Time-differenced carrier phase (TDCP) is a commonly used method of precise velocimetry, but when the receiver is in a dynamic or complex observation environment, the estimation accuracy is reduced. Doppler velocimetry aims at estimating instantaneous velocity, and the accuracy is restricted by the accuracy of measurement. However, in such unfavourable cases, the Doppler measurement is more reliable than the carrier phase measurement. This paper derives the relationship between Doppler observation and TDCP observation, then proposes a Doppler enhanced TDCP algorithm, for the purpose of improving the velocity estimation accuracy in dynamic and complex observation environments. In addition, considering the error caused by the constant speed state update model in the robust Kalman filter (RKF), this paper designs a terrain adaptive and robust Kalman filter (TARKF). After three experimental tests, the improved TDCP algorithm can significantly increase the speed measurement accuracy to sub-metre per second, and the accuracy can be further improved after using TARKF.

The design of new rules on seaways, such as traffic restrictions, requires determining the degree of improvement in marine traffic safety beforehand by considering the occurrence of new hazardous factors. This study proposes a method to predict the future traffic behaviour and ship encounter frequency (EF) with the introduction of a new traffic rule. First, a sensitivity analysis is conducted to identify the factors affecting the EF. A method of predicting future traffic behaviour and EF is presented based on the analysis of changes in the traffic flow in an area with a temporal restriction. Results show that the method appropriately predicts the location and degree of the occurrence of encounters in the sea area. The proposed method contributes to the discussion of future traffic safety, when sailing in a specific area is restricted by new regulations, installations of new offshore wind farms and fishing reefs.

Because of the high photon flux, the Crab nebula pulsar is widely used as the observation target for X-ray pulsar-based navigation. The built profile of the Crab pulsar will change over time, however, which means that the pre-calibrated template cannot be used for the long term. In this paper, a novel pulsar-based template-independent navigation method is proposed. The detected phase propagation model is given as a term of position of the vehicle, taking the orbital motion into account. A different method of time-of-arrival process between the recovered profiles is introduced. With the aid of orbital transition matrix, a measurement model is derived to be a term of velocity error of the vehicle varying with time. The state errors of the vehicle are transformed into velocity errors by performing multi-segment observations to achieve the navigation system observability. The navigation equations of the system are then established and can be solved directly. Some simulations are performed to verify the method and suggest that the proposed method is feasible, effective and easy to implement. The precise orbit information of the vehicle can be determined. The state estimation accuracy is basically consistent with the traditional filtering algorithms, and the computational cost is still very low.

Demonstrations and local tests of several maritime autonomous surface ships (MASS) have recently been carried out. From a technological standpoint, MASS are becoming able to handle actual operations in certain sea areas. Since 2017, the MSC (Maritime Safety Committee) of the IMO (International Maritime Organization) has been discussing legal problems with the Regulations for Preventing Collisions at Sea (COLREGs) with regard to MASS operation. The purpose of this paper is to clarify the rules from the perspective of seafarers, who need to interpret COLREGs when dealing with MASS in ship handling situations on the sea, and also to discuss possible required amendments to COLREGs. This paper attempts to clarify the extent of current interpretations while also taking into account the answers to questionnaires received from 130 pilots, ship captains and navigation officers concerning COLREGs for MASS operation. Given the four common principles of COLREGs, it is considered whether the principles need to be changed with the introduction of MASS from the viewpoint of seafarers.

Distance measuring equipment (DME/DME) as the main reversionary method provides alternative positioning, navigation and timing (A-PNT) services for use during a Global Navigation Satellite System (GNSS) outage. Considering the geometry limitation of DME/DME, multi-DMEs with better geometry can be used to increase the accuracy and integrity performance of positioning. This paper discusses the opportunities and challenges related to use of multi-DMEs as an alternate source of positioning, navigation and timing. To support the performance for A-PNT, the basic idea is considering the existing installed equipment. In this paper, barometer altimeter and TACAN are used to help improve the performance of A-PNT provided by multi-DMEs both in accuracy and integrity. Based on the database of EUROCONTROL, the test results demonstrate that 79⋅7% of a reference area roughly matching with the continental European locations achieve RNP 1 using multi-DMEs when the DME measurement accuracy is 0⋅2 NM (95%). When the DME measurement accuracy is 0⋅1 NM (95%), 87⋅9% of the reference area can achieve RNP 1 using multi-DMEs. The usage of barometer/TACAN measurements aided multi-DMEs improves the performance of the accuracy and integrity monitoring.

