GPS Solutions

Abstract

Integrated Water Vapor (IWV) is crucial in environmental research, offering insights into atmospheric dynamics. Direct IWV measurement is challenging, necessitating alternative estimation technologies. Existing methods including Global Navigation Satellite System (GNSS), radiosondes, water vapor radiometers (WVR), satellite remote sensing, and numerical weather models (NWM), have specific limitations. GNSS and WVR provide high precision and temporal resolution (e.g., 5 min) but are limited to specific locations. Radiosondes, while accurate, have sparse spatial distribution and low temporal resolution (e.g., twice daily). Satellite remote sensing offers broad spatial resolution but lower temporal resolution (hours to days) and reduced accuracy under cloudy conditions and due to satellite tracks. NWMs provide global hourly products but their accuracy depends on meteorological data and model precision.

This study introduces a regional IWV predictive model using Machine Learning to address these challenges. Utilizing IWV data from GNSS stations, the study develops a predictive model based on least squares support vector machine, which autonomously determines optimal parameters to enhance performance. The model enables accurate IWV estimation at any location within a region, using inputs such as latitude, longitude, altitude, and temperature, achieving an average root mean square error of 0.95 mm. The model’s performance varies across seasons and terrains, showing adaptability to diverse conditions. The model’s reliability is validated by comparing its predictions with the conventional ERA5 IWV method, showing a 61% improvement rate. This refined IWV estimation model is applied for regional climate analysis, demonstrating its practical utility in environmental research, specifically for the Upper Rhine Graben Region.

Abstract

The real-time ionospheric data streams are continuously being provided by a number of International GNSS service analysis centers such as Centre National d’Etudes Spatiales (CNES), Chinese Academy of Sciences (CAS), Universitat Politècnica de Catalunya (UPC), and Wuhan University, however, the performance evaluation of these Real-Time Global Ionosphere Map (RT-GIM) products is essential. We assess the quality and consistency of these RT-GIM products from the declining phase of solar cycle 24 (year 2017) to the maximum of solar cycle 25 (year 2024) by comparing with Final GIMs provided by Center for Orbit Determination in Europe (CODE) and Jason-3 altimetry satellite. The results suggest that during the low solar activity periods (2017–2022), all the RT-GIMs perform almost similar. However, the performance of the CNES and CAS RT-GIMs strongly deteriorates as the solar cycle proceeds towards the maximum (2022–2024) with annual RMS values remains between 9 and 7.5 TECU. The external validation vs Jason-3 during this maximum period suggested that the accuracy of the UPC RTGIMs is nearly identical to the final CODE GIMs at typically 4–10 TECU in standard deviation over oceans, while performance degradations are recorded for rest of the RTGIMs exhibiting high standard deviations. Results suggest that the high RMS errors in GIMs from CNES and CAS might be related to the geomagnetic inclination misalignments followed by the map projections as both maps form single peak along geomagnetic equator during high solar activities. In addition, under the presence of a severe G4-class geomagnetic storm, CNES RT-GIMs undergoes severe accuracy degradation across all continents recording a − 20 to − 40 TECU bias offset. Meanwhile, UPC RT-GIM remain the most consistent and stable performer (both, globally and over oceans) that provides accurate global ionospheric information which is promising for their applications in real-time precise GNSS positioning.

Abstract

Spoofing detection is an essential process in global navigation satellite system anti-spoofing. Signal quality monitoring (SQM) methods have been widely studied as simple and effective means to detect spoofing. However, the disadvantages of the existing SQM methods, such as long alarm times and low detection rates, necessitate the study of new methods. Therefore, to address these challenges, this paper proposes a novel SQM method based on a long short-term memory-detect (LSTM-Detect) model with a strong capacity for sequential signal processing. In particular, this method evaluates the distortion of the autocorrelation function (ACF) by the trained LSTM-Detect model for spoofing detection. The simulation results demonstrate that the LSTM-Detect model can detect a wide range of spoofing signals, varying in signal power advantages, code phase differences, and carrier phase differences. In the Texas Spoofing Test Battery datasets 2–6, the detection rate exceeds 98.5%, with an alarm time of less than 5 ms. Compared with five existing SQM methods, the LSTM-Detect model exhibits a more comprehensive spoofing detection performance.

