Enhancing GNSS timing and positioning performance through receiver clock noise modeling

Mitigation of the multipath effect in BDS-based time transfer using a wave-absorbing shield

Today’s society is highly reliant on time and frequency synchronization, e.g., in communications systems and financial networks. Precise timing is more and more derived from satellite navigation receivers that are unfortunately very susceptible to various signal threats. We studied the performance of global navigation satellite system (GNSS) timing under different operating conditions and tested the effectiveness of different techniques that improve timing receiver robustness. These features were tested under various threat scenarios related to specific vulnerabilities in GNSS-based timing, such as interference and navigation message errors, and their efficiency was analyzed against the corresponding scenarios. We found that interference or meaconing-type spoofing can threaten GNSS timing, but it can be detected by means of automatic gain control (AGC) and carrier-to-noise ratio-based methods. GNSS interruptions due to interference can be bridged by a local oscillator holdover technique based on a Kalman filter whose parameters are based on a GNSS time solution. Navigation message errors are mitigated by the European Geostationary Navigation Overlay Service (EGNOS), and constellation-wide timing errors can be detected by the use of a dual-constellation [global positioning system (GPS)-Galileo] cross-check. Dual-frequency operation for timing, in addition to mitigating first-order ionospheric effects, was found to be more robust to interference with the option to fall back to single frequency.

A wide-range utilisation of Global Navigation Satellite Systems (GNSS) across technology and socioeconomic domains renders the satellite navigation one of the pillars of the modern civilisation. Tackling and overcoming The inherent shortcomings and emerging threats to provision of robust and resilient GNSS Positioning, Navigation and Timing (PNT) services have become a research subject of the utmost importance. An open access to the GNSS positioning estimation process is fundamental for development of advanced methods for robust and resilient GNSS position estimation. Recent introduction of Google Android 7.0 revision allows for direct access to raw GNSS pseudoranges observed by smartphones. Here we address the opportunities for GNSS positioning estimation improvements, given through exploitation of Google Android Location API, in creation of bespoke GNSS position estimation process in navigation application domain of a GNSS Software-Defined Radio (SDR) receivers in smartphones. We present and validate opportunities for improvement of GNSS position estimation process through utilisation of distributed computing architectures, trusted sources of GNSS augmentation data and utilisation of GNSS positioning methods suitable for targeted classes of GNSS applications Authors are members of European GNSS Agency's GNSS Raw Measurements Task Force, and co-authored the white-paper on GNSS-related Google Android Location API applications.

Time and navigation are intimately linked and rely on each other. Global navigation satellite system (GNSS ) positioning is based on the measurement of time intervals needed by the signal to travel from satellites to the receiving station on the Earth or nearby. The precision of GNSS positioning is reached thanks to atomic frequency standards onboard the satellites and the possibility to determine their synchronization differences at the subnanosecond level. Time is thereby the core of GNSS. Inversely GNSS is widely used for accurate time and frequency dissemination, as well as for the comparison of distant clocks as needed for time and frequency metrology. All these aspects of using GNSS for time/frequency applications will be presented in this chapter.

In this paper, a data-driven Inertial navigation systems (INS) and Global Navigation Satellite System (GNSS) fusion algorithm based on the use of the Gated Recur-rent Unit (GRU) is proposed. In this project, we trained the GRU neural network with Inertial Measurement Unit (IMU) raw data and GNSS Position, Velocity and Timing (PVT) solutions as input and the position difference between GNSS and ground truth as labels. Therefore, the trained model can estimate the rover’s positions by subtracting the predicted GNSS error from GNSS positions given IMU raw measurements and GNSS PVT solutions. To evaluate the performance of GNSS/INS fusion algorithms in realistic scenarios, we developed an experimental platform. Our experimental platform consists of a moving test rig and an external validation system. The moving test rig consists of a rover equipped with an LPMS-CU2: 9-Axis Inertial Measurement Unit (IMU) and U-Blox ZED-F9P GNSS receiver. For validation purposes, we employ an onboard real-time kinematic positioning (RTK)-GNSS receiver. The test scenarios include both open-sky and challenging conditions near buildings, which is beneficial for devolving and testing urban navigation systems. After training with collected experimental data in multiple test scenarios, the proposed algorithm is able to improve GNSS positioning accuracy by more than 60% for the open-sky environment and 30% for the urban environment.

