Global Navigation Satellite System Pseudorange Research Articles

100 Picosecond/Sub-10−17 Level GPS Differential Precise Time and Frequency Transfer

A Global Navigation Satellite System (GNSS) is a high-precision method for comparing clocks and time transfer. The GNSS carrier phase can provide more precise observable information than pseudorange. However, the carrier phase is ambiguous, and only pseudorange can provide the absolute time difference between two clocks. In our study, by taking full advantage of GNSS pseudorange and carrier-phase observables, a differential precise time transfer (DPT) method with a clustering constraint was employed to estimate the time difference between two clocks, aiming to achieve accurate and precise time and frequency transfer. Using this method, several time transfer results were analyzed for different baselines. For the common clock experiment, the time transfer results showed good consistency across different days, with an intra-day accuracy of within 20 ps. Furthermore, we evaluated the self-consistency of DPT using closure among three stations. DPT closure of the three stations had a peak-to-peak value of closure of about 25 ps. The closure did not change over time, indicating the self-consistency of the DPT processing in time transfer. Moreover, our results were compared to station clock solutions provided by the International GNSS Service (IGS), and the standard deviations (STDs) of the four baselines were all less than 100 ps within one month, confirming the time and frequency stability of the DPT method. In addition, we found that the time stability of DPT was less than 20 ps within one week. As for frequency stability, DPT achieved a 10−16 level of modified Allan deviation (MDEV) at an averaging time of about 1 day and a sub-10−17 level at an averaging time of one week.

Vehicular Relative Positioning With Measurement Outliers and GNSS Outages

Relative positioning among vehicles finds many applications regarding location-based services in intelligent transportation systems (ITSs). This article introduces a hybrid relative positioning strategy integrating global navigation satellite system (GNSS), inertial navigation system (INS), and ultrawideband (UWB) observations, which addresses measurement outliers and GNSS outages simultaneously. An improved extended Kalman filter (IEKF) based on tracking an appropriately weighted window of past innovations is developed to deal with measurement outliers. To perform relative positioning during GNSS outages, a nonlinear autoregressive network with exogenous inputs (NARX) is developed to predict GNSS measurements increments, with the least-squares support vector machine (LSSVM) algorithm identifying the NARX model. The NARX-LSSVM module learns the relationship between GNSS pseudorange and Doppler shift increments of a target vehicle and its local and neighbors’ dynamics. Whereas during GNSS outages, the increments of GNSS measurements are generated by this prediction algorithm. The feasibility of the proposed methodology is evaluated on empirical road data, and improved positioning accuracy is achieved in cooperative positioning (CP) systems.

Instantaneous velocity determination and positioning using Doppler shift from a LEO constellation

To provide backup and supplementation for the Global Navigation Satellite System (GNSS), Doppler shift from Low Earth Orbit (LEO) satellites can be used as signals of opportunity to provide positioning, navigation, and timing service. In this contribution, we first investigate the model and performance of instantaneous velocity determination and positioning with LEO satellites. Given a LEO constellation with 288 satellites, we simulate Doppler shift observations at nine multi-GNSS experiment stations. Owing to the lower orbit, the performance of LEO velocity determination is much more sensitive to the initial receiver position error than that of GNSS. Statistical results show that with the initial receiver position error increased from 0.1 to 10 m, the Root Mean Square Errors (RMSEs) increase from 0.73 to 2.65 cm/s, 0.68 to 2.96 cm/s, and 1.67 to 4.15 cm/s in the east, north, and up directions, respectively. The performances with GPS are compared with GPS + LEO, and it is found that LEO Doppler shift observations contribute to GPS velocity determination. As for LEO Doppler positioning, even if more than 30 visible LEO satellites are available, the position dilution of precision values can reach several hundreds. Assuming that the error of LEO Doppler measurements is 0.01 m/s, the instantaneous Doppler positioning accuracy can achieve about a few meters, which is comparable to that of GNSS pseudorange positioning. A constant velocity model is adopted for state transition. Static LEO Doppler positioning results show that an accuracy at centimeter to decimeter level can be achieved after solution convergence. For a static simulated kinematic positioning test, the RMSEs range from a few decimeters to several meters in different regions by giving different constraints. For a dynamic positioning test, the RMSEs are about 2–3 m in high latitude region.

Robust train localisation method based on advanced map matching measurement-augmented tightly-coupled GNSS/INS with error-state UKF

AbstractThis 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.

