An algorithm for Global Navigation Satellite System satellite atomic clock integrity monitoring based on an extended measurement model is proposed. A detection statistic achieved by parity transformation is used to detect clock anomalies, and the concept of the optimal accumulation number, with a method to find it, is provided. Numerical simulations are adopted to verify the validity of detecting two typical anomalies.

The accuracy of the Global Positioning System (GPS) observable, especially for the code observable, has improved with the development of Global Navigation Satellite System (GNSS) receiver technology. An evaluation of the GPS code observable is presented in this paper, together with a stochastic model for the code and phase observables in Precise Point Positioning (PPP), established using the evaluated results. The results show that the code observables of Leica GNSS receivers are generally better than those of some other brand receivers and the Root Mean Square (RMS) for the code observables of the Leica GRX1200PRO, which includes the multipath effect, reaches 0·71 m, although Coarse/Acquisition (C/A) code observables are tracked. The static positioning of the code observable can reach centimetre level and the convergence time for the JPLM station is just 2·5 hours. The positioning results show that it is difficult to converge the Up direction to the centimetre level, compared with the North and East directions. The results show that static positioning can be correlated with the accumulation characteristic of the error for the code observable, while that that of the kinematic mode can be correlated to the error value. The shortened PPP convergence times verify that the presented stochastic models are effective.

This article discusses the technique of observing lunar distance - that is, angular distance between the moon and another celestial body - to establish universal time and longitude, from a practitioner's point of view. The article presents a brief overview of the principles underlying the lunar distance observation and its use in celestial navigation. A discussion follows of two different methods for finding universal time by observing lunar distance, Dr. Wendel Brunner's calculator-based method and the specialised inspection tables created by Bruce Stark. The article compares the two methods against each other for ease of use and accuracy. The author concludes that either method will provide satisfactory results, but that the technique of observing lunar distance is unlikely to regain relevance in the modern-day practice of navigation and is primarily useful as a skill-building exercise in making sextant observations.

In dense networks, the tremendous computational complexity and communication overhead of cooperative localisation are the two main bottlenecks that limit practical application. In this study, we introduce a bootstrap percolation scheme into Gaussian message passing-based cooperative localisation for precise positioning, aimed at reducing the system overhead. Considering the uncertainty information and geometric distribution of neighbours, an approximate collinear detection criterion is proposed to detect the possible flip ambiguities in cooperative localisation. According to the detection result and our connection constraint, agents are divided into three categories and are approximated by different distribution families. A message passing rule is designed to control the propagation direction from high precision to low precision, thereby mitigating potential error propagation. Additionally, a layer-by-layer positioning mechanism is established where the agents are located gradually. Analytical and simulation results indicate that when the ranging standard deviation is 0·2 m, 89·3% of the agent nodes can be located within 0·4 m using the proposed algorithm. Compared with the Hybrid Sum-Product Algorithm over A Wireless Network (H-SPAWN), this ratio is increased by 8·4% and the computational complexity is reduced by 72%.

A probabilistic methodology for separation loss probability assessments is proposed in this paper. The key focus is on the effect of uncertainties from multiple Automatic Dependent Surveillance-Broadcast (ADS-B) systems on the separation loss probability assessment. First, a brief review of the ADS-B system and its associated uncertainty quantification metrics is discussed. It is found that most existing studies focus on the individual ADS-B uncertainty quantification for a single aircraft, which is not sufficient for separation loss probability assessment when two or more aircraft are involved. Next, a probabilistic positioning model with multiple aircraft is proposed and various types of uncertainties are included in the proposed model. Numerical simulations show that a navigation satellite fault can significantly affect separation error when individual aircraft see different satellite sets. Following this, several demonstration examples are illustrated to show the bounds for separation loss probability estimation. Finally, several conclusions and suggestions are discussed based on this study. One major finding is that the separation risk significantly increases when two nearby aircraft use different satellite sets to navigate. Real-time assessment of this risk should be performed.

This article presents research on how frequently seafarers utilise functions and information available on an Integrated Navigation System to perform navigation duties. Using an online questionnaire, the study collected data from 601 members of the global seafaring community. The results provide an overview of the frequency of use for each feature, together with factors affecting the use and associated usability issues. The study finds that the use of navigation equipment is situation-dependent and affected by administrative factors, experience and professional habits, characteristics of the sailing area, traffic conditions, weather conditions, ship management factors and geographical location. Additionally, information overload, particularly with overlay and alert management functions, was found to be the major issue with existing systems. The findings of this study can be applied to improve menu tree structure, display layout, and interaction methods on the interface of navigation systems, such as making frequently-used features more readily available or easier to access.

