A closed-loop EKF and multi-failure diagnosis approach for cooperative GNSS positioning

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 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.

To achieve an accurate and robust localization result under Global Navigation Satellite System (GNSS) denied environment, coupling GNSS with other sensors tends to be a promising solution, also known as the sensor fusion system. One of the most challenging scenarios in sensor fusion is to couple vision navigation system with GNSS, especially the tightly-coupled fusion. Compared with those loosely coupled ones, it performs the information fusion on a more intrinsic level, which can benefit the accuracy and robustness of the system. However, the major barrier lying in front of tightly coupling method is the way to unify the heterogeneous and asynchronous GNSS observations with vision observations. To solve this problem, we start from the Vison Simultaneous Localization and Mapping (V-SLAM) method, which has already become the mainstream in vision navigation domain. By utilizing existing attempts on graph-optimization-based GNSS data processing, we propose a joint graph optimization combining vision-SLAM with GNSS pseudorange. It is a tightly coupled fusion of GNSS and stereo camera, implemented by considering GNSS satellites as vision feature points. Based on the framework of mature state-of-art pose-graph SLAM, a graph optimization is applied simultaneously on GNSS and vision positioning, to achieve a robust, accurate, yet versatile fusion system.

For global navigation satellite system (GNSS), ionospheric disturbances caused by the geomagnetic storm can reduce the accuracy and reliability of precision point positioning (PPP). At present, common stochastic models in GNSS PPP, such as the elevation angle stochastic (EAS) model or carrier‐to‐noise power‐density ratio () based SIGMA‐ model, do not properly consider storm effects on GNSS measurements. To mitigate severe storm effects on GNSS PPP, this study further implements the rate of total electron content index (ROTI) parameter into the EAS model referred to as the EAS‐ROTI model. This model contains two operations. The first one is to adjust variance of GNSS measurements using ROTI observations on EAS model. The second one is to determine the ratio of the priori variance factor between pseudorange and carrier phase measurements during severe storm conditions. The performance of EAS‐ROTI model is verified by using a large number of international GNSS service stations datasets on 17 March and 23 June in 2015. Experimental results indicate that on a global scale, the EAS‐ROTI model improves the PPP accuracy in 3D direction by approximately 12.9%–14.7% compared with the EAS model, and by about 24.8%–45.9% compared with the SIGMA‐ model.

Relative Navigation for Satellite Formation Flying based on Radio Frequency Metrology

Integer ambiguity resolution (AR) is the key to the attitude determination with global navigation satellite system (GNSS) differential carrier phases. Traditional applications in surveying field are generally performed in open areas with geodeticgrade receivers, and solve the AR problem in ambiguity domain. However, for some applications such as urban vehicle/unmanned air vehicle (UAV) attitude determination with single-frequency low-cost receivers, the AR success rate is not as satisfactory as the one in surveying field. Due to the reasons such as low-cost receivers’ inferior pseudorange quality, multipath interference and frequent cycle slips in complicated urban environment, it is difficult to give an accurate estimation for the float ambiguities which is used as the search center of the traditional AR methods in ambiguity domain, thus leading to the failure of finding the correct ambiguities. Here, we propose a single-epoch AR method in position domain to improve the AR success rate of urban attitude determination for ultra-short baselines. To get rid of the effect of the large pseudorange noise, our proposed algorithm abandons both the pseudorange measurements and the traditional idea of estimating the float ambiguities. With the known baseline length, the 3-D position search space can be compressed to a spherical surface, and by a 2-D traversal in angle domain, we can get a set of candidate position points. With the use of the integer property of the ambiguities and the geometric relationship between the position search space and carrier phase measurements, we establish an objective function whose performance relies on the carrier phases and geometric distribution only, and thus, the algorithm can provide a higher AR success rate. The corresponding 2-D traversal method and acceptance test method for validity judgment are also addressed in the paper. The results of both the simulation and the experiment under actual multipath environment are presented at the end of the paper.

GNSS (Global Navigation Satellite System) positioning accuracy depends on a complicated interaction of various factors. According to the GNSS signal propagation trajectory, accuracy depends on the quality of the pseudorange and carrier phase measurements as well as the broadcasted ephemeris data. The factors are reflected by measurement error, a fundamental assumption is made as the error can be allocated to individual satellite pseudorange. It is common to separate a geometry-related quality factor from the measurement error which called the dilution of precision (DOP) and errors in the pseudo-range measurement called user-equivalent range error (UERE). UERE is further divided into signal-in-space range error (SISRE) and user equipment error (UEE). This paper mainly takes GPS as an example, considering environment obstruction in the HDOP calculation, and estimates the UERE value by modeling and empirical values. An algorithm is designed to determine the visibility of the satellite based on the fish-eye image. The actual data and the estimation results are also compared and the UERE estimation value is corrected. Finally, the results of the analysis are compared to obtain the conclusion that the GPS positioning error in an open environment is lower than that in the more obstructed environment, and one of the main reasons for different UERE in different scenarios is multipath error.

