The Bombyx mori G protein ß subunit 1 (BmGNß1) gene inhibits BmNPV infection.

G protein ß subunit 1 (GNß1) has several functions, including cell growth regulation, the control of second messenger levels, and ion channel switching. Previous transcriptome analyses in our laboratory have shown that BmGNß1 transcription is reduced following infection with Bombyx mori nucleopolyhedrovirus (BmNPV), but it is unknown what role this gene may have in the host response to BmNPV infection. In this study, the BmGNß1 gene was cloned using the RACE method. After BmNPV infection, BmGNß1 was downregulated in Baiyu strains in tissues such as the hemolymph and midgut. Indirect immunofluorescence showed that BmGNß1 was localized to the cytoplasm. We further constructed a BmGNß1-pIZ/V5-His-mCherry overexpression plasmid and designed siRNA to evaluate the role of BmGNß1 in host response to infection. The results showed that BmGNß1 overexpression inhibited BmNPV proliferation, while knockdown of BmGNß1 was correlated with increased BmNPV proliferation. The siRNA-mediated reduction of BmGNß1 was correlated with an increase in BmNPV infection of BmN cells, increased BmNPV vp39 transcription, and reduced survival time of BmNPV-infected B. mori. Overexpression of BmGNß1 in BmN cells was also correlated with apoptosis and a modification in transcript levels of genes involved in host response to BmNPV infection (PI3K, AKT, Bmp53, BmFOXO, Caspase-1, Bmp21, BmPKN and BmCREB), suggesting that BmGNß1 may influence the apoptotic host response of infected B. mori through the PI3K-AKT pathway. This study provides potential targets and theoretical support for breeding BmNPV-resistant silkworm varieties.

Performance and micro-pacing in sprint cross-country skiing: A comparison of individual time-trial and head-to-head race formats.

This study compared performance strategies and sub-technique selection in cross-country skate skiing sprint races, specifically individual time-trial (ITT) and head-to-head (H2H) formats. Fourteen male cross-country skiers from the Chinese national team participated in the FIS-sanctioned sprint race day. GNSS and heart rate sensors recorded positioning, skiing speeds, heart rate, sub-technique usage, and skiing kinematics. Statistical parametric mapping (SPM) was used to determine the course positions (clusters) where instantaneous skiing speed was significantly associated with section time. One-way analyses of variance were used to examine differences between the ITT and H2H. H2H race speeds were 2.4 ± 0.2% faster than the ITT race (p < 0.05).Variations in sub-technique and skiing kinematics were observed between race formats, indicating different strategies and tactics employed by athletes. SPM identified specific clusters (primarily uphill) where the fastest athlete gained significant time over the slowest. The greatest time gains were associated with higher G3 sub-technique usage and longer G3 cycle length on steep uphill terrain (9-13% gradients). Integrating SPM analyses and sub-technique assessments can help optimise performance and tactics in sprint races. This study enhances our understanding of cross-country skiing dynamics and performance variations among elite competitors.

An Experimental Performance Assessment of Galileo OSNMA.

We present Galileo Open Service Navigation Message Authentication (OSNMA) observed operational information and key performance indicators (KPIs) from the analysis of a ten-day-long dataset collected in static open-sky conditions in southern Finland and using our in-house-developed OSNMA implementation. In particular, we present a timeline with authentication-related events, such as authentication status and type, dropped navigation pages, and failed cyclic redundancy checks. We also report other KPIs, such as the number of simultaneously authenticated satellites over time, time to first authenticated fix, and percentage of authenticated fixes, and we evaluate the accuracy of the authenticated position solution. We also study how satellite visibility affects these figures. Finally, we analyze situations where it was not possible to reach an authenticated fix, and offer our findings on the observed patterns.

A Study of Outliers in GNSS Clock Products.