<title>Abstract</title> Since the availability of raw global navigation satellite system (GNSS) measurements in Android devices in 2016, smartphone users have acquired the ability to not only process GNSS position, velocity, and time (PVT) solutions from chipsets, but also to utilize raw measurements to carry out their own GNSS postprocessing. Consequently, rather than relying on black-box algorithms inside the chipsets, it has become possible to understand and configure the navigation algorithms. To date, most publicly available navigation algorithms and corresponding publications that use Android raw GNSS measurements have focused on GNSS-only solutions. Furthermore, the top three participants of the Google Smartphone Decimeter Challenge in 2021 and 2022 were either unsuccessful in implementing an effective extended Kalman filter (EKF) using both GNSS and inertial navigation sensors (INSs) or found no significant improvements to their solutions arising from the use of non-GNSS sensors. This paper provides insight into the challenges of effectively implementing a traditional GNSS/INS EKF for smartphones and explores the reason behind the limited performance enhancements compared with GNSS-only solutions under benign environments. This work addresses these issues and provides solutions to alleviate these shortcomings by describing an algorithm to successfully fuse inertial sensors with raw GNSS measurements. The algorithm provides a robust solution by using not only the code, Doppler, and carrier-phase measurements in the PVT computation, but also the inertial sensors to assist in GNSS fault detection and exclusion (FDE) and to improve solution accuracy and availability. The novelties of this paper lie in the incorporation of a tightly coupled GNSS/INS EKF for sensor fusion, single-differenced GNSS measurements to eliminate the effects of receiver clock components, empirical modeling of GNSS and INS errors for statistical accuracy, utilization of both carrier-phase and Doppler measurements for accurate benign and challenging environment operations, and the application of INS for GNSS measurement FDE and navigation availability improvements.

Synchronization between system times of Global Navigation Satellite Systems (GNSSs), or GNSS time interoperability, is one of the prerequisites of GNSS interoperability. We explored the fractal behavior of time offsets between Coordinated Universal Time (UTC) and GNSS time scales (GNSST). A fractal-based prediction method for forecasting UTC-GNSST time offsets is developed. Through data analysis, the self-similarity behavior in UTC-GNSST time offsets is revealed, which is proven by calculating the Hurst exponent. The values of the fractal dimension and correlation metric indicated that the time series of UTC-GNSST time offsets have long memory, of which the memory span is 1247 days and could be obtained from V-statistics. Subsequently, the fractal interpolation-based mathematic model was built, and the prediction accuracy was tested through numerical experiments. Compared with the polynomial and gray prediction models, the fractal interpolation forecast model was found to have higher prediction accuracy. The prediction accuracies of UTC-GPST and UTC-GLOT using fractal interpolation forecast model in short term are less than 1.3 and 5.5 ns, and in long term are less than 2.3 and 8.3 ns, with an improvement by at least 50 and 30% compared to polynomial and gray model.

Global Navigation Satellite System (GNSS)-based applications rely on the quality of the GNSS position, navigation, and timing (PNT) services, accomplished through measurement and processing of satellite signals propagation characteristics in a process commonly known as satellite navigation. GNSS positioning performance is in the foundation of the quality of service of GNSS-based applications including the growing number of them in transport, traffic and Intelligent Transport Systems segments, thus a need for a common and independent approach. Here, we propose a novel method for the assessment of the contribution of a single cause to the over-all GNSS positioning error. Proposed method is demonstrated in the case of the GNSS multipath effects, resulting with the experimental predictive model of the direct multipath contribution to GNSS positioning error. The predictive models developed in this research is aimed at deployment in the GNSS positioning performance assessment for GNSS-based applications in transport and telecommunications.