A Comprehensive Analysis of Smartphone GNSS Range Errors in Realistic Environments.

Precise positioning using smartphones has been a topic of interest especially after Google decided to provide raw GNSS measurement through their Android platform. Currently, the greatest limitations in precise positioning with smartphone Global Navigation Satellite System (GNSS) sensors are the quality and availability of satellite-to-smartphone ranging measurements. Many papers have assessed the quality of GNSS pseudorange and carrier-phase measurements in various environments. In addition, there is growing research in the inclusion of a priori information to model signal blockage, multipath, etc. In this contribution, numerical estimation of actual range errors in smartphone GNSS precise positioning in realistic environments is performed using a geodetic receiver as a reference. The range errors are analyzed under various environments and by placing smartphones on car dashboards and roofs. The distribution of range errors and their correlation to prefit residuals is studied in detail. In addition, a comparison of range errors between different constellations is provided, aiming to provide insight into the quantitative understanding of measurement behavior. This information can be used to further improve measurement quality control, and optimize stochastic modeling and position estimation processes.

Achieving Reliable Intervehicle Positioning Based on Redheffer Weighted Least Squares Model Under Multi-GNSS Outages.

Achieving reliable intervehicle positioning is one of the most fundamental elements for many vehicular applications, including collision avoidance and autonomous driving. Vehicle position is generally provided by a global navigation satellite system (GNSS), which unfortunately suffers from inaccuracy to varying degrees in challenging environments, for example, GNSS outages. In this article, a reliable fusion technique, called non-Gaussian Redheffer weighted least squares ( n GRWLSs), is proposed. This new approach highlights the intervehicle positioning estimation in multi-GNSS outage environments, such as complete, partial, and free GNSS pseudorange outages. The proposed method combines, on the one hand, the benefits of the Gaussian dynamical matrix principle and the Redheffer distribution function for the sparse property in complete GNSS pseudorange outages and, on the other hand, the use of the optimal window size to regulate the data flow generated by both the inertial navigation systems (INSs) and GNSS during a partial GNSS pseudorange outage. During the free GNSS pseudorange outage, the process ignores data from the INS, and instead, GNSS pseudorange information alone will be considered to compute the intervehicle positioning information. Consequently, weighted least squares is used as an intervehicle positioning estimator. To address the pseudorange uncommon and INS measurement noises, the generalized error distribution (GED) is used to estimate the non-Gaussian densities. Finally, road-test experiments are implemented to evaluate the consistency of the proposed approach. The experimental results show that the proposed n GRWLS can accurately estimate the intervehicle positioning under various conditions (free, partial, and complete GNSS pseudorange outages).

Resilient Smartphone Positioning Using Native Sensors and PPP Augmentation

<h3>Abstract</h3> With the ubiquitous use of global navigation satellite system (GNSS) receivers, navigation solutions from smartphones have become integrated in various applications throughout our lives. These ultra-low-cost GNSS receivers have the drawbacks of insufficient observations and poorer signal reception quality than higher-cost receivers. Since 2016, smartphones using the Android operating system have been able to output raw GNSS pseudorange and carrier-phase measurements, thereby enabling improved navigation capabilities. The realm of sensor fusion is also being explored by using smartphone sensors, including inertial measurement units (IMUs), cameras, and other fusion techniques. The research presented herein deployed only IMU and GNSS sensors native to existing smartphones and achieved a standalone solution using PPP/IMU integration that outperformed standard techniques. In open-sky vehicle experiments, the sensor integration algorithm achieved 1.6-m horizontal RMS, thus reducing 80% of horizontal errors in GNSS-challenging environments through a tightly coupled GNSS-PPP solution that is yet to appear in publications.