Time is an extremely important element in the field of GNSS positioning. In precise positioning with a single-centimetre accuracy, satellite clock corrections are used. In this article, the longest available data set of satellite clock corrections of four GNSS systems from 2014 to 2021 was analysed. This study covers the determination of the quality (outliers number and magnitude), availability, stability, and determination of the specificity and nature of the clock correction for each satellite system. One problem with the two newest satellite systems (Galileo and BeiDou) is the lack of availability of satellite signals in the early years of the analysis. These data were available only in the later years of the period covered by the analysis, as most of the satellites have only been in orbit since 2018-2019. Interestingly, the percentage of outlying observations was highest in Galileo and lowest in BeiDou. Phase and frequency plots showed a significant number of outlying observations. On the other hand, after eliminating outlying observations, each system showed a characteristic graph waveform. The most consistent and stable satellite clock corrections are provided by the GPS and GLONASS systems. The main problems discussed in this paper are the determination of the number and magnitude of outliers in clock products of four GNSS systems (GPS, GLONASS, Galileo, Beidou) and the study on the long-term stability of GNSS clocks analysis, which covers the years 2014-2021.

Implementation of a High-Sensitivity Global Navigation Satellite System Receiver on a System-on-Chip Field-Programmable Gate Array Platform.

This paper presents the design, proof-of-concept implementation, and preliminary performance assessment of an affordable real-time High-Sensitivity (HS) Global Navigation Satellite System (GNSS) receiver. Specifically tailored to capture and track weak Galileo E1b/c signals, this receiver aims to support research endeavors focused on advancing GNSS signal processing algorithms, particularly in scenarios characterized by pronounced signal attenuation. Leveraging System-on-Chip Field-Programmable Gate Array (SoC-FPGA) technology, this design merges the adaptability of Software Defined Radio (SDR) concepts with the the robust hardware processing capabilities of FPGAs. This innovative approach enhances power efficiency compared to conventional designs relying on general-purpose processors, thereby facilitating the development of embedded software-defined receivers. Within this architecture, we implemented a modular GNSS baseband processing engine, offering a versatile platform for the integration of novel algorithms. The proposed receiver undergoes testing with live signals, showcasing its capability to process GNSS signals even in challenging scenarios with a carrier-to-noise density ratio (C/N0) as low as 20 dB-Hz, while delivering navigation solutions. This work contributes to the advancement of low-cost, high-sensitivity GNSS receivers, providing a valuable tool for researchers engaged in the development, testing, and validation of experimental GNSS signal processing techniques.

Sea Surface Height Measurements Based on Multi-Antenna GNSS Buoys.

Sea level monitoring is an essential foundational project for studying global climate change and the rise in sea levels. Satellite radar altimeters, which can sometimes provide inaccurate sea surface height data near the coast, are affected by both the instrument itself and geophysical factors. Buoys equipped with GNSS receivers offer a relatively flexible deployment at sea, allowing for long-term, high-precision measurements of sea surface heights. When operating at sea, GNSS buoys undergo complex movements with multiple degrees of freedom. Attitude measurements are a crucial source of information for understanding the motion state of the buoy at sea, which is related to the buoy's stability and reliability during its development. In this study, we designed and deployed a four-antenna GNSS buoy with both position and attitude measurement capabilities near Jimiya Wharf in Qingdao, China, to conduct offshore sea surface monitoring activities. The GNSS data were processed using the Precise Point Positioning (PPK) method to obtain a time series of sea surface heights, and the accuracy was evaluated using synchronous observation data from a small sea surface height radar. The difference between the GNSS buoy and the full-time radar was calculated, resulting in a root-mean-square error (RMSE) of 1.15 cm. Concurrently, the attitude of the GNSS buoy was calculated using multi-antenna technology, and the vertical elevation of the GNSS buoy antenna was corrected using the obtained attitude data. The RMSE between the corrected GNSS buoy data and the high ground radar was 1.12 cm, indicating that the four-antenna GNSS buoy can not only acquire high-precision coastal sea level data but also achieve synchronous measurement of the buoy's attitude. Furthermore, the data accuracy was also improved after the sea level attitude correction.

A Novel Machine Learning-Based ANFIS Calibrated RISS/GNSS Integration for Improved Navigation in Urban Environments.

