Algorithm for tropospheric delay estimation using genetic algorithm for calculating the coordinates of a stationary GNSS receiver

In urban road environments, global navigation satellite system (GNSS) signals may be interrupted due to occlusion by buildings and obstacles, resulting in reduced accuracy and discontinuity of combined GNSS/inertial navigation system (INS) positioning. Improving the accuracy and robustness of combined GNSS/INS positioning systems for land vehicles in the presence of GNSS interruptions is a challenging task. The main objective of this paper is to develop a method for predicting GNSS information during GNSS outages based on a long short-term memory (LSTM) neural network to assist in factor graph-based combined GNSS/INS localization, which can provide a reliable combined localization solution during GNSS signal outages. In an environment with good GNSS signals, a factor graph fusion algorithm is used for data fusion of the combined positioning system, and an LSTM neural network prediction model is trained, and model parameters are determined using the INS velocity, inertial measurement unit (IMU) output, and GNSS position incremental data. In an environment with interrupted GNSS signals, the LSTM model is used to predict the GNSS positional increments and generate the pseudo-GNSS information and the solved results of INS for combined localization. In order to verify the performance and effectiveness of the proposed method, we conducted real-world road test experiments on land vehicles installed with GNSS receivers and inertial sensors. The experimental results show that, compared with the traditional combined GNSS/INS factor graph localization method, the proposed method can provide more accurate and robust localization results even in environments with frequent GNSS signal loss.

Due to the low signal power, the Global Navigation Satellite System (GNSS) signal is vulnerable to interference and even cannot be captured or tracked in harsh environments. As an alternative, the Low Earth Orbit (LEO) satellite has been widely used in the navigation field due to the advantages of low cost and strong signals. It is becoming a significant component of the new combined navigation system with GNSS. The combination of an LEO Doppler signal and GNSS observables can improve the positioning accuracy and high-precision positioning convergence time of the GNSS receiver. However, the GNSS signal receiving capability cannot be improved from this data fusion level. We propose a novel assisted structure where GNSS signal acquisition and Doppler tracking are assisted by LEO Doppler positioning. The receiver uses the LEO signal to achieve Doppler positioning firstly. Then, the coarse position with the GNSS navigation messages received from LEO, as well as the estimated clock information, is used to assist in the acquisition and tracking of GNSS. In this way, the GNSS receiver’s sensitivity can get the benefit from this integrated system. The paper presents the structure of the assisted receiver and analyzes the assisted GNSS signal acquisition and carrier tracking performance in detail. Simulation experiments of this assisted structure are carried out to verify its superiority of acquisition and tracking sensitivity in comparison with standalone GNSS receivers. Theoretical analysis and experimental results show that the proposed acquisition method can achieve 90% detection probability at a carrier-to-noise ratio (C/N0) of 15 dB-Hz, which is about 8 dB higher than the conventional acquisition method without assistance; the proposed tracking method can track weak signals of 5 dB-Hz, which is about 4 dB higher than the conventional method. Therefore, this novel LEO-assisted receiver has significantly improved weak signal acquisition and tracking sensitivity.

With the ever-increasing number of small satellites launched into space, on-board orbit determination is becoming more and more important. Precise satellite positions are needed for constellation maintenance, formation flying, communication optimization, collision avoidance and Earth observation. In addition, accurate time information is required for the functioning of the instruments on board. Low-cost off-the-shelf Global Navigation Satellite System (GNSS) receivers and antennas, adapted to the small size and weight of the satellite, allow precise on-board orbit determination and time synchronization for even the smallest satellites.We analysed more than one year of on-board navigation solutions (NAVSOL) from 8 Astrocast CubeSats, which are equipped with our multi-GNSS single-frequency payload. Based on the residuals from a dynamic orbit fitting, we found that the quality of the NAVSOL from the Astrocast satellites varies strongly both over time and between satellites, with an RMS ranging from a few meters to several tens of meters.In this study, we focus on three main effects that influence the quality of the NAVSOL from the Astrocast satellites: (1) The orbit-fit residuals show a positive radial offset in the range of about 6 m to 15 m, which is caused by ionospheric refraction. Our data show that GNSS signals at negative elevations are very strongly affected by the ionospheric refraction and thus account for the major part of the radial offset. (2) Discrepancies between the NAVSOL positions and velocities, and simulations with a GNSS signal generator show a once-per-revolution periodicity in the out-of-plane component, with amplitudes of 2 m and 5 cm/s in position and velocity, respectively. This effect is probably due to an inappropriate dynamic model used in the real-time navigation algorithm of the GNSS receiver. (3) Depending on the location of the GNSS antenna on board the satellite, the noise level varies by a multiple. This is assumed to be due to the antenna orientations, interference of the GNSS signals with electromagnetic waves coming from the satellite platform, signal attenuation during the transmission from the antenna to the receiver and differences in the soldering or tuning of the individual GNSS antennas.These findings help us refine hardware configurations and firmware settings in preparation for future Astrocast satellites or other nanosatellite missions. By eliminating or minimizing the mentioned effects, we expect to consistently achieve an accuracy on the level of a few meters for the real-time navigation solution of commercial off-the-shelf single-frequency GNSS receivers in space.