Airborne-Pseudolite (A-PL) systems have been proposed to augment Global Navigation Satellite Systems (GNSSs) in difficult areas where GNSS-only navigation cannot be guaranteed due to signal blockages, signal jamming, etc. One of the challenges in realising such a system is to determine the coordinates of the A-PLs to a high accuracy. The GNSS Precise Point Positioning (PPP) technique is a possible alternative to differential GNSS techniques such as those that generate Real-Time Kinematic (RTK) solutions. To enhance the A-PL positioning performance in GNSS challenged areas, it is assumed that inter-PL range measurements are also used in addition to GNSS measurements. When processing these new measurements, cross-correlations among A-PL estimated states introduced during measurement updates need to be accounted for so as to obtain consistent estimated states. In this paper, a distributed algorithm based on a Split Covariance Intersection Filter (SCIF) is proposed. Three commonly used means of implementing the SCIF algorithm are analysed. Another challenge is that real-time GNSS PPP relies on the use of precise satellite orbit and clock information. One problem is that these real-time orbit and satellite clock error corrections may not be always available, especially for moving A-PLs in challenging environments when signal outages occur. To maintain A-PL positioning accuracy using GNSS PPP, it is necessary to predict these error corrections during outages. Different prediction models for orbit and clock error corrections are discussed. A test was conducted to evaluate the A-PL positioning based on GNSS PPP and inter-PL ranges, as well as the performance of error prediction modelling. It was found that GNSS PPP combined with inter-PL ranges could achieve better converged positioning accuracy and a reduction in convergence time of GNSS PPP. However, the performance of GNSS PPP with inter-PL ranges was degraded by observing A-PLs with limited positioning accuracy. Although the performance improvement achieved by the SCIF-based distributed algorithms was smaller than that by the centralised algorithm, greater robustness in dealing with deteriorated observed A-PLs' trajectory data was demonstrated by the distributed algorithms. In addition, short-term prediction models were analysed, and their performance was shown to reduce the effect of error correction outages on A-PL positioning accuracy.

The tourist attraction of a cruise itinerary is composed of the on board experience plus the shore-based experience. Due to the positive dynamism of the cruise industry since the beginning of the twenty-first century, cruise lines are driven to innovate to create new experiences that help maintain high demand rates. From the point of view of creating new experiences on land, cruise lines move their vessels from one destination region to another to maximise the vessel's occupancy and to offer itineraries with a wider variety of shore-based attractions. These new itinerary designs lead to alterations in the seasonality patterns of the neighbouring regions. In this work, the 17 most important cruise ports located in the northeast quadrant of the Atlantic Ocean are analysed to find groups of ports with homogeneous seasonality patterns using clustering techniques. The analysis showed two different seasonality patterns. Consequently, some implications to improve the use of the ports of both clusters are included.

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 new Global Positioning System (GPS) Civil Navigation Message (CNAV) has been transmitted by Block IIR-M and Block IIF satellites since April 2014, both on the L2C and L5 signals. Compared to the Legacy Navigation Message (LNAV), the CNAV message provides six additional parameters (two orbit parameters and four Inter-Signal Correction (ISC) parameters) for prospective civil users. Using the precise products of the International Global Navigation Satellite System Service (IGS), we evaluate the precision of satellite orbit, clock and ISCs of the CNAV. Additionally, the contribution of the six new parameters to GPS Single Point Positioning (SPP) is analysed using data from 22 selected Multi-Global Navigation Satellite System Experiment (MGEX) stations from a 30-day period. The results indicate that the CNAV/LNAV Signal-In-Space Range Error (SISRE) and orbit-only SISRE from January 2016 to March 2018 is of 0·5 m and 0·3 m respectively, which is improved in comparison with the results from an earlier period. The ISC precision of L1 Coarse/Acquisition (C/A) is better than 0·1 ns, and those of L2C and L5Q5 are about 0·4 ns. Remarkably, ISC correction has little effect on the single-frequency SPP for GPS users using civil signals (for example, L1C, L2C), whereas dual-frequency SPP with the consideration of ISCs results have an accuracy improvement of 18·6%, which is comparable with positioning accuracy based on an ionosphere-free combination of the L1P (Y) and L2P (Y) signals.