Autonomous vehicles (AVs) require accurate navigation, but the reliability of Global Navigation Satellite Systems (GNSS) can be degraded by signal blockage and multipath interference in urban areas. Therefore, a navigation system that integrates a calibrated Reduced Inertial Sensors System (RISS) with GNSS is proposed. The system employs a machine-learning-based Adaptive Neuro-Fuzzy Inference System (ANFIS) as a novel calibration technique to improve the accuracy and reliability of the RISS. The ANFIS-based RISS/GNSS integration provides a more precise navigation solution in such environments. The effectiveness of the proposed integration scheme was validated by conducting tests using real road trajectory and simulated GNSS outages ranging from 50 to 150 s. The results demonstrate a significant improvement in 2D position Root Mean Square Error (RMSE) of 43.8% and 28% compared to the traditional RISS/GNSS and the frequency modulated continuous wave (FMCW) Radar (Rad)/RISS/GNSS integrated navigation systems, respectively. Moreover, an improvement of 47.5% and 23.4% in 2D position maximum errors is achieved compared to the RISS/GNSS and the Rad/RISS/GNSS integrated navigation systems, respectively. These results reveal significant improvements in positioning accuracy, which is essential for safe and efficient navigation. The long-term stability of the proposed system makes it suitable for various navigation applications, particularly those requiring continuous and precise positioning information. The ANFIS-based approach used in the proposed system is extendable to other low-end IMUs, making it an attractive option for a wide range of applications.

GNSS Receiver Fingerprinting Based on Time Skew of Embedded CSAC Clock.

GNSS spoofing has become a significant security vulnerability threatening remote sensing systems. Hardware fingerprint-based GNSS receiver identification is one of the solutions to address this security issue. However, existing research has not provided a solution for distinguishing GNSS receivers of the same specification. This paper first theoretically proves that the CSACs (Chip-Scale Atomic Clocks) used in GNSS receivers have unique hardware noise and then proposes a fingerprinting scheme based on this hardware noise. Experiments based on the neural network method demonstrate that this fingerprint achieved an identification accuracy of 94.60% for commercial GNSS receivers of the same specification and performed excellently in anomaly detection, confirming the robustness of the fingerprinting method. This method shows a new real-time GNSS security monitoring method based on CSACs and can be easily used with any commercial GNSS receivers.

Spatial-Temporal Dynamic Evolution of Land Deformation Driven by Hydrological Signals around Chaohu Lake.

The frequent occurrence of extreme climate events has a significant impact on people's lives. Heavy rainfall can lead to an increase of regional Terrestrial Water Storage (TWS), which will cause land subsidence due to the influence of hydrological load. At present, regional TWS is mostly obtained from Gravity Recovery and Climate Experiment (GRACE) data, but the method has limitations for small areas. This paper used water level and flow data as hydrological signals to study the land subsidence caused by heavy rainfall in the Chaohu Lake area of East China (June 2016-August 2016). Pearson's correlation coefficient was used to study the interconnection between water resource changes and Global Navigation Satellites System (GNSS) vertical displacement. Meanwhile, to address the reliability of the research results, combined with the Coefficient of determination method, the research findings were validated by using different institutional models. The results showed that: (1) During heavy rainfall, the vertical displacement caused by atmospheric load was larger than non-tidal oceanic load, and the influence trends of the two were opposite. (2) The rapidly increasing hydrologic load in the Chaohu Lake area resulted in greater subsidence displacement at the closer CORS station (CHCH station) than the more distant CORS station (LALA station). The Pearson correlation coefficients between the vertical displacement and water level were as high as -0.80 and -0.64, respectively. The phenomenon confirmed the elastic deformation principle of disc load. (3) Although there was a systematic bias between the different environmental load deformation models, the deformation trends were generally consistent with the GNSS monitoring results. The average Coefficients of determination between the different models and the GNSS results were 0.63 and 0.77, respectively. The results demonstrated the effectiveness of GNSS in monitoring short-term hydrological load. This study reveals the spatial-temporal evolution of land deformation during heavy rainfall around Chaohu Lake, which is of reference significance for water resource management and infrastructure maintenance in this area.

Research on Robust Adaptive RTK Positioning of Low-Cost Smart Terminals.