Abstract

Low-cost (LC) Global Navigation Satellite System (GNSS) receivers are argued as an alternative solution to geodetic GNSS counterparts for different applications. Single-frequency low-cost (SF-LC) GNSS receivers have been in the market for many years while their inability to acquire GNSS observations in second frequency limited their use. A few years ago, dual-frequency low-cost (DF-LC) GNSS receivers with enhanced capabilities entered the mass market, considering the advancements they have been tested and evaluated by many researchers. Lastly, multi-frequency low-cost (MF-LC) GNSS receivers become available. With the ability to track more satellite signals, these GNSS receivers are expected to obtain better overall performance. This review article aims to analyze recent advances and applications of LC GNSS receivers. To provide answers to the research question relevant articles were selected and analyzed. From the reviewed articles, it was concluded that the performance of SF-LC and DF-LC GNSS receivers is comparable to that of geodetic counterparts only in open-sky conditions. However, in adverse conditions, the differences become more highlighted. In such environments, SF and DF-LC GNSS receivers face challenges not only with positioning quality but also with their proper work. Limited studies on MF-LC receivers have reported comparable observations and positioning performance to geodetic GNSS receivers. Despite drawbacks, LC GNSS receivers have been successfully applied in surveying, mapping, geodetic monitoring, precision agriculture, navigation, atmosphere monitoring, Earth surface monitoring, and other fields.

Abstract

Global ionospheric total electron content (TEC) map prediction is important for improving the accuracy of global navigation satellite systems. There are two main issues with the current TEC prediction: (1) The deep learning models used for TEC prediction are mainly designed using a stacked structure. When stacking multiple layers, the input data will undergo continuous multi-layer convolution operations, leading to the loss of fine-grained features and the degradation of model performance; (2) The model optimization methods for TEC prediction are relatively outdated, mainly using manual optimization or grid search methods. To address these two issues, an automatic framework for global TEC map prediction and optimization is proposed, named as CGAOA-STRA-BiConvLSTM. It includes a global TEC map prediction model, STRA-BiConvLSTM, which can simultaneously extract both coarse-grained and fine-grained spatiotemporal features. It also contains an optimization algorithm, CGAOA, to optimize the model. We first experimentally verified the effectiveness of CGAOA. Then, the effectiveness of STRA-BiConvLSTM was verified through ablation experiments. Finally, we conducted comparative experiments from multiple perspectives between our framework and 5 mainstream methods: C1PG, C2PG, ConvLSTM, ConvGRU, and ED-ConvLSTM. The results show that in all cases, the proposed CGAOA-STRA-BiConvLSTM outperforms the comparative models.

Abstract

On February 6, 2023 the Kahramanmaraş Earthquake Sequence caused significant ground shaking and catastrophic losses across south-central Türkiye and northwest Syria. These seismic events produced ionospheric perturbations detectable in Global Navigation Satellite System (GNSS) total electron content (TEC) measurements. This work aims to develop and incorporate a near-real-time (NRT) ionospheric disturbance detection method into JPL’s GUARDIAN system. Our method uses a Long Short-Term Memory (LSTM) neural network to detect anomalous ionospheric behavior, such as co-seismic ionospheric disturbances among others. Our method detected an anomalous signature after the second \(M_w\)  7.5 earthquake at 10:24:48 UTC (13:24 local time) but did not alert after the first \(M_w\)  7.8 earthquake at 01:17:34 UTC (04:17 local time), which had a visible disturbance of smaller amplitude likely due to lower ionization levels at night and potentially the multi-source mechanism of the slip.