Aircraft accidents are extremely rare in the aviation sector. However, their consequences can be very dramatic. One of the most important problems is runway excursions, when an aircraft exceeds the end (overrun) or the side (veer-off) of the runway. After performing exploratory analysis and hypothesis tests, a Bayesian-network-based approach was considered to provide information from risk scenarios involving landing procedures. The method was applied to a real database containing key variables related to landing operations on three runways. The objective was to analyse the effects over runway overrun excursions of failing to fulfil expert recommendations upon landing. For this purpose, the most influential variables were analysed statistically, and several scenarios were built, leading to a runway ranking based on the risk assessed.

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 switching between a damped and an undamped Inertial Navigation System (INS) is an important technical method to ensure its long-term accuracy. The stability of switching is of great importance. This paper studies the switching stability problem between a damped and an undamped INS. A model of an inertial navigation switching system is established by introducing switched control. The average dwell time method is used to analyse stability and a sufficient condition of exponential stability is given. The condition is also extended to the switched system containing constant disturbance and the sufficient condition of exponential stability. The effect of introducing switched control for the smooth operation of the system is verified and the accuracy of a long-term INS is improved effectively.

The Navigation with Indian Constellation (NavIC)/Indian Regional Navigation Satellite System (IRNSS) is an emerging satellite navigation system that provides an independent navigation system for positioning and timing services in India and up to 1,500 km from its borderline. The dual frequency NavIC system uses the L5 frequency and S-band for navigation. These navigation signals are extremely weak and susceptible to interference when they are received on Earth's surface. Moreover, the performance of these bands may be degraded by other band or out-of-band communication systems, which can become the major threat to the performance of a NavIC receiver. The main focus of this paper is to detect real-time interference of Wi-Fi signals in the S-band of the NavIC receiver. The results are prepared with respect to the Power Spectral Density (PSD), execution of acquisition stage and the detection of Wi-Fi interference with two sample hypothesis testing methods including the Kolmogorov-Smirnov (KS)-test, the t-test and the Variance (var)-test. A performance analysis of the p-value is used to measure the evidence of interference existence for hypothesis testing, decision hypothesis and probability of detection are evaluated for each hypothesis method. The results show the severity of the Wi-Fi signal as a potential source of interference for future NavIC applications.

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.

In this paper, adaptive noise estimation is used along with a previously proposed Huber-based robust algorithm for cooperative localisation of Autonomous Underwater Vehicles (AUVs). The Huber-based robust cooperative localisation algorithm named Huber-based Iterative Divided Difference Filtering (HIDDF), proposed in our previous work, effectively achieved a robust result against abnormal measurement noise, enhanced the stability of the filtering algorithm and improved the performance of cooperative localisation state estimation. However, its performance could be significantly further improved if it could estimate the system's noise statistical properties online in real time and then adaptively adjust the filtering gain matrix accordingly. In this paper, a novel adaptive noise estimation algorithm is proposed based on a covariance matching method. The proposed algorithm is suitable for adaptively estimating Gaussian and non-Gaussian measurement as well as process noise. The efficacy of the proposed algorithm has been verified through simulation results. In order to further verify the effectiveness of the proposed algorithm in practical systems, lake tests were conducted. Then, based on offline test data, the performance of the cooperative positioning algorithm under dual-pilot and single-pilot schemes was simulated. The advantages and feasibility of the algorithm are analysed and compared through performance comparison. Cooperative localisation accuracy of the previously proposed Huber-based robust algorithm has been enhanced significantly when used with the proposed adaptive noise estimation algorithm.

Operational deep-sea manned submersibles are important underwater vehicles that provide strong technical support for international deep-sea research. Navigation and positioning technologies are expected to facilitate the complete exploitation of the scientific value of samples and data collected by such submersibles, improve their underwater operation efficiency and enhance their safety. This paper first briefly describes six operational deep-sea manned submersibles that can dive to depths of more than 4,500 m. Then, the paper focuses on the navigation and positioning technologies used in these submersibles. Finally, considering the existing problems in the navigation and positioning systems of China's manned submersible Jiaolong, the paper discusses future development trends of the navigation and positioning technologies used in operational deep-sea manned submersibles.

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.