Noises in Double-Differenced GNSS Observations

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.

Urban environments present major challenges to the global navigation satellite system (GNSS) positioning to estimate the position of a self-driving vehicle. GNSS signals are often obstructed by buildings and other obstacles, leading to reflected and diffracted signals, which cause major positioning errors and known as line-of-sight (LOS) and non-line-of-sight (NLOS) multipath errors. Particularly, real-time kinematic (RTK)-GNSS, which can estimate the position in the centimeter-level accuracy, cannot estimate the precise position when there exist NLOS multipath errors. If we use NLOS GNSS code and carrier phase multipath measurements into the RTK-GNSS algorithm, carrier phase integer ambiguity cannot be solved, or wrong integer ambiguities are estimated. As a result, integer ambiguity resolved to fix solutions cannot be estimated, or wrong fix solutions which have large position error are estimated. That is a major barrier to using RTK-GNSS in autonomous driving. In this paper, we propose a novel NLOS detection and exclusion technique to enhance existing RTK-GNSS positioning in urban areas using only GNSS measurements alone. The key idea behind the proposed technique is that the NLOS pseudorange error will always be a positive value. NLOS pseudorange is longer than the true range, which is the distance between the GNSS antenna and satellite, due to the time delay caused by reflection and diffraction. The distribution of the NLOS error is not along with a Gaussian distribution. We use this phenomenon to detect the NLOS signals. We propose a technique to detect and eliminate the NLOS multipath using double-differenced pseudorange residuals (DD-PR). In the RTK-GNSS, DD GNSS measurement between the rover and base station is typically used. Here, we compute the DD-PR to detect the NLOS signals. In order to compute the DD-PR, the true position of the vehicle must be determined in advance. To solve this contradiction, we use a particle filter. The particle filter generates the position hypotheses, which is called as “particle”. These particles are used as the position candidate for estimating the DD-PR. When the DD-PR can be calculated at each particle position, we detect the large positive errors in DD-PR as NLOS signals. Then we compute the integer ambiguity of only the LOS DD carrier phase to estimate the precise vehicle position. The flow of the proposed technique is as follows: (1) The hypothetical user positions are created as particles, where the state vectors of these particles are 3D positions, x, y, and z. The initial particles are distributed based on the solution of the normal GNSS point positioning and its variance. (2) In the prediction step of the particle filter, the particle state in the next time step is estimated using the velocity of each particle computed from GNSS Doppler measurements. (3) Next, we compute the DD-PR at each particle location. The receiver clock bias, satellite clock bias, ionosphere error, and troposphere error in GNSS pseudorange are canceled through DD computation. As a result, DD geometrical range between receiver and satellite and DD multipath errors remain in the DD measurement. We compute DD-PR using the particle position. As a result, the only multipath error remains if the particle is close to the true position. NLOS multipath error is always positive value; we generate the subset of the LOS measurement hypothesis at each particle using a simple threshold test. (4) Next, we compute the RTK-GNSS position solution using the generated subset of the LOS measurement hypothesis at each particle location. It is expected that the RTK-GNSS fix solution can be calculated if the particle location is close to the true position because the NLOS signal has been eliminated. By contrast, if the particle is far from true position, the integer ambiguity cannot be solved because of using the incorrect subset of LOS measurements. The likelihood of each particle is computed from a distance between the particle location and the RTK-GNSS fix solution. The particle that is closest to the true position has a higher likelihood than the other particles. The probabilistic weight of each particle is then updated based on its likelihood. (5) Finally, all the particles are resampled based on their new weights. Particles that are sufficiently close to the true position survive this resampling step, and the average position of the remaining particles are employed as the final estimated user position. To confirm the effectiveness of the proposed technique, a kinematic positioning test was performed in Shinjuku, Tokyo, Japan. From the several positioning tests, the proposed technique could dramatically improve the availability and accuracy of RTK-GNSS fix solutions in the dense urban canyon where there exist a lot of NLOS multipath signals.

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.

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.