Plain Language Summary Seismic activity, including the destructive Kahramanmaraş Earthquake Sequence on February 6, 2023 in the Republic of Türkiye, result in vertical ground displacement that cause atmospheric waves. These waves propagate upwards to the outer atmosphere, disturbing the ionospheric electron content. This disturbance impacts the signals broadcast by positioning satellites (such as GPS) and received by ground-based receivers. If the receiver position is known, the impact to these signals can be used to measure the electron density disturbance caused by these seismically-induced atmospheric waves. Such studies usually rely on being aware of the event a priori. Using deep learning neural networks, we instead aim to detect anomalous signals automatically. We propose to utilise this method to detect seismically-induced disturbances over a large geographical area. The detection method proposed in this paper successfully detected an anomalous event in the ionosphere approximately ten minutes after the second earthquake in the Kahramanmaraş Earthquake Sequence.

Abstract

This study addresses the frequent convergence issues of satellite clocks within regional network, with a particular focus on the multifrequency advantages using data from 25 uniformly distributed reference stations across China. Experimental results demonstrate that incorporating the third frequency significantly enhances the accuracy of BDS-3 clock solutions, reducing the root mean square (RMS) by 44.5%. Additionally, employing a 2-min smoothing interval, multifrequency inclusion increases the wide-lane (WL) fixing rate by 30.4% at low elevation angles, which in turn leads to a marked improvement in narrow-lane (NL) ambiguity resolution. By leveraging phase-wide-lane observations, the stable wide-lane phase bias enables the continuous generation of inter-frequency clock bias (IFCB), ensuring reliable cyclic sequence construction even when satellites exit the observed region. The effectiveness of regional observable specific bias (OSB) on ambiguity resolution at the user level is highlighted, and over 95% of GPS, BDS-3, and Galileo NL fractional biases below 0.15 cycles could be achieved. Furthermore, the single-epoch convergence rates of multi-constellation precise point positioning (PPP) reach horizontal 91.9% and vertical 84.5% for multifrequency, a substantial improvement over the dual-frequency, which does not exceed 25%.

Abstract

In this paper, we propose a novel algorithm for fast frequency and phase synchronization of high-stability oscillators synchronized with 1 PPS signal from satellite navigation systems. The algorithm uses a model of a control object in the space of state variables and controls the frequency of an oscillator operating in a phase-locked loop. A new element is the introduction to the theoretical analysis and the design process, the time of entering synchronization. Currently, the literature lacks theoretical analysis and design methodology that considers the impact of the synchronization time on the choice of the steering algorithm and its parameters. All the data needed to determine the numerical values of the model were found experimentally for three different classes of control objects. Short synchronization times, a detailed description of the design methodology, and the use of values measured in the real system distinguish the proposed algorithm from the solutions described in the literature. The effect of optimization was achieved thanks to the algorithm’s two-stage operation. In the first stage, the algorithm aims to minimize the phase error quickly. The best solution for this stage is Sliding Mode Control (SMC). In the second stage, the algorithm strives to maximize the control quality, understood as minimizing the values of Maximum Time Interval Error (MTIE) and Time Deviation (TDEV). The Model Predictive Control (MPC) and Linear-Quadratic Regulator (LQR) optimal control algorithms were used at this stage. The paper also investigated the influence of the tuning parameters of these algorithms (weights as a function of cost) on the long-term behavior of the control system.

Abstract

In order to further improve the convergence rate and positioning accuracy of multi-frequency multi-system precise point positioning (PPP), an open-sourced software for fractional cycle bias (FCB) estimation (M_FCB) was produced based on MATLAB 2016a for GPS, BDS-2, Galileo, and BDS-3 satellite users. Based on raw frequency float ambiguity, the software can estimate ultra-wide-lane, wide-lane, narrow-lane combined FCB and raw frequency FCB. To validate the usability of the M_FCB software, 180 and 24 globally uniformly distributed multi-GNSS experiment stations were used to perform FCB estimation and triple-frequency uncombined PPP ambiguity resolution performance evaluation. The results show that the M_FCB software can generate stable and reliable FCB products. Particularly, Galileo satellites presented the best FCB stability. In addition, taking GPS/Galileo/BDS-2/BDS-3 fusion positioning as an example, the kinematic PPP after ambiguity resolution was significantly improved in terms of three-dimensional coordinate accuracy and positioning stability. Relative to the float solution, the average root mean square of the fixed-solution coordinate residuals in the east, north and vertical directions decreased by 30.3%, 12.5% and 16.0%, respectively.