A Tightly Coupled Integration Approach for Cooperative Positioning Enhancement in DSRC Vehicular Networks

Intelligent transportation system significantly relies on accurate positioning information of land vehicles for both safety and non-safety related applications, such as hard-braking ahead warning and red-light violation warning. However, existing Global Navigation Satellite System (GNSS) based solutions suffer from positioning performance degradation in challenging environments, such as urban canyons and tunnels. In this paper, we focus on the positioning performance enhancement of land vehicles via cooperative positioning under a partial GNSS environment in a Vehicular Ad-hoc NETwork (VANET). The availability of Time-of-Flight (ToF) based inter-vehicle or vehicle-to-infrastructure ranges is verified via 5.9 GHz Dedicated Short-Range Communication (DSRC) vehicle-to-everything communication with RTS/CTS unicast mechanism. An inertial navigation sensor aided, tightly coupled integration approach for land vehicle cooperative positioning using DSRC ToF ranges and carrier frequency offset range-rates is proposed, where a digital map is used to constrain the position estimates. If available, the GNSS pseudorange and Doppler shift under partial GNSS environment can also be incorporated. A Rao–Blackwellized particle filter is utilized to estimate the unknown variables allowing for reduced computational complexity in comparison with the conventional particle filter. The posterior Cramer–Rao lower bound is also derived to give a theoretical performance guideline. Both simulation and experimental results show the validity of our proposed approach.

Research on Blunder Detection Methods of Pseudorange Observation in GNSS Observation Domain

Global Navigation Satellite System (GNSS) signal quality, type of receiver equipment, and external environment can cause GNSS observations to be anomalous, and these anomalies are sometimes reflected in GNSS pseudorange observations rather than phase observations. To better detect blunders in pseudorange observations, this paper proposes three pseudorange blunder detection methods under the same frequency and different code types (case1), and the same code type and different frequencies (case2), of pseudorange observations, which are the Code Observation Difference Method (CODM), the Inter-satellite Code Observation Difference Method (ICODM), and the Inter-epoch and Inter-satellite Code Observation Difference Method (IICODM). The corresponding thresholds for the constructed test statistics of the three detection methods were derived based on the Bessel formula. Performance analysis of the three detection methods was performed under case1 based on C2 and P2 code observation data of Global Positioning System (GPS) at 137 Multi-GNSS Experiment (MGEX) stations, and case2 based on BDS B1I and B3I frequency observation data of BeiDou Navigation Satellite System (BDS) at 232 MGEX stations, on 29 July 2022. The results show that the statistical information value of the three methods in case1 was significantly smaller than that in case2. In the first case, the maximum values of test statistics, RMSE and threshold mean values were 0.526, 0.752 and 2.243 m, respectively, while the corresponding values in case2 were 7.066, 4.490 and 13.480 m respectively. The reason for this is that the data quality of global GPS is higher than that of BDS and the differential observation equation eliminates or weakens more errors with the same frequency and different types of code pseudorange observations. Under the same conditions, compared with ICODM and IICODM, CODM has high computational efficiency and a simple mathematical model. It is recommended to use CODM first for pseudorange blunder detection in the GNSS observation domain. According to the RMSE of 3 times as the limit, it is recommended that the threshold be set to 5 m under case1 for GPS and 15 m under case2 for BDS, which is half the existing reference value. Finally, the blunder detection methods proposed can improve positioning performance through actual data verification.

Continuous and Precise Positioning in Urban Environments by Tightly Coupled Integration of GNSS, INS and Vision

Accurate, continuous and seamless state estimation is the fundamental module for intelligent navigation applications, such as self-driving cars and autonomous robots. However, it is often difficult for a standalone sensor to fulfill the demanding requirements of precise navigation in complex scenarios. To fill this gap, this letter proposes to exploit the complementariness of the global navigation satellite system (GNSS), inertial measurement unit (IMU) and vision via a tightly coupled integration method, aiming to achieve continuous and accurate navigation in urban environments. Specifically, the raw GNSS carrier phase and pseudorange measurements, IMU data, and visual features are directly fused at the observation level through a centralized Extended Kalman Filter (EKF) to make full use of the multi-sensor information and reject potential outlier measurements. Furthermore, the widely used high-precision GNSS models including precise point positioning (PPP) and real-time kinematic (RTK) are unified in the proposed integrated system to increase usability and flexibility. We validate the performance of the proposed method on several challenging datasets collected in urban canyons and compare against the loosely coupled and state-of-the-art methods.

GNSS NLOS Signal Classification Based on Machine Learning and Pseudorange Residual Check.

