicles (AUVs). Terrain matching navigation can realise long-term, subtle, all-weather, and high-precision underwater AUV navigation. In this paper, the research status of the application of AUV underwater terrain matching navigation is reviewed, the system composition, theory and terrain matching methods of underwater terrain matching navigation are summarised and the advantages of a multi-beam bathymetric system in underwater terrain matching navigation are discussed. The current research thoughts are summarised, the key issues are pointed out, and possible future development trends are discussed.

The predictions of Length-Of-Day (LOD) are studied by means of Gaussian Process Regression (GPR). The EOP C04 time-series with daily values from the International Earth Rotation and Reference Systems Service (IERS) serve as the data basis. Firstly, well known effects that can be described by functional models, for example effects of the solid Earth and ocean tides or seasonal atmospheric variations, are removed a priori from the C04 time-series. Only the differences between the modelled and actual LOD, i.e. the irregular and quasi-periodic variations, are employed for training and prediction. Different input patterns are discussed and compared so as to optimise the GPR model. The optimal patterns have been found in terms of the prediction accuracy and efficiency, which conduct the multi-step ahead predictions utilising the formerly predicted values as inputs. Finally, the results of the predictions are analysed and compared with those obtained by other prediction methods. It is shown that the accuracy of the predictions are comparable with that of other prediction methods. The developed method is easy to use.

The Rotterdam Rules, as the latest marine cargo convention, seek to promote legal uniformity of multimodal transport. The network-liability approach of this convention attempts to harmonise conflicts of liability regimes among different types of navigation in multi-modal transport. However, its Articles 26 and 82 only harmonise limited scenarios among all the potential conflicts of interest. Additionally, the network-liability approach itself relies on localising any occurrence of damage to or loss of goods, which corresponds to different degrees of liability among marine, land and air navigation. Thus, it is impossible for carriers and navigators to anticipate their liabilities when entering into a contract of multimodal transport. Through analysing UNCITRAL negotiating documents, a comprehensive safeguard is proposed to solve these problems.

This article proposes a batch-mode algorithm to handle the large databases generated from experimentations using probe vehicles. This algorithm can locate raw Global Positioning System (GPS) positions on a map, but can also be used to correct map-matching errors introduced by real time map-matching algorithms. For each journey, the algorithm globally searches for the closest path to the GPS positions, and so is inspired from the “path to path” algorithm's family. It uses the Multiple Hypothesis Technique (MHT) and relies on an innovative weighting system based on the area between the GPS points and the arcs making up the path. For high performance, the algorithm uses an iterative program and the data is stored in tree form.

Based on the candidate architectures of the libration point satellite navigation system proposed in our previous work, a navigation performance study is conducted in this paper to verify the cislunar navigation ability of the proposed system. Using scalar satellite-to-satellite range measurement between the user and libration point navigation satellites, a virtual lunar exploration mission scenario is developed to verify the navigation performance of the candidate Earth-Moon L1,2,4,5 four-satellite constellations. The simulation results indicate that the libration point satellite navigation system is available for cislunar navigation and the navigation accuracy of a few tens of metres can be achieved for both the trans-lunar cruise and lunar orbit phase. Besides that, it is also found that the navigation accuracy of the libration point satellite navigation system is sensitive to the orbit of the L1 satellite. Once the L1 navigation satellite is located in the Halo orbit or vertical Lyapunov orbit, the proposed system can present a better navigation performance in cislunar space.

Marine accident analysis is a sophisticated and complex official interpretation that requires a professional and fair judgment. For accidents such as a collision, contact and other incidents in the maritime field, the judgment mechanism of the courts depends on the decision process of the field experts. Field experts define the “Fraction Defectives” (FDs) of the vessels for the intended case based on the existing evidence and navigational specifications. However, evaluation of human judgment can be limited and problematic in analysing many aspects of a case. In this paper, a pairwise comparison method is used to simplify and clarify the judgment process. We aim to assess marine accidents in a stepwise approach that is inaccurately carried out in a holistic perspective by the field experts. A real accident that occurred in the past is simulated in front of the field experts. After conducting an expert consultation, FDs are re-calculated to compare both the regular judgment and the results in our suggested Generic Fuzzy Analytical Hierarchy Process (GF-AHP) approach.