The performance of low-cost smart terminals is limited by the performance of their low-cost Global Navigation Satellite System (GNSS) hardware and chips, as well as by the impact of complex urban environments, which affect the positioning accuracy and stability of GNSS services. To this end, this paper proposes a robust adaptive Kalman filter for different environments that can be applied after data preprocessing. Based on the Kalman filter algorithm, a robust estimation approach is introduced into real-time kinematic (RTK) positioning to make judgments on the abnormal observation values of low-cost smart terminals, which amplifies the variance and covariance of the outlier observation equation, and reduces the impact of outliers on positioning performance. The Institute of Geodesy and Geophysics III (IGG III) function is used for regulation purposes, where prior information is modified and refreshed using the equivalent weight matrix and adaptive factors, thus reducing the impact of system model errors on system state estimation results. In addition, a robust factor is defined to adjust positioning deviation weighting between the pre- and post-test robust estimates. The experimental results show that after robust RTK positioning in the static experiments, the overall improvement in positioning accuracies of the Xiaomi 8, Huawei P40, Huawei mate40, and low-cost M8 receiver reached 29.6%, 31.3%, 32.1%, and 30.7%, respectively. Similarly, after applying the proposed robust method in the dynamic experiments, the overall positioning accuracies of the Xiaomi 8, Huawei P40, Huawei mate40, and the low-cost M8 receiver improved by 28.3%, 32.9%, 35.4%, and 26.2%, respectively. The experimental results reveal that an excellent positioning effect of a smartphone is positively correlated with robust RTK positioning performance. However, it is worth noting that when the positioning accuracy reaches a high level, such as the positioning results achieved using low-cost receivers, the robustness performance shows a relatively decreasing trend. This finding suggests that under the condition of high positioning accuracy, the sensitivity of specific positioning equipment to interference sources may increase, resulting in a decline in the effect of robust RTK positioning.

Flying Target Detection Technology Based on GNSS Multipath Signals.

In this study, a passive radar system that detects flying targets is developed in order to solve the problems associated with traditional flying target detection systems (i.e., their large size, high power consumption, complex systems, and poor battlefield survivability). On the basis of target detection, the system uses the multipath signal (which is usually eliminated as an error term in navigation and positioning), enhances it by supporting information, and utilizes the multi-source characteristics of ordinary omnidirectional global navigation satellite system (GNSS) signals. The results of a validation experiment showed that the system is able to locate a passenger airplane and obtain its flight trajectory using only one GNSS receiving antenna. The system is characterized by its light weight (less than 5 kg), low power consumption, simple system, good portability, low cost, and 24/7 and all-weather work. It can be installed in large quantities and has good prospects for development.

A Study on Graph Optimization Method for GNSS/IMU Integrated Navigation System Based on Virtual Constraints.

In GNSS/IMU integrated navigation systems, factors like satellite occlusion and non-line-of-sight can degrade satellite positioning accuracy, thereby impacting overall navigation system results. To tackle this challenge and leverage historical pseudorange information effectively, this paper proposes a graph optimization-based GNSS/IMU model with virtual constraints. These virtual constraints in the graph model are derived from the satellite's position from the previous time step, the rate of change of pseudoranges, and ephemeris data. This virtual constraint serves as an alternative solution for individual satellites in cases of signal anomalies, thereby ensuring the integrity and continuity of the graph optimization model. Additionally, this paper conducts an analysis of the graph optimization model based on these virtual constraints, comparing it with traditional graph models of GNSS/IMU and SLAM. The marginalization of the graph model involving virtual constraints is analyzed next. The experiment was conducted on a set of real-world data, and the results of the proposed method were compared with tightly coupled Kalman filtering and the original graph optimization method. In instantaneous performance testing, the method maintains an RMSE error within 5% compared with real pseudorange measurement, while in a continuous performance testing scenario with no available GNSS signal, the method shows approximately a 30% improvement in horizontal RMSE accuracy over the traditional graph optimization method during a 10-second period. This demonstrates the method's potential for practical applications.

Validity of Current Smartwatches for Triathlon Training: How Accurate Are Heart Rate, Distance, and Swimming Readings?