Global navigation satellite system (GNSS) positioning has recently garnered attention for autonomous driving, machine control, and construction sites. With the development of low-cost multi-GNSS receivers and the advent of new types of GNSS, such as Japan’s Quasi-Zenith Satellite System, the potential of GNSS positioning has increased. New types of GNSS directly increase the number of line-of-sight (LOS) signals in dense urban areas and improve positioning accuracy. However, GNSS receivers can observe both LOS and non-line-of-sight (NLOS) signals in dense urban areas, and more NLOS signals are observed under static conditions than under dynamic conditions. The classification of LOS and NLOS signals is important, and various methods have been proposed, such as C/N0, using three-dimensional maps, fish-eye view, and GNSS/inertial navigation system integration. Multipath detection based on machine learning has also been reported in recent years. In this study, we propose a method for detecting NLOS signals using a support vector machine (SVM) classifier modeled with unique features that are calculated by receiver independent exchange format-based information and GNSS pseudorange residual check. We found that using both the SVM classifier and GNSS pseudorange residual check effectively reduced the error due to NLOS signals. Several static tests were conducted near high-rise buildings that are likely to receive some NLOS signals in downtown Tokyo. For all static tests, the percentage of positioning errors within 10 m in the horizontal positioning error was improved by >80% by detecting and eliminating satellites receiving NLOS signals.

Kalman–Hatch dual‐filter integrating global navigation satellite system/inertial navigation system/on‐board diagnostics/altimeter for precise positioning in urban canyons

For improved positioning in urban canyons, this study proposes an efficient dual-filter method integrating multi-constellation global navigation satellite system (GNSS), an inertial navigation system (INS), a barometric altimeter and an on-board diagnostics (OBD) module. The proposed method consists of a position-domain (PD) Hatch filter and velocity Kalman filter. The Hatch filter is operated as the main positioning filter and the Kalman filter is operated as a sub-filter to aid the main filter for the occasional GNSS outages. The Hatch filter combines barometric altimeter measurements with GNSS pseudorange and carrier phase measurements. The Kalman filter integrates the inertial measurement unit (IMU) measurements with GNSS Doppler shift and OBD speed measurements. A semi-simulation method is applied for the accurate performance evaluation of the proposed method compared with the several conventional methods under deficient satellite visibility, multipath errors and cycle slips caused by urban canyons. By the test results, it is demonstrated that the proposed method can bound the positioning errors effectively by utilising low-cost all-weather sensors. The RMSEs of the proposed Kalman–Hatch dual-filter algorithm were shown as 0.05, 0.19 and 0.11 m, respectively, and the maximum errors were shown as 0.16, 0.26 and 0.40 m, respectively, in the east, north and upward directions.

Predicting State Uncertainty Bounds Using Non-Linear Stochastic Reachability Analysis for Urban GNSS-Based UAS Navigation

Unmanned aircraft systems (UAS) generally use Global Navigation Satellite System (GNSS) measurements to estimate their state (position and orientation) for outdoor navigation. However, in urban environments, GNSS pseudorange measurements contain biases due to multipath effects and signal blockages by nearby buildings. For safe navigation in such environments, it is beneficial to predict the state uncertainty while accounting for the effect of measurement biases. Reachability analysis is a commonly used tool to predict the state uncertainty of a system. However, existing works do not account for the effect of measurement biases on state estimation, which consequently affects the predicted state uncertainty. Additionally, majority of the existing literature focuses on linear systems, whereas the dynamics of widely used practical systems are better captured by non-linear models. Thus, in this paper we present a non-linear stochastic reachability analysis to predict bounds on the state uncertainty while accounting for measurement biases. We derive the analysis for a fixed-wing UAS navigating using ranging measurements. In order to evaluate our predicted bounds for GNSS-based navigation, we simulate a 3D urban environment and the pseudorange biases due to multipath effects. We validate the predicted bounds for multiple trajectories in the simulated environment. Finally, we demonstrate the applicability of our predicted bounds towards ensuring safe UAS navigation in a shared airspace.

Recurrence plot analysis of GPS ionospheric delay time series in extreme ionospheric conditions