This paper, in allusion to the limitations of traditional transfer alignment methods based on the external measurement equipment or the empirical model of angular deformation, proposes a rapid and accurate transfer alignment method without relying on the empirical angular deformation model. Firstly, the relationship between the actual angular deformation and the angular velocities measured by the gyroscopes in the master and slave inertial navigation systems (INSs) is derived to roughly estimate the angular deformation. Secondly, according to the error characteristics of gyroscopes, the error model of angular deformation is established. Thirdly, expanding the angular deformation error instead of the installation error angle, flexure angle and flexure angle rate into the state vector, a low-order transfer alignment filtering model independent of the empirical angular deformation model is established. The proposed method not only gets rid of the dependence on an empirical angular deformation model, but also realises the rapid and accurate initial alignment of the slave INS without adding any external measurement equipment. The simulations and experiments evidence the validity of the proposed transfer alignment method.

Inland waterway transportation is one of the most important means to transport cargo in rivers and canals. To facilitate autonomous navigation for ships in inland waterways, this paper proposes a data-driven approach for predictions and control of underactuated ships with unknown dynamics, which integrates model predictive control (MPC) with an iterative learning control (ILC) scheme. In each iteration, kernel-based linear regressors are used to identify the relations between the evolution of ship states and control inputs based on the stored data from previous iterations and the collected data during operation, so as to build the system prediction model. The data are dynamically used to fix the prediction model over iterations, as well as to improve the controller performance until it converges. The proposed approach does not require prior knowledge regarding the hydrodynamic coefficients and ship parameters, but learns from the data instead. In addition, it exploits the advantages of MPC in handling constraints with minimised overall cost. Simulation results show that the controller could start from a nominal, linear data-driven ship model and then learn to reduce the path-following errors based on the data obtained over iterations.

Following substantial progress achieved recently, the Galileo constellation provides a considerable satellite resource for the GNSS applications. In this regard, the performance assessment of real-time single-frequency precise positioning with Galileo satellites is the main objective of this research. For this purpose, several experimental tests were conducted in this study with two single-frequency positioning models, namely single-frequency code-based positioning and code-phase combination. The results show that Galileo presents an adequate number of visible satellites sufficient for single-frequency positioning. Also, the study demonstrates that, in comparison to GPS observations, Galileo observations have a significantly lower noise level. For the single-frequency code-based positioning, Galileo presents a better positioning accuracy than GPS by 25⋅8% on average. When compared with GPS, a 9⋅4% better positioning accuracy is acquired from Galileo for the single-frequency code-phase combination, with its average convergence time shorter than GPS by a ratio of 24⋅4%.

Integrated navigation systems made up of a strap-down inertial navigation system (SINS) and global positioning system (GPS) are increasingly being used to improve the position, speed, and attitude information of unmanned surface vessels (USV). However, a GPS outage could occur due to the dependence of GPS performance on the external environment and the number of available satellites. This study uses an innovative combination of Dempster–Shafer (DS) theory and broad learning (BL) method to design a SINS/GPS integrated navigation system. First, the velocity and position information derived from the SINS and their corresponding GPS were fused using DS fusion rules, while the SINS error was modelled using the BL method. A ‘virtual’ GPS was then designed using the proposed DS–BL approach to provide the speed and position information when the GPS signal was interrupted, thereby ensuring the continuous navigation of the USV. The results of both simulation and sea trial demonstrate that the proposed virtual GPS estimation approach is effective, and the navigational accuracy of the proposed method is superior to other methods.

