Missed detection probability is a critical metric for the integrity performance of receiver autonomous integrity monitoring (RAIM) in the presence of faults. The traditional missed detection probability evaluation method for RAIM is limited by impractical time consumption because of the absence of accurate searching interval for the magnitude of a worst-case fault. To address this issue, the searching interval for the magnitude of a worst-case fault is constructed by the combination of minimum detectable magnitude and minimum hazardous magnitude, and the searching interval adjustment is designed to avoid the absence of worst-case fault magnitude so that the maximum missed detection probability can be accurately evaluated. The simulation result indicates that the proposed method can achieve higher accuracy for the worst-case fault magnitude searching. Furthermore, the accuracy of worldwide evaluated missed detection rate can achieve an improvement of 57·66% at most by the proposed method for the different classical RAIM algorithms.

This paper introduces a tri-band stacked elliptical patch antenna featuring a right-handed circular polarized, designed to operate at the L2, L5, and L1 Global Navigation Satellite System bands. Initially, an elliptic patch is constructed and fed by a probe feed to generate TM110 and TM210 modes at resonance frequencies calculated using Mathieu functions. The probe position is precisely adjusted to excite the quasi-orthogonal mode of TM110 to generate circularly polarized (CP) waves at the L2 and L5 bands. Subsequently, an eye-shaped aperture is engraved into the elliptical patch to enhance the axial ratio (AR) beamwidth in the L2 and L5 bands and stimulate the orthogonal mode of TM210 to produce CP waves at the L1 band. Lastly, a stacked partially elliptical parasitic element is placed beneath the upper slotted elliptical patch to enhance the orthogonality of TM210 surface current versions and thus improve the AR beamwidth at the L1 band. The proposed antenna shows low reflection coefficient values at 1.12–1.33 (L2/L5), and 1.5–1.66 GHz (L1). The AR beamwidths are 133/213∘, 167/163∘, and 36/103∘ at two orthogonal cutplanes at L5, L2, and L1 bands, respectively. The antenna also has decent gains of 6–6.9 dBic across the three bands.

In this article, the cylindrical conformation of a linearly polarized cavity-backed magnetoelectric (ME) antenna is studied. Starting from a planar ME antenna presenting a wide bandwidth due to a specific design of its feeding probe, the impact of conformation is shown; the coupling between the ME dipole and the cavity walls is demonstrated to be the key element to keep a wideband behavior. Conformal antennas offering the same impedance bandwidth as the planar antenna are presented operating at Global Navigation Satellite System frequencies (1.164–1.61 GHz). As a result of the conformation, the antenna size has to be reduced to maintain the coupling and a wideband behavior. A prototype conformed to a 44-mm radius cylinder was built using low-cost additive manufacturing. External dimensions of 62 × 62 × 35 mm3 (0.285 × 0.285 × 0.16λ03, where λ0 is the wavelength at 1.38 GHz) were obtained, showing a ground plane area reduction of 46% compared to the planar antenna with the same materials. The conformal antenna also exhibits very steady radiation properties with a gain of around 4.5 dBi and a very similar and stable 3 dB beamwidth around 113° in E- and H-planes. A relatively good agreement is found between measurements and simulation.

The mass balance of glaciers requires more detailed and continuous observations to understand their seasonal change in relation to climate. Here, we designed and installed an automated real-time monitoring platform at 4645 m a.s.l. on the Baishui River Glacier No.1 to collect continuous high-resolution observational data, and analyzed the seasonal dynamic from glacier movement and surface mass balance from glacier melting and snow accumulation. The results showed that the platform moved northeastward ~12.9 m at a rate of 0.06 ± 0.02 m d−1 between September 2021 and April 2022. The surface mass balance showed a varied temporal period. July and August were the main ablation periods, while ablation decreased and ceased in September. The glacier neither melted nor accumulated much between October and December, but began to have rapid snow accumulation in January. The glacier surface temperature varied with the air temperature and showed significant inter-seasonal differences among monsoon, post-monsoon and winter seasons. The surface mass balance also exhibited a strong response to the air temperature changes, with an average decrease of 1°C the point mass balance increased by 0.11 m w.e. from monsoon to post-monsoon and 0.22 m w.e. from post-monsoon to winter. Moreover, we found snowfall caused a decrease in the glacier surface temperature by increasing the surface albedo.