With provision of Positioning, Navigation, and Timing (PNT) services, satellite navigation systems have become a pillar of modern society. These services lay the foundations of a growing number of technological and socio-economic systems and constitute a key enabling technology for transportation systems, services and components. Mitigation of disruptions and degradation of Global Navigation Satellite System (GNSS) positioning performance and operation quality become critical issues for satellite navigation advancement and adoption. Ionospheric conditions are the single prime natural cause of GNSS positioning performance disruptions and degradations. Complex, non-linear and random nature of the ionospheric effects on GNSS positioning performance adds to the challenges of the suitable mitigation processes development. Here a contribution to the understanding of the ionospheric effects on GNSS positioning performance is provided through a study of Total Electron Content (TEC) and GNSS pseudorange measurement errors time series in the selected cases of characteristic ionospheric conditions, using the Recurrence Plot Analysis (RPA), a common procedure for studying general time series. Based on experimental GPS observations, this study found good alignment of TEC and TEC-rate time series with several characteristic schemes of dynamical behaviour, thus allowing for classification of ionospheric conditions and related TEC behaviour based on their dynamical properties. Further to this, the study identified several RPA predictors as precursors of developing ionospheric storm and the consequent disruptions and degradation of GNSS positioning performance. The study stressed the importance of TEC time series assessment, and initiates research challenges for consideration of TEC time series RPA predictors for mitigation, correction, and forecasting model development of GNSS pseudorange measurements, and GNSS position estimation errors, thus contributing to GNSS resiliency development against space weather and ionospheric effects.

Fast Time Synchronization on Tens of Picoseconds Level Using Uncombined GNSS Carrier Phase of Zero/Short Baseline.

Since the observation precision of the Global Navigation Satellite System (GNSS) carrier phase is on the order of millimeters, if the phase ambiguity is correctly solved, while calibrating the receiver inter-frequency bias, time synchronization on the order of tens of picoseconds is expected. In this contribution, a method that considers the prior constraints of the between-receiver inter-frequency bias (IFB) and its random variation characteristics is proposed for the estimation of the between-receiver clock difference, based on the uncombined GNSS carrier phase and pseudorange observations of the zero and short baselines. The proposed method can rapidly achieve the single-difference ambiguity resolution of the zero and short baselines, and then obtain the high-precision relative clock offset, by using only the carrier phase observations, along with the between-receiver IFBs being simultaneously determined. Our numerical tests, carried out using GNSS observations sampled every 30 s by a dedicatedly selected set of zero and short baselines, show that the method can fix the between-receiver single-difference ambiguity successfully within an average of fewer than 2 epochs (interval 30 s). Then, a clock difference between two receivers with millimeter precision is obtained, achieving time synchronization on tens of picoseconds level, and deriving a frequency stability of 5 × 10−14 for averaging times of 30,000 s. Furthermore, the proposed approach is compared with the precise point positioning (PPP) time transfer method. The results show that, for different types of receivers, the agreement between the two methods is between −6.7 ns and 0.2 ns.

Toward Accurate Intervehicle Positioning Based on GNSS Pseudorange Measurements Under Non-Gaussian Generalized Errors

Intervehicle accurate positioning information is a cardinal prerequisite for proper and efficient management for many vehicular applications, such as collision avoidance, navigation, and intelligent transportation systems (ITSs). To improve the positioning accuracy, collaborative vehicular localization techniques based on fused data from different sources have been proposed in vehicular ad hoc networks (VANETs). Although the existing positioning techniques achieve high precision, they heavily rely on large-scale infrastructures and/or on the support of specific hardware devices, some of which are not generally accessible or are expensive, so they are impractical in many scenarios. In this article, a novel collaborative vehicular localization approach termed non-Gaussian weighted least-squares (${n}$ GWLS) is proposed to estimate the intervehicle distances. In this approach, the global navigation satellite system (GNSS) pseudorange double-difference (PDD) measurements are adopted, whereas the position dilution of precision (PDOP) and the number of common satellites of two given GNSS receivers are used to evaluate the quality of the PDD. To achieve reliable pseudorange measurements, the uncommon noise specific to a GNSS receiver and satellite is utilized as non-Gaussian distributed, where the generalized error distribution (GED) is adopted as an approximation to non-Gaussian densities. Moreover, the weighted least-squares technique is exploited, which considers the signal quality of each pseudorange measurement. The comparison study based on real-world experiments and statistical analysis demonstrates that the proposed method can effectively obtain an accurate intervehicle distance estimation.