Abstract

Terrestrial scale is one of the key datum parameters in the realization of the International Terrestrial Reference Frame (ITRF), which is defined by Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) in the latest ITRF2020. Currently, the scale of GNSS is aligned to ITRF by estimating phase center offsets (PCOs) of GNSS satellites in a global adjustment with minimum constraints to ITRF. With the proposal of space tie concept in recent years, the co-location of different techniques on the same Low Earth Orbit (LEO) spacecraft provides a possible alternative to achieve this scale datum transfer between different techniques. In this study, we investigate the potential of terrestrial scale transfer between GNSS and SLR using the co-location onboard LEO satellites. The integrated precise orbit determination of GNSS and LEO satellites is performed based on one year of onboard GPS data and SLR observations from GRACE-FO and Swarm satellites as well as a global GNSS network. Two GNSS-only solutions and four GNSS + SLR combined solutions are generated. The results indicate that the scale determined by LEO gravitational constraint in the GNSS-only solution presents an average offset of -0.35 ppb w.r.t. ITRF2020. The space-ties onboard LEO satellites fail to transfer SLR scale information to GNSS network. With the inclusion of SLR observations to LEO satellites, the scale factor of the combined solution is only changed by less than 0.05 ppb with respect to the GNSS-only solution. The small changes of a few millimeters in GPS PCO of the orbital radial direction for the combined solution also demonstrate that the GPS z-PCOs cannot inherit any SLR scale information through LEO co-locations. Meanwhile, we find that the range biases of GRACE-FO and Swarm satellites achieve a good consistency for the majority of SLR stations, since these satellites carry the same type of laser retroreflector arrays and can achieve comparable orbit accuracy. The result indicates that estimating a common range bias parameter is sufficient for GRACE-FO and Swarm when using the SLR observations from these satellites.

Abstract

Vehicular attitude can be estimated using micro-electro-mechanical systems (MEMS) based magnetic, angular rate, and gravity (MARG) sensors or global navigation satellite systems (GNSS). In challenging environments external accelerations, magnetic distortions, and failure of GNSS will result in significant attitude estimation errors. We proposed a hybrid attitude estimation algorithm based on the low-cost dual-antenna GNSS/MEMS MARG sensor integration, in which the two GNSS antennas are connected to two separate low-cost receivers. Heading and pitch angles are obtained from the moving baseline spanned by the two antennas. An error state Kalman filter is built for data fusion, the filter shares the identical kinematic model but switches the measurement model according to the valid aiding sources. Six possible measurement update schemes are conditioned on the availability of GNSS-derived angles and the disturbances detected in the MARG sensor data. The accuracy degradation of attitude estimation caused by disturbances is alleviated by adjusting the measurement covariance matrix adaptively. A land vehicle-based dynamic experiment was performed to assess the proposed algorithm. Compared to the MARG sensor alone method, the root mean square errors of the proposed GNSS/MARG sensor integrated method were reduced by 38.9%, 65.8%, and 45.6% in the roll, pitch, and yaw angles, respectively.

Abstract

Atmospheric weighted mean temperature (Tm) is pivotal for converting zenith wet delay (ZWD) derived from global navigation satellite system (GNSS) signal to precipitable water vapor (PWV). Currently, most Tm models are developed based on radiosonde (RS) data or reanalysis data. These models are limited by the availability of measured surface temperature and the accuracy of input data used during modeling. Additionally, they face challenges in accounting for the diurnal effect on Tm. In this study, we innovatively use the latest AI weather model, Pangu-Weather, to estimate surface air temperature (Pangu-Ts) in 2016–2019. Compared with the measured surface temperature (RS-Ts) at RS stations, bias and root mean square error (RMSE) are − 0.75 K and 2.54 K, respectively. Subsequently, a Tm forecast model (RF-Tm) in China is developed based on this data using random forest (RF). The model only requires the input of time, 3D coordinates of stations, and predicted Pangu-Ts data to yield the forecasted Tm estimates. The validation results based on RS data show that bias of the RF-Tm is − 0.38 K and the RMSE is 2.47 K. Through comparison and validation with the Bevis model, GPT3, and the Tm forecast model (BP-Tm) developed using back propagation neural network (BPNN), RF-Tm demonstrates reductions in RMSE of 41.33%, 39.46%, and 2.76%, respectively. The mean values with theoretical RMSE and relative error of PWV derived from the RF-Tm are 0.171 mm and 0.90%. The RF-Tm proposed in this study can provide reliable and high-precision Tm estimation for real-time GNSS PWV retrieval.