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 performance of the Global Navigation Satellite System (GNSS)-based navigation is usually degraded in challenging environments such as deep urban and light indoors. In such environments, the satellite visibility is reduced, and the complex propagation conditions perturb the GNSS signals with attenuation, refraction, and frequent reflection. This paper presents a novel Artificial Intelligence (AI)-based approach, to tackle the complex GNSS positioning problems in deep urban, even light indoors. The new approach, called LIGHT, i.e., Light Indoor GNSS macHine-learning-based Time difference carrier phase, can select healthy GNSS carrier phase data for positioning thanks to Machine Learning (ML). The selected carrier phase data are fed into a Time Difference Carrier Phase (TDCP)-based Extended Kalman Filter (EKF) to estimate the user's velocity. Four trajectories including shopping mall, railway station, shipyard, as well as urban canyon scenarios over a 3.2 km total walking distance with a handheld device are tested. It is shown that at least half of the epochs are selected as usable for light indoor GNSS TDCP standalone positioning, and the accuracy of the velocity estimates can improve up to 88% in terms of the 75 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{th}$</tex-math></inline-formula> percentile of the absolute horizontal velocity error compared with the state-of-the-art non-ML approach. Furthermore, a newly designed hybridization filter LIGHT-PDR that fuses the LIGHT algorithm and Pedestrian Dead Reckoning (PDR) solution is applied to perform seamless indoor/outdoor positioning in a more robust manner.

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.

A distinctive feature of modern Global Navigation Satellite System (GNSS) signals is that they transmit multiple signal components at the same carrier frequencies. The idea of joints across the signal channels from the same carrier frequency and even across different frequencies has been presented in many studies for tracking purposes. Carrier joint tracking is required on the premise that the frequency and phase relationship between signals are nominal values, and the bias of carrier characteristics between signals is drowned in noise as the signal reaches the ground, which requires high-gain receiving equipment to restore the original signal. The space signal-quality monitoring and evaluation system built by the National Timing Center of the Chinese Academy of Sciences is based on a 40 m dish antenna, which can automatically track a single satellite and achieve a high-fidelity reception of navigation signals to a certain extent, realizing fine signal quality monitoring (SQM) of GNSS satellites. Based on this platform, we discuss four types of time distributions of the combined signals among different signal components and provide a method to estimate the carrier characteristic bias between GNSS signals. We derived the correction method of carrier characteristic bias in the joint reception by the joint tracking mathematical model. Under the conditions of narrow correlation and unobstructed case, the carrier characteristic deviation does not vary significantly with the correlator interval and the satellite elevation angle. Based on the results of stability analysis, it is recommended that the receivers should update the carrier frequency bias correction number of the intra-frequency signal and carrier phase bias correction number of the intra-frequency signal monthly. The carrier phase deviation correction number of the inter-frequency signal is performed daily. The measured data from satellites show that the phase accumulation error of the joint tracking carrier loop can be eliminated to achieve long-term stable tracking after frequency bias correction. After the carrier phase bias correction, the joint positioning accuracy of the B2a and B2b signals was improved by 0.81%, and those of the B1C, L1C, E1C, and B2a signals were improved by 0.35%, 0.04%, 0.20%, and 0.11%, respectively. The positioning accuracy improvement effect of inter-frequency signals was greater than that of intra-frequency signals after carrier phase correction.

On-board cooperative spacecraft relative navigation fusing GNSS with vision

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.

In global navigation satellite system (GNSS)-based positioning and applications, multipath is by far the most obstinate impact. To overcome paradoxical issues faced by current processing approaches for multipath, this paper employs an intrinsic method to identify and mitigate multipath based on empirical mode decomposition (EMD) and Hilbert–Huang transform (HHT). Frequency spectrum and power spectrum are comprehensively employed to identify and extract multipath from complex data series composed by combined GNSS observations. To systematically inspect the multipath from both code range and carrier phase, typical kinds of combinations of the GNSS observations including the code minus phase (CMP), differential correction (DC), and double differential (DD) carrier phase are selected for the suggested intrinsic approach to recognize and mitigate multipath under typical positioning modes. Compared with other current processing algorithms, the proposed methodology can deal with multipath under normal positioning modes without recourse to the conditions that satellite orbits are accurately repeated and surrounding environments of observing sites remain intact. The method can adaptively extract and eliminate multipath from solely the GNSS observations using intrinsic decomposition mechanism. From theoretical discussions and validating tests, it is found that both code and carrier phase multipath can be identified and distinguished from ionospheric delay and other impacts using the EMD based techniques. The resultant positioning accuracy is therefore improved to an obvious extent after the removal of the multipath. Overall, the proposed method can form an extensive and sound technical frame to enhance localization accuracy under typical GNSS positioning modes and harsh multipath environments.