Two metasurface-inspired antennas embedded in a metallic cavity are introduced here. They are expected to be integrated on fast moving platforms enduring harsh accelerations and shocks. The metasurface allows enlarging the antenna bandwidth that is intrinsically reduced for small antennas embedded in sub-wavelength metallic cavities. The first one is only 60 × 60 × 20 mm3 (0.23λ1 × 0.23λ1 × 0.08λ1 at the frequency of 1164 MHz) and presents a dual-band behavior, covering both the lower and upper global navigation satellite systems (GNSS) bands (all GNSS bands are covered). It is fed by four probes and a dedicated circuit, ensuring the phase quadrature between adjacent feeds to achieve circular polarization over these two bands. For the second proposed antenna, circular polarization is achieved using two feed points connected to the radiating aperture of size 50 × 50 × 20 mm3 (0.26λ0 × 0.26λ0 × 0.10λ0 at the frequency of 1559 MHz). It covers the E1, L1, B1, and G1 GNSS bands. The numerical results are successfully validated by measurements.

In missile test ranges, complex missions demand precise trajectory generated by radar. Both the radar and Global Navigation Satellite System (GNSS) signals are affected by atmospheric effects, degrading their accuracy and performance. The Indian Regional Navigation Satellite System/Navigation with Indian Constellation (IRNSS/NavIC) transmits signals in the S-band together with the L-band. This paper presents a novel experimental technique to improve the tracking accuracy of S-band radars using the concurrent NavIC S-band signal. The ionospheric delay using the NavIC S-band signal is calculated first, and the results are used to improve the trajectory data of simultaneously operating S-band radars. This is a unique application of the NavIC S-band signals apart from its conventional usage. During a launch mission, for low elevation angles, the ionospheric error is found to be ~130 m while at higher elevation angles the error values are found to be ~1–3 m. The concept is validated using data from a missile test mission. This report on the use of S-band GNSS signals for the correction of S-band radar range data offers a clear advantage of simplicity and accuracy.

It has been acknowledged that the Doppler is beneficial to the GNSS positioning of smartphones. However, analysis of Doppler precision on smartphones is insufficient. In this paper, we focus on the characteristic analysis of the raw Doppler measurement from Android smartphones. A comprehensive investigation of the Doppler was conducted. The results illustrate that the availability of Doppler is stable and higher than that of carrier measurements, which means that the Doppler-smoothed code (DSC) method is more effective. However, there is a constant bias between the Doppler and the code rate in Xiaomi MI8, which indicates that extra processing of the DSC method is necessary for this phone. Additionally, it is demonstrated that the relationship between the Doppler and C/N0 can be expressed as an exponential function, and the fitting parameters are provided. The numerical experiment in car-borne and hand-held scenes was conducted for evaluating the performance of the Doppler-aided positioning algorithm. For positioning, the improvement reaches 37 ⋅ 69%/37 ⋅ 14%/26 ⋅ 61% in the east, north and up components, respectively, after applying the Doppler aiding. For velocity estimation, the improvement reaches 29 ⋅ 62%/39 ⋅ 63%/29 ⋅ 37% in the three components, respectively.