Initial analysis for characterizing and mitigating the pseudorange biases of BeiDou navigation satellite system

Pseudorange bias has become a practical obstacle in the field of high-precision global navigation satellite system (GNSS) applications, which greatly restricts the further development of high-precision applications. Unfortunately, no studies have been conducted on the pseudorange biases of the BeiDou navigation satellite system (BDS). To mitigate the effects of pseudorange biases on the BDS performance to the greatest extent possible, the origin of such BDS pseudorange biases are first thoroughly illustrated, based upon which the dependency of the biases on the receiver configurations are studied in detail. Owing to the limitations regarding the parameter re-settings for hardware receivers, software receiver technology was used to achieve the ergodicity of the receiver parameters, such as the correlator spacing and front-end bandwidth, using high-fidelity signal observations collected by a 40-m-high gain dish antenna at Haoping Observatory. Based on this, the pseudorange biases of the BDS B1I and B3I signals and their dependency on different correlator spacings and front-end bandwidths were adequately provided. Finally, herein, the suggested settings of the correlator spacing and front-end bandwidth for BDS receivers are in detail proposed for the first time. As a result, the pseudorange biases of the BDS signals will be less than 20 cm, reaching even under 10 cm, under this condition. This study will provide special attention to GNSS pseudorange biases, and will significantly promote a clear definition of the appropriate receiver parameter settings in the interface control documents of BDS and other individual satellite systems.

GNSS pseudorange and time‐differenced carrier phase measurements least‐squares fusion algorithm and steady performance theoretical analysis

In Global Navigation Satellite System (GNSS) community, pseudorange observables, without integer ambiguity, have large measurement noise, while carrier phase observables, with high measurement accuracy, have integer ambiguity, which restricts the direct use either of them for high-accuracy navigation and positioning. In this regard, fusing pseudorange and ambiguity-free time-differenced carrier phase (TDCP) is a popular data processing technique. In this Letter, the least-squares fusion is studied. A theoretical analysis of the steady performance of this fusion is conducted. A set of formulas of the steady performance is derived, based on which simulations are carried out for different pseudorange-carrier-phase precision ratios. Results showed that the steady accuracy of fusion pseudorange is about two orders of magnitude higher than that of the original pseudorange, and is close to that of carrier phase observables. Besides, the convergence speed and the comparison to the Hatch filter are also checked in the simulations.

Calibration of BeiDou Triple-Frequency Receiver-Related Pseudorange Biases and Their Application in BDS Precise Positioning and Ambiguity Resolution.

Global Navigation Satellite System pseudorange biases are of great importance for precise positioning, timing and ionospheric modeling. The existence of BeiDou Navigation Satellite System (BDS) receiver-related pseudorange biases will lead to the loss of precision in the BDS satellite clock, differential code bias estimation, and other precise applications, especially when inhomogeneous receivers are used. In order to improve the performance of BDS precise applications, two ionosphere-free and geometry-free combinations and ionosphere-free pseudorange residuals are proposed to calibrate the raw receiver-related pseudorange biases of BDS on each frequency. Then, the BDS triple-frequency receiver-related pseudorange biases of seven different manufacturers and twelve receiver models are calibrated. Finally, the effects of receiver-related pseudorange bias are analyzed by BDS single-frequency single point positioning (SPP), single- and dual-frequency precise point positioning (PPP), wide-lane uncalibrated phase delay (UPD) estimation, and ambiguity resolution, respectively. The results show that the BDS SPP performance can be significantly improved by correcting the receiver-related pseudorange biases and the accuracy improvement is about 20% on average. Moreover, the accuracy of single- and dual-frequency PPP is improved mainly due to a faster convergence when the receiver-related pseudorange biases are corrected. On the other hand, the consistency of wide-lane UPD among different stations is improved significantly and the standard deviation of wide-lane UPD residuals is decreased from 0.195 to 0.061 cycles. The average success rate of wide-lane ambiguity resolution is improved about 42.10%.

GNSS Code Multipath Short-time Fourier Transform Analysis

Global Navigation Satellite System pseudorange multipath errors cannot be analyzed with the Fourier transform as they are non-stationary; thus, other tools must be used. The objective of this paper is to investigate short-time Fourier transform (STFT) performance in detecting Global Positioning System code multipath and analyzing its frequency content. Multipath estimation was achieved by using the code-minuscarrier and the pseudorange multipath observable. Two real datasets were analyzed. A first experiment was carried out using data provided by the Jiufeng (China) International GNSS Service station. The theoretical multipath time-frequency signature was identified by analyzing time series provided by a simulator under the same conditions of the analyzed station. The spectrograms calculated on the real data and those calculated on the simulated data show the same pattern, assessing the effectiveness of the STFT performance. Based on these results, the STFT analysis was applied to a second dataset collected in a strong multipath scenario in Naples (Italy), allowing identification of the multipath sources.