Abstract

Jamming of Global Navigation Satellite System (GNSS) signals severely affects the security of critical infrastructures and applications. The localization of intentional jamming sources, jammers, is an important step in securing GNSS resilience as it provides the authorities with technical tools to prevent the jamming. However, jammers are difficult to localize in dense urban areas because the existence of multipath and non-line-of-sight propagation challenges conventional methods significantly. This challenge has not been comprehensively addressed in previous research. Motivated by this gap, a ray-tracing tool using 3-D city models is established to simulate jamming signal propagation with high precision and thereby augment the existing signal simulators, and measurements for localization are modeled by characterizing a commercial GNSS receiver under jamming conditions. Then, we propose a novel two-step strategy which consists of an ensemble subspace k-Nearest-Neighbor (KNN) as a raw-predictor and an improved gravitational searching algorithm (GSA) as a fine-optimizer. Based on this, two cloud-computing-based schemes using signal-matching and joint-localization in fine-optimizing stage are proposed. Finally, the proposed methods are evaluated in three typical urban areas, and their effectiveness and superiority over conventional least-squares method based on an empirical path-loss model are validated.

Abstract

The accuracy of satellite clock bias (SCB) directly affects the precision and reliability of positioning in Global Navigation Satellite System. Through precise clock bias prediction, positioning errors can be effectively reduced, and the overall reliability of the system can be improved. This paper proposes a deep learning model for SCB prediction based on the fusion of the Beluga Whale Optimization (BWO), Convolutional Neural Network (CNN), Bidirectional Gated Recurrent Unit (BiGRU), and an attention mechanism. The CNN is utilized to extract the spatiotemporal characteristic information from the clock bias sequence, while the BiGRU fully extracts relevant features through forward and backward propagation. The introduction of an attention mechanism aims to preserve essential features within the clock bias sequence to enhance feature extraction by both CNN and BiGRU networks. Additionally, the BWO is employed to optimize parameter selection in order to improve model accuracy. Experimental verification demonstrates that for the BeiDou Navigation Satellite System’s hydrogen-maser atomic clocks, the predicted clock bias for 6 h, 3 days, and 15 days are 0.078 ns, 0.475 ns, and 2.130 ns respectively, superior to the CNN-BiGRU-Attention, CNN-BiGRU, BiGRU, GRU, LSTM, BP, Kalman filter and ARIMA models.

Abstract

Currently, the susceptibility of Global Navigation Satellite System (GNSS) signals underscores the importance of accurate GNSS time spoofing detection as a critical research area. Traditional spoofing detection methods have limitations in applicability, while the current learning-based algorithms are only applicable to the judgment of collected data, which is difficult to apply to real-time detection. In this paper, a real-time spoofing detection framework based on feature processing is proposed. The approach involves feature integration and correlation coefficient screening on each epoch of multi-satellite data. Additionally, special standardization strategy is employed to enhance the feasibility of real-time application. In the experimental phase, apart from utilizing the open dataset, an experimental platform is developed to generate dual-system data for experimentation purposes. Compared with the traditional clock difference detection method, this algorithm improves the detection performance by about 25%. Furthermore, the framework proposed can improve the detection F1 score of basic machine learning models and greatly reduce the computation time by more than ten times. On most datasets, models incorporating the framework achieved F1 scores of more than 99% and average response times of less than 10 μs. In summary, this study provides an effective intelligent solution for the application of real-time receiver spoofing detection.