Smartwatches are one of the most relevant fitness trends of the past two decades, and they collect increasing amounts of health and movement data. The accuracy of these data may be questionable and requires further investigation. Therefore, the aim of the present study is to validate smartwatches for use in triathlon training. Ten different smartwatches were tested for accuracy in measuring heart rates, distances (via global navigation satellite systems, GNSSs), swim stroke rates and the number of swim laps in a 50 m Olympic-size pool. The optical heart rate measurement function of each smartwatch was compared to that of a chest strap. Thirty participants (15 females, 15 males) ran five 3 min intervals on a motorised treadmill to evaluate the accuracy of the heart rate measurements. Moreover, for each smartwatch, running and cycling distance tracking was tested over six runs of 4000 m on a 400 m tartan stadium track, six hilly outdoor runs over 3.4 km, and four repetitions of a 36.8 km road bike course, respectively. Three swimming protocols ranging from 200 m to 400 m were performed in triplicate in a 50 m Olympic-size pool, evaluating the tracked distance and the detected number of strokes. The mean absolute percentage errors (MAPEs) for the average heart rate measurements varied between 3.1% and 8.3%, with the coefficient of determination ranging from 0.22 to 0.79. MAPE results ranged from 0.8% to 12.1% for the 4000 m run on the 400 m track, from 0.2% to 7.5% for the 3.4 km outdoor run, and from 0.0% to 4.2% for the 36.8 km bike ride. For the swimming tests, in contrast, the deviations from the true distance varied greatly, starting at a 0.0% MAPE for the 400 m freestyle and reaching 91.7% for the 200 m medley with style changes every 25 m. In summary, for some of the smartwatches, the measurement results deviated substantially from the true values. Measurements taken while road cycling over longer distances with only a few curves were in relative terms more accurate than those taken during outdoor runs and even more accurate than those taken on the 400 m track. In the swimming exercises, the accuracy of the measured distances was severely deteriorated by the medley changes among the majority of the smartwatches. Altogether, the results of this study should help in assessing the accuracy and thus the suitability of smartwatches for general triathlon training.

Distributed Resources Allocation Method for Space-Ground Integrated Mobile Communication System.

This paper presents an innovative approach towards space-ground integrated communication systems by combining terrestrial cellular networks, UAV networks, and satellite networks, leveraging advanced slicing technology. The proposed architecture addresses the challenges posed by future user surges and aims to reduce network overhead effectively. Central to our approach is the introduction of a marginal mobile station (MS)-assisted network resource allocation decision architecture. Building upon this foundation, we introduce the DP-DQN model, an enhanced decision-making algorithm tailored for MSs in dynamic network environments. Furthermore, this study introduces a feedback mechanism to ensure the accuracy and adaptability of the marginalization model over time. Through extensive simulations and experimental validations, our DP-DQN-based edge decision method demonstrates substantial potential in alleviating core network overhead while improving success access ratios compared to conventional methods.

An Enhanced FGI-GSRx Software-Defined Receiver for the Execution of Long Datasets.

The Global Navigation Satellite System (GNSS) software-defined receivers offer greater flexibility, cost-effectiveness, customization, and integration capabilities compared to traditional hardware-based receivers, making them essential for a wide range of applications. The continuous evolution of GNSS research and the availability of new features require these software-defined receivers to upgrade continuously to facilitate the latest requirements. The Finnish Geospatial Research Institute (FGI) has been supporting the GNSS research community with its open-source implementations, such as a MATLAB-based GNSS software-defined receiver `FGI-GSRx' and a Python-based implementation `FGI-OSNMA' for utilizing Galileo's Open Service Navigation Message Authentication (OSNMA). In this context, longer datasets are crucial for GNSS software-defined receivers to support adaptation, optimization, and facilitate testing to investigate and develop future-proof receiver capabilities. In this paper, we present an updated version of FGI-GSRx, namely, FGI-GSRx-v2.0.0, which is also available as an open-source resource for the research community. FGI-GSRx-v2.0.0 offers improved performance as compared to its previous version, especially for the execution of long datasets. This is carried out by optimizing the receiver's functionality and offering a newly added parallel processing feature to ensure faster capabilities to process the raw GNSS data. This paper also presents an analysis of some key design aspects of previous and current versions of FGI-GSRx for a better insight into the receiver's functionalities. The results show that FGI-GSRx-v2.0.0 offers about a 40% run time execution improvement over FGI-GSRx-v1.0.0 in the case of the sequential processing mode and about a 59% improvement in the case of the parallel processing mode, with 17 GNSS satellites from GPS and Galileo. In addition, an attempt is made to execute v2.0.0 with MATLAB's own parallel computing toolbox. A detailed performance comparison reveals an improvement of about 43% in execution time over the v2.0.0 parallel processing mode for the same GNSS scenario.