This study evaluates the suitability of compact, lowcost Global Navigation Satellite System (GNSS) receiver module in estimating the effects of tropospheric delay on accuracy of GNSS position solution at GNSS laboratory, the University of Burdwan, West Bengal, India with geographical coordinate of 23.2545°N, 87.8467°E, −11.402 m, using compact, low-cost uBlox F9P GNSS module and high cost Leica GR 50 geodetic receiver in March 2023. GNSS observation data were logged by the two receivers for 24 hours at 1Hz dual-frequency and converted into Rinex observation files in GPS-only, GLONASS-only, and GPS+GLONASS hybrid modes. The converted Rinex observation data were uploaded to the Natural Resources of Canada (NRCan) online service to obtain the user fixed values of latitude, longitude and attitude, and the wet and dry tropospheric delay files via email. The converted Rinex observation files were post-processed using GNSS positioning analysis tool that estimate the GNSS positioning accuracy parameters namely Distance Root Mean Square (2DRMS), Circle of Error Probable (CEP), Spherical Error Probable (SEP), and Mean Radian Spherical Error (MRSE) from the users defined known fixed values of latitude, longitude and altitude. The total delay obtained from the two GNSS receivers were compared with their positioning accuracy parameters. The results showed better position solution on observation days with the least total zenith delay in all the constellations considered. The Leica GR 50 shows an average total zenith delay of 2.476 m in GPS mode, 2.486 m in GLONASS mode and 2.4680 m in GPS+GLONASS hybrid mode while the uBlox F9P shows 2.477 m in GPS mode, 2.494 m in GLONASS mode and 2.4684 m in GPS+GLONASS hybrid mode of operation. The GPS+GLONASS hybrid mode of operation reduces the total zenith delay and enhanced the position solution. Hence, there is no distinct difference between the two GNSS receivers, suggesting that compact, low-cost, GNSS receiver modules can be used for tropospheric study.

Global Navigation Satellite Systems (GNSS) rely on one-way signal travel time measurements from satellites to receivers. To ensure accurate ranging, GNSS must estimate and compensate for clock offsets on at least one end of the transmitter-receiver system. Consequently, clock offsets are highly correlated with GNSS-derived parameters such as station coordinates, tropospheric delay estimates, satellite radial orbit parameters, and apparent geocenter coordinates. Improper handling of clock offsets can lead to their absorption into these parameters, degrading geodetic product accuracy. Traditionally, clocks have been handled within individual techniques without being specially addressed. However, some research efforts and experimental trials have explored using VLBI to synchronize clocks for GNSS and refining clock models to reduce correlations with other estimated parameters in GNSS, thereby improving overall precision.With recent advancements, high-precision optical clocks and fiber-optic time transfer technologies provide new possibilities for enhancing clock synchronization in GNSS. Optical fiber offers a stable, interference-free medium for time and frequency transfer, eliminating atmospheric effects such as ionospheric and tropospheric delays that impact GNSS-based synchronization. Moreover, fiber-optic time transfer is inherently two-way, removing the need for external clock offset estimation. Thus, fiber-optic clock synchronization represents the most precise timing technique currently available. Establishing a common clock by connecting multiple GNSS receivers via optical fiber could significantly reduce the number of estimated clock parameters in GNSS solutions, leading to improved geodetic measurement precision and a more accurate geodetic reference frame.Despite its potential, the approach of implementing a common clock with optical fiber for GNSS receivers remains largely untested. Although optical fiber links have been successfully used in clock synchronization, their integration into GNSS receiver clocking is still in an experimental stage. Notable existing efforts include: (1) the Geodetic Observatory Wettzell, where multiple receivers are connected to a single clock via optical fiber, representing a local baseline setup, and (2) the GFZ experiment, where a receiver is linked to the ultra-stable clock of PTB, representing a regional baseline approach.This study characterizes existing fiber-optic connections among GNSS receivers to identify practical challenges and evaluate their impact on GNSS parameter estimation. We process data from receivers sharing a common clock using Bernese GNSS Software. Initially, PPP will be performed to compare GNSS-derived clock parameters across receivers sharing a common clock, verifying the effectiveness of fiber-optic clock synchronization. Following this validation, we will leverage GNSS-derived clock parameters to evaluate inter-receiver clock differences measured via optical fiber. Subsequently, we will implement a strategy in which only one receiver’s clock parameters are estimated, using fiber-measured clock differences as a priori constraints for other receivers in the PPP solution. This approach reduces the number of estimated clock parameters and serves as a preliminary test of the feasibility of a GNSS common clock framework.Future developments will focus on refining our analysis framework to enable simultaneous estimation of GNSS receivers operating under a common clock. This research contributes to the broader goal of integrating ultra-stable clocks into global GNSS networks, ultimately enhancing the stability of geodetic reference frames and improving GNSS-derived geodetic products.