The paper reviews the optimisation methods of the flight trajectory for airliners. In contrast to maritime navigation, where the shortest route (the orthodrome) is preferred, in air navigation, the brachistochrone is the optimal flight trajectory on the sphere or on the ellipsoid, considering the wind vector field (maximising the tail wind and minimising the head wind over the duration of the flight). The major impact of the wind on the flight trajectory results from the possible significant velocity at the normal cruise flight levels, which could reach 200 kts, or 40% of the aircraft true airspeed (TAS). Brachistochrone is independent of the flight performance optimisation (range versus speed), as computed by the flight management system. Whichever cost index (CI) is selected (and consequently, the cruise Mach number), the brachistochrone is the minimum time of flight trajectory at that target Mach number. In cruise flight, the minimum time of flight is also equivalent to the minimum fuel consumption. It concerns just the wind velocity field. All these qualify the brachistochrone as the greenest trajectory, the most fuel and emissions efficient solution relative to the atmosphere. The paper classifies the brachistochrone problems (2D, 3D and 4D brachistochrones, with or without flexible time of departure). Some numerical examples are provided. The overall optimal 4D trajectory considers many aspects, including safety, by minimisation of total costs and risks of the 4D trajectory.

Estimating the collision frequency of ships (F) is important for assessing collision risk on waterways. To date, F has been estimated as the product of the number of collision candidates $({N_{a }})$ and the causation probability $({P_c})$: $F = {N_{a}} \cdot {P_c}$, where ${N_{a }}$ represents the number of collisions that occur when related ships continue on course with no intervention, and ${P_c}$ is the probability that collision avoidance fails. Fujii developed a general method and Pedersen formulated it to estimate ${N_{a }}$ in an intersectional area. Their method is generally called ‘the geometric method’ because collision candidates are estimated only from the geometric relationship between two ships. The method has been used in many projects to estimate F in waterways; however, its use should be limited to intersection angles ranging from 10° to 170°. This paper presents a method, statistically verified by computer simulation, that can be used at all intersection angles to overcome this limitation. Moreover, it demonstrates strong agreement with Pedersen's method at intersection angles of 10° to 170°.

Pedestrian dead reckoning (PDR) is widely used in handheld indoor positioning systems. However, low-cost inertial sensors built into smartphones provide poor-quality measurements, resulting in cumulative error which consists of heading estimation error caused by gyroscope and step length estimation error caused by an accelerometer. Learning more motion features through limited measurements is important to improve positioning accuracy. This paper proposes an improved PDR system using smartphone sensors. Using gyroscope, two motion patterns, walking straight or turning, can be recognised based on dynamic time warp (DTW) and thus improve heading estimation from an extended Kalman filter (EKF). Joint quasi-static field (JQSF) detection is used to avoid bad magnetic measurements due to magnetic disturbances in an indoor environment. In terms of periodicity of angular rate while walking, peak–valley angular velocity detection and zero-cross detection is combined to detect steps. A step-length estimation method based on deep belief network (DBN) is proposed. Experimental results demonstrate that the proposed PDR system can achieve more accurate indoor positioning.

To address the shortcomings of existing methods for rotorcraft searching, positioning, tracking and landing on a ship at sea, a dual-channel LIDAR searching, positioning, tracking and landing system (DCLSPTLS) is proposed in this paper, which utilises the multi-pulse laser echoes accumulation method and the physical phenomenon that the laser reflectivity of the ship deck in the near-infrared band is four orders of magnitude higher than that of the sea surface. The DCLSPTLS searching and positioning model, tracking model and landing model are established, respectively. The searching and positioning model can provide estimates of the azimuth angle, the distance of the ship relative to the rotorcraft and the ship's course. With the above parameters as inputs, the total tracking time and the direction of the rotorcraft tracking speed can be obtained by using the tracking model. The landing model can calculate the pitch and the roll angles of the ship's deck relative to the rotorcraft by using the least squares method and the laser irradiation coordinates. The simulation shows that the DCLSPTLS can realise the functions of rotorcraft searching, positioning, tracking and landing by using the above parameters. To verify the effectiveness of the DCLSPTLS, a functional test is performed using a rotorcraft and a model ship on a lake. The test results are consistent with the results of the simulation.