The global navigation satellite system (GNSS) signal modulation type plays a crucial role in determining the performances of positioning, navigation and timing (PNT) services. Currently, the binary offset carrier (BOC) modulation signal and binary coded symbol (BCS) modulation signal are both bipolar signals, which greatly restrict the room of improving the GNSS signal performance. Therefore, multi-level coded symbol (MCS) modulation has received great attention in the field of GNSS signal design. The MCS modulation is the most extensive step-coded symbol modulation mode, where BOC modulation and BCS modulation are its special cases. Since the waveform symbol of the MCS modulation signal can be arbitrarily valued, the optimal GNSS signal can be designed. However, like the BOC modulation signal, the MCS modulation signal also has the problem of ambiguous tracking, and then results in a large pseudo range measurement error, which is unacceptable for the new generation GNSS with high accuracy. In recent years, the unambiguous tracking of GNSS signals has become a hot research subject in the navigation signal processing domain and many methods are presented, and those methods can be divided into three categories:BPSK-like method, bump jump (BJ) method, and side-peak cancellation (SC) method. However, these methods are designed for BOC signal, and they are not suitable for MCS signal. Therefore, in this paper we propose a general unambiguous tracking algorithm based on the pseudo correlation function (PCF), which is suitable for MCS modulated signals. Firstly, the unitary expression of MCS modulated signal based on waveform value vector is given, then the unitary formula of cross-correlation function for MCS signal is derived and the definition of PCF is given. Then the constraint condition which should be satisfied to realize unambiguous tracking is analyzed in depth, and the universal constructing method of two reference signals and the relationship between each other are derived according to this constraint condition, which brings great convenience for solving the specific MCS signal. The code tracking loop model of GNSS receiver based on the proposed method is illustrated. It is observed that the proposed method can receive different MCS signals under the same receiver loop framework, and can simplify the design of the receiver while eliminating the tracking ambiguous problem. Finally, as a special case of MCS signal, the applications of the proposed method in four kinds of BOC signals are discussed respectively, and then the waveform value vector of the reference signal and the unitary expression of code discriminator are derived. Simulation results show that the proposed method can effectively solve the ambiguous tracking problem of MCS signal, which has good performance and broad application prospect.

Abstract. For the azimuth observation to be made at its magnetic observatories routinely, Japan Meteorological Agency (JMA) has adopted a traditional method based on Polaris sighting. Due to its difficulty to implement under overcast weather conditions and to its demand on observers, for overtime work into the evening, we are motivated to seek for an alternative method based on the Global Navigation Satellite Systems (GNSS) observation that might potentially relieve those two disadvantages. An experiment is made at Kakioka to assess the eligibility and effectiveness of the GNSS method for JMA's unmanned observatories, Memambetsu and Kanoya. The GNSS observations themselves achieve as high a precision as approximately 1 arcsec, as far as they are analyzed with Static mode. Derived from the results of GNSS observation and some supplementary horizontal angle measurements, the azimuth of the azimuth mark for the absolute measurement is determined with a precision of a few arcsecond, which is comparable to the azimuth precision achieved by the Polaris sighting. However, we end up with their significant difference by about 10 arcsec. We discuss this discrepancy to be possibly due to a local geoid gradient. The Polaris observation is made with a theodolite tilted in the gravitational direction, also known as the vertical line deviation, whereas the GNSS observations are based on the azimuth of the compliant ellipsoid plane.

This paper presents one of the solutions to the problem of multipath propagation and effects on Global Navigation Satellite Systems (GNSS) signals in urban canyons. GNSS signals may reach a receiver not only through Line-of-Sight (LOS) paths, but they are often blocked, reflected or diffracted from tall buildings, leading to unmodelled GNSS errors in position estimation. Therefore in order to detect and mitigate the impact of multipath, a new ray-tracing model for simulation of GNSS signals reception in urban canyons is proposed - based on digital 3D maps information, known positions of GNSS satellites and an assumed position of a receiver. The model is established and validated using experimental, as well as real data. It is specially designed for complex environments and situations where positioning with highest accuracy is required - a typical example is navigation for blind people.

Compared with the traditional GPS L1 C/A BPSK-R(1) signal, wideband global navigation satellite system (GNSS) signals suffer more severe distortion due to ionospheric dispersion. Ionospheric dispersion inevitably introduces additional errors in pseudorange and carrier phase observations that cannot be readily eliminated by traditional methods. Researchers have reported power losses, waveform ripples, correlation peak asymmetries, and carrier phase shifts caused by ionospheric dispersion. We analyze the code tracking bias induced by ionospheric dispersion and propose an efficient all-pass filter to compensate the corresponding nonlinear group delay over the signal bandwidth. The filter is constructed in a cascaded biquad form based on the estimated total electron content (TEC). The effects of TEC accuracy, filter order, and fraction parameter on the filter fitting error are explored. Taking the AltBOC(15,10) signal as an example, we compare the time domain signal waveforms, correlation peaks, code tracking biases, and carrier phase biases with and without this all-pass filter and demonstrate that the proposed delay-equalization all-pass filter is a potential solution to ionospheric dispersion compensation and mitigation of observation biases for wideband GNSS signals.