The absence of a regional, open water vessel collision risk assessment system endangers maritime traffic and hampers safety management. Most recent studies have analysed the risk of collision for a pair of vessels and propose micro-level risk models. This study proposes a new method that combines density complexity and a multi-vessel collision risk operator for assessing regional vessel collision risk. This regional model considers spatial and temporal features of vessel trajectory in an open water area and assesses multi-vessel near-miss collision risk through danger probabilities and possible consequences of collision risks via four types of possible relative striking positions. Finally, the clustering method of multi-vessel encountering risk, based on the proposed model, is used to identify high-risk collision areas, which allow reliable and accurate analysis to aid implementation of safety measures.

An airport can be a stressful place for passengers. One of the reasons to get stressed might be the result of poor wayfinding. Current wayfinding signs are often static, which makes them difficult to adapt to new situations. In contrast, dynamic signs can be updated and adjusted accordingly. Light projections can be used as dynamic signs. The aim of this study is to understand if the use of animated projections onto the floor can improve the wayfinding experience. Four animations have been developed and tested within a controlled testing environment of which one animation has been tested in a real airport environment. Results indicate that animation for wayfinding purposes should show a clear vertical motion to guide towards a certain direction. Additionally, higher velocity in the animation was perceived as more positive. The observation in the airport showed that a projection in clear daylight and on the floor is not noticed by the passengers walking by.

Dynamic trajectory prediction is an important topic in the field of navigation and positioning. Due to the drawbacks of a Global Navigation Satellite System (GNSS) receiver, the trajectory of the position always lags behind the dynamic platform's actual position, especially in highly dynamic situations. In order to solve the prediction of a dynamic trajectory, a generalised extension extrapolated model is proposed in this paper. The model utilises the current motion state and a priori position data of the platform, combines the interpolation and fitting method, adds the angle information as a constraint condition and solves the platform position prediction. In this paper, the feasibility of the generalised extended extrapolation algorithm is analysed theoretically and practically. Simulation results show that the prediction error is within 0.2 metres and experimental results show that the algorithm still has high prediction accuracy when a land vehicle platform is turned through a large angle.

The performance of Global Navigation Satellite System (GNSS) and Micro-Electro-Mechanical System (MEMS)-based Inertial Navigation System (INS) integrated navigation is reduced during GNSS outages. To bridge the period during GNSS outages, a novel hybrid intelligent algorithm incorporating a Discrete Grey Predictor (DGP) and a Multilayer Perceptron (MLP) neural network (DGP-MLP) is proposed. The DGP-MLP is used to provide a pseudo-GNSS position to correct the INS errors during GNSS outages; the DGP uses the GNSS position information of the latest few moments to predict the position of future moments; in the process of DGP-MLP, the MLP is used to modify the prediction errors of DGP, and the MLP is improved by adding momentum terms and adaptively adjusting the learning rate and momentum factor. To evaluate the effectiveness of the proposed methodology, four GNSS outages in different cases over a real field test data were employed. The experimental results demonstrate that the proposed methodology can significantly improve positioning accuracy during GNSS outages.

The accuracy of speed prediction error to the next waypoint is a key factor in maintaining longitudinal separation on oceanic routes. This estimation is often used by air traffic control to estimate the future position of aircraft, and the estimation errors result in potential separation infringement. While most aircraft can calculate the estimated time at each future waypoint using the onboard Flight Management System, the factors affecting the inaccuracy of the estimation require more clarification. This paper investigates the accuracy of the speed prediction error on oceanic routes and examines the main factor of error using airline flight data. The results show that wind prediction error is a main source of speed prediction error, and significant differences of the speed prediction error among airlines and aircraft types were observed.