Standalone Global Navigation Satellite System (GNSS) applications demand higher precision than is typically achieved using differential processing. While differential processing removes the effects of most common-mode error sources, it provides limited compensation for distortions caused by multipath or pseudorange measurement biases from dissimilar receiver hardware due to subtle space vehicle-borne signal deformations. These naturally occurring phenomena directly impact system integrity and lead to ranging error in the GNSS receiver solution. Signal Quality Monitoring (SQM) has the objective of providing confidence in the GNSS Positioning, Navigation, and Timing (PNT) solution, and aims to offer timely warning in the event that SV signal conditions degrade to unsafe levels. Several methods of SQM have been previously introduced and implemented to augment civilian Safety-of-Life (SoL) applications. The methods considered in this work focus on implementing effective SQM using low-cost Commercial Off-theShelf (COTS) equipment, a Software-Defined Radio (SDR), and a typical software GNSS receiver architecture that tracks the Galileo E1 signals and the Global Positioning System (GPS) L1 Coarse-Acquisition (C/A) signals. The techniques here are centered on acquiring and discriminating signal chip shapes with a goal of identifying both ‘clean’ and ‘deformed’ signals. The demonstrated identification method is relevant to the growing significance of SQM for SoL applications while providing benefit for confidently monitoring received GNSS signal integrity without requiring specialized receiver hardware.

Robust Interference Mitigation (RIM) is a class of techniques that can significantly improve the performance of Global Navigation Satellite System (GNSS) receivers in the presence of jamming and interference. While RIM enables receiver operations in the presence of significant levels of jamming, biases and other distortions could be introduced in the final navigation solution. This paper experimentally analyses the impact of RIM on the timing solution of a GNSS receiver acting as a timing device. In this case, the user coordinates are fixed and the receiver only computes the clock bias and drift. Several tests have been performed and different GNSS modulations have been considered. From the analysis, it emerges that GNSS does not introduce biases. Moreover, the stability of the timing solution, as quantified by the Allan Deviation (ADEV), is not affected by RIM.

The analysis of the Global Navigation Satellite System (GNSS) time series provides valuable information for geodesy and geodynamics research. Precise data analysis strategies are crucial for accurately obtaining the linear velocity of GNSS stations, enabling high-precision applications of GNSS time series. This study investigates the impact of different stochastic noise models on velocity estimations derived from GNSS time series, specifically under conditions of environmental loading correction and common mode error (CME) removal. By comparing data from various data centers, we find that post-correction, different analysis strategies exhibit high consistency in their noise characteristics and velocity estimation results. Across various analysis strategies, the optimal noise models were predominantly Power Law with White Noise (PLWN) and Flicker Noise with White Noise (FNWN), with the optimal noise models including COMB/JPL, COMB/SOPAC, and COMB/NGL for approximately 50% of the datasets. Most of the stations (approximately 80%) showed velocity differences below 0.3 mm/year and velocity estimation uncertainties below 0.1 mm/year. Nonetheless, variations in amplitudes and periodic signals persisted due to differences in the processing of raw GNSS observations. For instance, the NGL and JPL datasets, which were processed using GipsyX 2.1 software, showed higher amplitudes of the 5.5-day periodic signal. These findings provide a solid empirical foundation for advancing data analysis methods and enhancing the reliability of GNSS time series results in future research.