This paper presents a robust train localisation system by fusing a Global Navigation Satellite System (GNSS) with an Inertial Navigation System (INS) in a tightly-coupled (TC) strategy. To improve navigation performance in GNSS partly blocked areas, an advanced map-matching (MM) measurement-augmented TC GNSS/INS method is proposed via an error-state unscented Kalman filter (UKF). The advanced MM generates a matched position using a one-step predicted position from a UKF time update step with binary search algorithm and a point–line projection algorithm. The matched position inputs as an additional measurement to fuse with the INS position to augment the degraded GNSS pseudorange measurement to optimise the state estimation in the UKF measurement update step. Both the real train test on the Qinghai–Tibet railway and the simulation were carried out and the results confirm that the proposed advanced MM measurement-augmented TC GNSS/INS with error-state UKF provides the best horizontal positioning accuracy of 0 ⋅ 67 m, which performs an improvement of about 71% and 90% with respect to TC GNSS/INS with only error-state UKF and only error-state Extended Kalman filter in GNSS partly blocked areas.

Due to the exceptional complexity of the propulsion system (sails), square-riggers form a special group of sailing vessels. In modern pleasure and sport sailing, simple Bermuda (triangular) sailing rigging prevails, which is widely discussed in the literature, both in terms of theory and numerous experiments. The literature on the theory on square-riggers is, in turn, limited mainly to the description of good sailing practice developed over the centuries. Its important element was maximising vessel speed, but this discussion has not been documented by scientific research. This paper presents the significant parameters influencing the speed of a square-rigged sailing vessel and selects those which are the most important from the point of view of its maximisation. The paper also proposes methods and measurement systems which optimise selected parameters affecting the achievement of higher speeds. The paper describes the types of speeds of typical sailing vessels, provides a historical synthesis of sailing ships with respect to their speed, and presents a selection and description of the parameters affecting the speed of modern square-rigged vessels. The paper ends with a proposed method and measurement system for experimental research aiming at rigging optimisation in a square-rigged sailing vessel from the point of view of maximising its speed.

The high-precision global navigation satellite system (GNSS) positioning technique on smartphones has been attracting increasing interest in recent years. However, the low-cost GNSS chip and linearly polarised antenna embedded inside smartphones result in data lack and quality degradation, which hinders the high-precision GNSS positioning on smartphones. In this study, a mixed single- and dual-frequency quad-constellation precise point positioning (MSDQ-PPP) model is proposed to improve the positioning performance on smartphones by taking advantage of all available GNSS observations. Static and kinematic tests were made using a Xiaomi Mi8 smartphone to fully assess the MSDQ-PPP performance with comparisons to single-frequency PPP (SF-PPP) and dual-frequency PPP (DF-PPP) models. The static test results show that the MSDQ-PPP can reach an accuracy level of 0⋅39 m and 0⋅50 m in the horizontal and vertical directions with a convergence time of less than 10 min in most sessions. The MSDQ-PPP improves the positioning accuracy by 53% and 31% over the DF-PPP in the horizontal and vertical directions, respectively. In contrast to the SF-PPP, the positioning accuracy and convergence time improvement can reach 62% and 90% in the horizontal direction, respectively. In the kinematic test, the MSDQ-PPP achieves an accuracy of 0⋅7 m and 1⋅5 m in the horizontal and vertical directions, respectively. The accuracy improvement rates reach 78% and 76% over the DF-PPP, and 13% and 38% over the SF-PPP, respectively. Both static and kinematic MSDQ-PPP tests indicate significantly enhanced positioning performance.

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.

In urban areas, the Global Navigation Satellite System (GNSS) can lead to position errors of tens of meters due to signal obstruction and severe multipath effects. In cases of 3D-positioning, the vertical coordinate is estimated less accurately than are the horizontal coordinates. Multisensor systems can enhance navigation performance in terms of accuracy, availability, continuity and integrity. However, the addition of multiple sensors increases the system cost, and thereby the applicability to low-cost applications is limited. By using the concept of receiver clock modelling (RCM), the position estimation can be made more robust; the use of high-sensitivity (HS) GNSS receivers can improve the system availability and continuity. This paper investigates the integration of a low-cost HS GNSS receiver with an external clock in urban conditions; subsequently, the gain in the navigation performance is evaluated. GNSS kinematic data is recorded in an urban environment with multiple geodetic-grade and HS receivers. The external clock stability information is incorporated through the process noise matrix in a Kalman filter when estimating the position, velocity and time states. Results shows that the improvement in the precision of the height component and vertical velocity with both receivers is about 70% with RCM compared with the estimates obtained without applying RCM. Pertaining accuracy, the improvement in height with RCM is found to be about 70% and 50% with geodetic and HS receivers, respectively. In terms of availability, the HS receiver delivers an 100% output compared with a geodetic receiver, which provides an output 99⋅4% of the total experiment duration.