The impact of L‐band equatorial ionospheric scintillation on Global Navigation Satellite Systems (GNSS) receivers is investigated in this paper using both real and synthetic scintillation data. To this end, various low‐latitude data sets, recorded during the most recent solar maximum, are exploited in post‐processing to develop and verify realistic simulation tools and evaluate GNSS receiver performance. A scintillation simulation model is implemented based on the phase screen formulation of Dr. Charles Rino (1979, 1982, and 2011) which allows oblique signal propagation in an anisotropic propagation medium with multiple irregularity layers (or phase screens) for multiple GNSS frequencies. The observed real scintillation parameters are used to drive GNSS signal simulations. The subsequent simulated GNSS signal time series are verified through comparison with real data for different signal tracking states including the most severe and challenging tracking scenarios. Using both real and synthetic data sets, the impact of scintillation on observation quality and receiver performance is evaluated in terms of probability of loss of phase and frequency lock, as well as the correlation of disturbed L‐band signals transmitted by GNSS satellites on the same transionsopheric path.

People have to move between indoor and outdoor frequently in city scenarios. The global navigation satellite system signal cannot provide reliable indoor positioning services. To solve the problem, this article proposes a seamless positioning system based on an inverse global navigation satellite system signal, which can extend the global navigation satellite system service into the indoor scenario. In this method, a signal source is arranged at a key position in the room, and the inverse global navigation satellite system signal is transmitted to the global navigation satellite system receiver to obtain a preset positioning result. The indoor positioning service is continued with the inertial navigation system after leaving the key position. The inverse global navigation satellite system seamless positioning system proposed in this article can unify indoor and outdoor positioning using the same receiver. The receiver does not need to re-receive navigation information when the scene changes, which avoids the switching process. Through the design of signal layer coverage, the receiver is in a warm start state, and the users can quickly fix the position when the scenario changes, realizing quick access in a true sense. This enables the ordinary commercial global navigation satellite system receiver to obtain indoor positioning capability without modification, and the algorithm can perform accurate positioning indoors and outdoors without switching.

Implementing the International GNSS Service 2021+ Strategic Plan: Vision and Use Cases

In the recent years, the threat of radio frequency interference (RFI) to Global Navigation Satellite Systems (GNSS) receivers has been increasing due to an escalating number of RFI related GNSS issues, and enhanced complexity of jammers and spoofers. This poses significant integrity threats to various systems that depend on GNSS measurements for navigation and guidance. One of the most versatile methods to detect such instances of spoofing is the use of Automatic Gain Control (AGC) measurements provided by GNSS receivers. AGC is indicative of the change in thermal noise levels observed by the frontend of the receiver, thus it can be used to detect presence of RFI. If AGC is coupled with the carrier to noise ratio density (??/????) values of visible GNSS satellites, it is possible to gain insight into which specific constellations or satellites may have been spoofed. Although AGC has been available in some commercial GNSS receivers and customized frontends for some time, the introduction of raw GNSS measurements in Android 7 has recently allowed it to be accessible in some smartphones as well. This study looks at AGC measurements from multiple smartphone models which have different GNSS chipsets, assesses their behavior under RFI, points out the current limitations, and proposes future improvements that would assist in its usage as a GNSS RFI indicator. Furthermore, the paper discusses the future of AGC measurements that would assist in broadening their applications to all GNSS receivers.