The technique of tracking a non-cooperative manoeuvring satellite is important for Space Situation Awareness (SSA). However, the classical extended Kalman filter cannot work successfully in this situation. Motivated by this problem, a novel Extended Kalman Filter with Input Detection and Estimation (EKF/IDE) method is proposed in this paper for tracking a non-cooperative satellite with impulsive manoeuvres. The impulsive manoeuvre is modelled as an unknown acceleration without any prior information. An unbiased minimum-variance input and state estimation method is introduced to estimate the manoeuvre acceleration. An approach based on the Mahalanobis distance of the manoeuvre estimate error is proposed for manoeuvre detection. With the impulsive manoeuvre being detected and estimated accurately, an adaptive extended Kalman filter is proposed to estimate the state of the target. An approach of covariance inflation is proposed to deal with the manoeuvre during the unobserved period. Simulations and Monte Carlo experiments are implemented to demonstrate the feasibility and validity of the proposed method. The results of simulations show that the proposed method can accurately detect and estimate unknown impulsive manoeuvres of a non-cooperative satellite. Through the compensation of the estimated manoeuvre, the estimation of position and velocity after the manoeuvre maintains the accuracy of the pre-manoeuvre period, demonstrating the robustness of the proposed method against unknown manoeuvres.

The Carrier-Phase (CP) technique used in the Global Positioning System (GPS) has proved to be a useful spatial tool for remote precise time transfer. Galileo is a Global Navigation Satellite System like GPS. However, currently, given the low number of satellites at any one observation epoch, Galileo's accuracy and continuity of time transfer leave much to be desired. To achieve better performance of time transfer for Galileo, this study has developed a new approach for Galileo CP time transfer, using prior constraint information such as precise coordinates and troposphere zenith delay constraints. The new approach was applied for precise time transfer in real-time mode and post-processed mode for short baseline and long baseline observations. For the short baseline time link in real-time mode, compared with the standard Galileo CP, the standard deviation improved by 51·4% for the troposphere zenith delay constraint, 47·6% for the station coordinates constraint, and 49·5% when considering both constraints simultaneously. At a 10,000 s time interval, in comparison to the standard CP, the three constraint approaches show stable results as well as improvements of nearly an order of magnitude. In post-processed mode, the constraint approach for Galileo time transfer showed little improvement compared to the standard CP technique for both the short baseline and long baseline time links.

This paper first investigates the influencing factors of between-receiver Differential Inter-System Bias (DISB) between overlapping frequencies of the Global Positioning System (GPS), Galileo and the Quasi-Zenith Satellite System (QZSS). It was found that the receiver reboot and the type of observations may have an impact on DISBs. The impact of receiver firmware upgrades and the activation of anti-multipath filters are also investigated and some new results are presented. Then a performance evaluation is presented of tightly combined relative positioning for a short baseline with GPS/Galileo/QZSS L1-E1-L1/L5-E5a-L5 observations with the current constellations, in which the recently launched Galileo and QZSS satellites will also be included. It is demonstrated that when DISBs are a priori calibrated and corrected, the tightly combined model can deliver a much higher empirical ambiguity resolution success rate and positioning accuracy with respect to the classical loosely combined model, especially under environments where the observed satellites for each system are limited and only single-frequency observations are available. The ambiguity dilution of precision, bootstrapping success rate, and ratio values are analysed to illustrate the benefits of the tightly combined model as well.

To evaluate the aptness of a navigation system in a particular application, the designer needs to assess its performance over typical trajectories travelled by the vehicle itself. Moreover, he or she may be required to judge which components of the kinematics state may be better estimated (and which will not). The main contributions of this work are two novel and complementary performance measures that, in concert, allow for the assessment of a navigation system within the actual context of its application over specific trajectories. For a given on board instrumental configuration, the “excitability metric” permits the isolation of the contribution of the information conveyed by the vehicle's motion itself, while, the “sensability metric” measures the resultant overall quality of the kinematics state estimation. The same tools could help the designer planning appropriate vehicles manoeuvres in order to obtain a required precision for each estimated component. While emphasis is given on the mathematical justification of those metrics, their use is also illustrated with real flight data recorded from a sounding rocket.

In this paper, a novel method for autonomous navigation for an extra-terrestrial body landing mission is proposed. Based on state-of-the-art crater detection and matching algorithms, a crater edge-based navigation method is formulated, in which solar illumination direction is adopted as a complementary optical cue to aid crater edge-based navigation when only one crater is available. To improve the pose estimation accuracy, a distributed Extended Kalman Filter (EKF) is developed to encapsulate the crater edge-based estimation approach. Finally, the effectiveness of proposed approach is validated by Monte Carlo simulations using a specifically designed planetary landing simulation toolbox.