Assessment of Noise of MEMS IMU Sensors of Different Grades for GNSS/IMU Navigation.

Inertial measurement units (IMUs) are key components of various applications including navigation, robotics, aerospace, and automotive systems. IMU sensor characteristics have a significant impact on the accuracy and reliability of these applications. In particular, noise characteristics and bias stability are critical for proper filter settings to perform a combined GNSS/IMU solution. This paper presents an analysis based on the Allan deviation of different IMU sensors that correspond to different grades of micro-electromechanical systems (MEMS)-type IMUs in order to evaluate their accuracy and stability over time. The study covers three IMU sensors of different grades (ascending order): Rokubun Argonaut navigator sensor (InvenSense TDK MPU9250), Samsung Galaxy Note10 phone sensor (STMicroelectronics LSM6DSR), and NovAtel PwrPak7 sensor (Epson EG320N). The noise components of the sensors are computed using overlapped Allan deviation analysis on data collected over the course of a week in a static position. The focus of the analysis is to characterize the random walk noise and bias stability, which are the most critical for combined GNSS/IMU navigation and may differ or may not be listed in manufacturers' specifications. Noise characteristics are calculated for the studied sensors and examples of their use in loosely coupled GNSS/IMU processing are assessed. This work proposes a structured and reproducible approach for working with sensors for their use in navigation tasks in combination with GNSS, and can be used for sensors of different levels to supplement missing or incorrect sensor manufacturers' data.

Monitoring Surface Deformations in a Fossil Landslide Zone and Identifying Potential Failure Mechanisms: A Case Study of Gümüshane State Hospital.

The escalating occurrence of landslides has drawn increasing attention from the scientific community, primarily driven by a combination of natural phenomena such as unpredictable seismic events, intensified precipitation, and rapid snowmelt attributable to climate fluctuations, compounded by inadequacies in engineering practices during site selection. Within the scope of this investigation, contemporary geodetic techniques using the GNSS were employed to monitor structural and surface deformations in and around a hospital edifice situated within an ancient fossil landslide region. Additionally, inclinometer measurements facilitated the determination of slip circle parameters. A subsequent analysis integrated these datasets to scrutinize both the hospital structure and its surrounding slopes. In addition to the finite element method, four different limit equilibrium methods (Bishop, GLE-Morgenstern-Price, Spencer, and Janbu) were used in the evaluation of stability. Since the safety number determined in all analyses was <1, it was determined that the slope containing the hospital building was unstable. The movement has occurred again due to the additional load created by the hospital building built on the currently stable slope, the effect of surface and groundwater, and the improperly designed road route. As a result of geodetic monitoring, it was determined that the sliding speed on the surface was in the N-E direction and was approximately 3 cm, and this situation almost coincided with inclinometer measurements.

GNSS Spoofing Detection via the Intersection Angle between Two Directions of Arrival in a Single Rotating Antenna.