Measurements of carrier frequency phase differences of global navigation satellite system signals between multiple antennas are used in many coordinate and navigation applications. Global navigation satellite systems signal simulators are used for controlling global navigation satellite systems receiver’s instrumental errors. Therefore, it is necessary to determine the systematic error of the carrier frequency phase of generated signals for signal simulators. For this purpose a new calibration method of global navigation satellite systems simulators was developed. Method is based on refined errors model of generated phase differences of two radio frequency channels of the simulator. The proposed method was implemented using a wideband oscilloscope as an analog-to-digital converter. Approbation of the calibration method was carried out by comparison with the measurement results obtained using the State secondary standard of units of complex transmission coefficients in the range of 0...–60 dB and complex reflection coefficients in the range of 0.002–1 in the frequency range of 0.05–65 GHz (registration No. 2.1.ZZT.0210.2015). The calibration method allows one to determine carrier frequencies phase offsets of navigation signals for global navigation satellite systems simulators with expanded uncertainty (with a coverage factor of 3) of 1°. The proposed method provides the required accuracy of generating phase differences of the carrier frequencies of global navigation satellite systems signals is ensured for modern types of global navigation satellite systems simulators.

The study of climate change is an important field of research. Monitoring of atmospheric variability especially the tropospheric precipitable water vapor (PWV) is a powerful way to investigate climate change. Global navigation satellite systems (GNSS) provide a good tool for studying atmospheric parameters as GNSS signals along its path from the satellites to the ground based receivers suffer a significant delay due to the refractivity of earth’s atmosphere. GNSS signals are not only delayed but also refracted in the neutral atmosphere. The zenith wet delays (ZWD) caused by the troposphere can be estimated during the geodetic processing of GNSS signals. Since the ZWD is tightly correlated to the PWV, GNSS observations can be used to study the changes of PWV. In this study GNSS data from the Egyptian permanent GNSS network (EPGN), International GNSS Service (IGS), EUREF Permanent Network (EPN) and Scripps Orbit and Permanent Array Center (SOPAC), for the years 2013 and 2014, were used. These GNSS stations provided a good geometrical coverage over the respective region. All GNSS data were processed using Bernese V 5.2 software. The needed product from GNSS data processing is the tropospheric zenith total delay (ZTD) over each GNSS site. The ZTD is divided based on physical parameters into zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). The ZWD is the basic observable used to calculate PWV. The values of the PWV were calculated and its variation over the study area was investigated. The quality of calculated PWV values from GNSS data evaluated against traditional Radiosonde (RS) measurements. The results of GNSS PWV showed good agreement with RS PWV when the PWV values were low, but this agreement became worse at high PWV values as the differences between the two techniques increased. The correlation coefficient between RS PWV and GNSS PWV varied from 0.31 to 0.84. Standard deviation of the differences between RS PWV and GNSS PWV ranged from 2.369 to 5.973 mm. The PWV estimated from GNSS observations had annual cycle, and its cycle in 2013 was different from that in 2014. The PWV differences between the 2 years clarified that the water vapor content over the east Mediterranean in most of 2014 days was higher than that in 2013. Furthermore, PWV variations were noted on both temporal and spatial scales. The highest temporal variation value was 25.41 mm whereas the maximum value of the spatial variation was 19.67 mm. The present study illustrated the importance of using geodetic networks to provide atmospheric information.