Abstract

The development of Global Navigation Satellite Systems (GNSS) results in large spatial geodetic networks with a distinct range of accuracy. Thus, classification of the GNSS stations is needed to determine which stations are appropriate for geodetic applications. Additionally, advanced Machine Learning (ML) techniques have been proposed. However, ML algorithms may sometimes be less sensitive due to a lack of samples or anomalies in input data. Therefore, this study introduces an approach in which human-based supervision is integrated into ML processes to improve the ML model’s performance in classifying the continuous GNSS stations. The human factor influences the ML processes through two sampling strategies: “suggest-decide” and “correct-retrain”, where the accuracy of ML models will be improved via human-based corrections. The idea is that the unsupervised ML-based clustering techniques are driven by human-based supervision to create samples for training the supervised ML-based classification models. In this study, we develop a MATLAB app to automate the clustering and labeling processes. Our finding demonstrates that applying these sampling strategies can enhance the accuracy of the ML-based classification models from under 50 % up to \(\sim\) 99 % after re-training. Also, this study categorizes almost 9000 continuous monitoring stations in the Nevada database, of which 1900 stations in Europe serve as samples for training the ML-based classification models. Furthermore, the methodologies developed in this study can be applied to warning systems, which utilize internal and external human resources to correct errors, address unusual situations, and provide timely feedback for better performance of ML-based forecasts.

Abstract

Displacement-based modal analysis has been proven to yield more robust and reliable modal parameter identification results compared to acceleration-based modal analysis. Global navigation satellite systems (GNSS) under real-time kinematic (RTK) mode is a widely used dynamic displacement monitoring technique. Notably, the monitoring accuracy of GNSS is limited due to the existence of multiple error sources such as multipath effect and satellite shielding effect. Particularly, blind source separation (BSS) can determine structural modal parameters from output-only responses. This method is advantageous compared with conventional modal analysis method because it does not require any prior knowledge of the structure. However, common BSS methodologies are susceptible to the local minima problem and are sensitive to low signal-to-noise ratio (SNR) signals. To address the aforementioned problems, this study first presents a combination filter strategy of Chebyshev and wavelet threshold (WT) to estimate the structural dynamic displacement based on GNSS RTK measurement. Then, a swarm-enhanced blind identification approach is proposed to determine structural modal parameters from the estimated displacement. The core of this approach is to develop a robust K-means clustering approach with swarm intelligence optimization to estimate the mixing matrix (i.e., mode shape matrix). Finally, the developed approach is verified in a four-degree-of-freedom numerical model and then implemented to a field test of a long-span cable-stayed bridge in engineering practice. The results illustrate that the designed combination filter can effectively weaken the influence of GNSS-RTK background noise while retaining the components related to structural dynamic vibration. Meanwhile, comparing with the conventional BSS approach (i.e., sparse component analysis), the developed swarm-enhanced blind identification approach exhibits higher robustness and convergence accuracy in determining structural modal parameters.

Abstract

For about three decades, the Global Navigation Satellite System (GNSS) has been used for high-precision positioning in scientific and engineering applications, such as deformation monitoring for seismicity and volcano eruption. Such high-precision positioning applications require millimeter-level positioning accuracy. There are many man-made and natural reflective surfaces near the GNSS receiving antennas. GNSS signals can be reflected and then arrive at the GNSS antenna. The multipath effect occurs when the direct signal is mixed with the reflected signal at the GNSS receiver. Choke-ring antennas are designed to mitigate the multipath effect of reflected signals from below the horizontal plane of the GNSS receiving antenna. Moreover, GNSS receiving antennas at network/permanent stations are usually installed on tall pillars or monuments to prevent multipath from “ground” reflected signals. However, part of the reflected signals can still arrive at the GNSS antenna center and cause multipath errors in GNSS measurements. How much can the multipath effect be on the real-time GNSS-measured displacements in studies on seismicity and volcano eruption? This work investigates the below-the-horizon multipath effect of choke-ring antennas on GNSS carrier-phase measurements. Here we show the differenced carrier-phase multipath errors of two commonly used GNSS antennas at the International GNSS Service (IGS) tracking stations can reach 8 mm, the maximum, with the mean and SD in a few millimeters at the 95% confidence level. The findings of this work should be applicable to other choke-ring antennas with similar architecture.