This paper presents a formulation of snapshot positioning as a mixed-integer least-squares problem. In snapshot positioning, one estimates a position from code-phase (and possibly Doppler-shift) observations of global navigation satellite system (GNSS) signals without knowing the time of departure (timestamp) of the codes. Solving the problem allows a receiver to determine a fix from short radio-frequency snapshots missing the timestamp information embedded in the GNSS data stream. This is used to reduce the time to first fix in some receivers, and it is used in certain wildlife trackers. This paper presents two new formulations of the problem and an algorithm that solves the resulting mixed-integer least-squares problems. We also show that the new formulations can produce fixes even with huge initial errors, much larger than permitted in Van Diggelen's widely-cited coarse-time navigation method.

The region of Ridge B in central East Antarctica is one of the last unexplored parts of the continent and, at the same time, ranks among the most promising places to search for Earth's oldest ice. In January 2020, we carried out the first scientific traverse from Russia's Vostok Station to the topographical dome of Ridge B (Dome B, 3807 m above sea level, 79.02°S, 93.69°E). The glaciological programme included continuous snow-radar profiling and geodetic positioning along the traverse's route, installation of snow stakes, measurements of snow density, collection of samples for stable water isotope and chemical analyses and drilling of a 20 m firn core. The first results of the traverse show that the surface mass balance at Dome B (2.28 g cm−2 year−1) is among the lowest in Antarctica. The firn temperature below the layer of annual variations is −58.1 ± 0.2°C. A very low value of heavy water stable isotope content (-58.2‰ for oxygen-18) was discovered at a distance of 170 km from Vostok Station. This work is the first step towards a comprehensive reconnaissance study of the Ridge B area aimed at locating the best site for future deep drilling for the oldest Antarctic ice.

Array antenna beam forming has high potential to improve the performance of the global navigation satellite system (GNSS) in urban areas. However, the widespread application of array antennas for GNSS multipath mitigation is restricted by many factors, such as the complexity of the system, the computation load and conflicts between required performance, cost budget and limited room for the antenna placement. The scope of this work is triplicate. (1) The pre-correlation beam forming structure is first suggested for multipath mitigation to decrease the system complexity. (2) With the pre-correlation structure, the equivalence of adaptive beam forming to quiescent beam forming is revealed. Therefore, the computational load for beam forming is greatly decreased. (3) A theoretical model is established to link the benefits of beam forming with GNSS performance improvement in terms of pseudorange quality. The model can be used by industry to balance the aforementioned restrictions. Numerical results with different array settings are given, and a 2 × 2 rectangle array with $0.4\lambda $ element spacing is suggested as a cost-effective choice in GNSS positioning applications in urban canyon areas.

In recent years, global navigation satellite system (GNSS) precise point positioning (PPP) has become a standard positioning technique for many applications with typically favourable open sky conditions, e.g. precision agriculture. Unfortunately, the long convergence (and reconvergence) time of PPP often significantly limits its use in difficult and restricted signal environments typically associated with urban areas. The modernisation of GNSS will positively affect and improve the convergence time of the PPP solutions, thanks to the higher number of satellites in view that broadcast multifrequency measurements. The number and geometry of the available satellites is a key factor that impacts on the convergence time in PPP, while triple-frequency observables have been shown to greatly benefit the fixing of the carrier phase integer ambiguities. On the other hand, many studies have shown that triple-frequency combinations do not usefully contribute to a reduction of the convergence time of float PPP solutions.