Conventional underwater navigation and positioning methods for Autonomous Underwater Vehicles (AUVs) either require the installation of acoustic arrays, which make AUVs less independent, or result in cumulative errors. This paper proposes an Underwater Terrain Positioning Method (UTPM) using Maximum a Posteriori (MAP) estimation and a Pulse Coupled Neural Network (PCNN) model for highly accurate navigation by AUVs. The PCNN model is used as a secondary discriminant to effectively identify pseudo-anchor points in flat terrain feature areas and to find the true positioning point, which significantly improves the matching positioning accuracy in these areas. Simulation results show that the proposed method effectively corrects Inertial Navigation System (INS) cumulative errors and has high matching positioning accuracy, which satisfy the requirements of AUV underwater navigation and positioning.

In some cases, navigation of aircraft or spacecraft may need to be conducted in a Global Navigation Satellite System (GNSS)-denied environment. So, additional sources of navigation information may need to be used to increase navigation precision and resilience. Such sources can include visual navigation systems such as visual shoreline navigation. The main feature of visual shoreline navigation is the severe variability of navigation errors depending on the shape of the observed shoreline, the distance and the view angle of the observation. Such variations are so great that it is not possible to use average values of errors. So, each measurement of an aircraft or spacecraft position should be accompanied with an estimation of the error covariance matrix in real time. It is proposed to use the Cramer-Rao lower bound of visual shoreline navigation errors as such a matrix. The method for constructing the Cramer-Rao lower bound is described in this paper.

A new unambiguous tracking technique based on combined correlation functions for sine Binary Offset Carrier (BOC) signals is proposed in this paper. The key to this method is to exploit two types of local reference signals: the BOC signal and a linear combination of a series of BOC signals with different delays. They are both correlated with the received signals. Then, a correlation function without any positive side peaks is obtained by multiplying the two correlation results to make tracking completely unambiguous. Theoretical analysis and simulation in the tracking stage show that the proposed method has the best code tracking accuracy among the method tracking BOC signals like Binary Phase-Shift Keying signals (BPSK-LIKE), the Pseudo correlation function based Unambiguous Delay Lock Loop (PUDLL), Symmetrical Pulse Ambiguity Removing (SPAR) technique, the method proposed by Shen Feng (SF) and the two methods proposed by Yan Tao (YT-V1 and YT-V2). In multipath environments, the proposed method has the best anti-multipath performance of all the tracking methods mentioned above. In conclusion, the proposed method can completely eliminate ambiguity and has significant performance advantages compared with the methods mentioned above.

Receiver Autonomous Integrity Monitoring (RAIM) provides an integrity service for Global Navigation Satellite Systems (GNSS). The conventional RAIM algorithm is based on the assumption of a single fault and typically uses the forward-backward method, which is based on the w-test or correlation analysis methods, to exclude the faults. It is suitable for single fault detection and exclusion, while it can lead to inefficiency, can be misleading and can even fail in the exclusion of multiple faults. To solve this problem, an improved method based on consensus voting of the w-test and correlation analysis methods is presented. To verify the performance of the improved method, tests using Global Positioning System (GPS)/BeiDou System (BDS) data have been carried out in comparison with the conventional methods in terms of false and correct faults exclusion rate and computational complexity in the case of a different number of faults. Results show that the improved method has almost the same correct exclusion rate compared to the conventional RAIM in the case of a single fault. It is worth noting that the improved method has a higher correct exclusion probability and computational efficiency as well as a lower possibility of false exclusion in the case of multiple faults.

In this paper, the spacecraft close-range safe proximity problem is investigated. In the presence of a “chief” spacecraft, a Multi-Equal-Collision-Probability-Curve (MECPC) method is developed. The influence of the chief spacecraft with a convex polygon shape is considered and the chief spacecraft is divided into several small components. Each component generates a corresponding separate repulsive force and the superposition of these forces is regarded as the ultimate avoidance force. As a result, the proposed MECPC method not only improves the system robustness against control and navigation uncertainties but is also analytically validated in collision avoidance. The MECPC method solves the safe proximity problem in the presence of a convex polygon shape. In addition, an Improved Linear Quadratic Regulator (ILQR) is designed to track the expected trajectory. Numerical simulations are performed in a close-range operation environment to verify the effectiveness of the proposed MECPC method.