Abstract

The ambiguity resolution (AR) technology effectively accelerates convergence and improves precise point positioning (PPP) accuracy. Many observations involved in the calculation can enhance the accuracy of parameter estimation. Still, it can also introduce unmodeled errors, making it difficult to fix ambiguities, especially in multiple global navigation satellite system (GNSS). This paper presents a novel PPP Partial-AR (PAR) method to enhance Precise Point Positioning (PPP) performance by selecting an ambiguity subset based on the variation of ambiguity check factors, including the ratio, ambiguity dilution of precision (ADOP), and Bootstrapping success rate. The proposed method is validated using post-processing and real-time static and kinematic datasets across five GNSS integration modes involving the global positioning system (GPS) and BeiDou navigation satellite system (BDS), demonstrating that PPP Partial-AR (PAR) outperforms the method that fixes all ambiguities, known as PPP Full-AR (FAR). The static and kinematic post-processing experiment shows that PPP-PAR, compared with PPP-FAR, increases the ambiguity epoch fixing rate from 84.6 and 79.5% to 94.2 and 91.9%, decreases the time to first fix (TTFF) from 21.4 and 31.1 min to 17.7 and 25.4 min, and reduces the root mean square error (RMSE) from 12.7/11.3/32.2 and 21.7/19.4/51.8 mm to 11.5/10.3/30.9 and 19.1/18.1/48.9 mm in the north-east-up directions, respectively. The static and kinematic real-time experiment shows that PPP-PAR, compared with PPP-FAR, increases the ambiguity epoch fixing rate from 80.1 and 71.7% to 91.8 and 86.6%, decreases the TTFF from 29.5 and 35.5 min to 25.2 and 28.7 min, and reduces the RMS from 22.4/19.4/45.9 and 33.8/26.9/65.2 mm to 18.6/17.1/42.0 and 29.2/23.6/60.5 mm in the north-east-up directions, respectively. Moreover, the real-time experiments with actual kinematic data show that the proposed method significantly improves the ambiguity epoch fixing rate from 43.3% for PPP-FAR to 50.7% for PPP-PAR, and increases the positioning accuracy with an RMS value of 0.28/0.21/0.57 m for the PPP float solution, 0.23/0.19/0.55 m for the PPP-FAR solution towards 0.21/0.18/0.53 m for the PPP-PAR solution.

Abstract

Although GNSS (Global Navigation Satellite System) is well-established for outdoor positioning, it still encounters challenges in urban occluded environments. Currently, multi-source fusion positioning has emerged as the primary solution. Since commonly used smartphones can simultaneously receive satellite signals and send 5G signals, researching GNSS/5G fusion positioning based on smartphones is a highly feasible solution. However, existing studies on GNSS/5G fusion positioning primarily rely on simulation data and TOA (Time of Arrival). On the one hand, simulation data often fail to accurately reflect positioning performance in real-world environments. On the other hand, while TOA often struggles to achieve high accuracy due to time synchronization errors, the AOA (Angle of Arrival) method, which does not depend on time synchronization, presents a promising alternative. Therefore, we propose a GNSS/5G tightly coupled fusion positioning method based on AOA measurements and conduct practical tests. For the first time, we use a smartphone to verify the performance of this method in urban occluded environments. The static experimental results indicate that SPP of the smartphone performs poorly in occluded environments. In contrast, AOA positioning demonstrates relatively stable performance. GNSS/5G fusion positioning yields the best positioning results, exhibiting a best improvement of 98.18% over SPP and 70.69% over AOA positioning. For the two dynamic routes with varying levels of occlusion, GNSS/5G fusion positioning shows considerable enhancements, achieving improvements of 39.39% and 9.32% over SPP, and 13.35% and 44.68% over AOA positioning. These results demonstrate that the fusion positioning method can effectively compensate for the shortcomings of satellite positioning in occluded environment.