Spoofing against the Global Navigation Satellite System (GNSS) is an attack with strong concealment, posing a significant threat to the security of the GNSS. Many strategies have been developed to prevent such attacks, but current detection methods based on signal direction for multi-agent spoofing require multiple antennas/receivers, leading to increased cost and complexity in implementation. Additionally, methods utilizing a moving single antenna cannot effectively detect multi-agent spoofing. Therefore, we introduce a novel spoofing-detection technique based on the intersection angle between two directions of arrival (IA-DOA) using a single rotating antenna. The essence of this approach lies in estimating the IA-DOA between a pair of signals by utilizing the carrier-to-noise ratio (CNR) and carrier phase single difference (CPSD) of the received signal. The estimation of IA-DOA should be consistent with the prediction when there is no spoofing. With spoofing, it is difficult to accurately simulate the directionality of navigation signals, which can disrupt the consistency between the estimation and prediction of IA-DOA. Therefore, estimations and predictions of IA-DOA can be used to establish detection variables through generalized likelihood ratio testing (GLRT) to detect multi-agent spoofing. We conducted a simulation to analyze the impact of the antenna's parameters on the detection performance and evaluated it through on-site experiments. The results indicate that the method proposed in this article can efficiently achieve real-time detection of multi-agent spoofing.

Determining the Antenna Phase Center for the High-Precision Positioning of Smartphones.

In recent years, smartphones have emerged as the primary terminal for navigation and location services among mass users, owing to their universality, portability, and affordability. However, the highly integrated antenna design within smartphones inevitably introduces interference from internal signal sources, leading to a misalignment between the antenna phase center (APC) and the antenna geometric center. Accurately determining a smartphone's APC can mitigate system errors and enhance positioning accuracy, thereby meeting the increasing demand for precise and reliable user positioning. This paper delves into a detailed analysis of the generation of Global Navigation Satellite System (GNSS) receiver antenna phase center errors and proposes a method for correcting the receiver antenna phase center. Subsequently, a smartphone positioning experiment was conducted by placing the smartphone on an observation column with known coordinates. The collected observations were processed in static relative positioning mode, referencing observations from geodetic-grade equipment, and the accuracy of the static relative positioning fixed solution was evaluated. Following weighted estimation, we determined the antenna phase center of the Xiaomi Mi8 and corrected the APC. A comparison of the positioning results of the Xiaomi Mi8 before and after APC correction revealed minimal impact on the standard deviations (STDs) but significant influence on the root mean square errors (RMSEs). Specifically, the RMSEs in the E/N/U direction were reduced by 59.6%, 58.5%, and 42.0%, respectively, after APC correction compared to before correction. Furthermore, the integer ambiguity fixing rate slightly improved after the APC correction. In conclusion, the determination of a smartphone's APC can effectively reduce system errors in the plane direction of GNSS positioning, thereby enhancing smartphone positioning accuracy. This research holds significant value for advancing high-precision positioning studies related to smartphones.

A Two-Step Regional Ionospheric Modeling Approach for PPP-RTK.

In the precise point positioning/real-time kinematic (PPP-RTK) technique, high-precision ionospheric delay correction information is an important prerequisite for rapid PPP convergence. The commonly used ionospheric modeling approaches in the PPP-RTKs only take the trend term of the ionospheric total electron content (TEC) variations into account. As a result, the residual ionospheric delay still affects the positioning solutions. In this study, we propose a two-step regional ionospheric modeling approach that involves combining a polynomial fitting model (PFM) and a Kriging interpolation (KI) model. In the first step, a polynomial fitting method is used to model the trend term of the ionospheric TEC variations. In the second step, a KI method is used to compensate for the residual term of the ionospheric TEC variations. Datasets collected from continuously operating reference stations (CORSs) in Hunan Province, China, are used to validate the PFM/KI method by comparing with a single PFM method and a combined PFM and inverse distance weighting interpolation (IDWI) method. The experimental results show that the two-step PFM/KI modeled ionospheric delay achieves an average root mean square (RMS) error of 1.8 cm, which is improved by about 48% and 23% when compared with the PFM and PFM/IDWI methods, respectively. Regarding the positioning performance, the PPP-RTK with the PFM/KI method takes an average of 1.8 min or 4.0 min to converge to a positioning accuracy of 1.3 cm or 2.5 cm in the horizontal and vertical directions, respectively. The convergence times are decreased by about 18% and 14% in the horizontal direction and 9% and 5% in the vertical direction over the PFM and the PFM/IDWI methods, respectively.