X-ray Pulsar Navigation (XPNAV) uses the Time Difference of Arrival (TDOA) of the pulsar signal between the spacecraft and Solar System Barycentre (SSB) to determine position. In this paper, a novel method to improve the performance of XPNAV via exploiting the pulsar position vector is proposed. First, the field of view of the collimator is utilised to find the pulsar orientation direction. Then, a searching strategy based on the modified Powell method under given coordinate frames is proposed. We also mathematically prove the existence of the extreme value of the searching strategy. Subsequently, an observation model based on the pulsar radiation vector is presented and applied to formulate the observation function together with pulsar time transfer function. Finally, an Adaptive Divided Difference Filter (ADDF) algorithm is introduced to iteratively estimate the position and velocity of the spacecraft. Numerical simulations show that the vector searching method is feasible and the pulsar radiation direction can improve the navigation performance by 75%. The simulation results also show that the ADDF performs better than Unscented Kalman Filtering (UKF) and DDF in position estimation.

Ionospheric scintillation effects degrade satellite-based radio communication/navigation links and influence the performance of Global Navigation Satellite Systems (GNSS). An adaptive wavelet-based decomposition technique, Synchrosqueezing Transform (SST), with a Detrended Fluctuation Analysis (DFA) algorithm has been implemented for time-frequency representation of GNSS multi-component signals and mitigation of scintillation effects. Synthetic In-phase (I) and Quadra-phase (Q) samples were collected from the Cornell Scintillation Model (CSM) and the CSM amplitude scintillation signal was processed with SST-DFA for the detection of noisy scintillation components and mitigation of ionospheric scintillation effects. Also, performance of the SST-DFA algorithm was tested for real-time GNSS ionospheric scintillation data collected from a GNSS Software Navigation Receiver (GSNRx) located at a low-latitude station in Rio de Janeiro, Brazil. The de-noising performance of the SST-DFA algorithm was further evaluated and compared with a low-pass Butterworth filter during different ionospheric scintillation time periods. The experimental results clearly demonstrated that the proposed method is reliable for mitigation of ionospheric scintillation noise both in time and frequency scales.

A round of three celestial sights yields three lines of position along which the observer's true position could lie. Due to measurement errors, the lines of position do not intersect at a point but rather form a triangle called the “cocked hat”. The probability that this encloses the observer's true position is well known to be 25% which is the average over all possible cocked hats that could arise when the sights are made. It does not apply to any specific set of sights and in that case the probabilities depend on the statistical distribution of the measurement errors. With fixed azimuths for the observed celestial bodies and assuming a normal distribution for the errors in their measured altitudes, a closed form analytic expression is derived for the probability of the observer's position falling inside the cocked hat and this is related back to the global average. Probabilities for exterior regions bounded by the lines of position are also obtained. General results are given that apply for any number of lines of position.

The High-degree Cubature Kalman Filter (HCKF) is proposed as a novel methodology based on the arbitrary degree spherical rule, which can achieve better performance than the traditional Kalman filter. However, it also has a large calculation burden when used in a high-dimension and high-degree of accuracy estimation system. The number of sampling points of an HCKF increases polynomially with increasing state-space dimensions, which further increases the calculation burden. The reduction of the number of the state-space dimensions is the main contribution of this study. A strategy for HCKF based on the partitioning of the state-space and orthogonal principle is introduced, referred to as the Multiple Robust HCKF (MRHCKF). It is shown that this technique can effectively reduce the calculation burden for the high-dimension system with robust performance. Numerical simulations are performed for the example of high-dimension relative position and attitude estimation to show that the proposed method can obtain nearly the same performance as the HCKF, while drastically reducing computational complexity.

The accuracy in an X-ray pulsar-based navigation system depends mainly on the accuracy of the pulse phase estimation. In this paper, a novel method is proposed which combines an epoch folding process and a cross-correlation method with the idea of “averaging multiple measurements”. In this method, pulse phase is estimated multiple times on the sampled subsets of arriving photons' time tags, and a final estimation is obtained as the weighted average of these estimations. Two explanations as to how the proposed method can improve accuracy are provided: a Signal to Noise Ratio (SNR)-based explanation and an “error-difference trade-off” explanation. Numerical simulations show that the accuracy in pulse phase estimation can be improved with the proposed algorithm.