The landscape of Global Navigation Satellite Systems (GNSS) signals is undergoing significant change. The parallel development of new, more robust and versatile signals along with two new GNSS systems with global reach is having a dramatic impact on the development of GNSS receivers. Receiver manufacturers are continually developing and implementing unique signal acquisition and tracking algorithms, advanced integrity monitoring algorithms, advanced multipath mitigation algorithms and a host of other enhancements in an effort to improve the performance of GNSS receivers and make their products stand out in a crowded field. The objective of this research is to develop a methodology for comparing the pseudorandom noise (PRN) code tracking performance of various receivers. While the overall performance of a receiver depends on many more factors, effective PRN code tracking is fundamental to the operation of a GNSS receiver. The methodology developed in this research requires three fundamental measurements from the receiver under test – code pseudorange, carrier pseudorange and carrier-to-noise-density ratio (C/No). These measurements are generated by all GNSS receivers but may not always be available to the user. Therefore, this methodology can only be performed on receivers that output these values. This methodology might be useful as a tool to evaluate the suitability of various receivers in certain environments or applications (e.g., weak signal environments, high dynamic environments, unfriendly radio frequency (RF) interference environments, etc.) and also as a means of comparing the relative performance of receivers in those environments or applications. Expectations for the research were that the data collection and analysis techniques would generate code loop tracking jitter plots that closely tracked with theoretical curves. In addition, it was expected that different receivers would yield slightly different jitter plots giving them a unique “signature.” Finally, it was expected that some receivers might incorporate scalar code tracking loops and others might incorporate vector tracking loops. The methodology was developed and refined using three receivers from three popular manufacturers, each with a unique set of capabilities. Raw data was collected from each receiver and processed using purpose built algorithms to estimate the code loop tracking jitter for each signal for each receiver. The code loop tracking observations for each of the three receivers tested were compared with theoretical curves generated using closed form equations published in previous papers. In most cases, the data compared favorably. However, there were some significant outliers that are worthy of additional research and analysis. In addition, the jitter plots for one receiver tested indicated that it used scalar code tracking loops and the jitter plots for the other two receivers indicated that they use vector tracking loops. It appears to be possible to determine if a receiver uses scalar tracking loops or vector tracking loops based on the jitter estimates generated in this research. This research indicated that the methodology might be a useful tool for 2 characterizing GNSS receivers and, eventually evaluating their performance in various environments. However, more data collection and analysis is required to further validate and refine the methodology. Also, more analysis of the signals that yielded “non-conforming” jitter plots should be examined in more detail.

A sparse global navigation satellite system (GLONASS) signal acquisition method based on compressive sensing and multiple measurement vectors is proposed. The nonsparse GLONASS signal can be represented sparsely on our proposed dictionary which is designed based on the signal feature. Then, the GLONASS signal is sensed by a normalized orthogonal random matrix and acquired by the improved multiple measurement vectors acquisition algorithm. There are 10 cycles of pseudorandom codes in a navigation message, and these 10 pseudorandom codes have the same row sparse structure. So, the acquisition probability can be raised by row sparse features theoretically. A large number of simulated GLONASS signal experiments show that the acquisition probability increases with the increase in the measurement vector column dimension. Finally, the practical availability of the new method is verified by acquisition experiments with the real record GLONASS signal. The new method can reduce the storage space and energy loss of data transmission. We hope that the new method can be applied to field receivers that need to record and transmit navigation data for a long time.

The Global Navigation Satellite System (GNSS) signals are often blocked or interfered in complex geographical or electromagnetic environments, which may make GNSS receivers unable to provide satisfying navigation and positioning services. There have been many ground-based or space-based GNSS augmentation systems to improve the resilience of GNSS positioning, of which most of them rely on additional infrastructures. In this study, a smartphone-based tightly-coupled positioning method was developed using the images from a build-in monocular camera and GNSS signals. In this method, the feature points with the known coordinates are regarded as 'visual pseudolite' and the distance between the camera and the feature points was calculated according to the photogrammetry approaches and used to estimate the user positioning with GNSS signals. The experimental results showed the feasibility of the tightly-coupled positioning algorithm and reached the positioning accuracy of ±5.56 m (1?), which is significantly higher than that of GNSS-only and vision-only positioning solutions.

The traditional measurement of signal bandwidth using single-carrier frequency sweeping is not suitable for global navigation satellite system (GNSS) signal. A new analysis technique of signal bandwidth with digital signal processing technique has been developed. After the GNSS signal is highly sampled, the spectrum of the actual GNSS signal and the ideal signal generated locally are evaluated in digital domain. The bandwidth of GNSS signal can be calculated. Simulation has been done for the proposed measurement technique using spectrum evaluation algorithm of the Periodogram and the Welch respectively. The simulation results shows that the GNSS signal bandwidth can be accurately estimated after the ideal and actual signal spectrum are evaluated and calculated using the Welch. The simulation results show that The estimating accurate of signal bandwidth can be higher than 99.9% in the case of the proper parameters have been set for Welch.