Global Navigation Satellite System (GNSS) typically use ranging signals to provide a global-coverage solution for positioning, velocity and timing applications. An accurate and stable clock is required for pseudorange estimation and GNSS timeline. The very accurate and long-time stable on-board atomic clocks on each GNSS satellite (SV), without any corrections after a certain period, will deviate from GNSS time and cause the significant reduction of position accuracies. To correct the atomic clocks bias, GNSS main ground-control stations accurately estimate the bias, usually having a residual approximately between 1 ns and 10 ns (corresponding to pseudorange error up to 0.3 – 3 m) respectively and re-transmit the correction to the SV. For critical application that require precise positioning at decimetre-level accuracy, an accurate clock bias correction, in the order of 3 ns (< 1 m pseudorange error) is required. For Global Positioning System (GPS), the clock bias correction interval is few hours with potential drift can be up to > 12 ns, leading to > 4 m pseudorange error. International GNSS Service (IGS) provides accurate clock bias corrections that can be openly accessed. IGS final product provides clock bias correction ±75 ps accuracy with availability 12-18 days. Alternatively, IGS ultra-rapid product provides clock bias correction with accuracy of 3 ns - 5 ns (pseudorange error up to 1.5 m). Another drawback of using IGS product is that the receiver data processing unit should be connected to internet and to download IGS clock-bias. In this paper, the development and performance evaluation of a Machine Learning (ML) time-series model, based on a transformer deep neural network, for SV clock bias correction prediction tool are presented. The main purpose of the developed ML software tool is to provide fast and reliable forecasting of clock bias correction for stand-alone single-frequency receivers without changing the infrastructure of the receivers and with prediction accuracy of < 2 ns. From the training results, the target prediction accuracy, up to two-hour time horizon, of < 2ns can be achieved. Performance analysis and comparison of the developed transformer model prediction with respect to IGS rapid, CODE-MGEX clock-bias product and holdover method are performed. In addition, prediction comparison among difference SV block and clock-types are also presented. From all the comparisons, the ML predictions perform up to 50% better than the other clock-bias prediction methods.

The received global navigation satellite system (GNSS) signal has a very low power due to traveling a very long distance and to the nature of the signal’s propagation medium. Thus, GNSS signals are easily susceptible to signal interference. Signal interference can cause severe degradation or interruption in GNSS position, navigation, and timing (PNT) services which could be very critical, especially in safety-critical applications. The objective of this paper is to evaluate the impact of the presence of jamming signals on a high-end GNSS receiver and investigate the benefits of using a multi-constellation system under such circumstances. Several jamming signals are considered in this research, including narrowband and wideband signals that are located on GPS L1 or GLONASS L1 frequency bands. Quasi-real dynamic trajectories are generated using the Spirent™ GSS6700 GNSS signal simulator combined with an interference signal generator through a Spirent™ GSS8366 unit. The performance evaluation was carried out using several evaluation metrics, including signal power degradation, navigation solution availability, dilution of precision (DOP), and positioning accuracy. The multi-constellation system presented better performance over the global positioning system (GPS)-only constellation in most cases. Moreover, jamming the GPS band caused more critical effects than jamming the GLONASS band.

Global navigation satellite systems (GNSS) are the most widely used positioning, navigation, and timing (PNT) technology. However, a GNSS cannot provide effective PNT services in physical blocks, such as in a natural canyon, canyon city, underground, underwater, and indoors. With the development of micro-electromechanical system (MEMS) technology, the chip scale atomic clock (CSAC) gradually matures, and performance is constantly improved. A deep coupled integration of CSAC and GNSS is explored in this thesis to enhance PNT robustness. “Clock coasting” of CSAC provides time synchronized with GNSS and optimizes navigation equations. However, errors of clock coasting increase over time and can be corrected by GNSS time, which is stable but noisy. In this paper, weighted linear optimal estimation algorithm is used for CSAC-aided GNSS, while Kalman filter is used for GNSS-corrected CSAC. Simulations of the model are conducted, and field tests are carried out. Dilution of precision can be improved by integration. Integration is more accurate than traditional GNSS. When only three satellites are visible, the integration still works, whereas the traditional method fails. The deep coupled integration of CSAC and GNSS can improve the accuracy, reliability, and availability of PNT.

The aim of this paper is to reduce the noise level in the time signals of the Global Navigation Satellite Systems (GNSS). This is done by finding patterns in the Common Generic GNSS Timing Transfer Standard (CGGTTS) data, as the pseudorange residuals in this data appear to include patterns that repeat every day. The reduced noise level allows for easier detection of possible anomalies in the time signals of individual GNSS satellites and hence increases the resilience of the GNSS time measurement. The observed patterns are explainable by multipath, repeating every time the satellite is at a certain position in its groundtrack.