To verify whether a graph is suitable for describing driver behaviour performance under the effects of navigation information, this study applies two types of prompt messages: simple and detailed. The simple messages contain only direction instructions, while the detailed messages contain distance, direction, road and lane instructions. A driving simulation experiment was designed to collect the empirical data. Two vehicle operating indicators (velocity and lateral offset), and two driver manoeuvre indicators (accelerator power and steering wheel angle) were selected, and T-test was used to compare the differences of behavioural performance. Driving behaviour graphs were constructed for the two message conditions; their characteristics and similarities were further analysed. Finally, the results of T-test of behavioural performance and similarity results of the driving behaviour graphs were compared. Results indicated that the two different types of prompt messages were associated with significant differences in driving behaviours, which implies that it is feasible to describe the characteristics of driving behaviours guided by navigation information using such graphs. This study provides a new method for systematically exploring the mechanisms affecting drivers’ response to navigation information, and presents a new perspective for the optimisation of navigation information.

This paper proposes a method for self-calibrating the star sensor on the Mars rover considering several years of exploration on the surface of Mars. The natural stars in the night sky are considered the control points, and a self-calibration model is deduced in detail according to an imaging model. An adaptive celestial positioning (ACP) algorithm is then introduced, and the calculation procedure is presented in detail to realise self-adjustment based on the self-calibration of the star sensor. Three field tests were conducted on Earth, the results of which show good self-calibration and celestial positioning performances. The positioning results indicate an obvious accuracy improvement using the ACP algorithm compared with that without calibration. Multiple positionings in one night can improve the celestial positioning accuracy to approximately 15 m. For future studies, this self-calibration model will be useful not only for star sensors but also for other optical sensors, such as sun sensors and binocular or stereo-vision cameras.

To solve the problem of spacecraft attitude manoeuvre planning under dynamic multiple mandatory pointing constraints and prohibited pointing constraints, a systematic attitude manoeuvre planning approach is proposed that is based on improved policy gradient reinforcement learning. This paper presents a succinct model of dynamic multiple constraints that is similar to a real situation faced by an in-orbit spacecraft. By introducing return baseline and adaptive policy exploration methods, the proposed method overcomes issues such as large variances and slow convergence rates. Concurrently, the required computation time of the proposed method is markedly reduced. Using the proposed method, the near optimal path of the attitude manoeuvre can be determined, making the method suitable for the control of micro spacecraft. Simulation results demonstrate that the planning results fully satisfy all constraints, including six prohibited pointing constraints and two mandatory pointing constraints. The spacecraft also maintains high orientation accuracy to the Earth and Sun during all attitude manoeuvres.

The fish-eye star sensor with a field of view (FOV) of 180° is an important piece of equipment for attitude determination, which improves the visibility of stars significantly. However, it also brings the star identification (star-ID) difficulties because of imprecise calibrations. Thus, a fish-eye star-ID algorithm supported by the integration of the precise point positioning/inertial navigation system (PPP/INS) is proposed. At first, a reference star map is generated in combination with the distortion model of the fish-eye camera based on the position and attitude information from the PPP/INS. Then the star points are extracted in a specific neighbourhood of the reference star points. Subsequently, the extracted star points are individually tested and identified according to angular distance error. Finally, the real-time precise attitude is determined based on the star-ID results. Experimental results show that, 270–310 stars can be identified in a fish-eye star map with an average time of 0.03 s if the initial attitude error is smaller than 1.5° and an attitude determination accuracy better than 10″ can be achieved by support from PPP/INS.

Location and navigation services based on global navigation satellite systems (GNSS) are needed for real-time high-precision positioning applications in relevant economic sectors, such as precision agriculture, transport, civil engineering or mapping. Real-time navigation users of GNSS networks have significantly increased all around the world, since the 1990s, and usage has exceeded initial expectations. Therefore, if the evolution of GNSS network users is monitored, the dynamics of market segments can be studied. The implementation of this hypothesis requires the treatment of big volumes of navigation data over several years and the continuous monitoring of customers. This paper is focused on the management of massive connection of GNSS users in an efficient way, in order to obtain analysis and statistics. Big data architecture and data analyses based on data mining algorithms have been implemented as the best way to approach the hypothesis. Results demonstrate the dynamic of users of different market segments, the increasing demand over the years and, specifically, conclusions are obtained about the trends, year-on-year correlation and business volume recovering after economic crisis periods.