This paper proposes novel GPS and Galileo triple-carrier ionosphere-free combinations that aim to enhance the observability of the narrow-lane ambiguities. Tests based on simulated data have shown that these combinations can reduce the convergence time of the float PPP solution by a factor of up to 2·38 with respect to the two-frequency combinations. This approach becomes effective only after the extra wide-lane and wide-lane ambiguities have been fixed. For this reason, a new fixing method based on low-noise pseudo-range combinations corrected by the smoothed ionosphere correction is presented. By exploiting this algorithm, no more than a few minutes are required to fix the WL ambiguities for Galileo, even in cases of severe multipath environments.

The tight combination model improves the positioning accuracy of the Global Navigation Satellite System (GNSS) in complex environments by increasing the redundancy of observation. However, the ambiguity cannot be calculated directly because of the correlation between it and the phase difference inter-system bias (DISB) in the model. This paper proposes a method of DISB estimation based on the principle of maximum ratio. From the data analysis, for the standard deviation of code DISB, the improvement of the method can up to 0·179 m with the poor quality data. In addition, compared to the parameter combination method, the standard deviation of all the phase DISB was deceased with the method in the paper. About the phase DISB of GPS L1/Galileo E1, the standard deviation decreased from 0·014/0·022/0·009/0·051 cycles to 0·006/0·015/0·004/0·029 cycles of four baselines, which represents the improvement of 57·14/31·82/55·56/43·14%. About the phase DISB of GPS L1/BDS B1, the standard deviation decreased from 0·014/0·061/0·010/0·052 cycles to 0·002/0·005/0·009/0·004 cycles of four baselines, which represents the improvement of 85·71/91·80/10·00/92·31%.

In recent years the availability of geolocation data has increased considerably and can be found in various portable devices such as smartphones. These devices are intended for navigation in general, but can be used to carry out topographical surveys that do not require high accuracy of the surveyed data. To verify the applicability and accuracy of these devices we conducted the topographic survey in an area of approximately 5 ha using a GPS with RTK technology as reference, a Commercial Navigation Receiver (RNC) and a popular brand smartphone with the mobile applications C7 GPS Data and GPS Essentials previously installed. The GPS RNC showed the best planimetric results and the Smartphone with C7 GPS Data obtained the best result altimetric. None of the receivers analyzed showed high accuracy in results obtained. However, they can be used for tasks where high precision is not required.

Global satellite navigation systems (GNSS) are nowadays used in many applications. GNSS receivers experience limitations in receiving weak signals in a degraded environment. Hence, tracking weak GNSS signals is a topic of interest to researchers in this field. Different methods have been proposed to address this issue, each of which has advantages and disadvantages. In this paper, a method based on the vector tracking method is proposed for weak signal tracking. This method has been developed based on a strong Kalman filter instead of the extended Kalman filter used in conventional vector tracking methods. In order to adjust important parameters of this filter, the fuzzy method is used. The results of tests performed with both simulated data and real data demonstrate that the proposed method performs better than previous ones in weak signal tracking.

To reduce the operational complexity of the multipath estimating delay lock loop (MEDLL) and improve its anti-multipath performance for strobe correlators, a combination anti-multipath scheme, namely, the MEDLL on-strobe correlation technique, is proposed for global navigation satellite system (GNSS) signal processing. Short-delay multipath rays are separated from the strobe correlation function by the MEDLL mechanism; the dot product between the estimation residue and the standard correlation function or the BOC-PRN correlation function is then computed to eliminate the potential tracking ambiguity. Finally, this non-coherent combination result is sent to the loop filter to obtain anti-multipath code tracking. The proposed method is analysed via simulator data with a software receiver under different front-end bandwidth conditions. The results corroborate the better multipath mitigation capability and lower computational burden, although it is still difficult to eliminate all multipath interference, especially when the front-end bandwidth is insufficient.