Precise data processing from the Global Navigation Satellite Systems (GNSS) reference station network is mainly based on a combination of double-differenced carrier phase and code observations. This approach allows most of the measurement errors to be removed or reduced and is characterized as the most accurate method. However, creating observation differences between two receivers and two satellites increases the measurement noise of the observations by a factor of 2. As a result, it increases the impact of the incorrect definition of the noise characteristic on the results of the estimation of the unknowns in the positioning model. This is especially important in Multi-GNSS solutions, which integrate measurements from different systems, for which the stochastic parameters of observation may differ significantly. In this paper, the authors prepared a complex analysis of the noise type in double-differenced GNSS (GPS, GLONASS and Galileo) observations, both carrier phase and code ones, with a 1 s sampling interval. The Autocorrelation Function (ACF) method, the Lomb–Scargle (L-S) periodogram method, and the Allan variance (AVAR) method were used. The results that were obtained for the weekly set of measurement data showed that, depending on the system and type of observation, the noise level and its type are significantly different. Among the code measurements, the lowest noise levels were obtained for the GPS C5Q and Galileo C7Q/C8Q observations, with the standard deviations not exceeding ±10 cm, while the noisiest observations were for the GLONASS C1C and C2C signals, which had standard deviations of about ±90 cm and ±45 cm, respectively. For the carrier phase observations, each signal type was characterized by very similar noise levels of ±1.5–3.5 mm. The ACF analysis showed that 1 Hz double-differenced GNSS data can only be treated as being not correlated to time for carrier phase observations; for code observations, an irrelevant autocorrelation may be considered for measurement intervals greater than 20 s. Depending on the GNSS signals, the spectral index k varies in a range from −1.3 to −0.2 for code data and k = 0.0 in the case of phase data. Using the modified Allan deviation (MDEV) allows for specific noise types for each signal and GNSS system to be determined. All of the code observations were characterized by either flicker PM or white PM. In the case of the phase observations, they were all uniquely characterized by white PM (GPS and Galileo or by white PM and flicker PM (GLONASS).

This paper describes an accurate attitude determination technique using multiple global navigation satellite system (GNSS) receivers and antennas for small unmanned aerial vehicles (UAVs). A laser survey using a small UAV needs highly accurate position and attitude information for reconstructing 3D models. The proposed technique uses the multiple GNSS antenna's positions computed by the GNSS carrier phase measurements to estimate the UAV's position and attitude. To solve the GNSS carrier phase ambiguity, the reliable ambiguity search is performed with a couple of constraints for the base line vector. The performance of the proposed technique is evaluated in the static test. From the test, the proposed technique could estimate UAV's attitude in 0.1 degree accuracy. Furthermore, the accurate UAV's position could be estimated in almost 100 % availability.

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.

The Kahramanmara&amp;#351; earthquakes of February 6, 2023 occurred in the tectonically active eastern Mediterranean region near the Kahramanmara&amp;#351; triple junction, where the Anatolian, Arabian, and African plates converge. This structurally complex boundary is characterized by significant strain accumulation, which frequently generates large-magnitude earthquakes. The significant ground shaking experienced in southeastern Turkey and surrounding areas implies the importance of high-resolution studies aimed at monitoring detailed seismotectonic processes in this region.Here, we present a kinematic rupture model of these destructive events derived from a joint inversion of high-rate Global Navigation Satellite System (GNSS) and strong ground motion (SGM) data. We combine GNSS-derived displacement time series from continuously operating stations with displacement waveforms extracted from SGM records. We assess the correlation between these two datasets by comparing stations in close proximity, thereby evaluating the consistency and precision of the derived ground motions. In addition, the earthquake hypocenter and the surface fault trace are taken into account by classifying and grouping the data based on source-to-station geometry. We employ different filtering approaches for near-field and far-field observations to extract the displacements appropriately. We also use the Precise Point Positioning (PPP) technique to obtain the coseismic displacement of GNSS observations. Instead of traditional differential techniques, we tested kinematic PPP while still preserving the effect of ambiguity resolution. Kinematic PPP solutions are derived from raw GNSS phase and pseudorange observations, yielding precise station positions at each epoch during each earthquake separately.To address the spatiotemporal evolution of fault slip, we apply finite fault modeling to the combined dataset and obtain a detailed kinematic rupture model for the earthquake sequence. We compare this model with previously published rupture models for the February 6, 2023 Kahramanmara&amp;#351; earthquakes, highlighting both similarities in overall fault geometry and slip patterns, and differences in rupture extent and timing. By integrating high-frequency strong ground motion observations with GNSS displacements, we emphasize the importance of combining multiple data sources to gain a more comprehensive understanding of earthquake source processes.

The precise point positioning (PPP)-based real-time-kinematic (RTK) method attracts increasing attention from both academia and industry because of its potential for high accuracy positioning with a shorter convergence time compared to the traditional PPP. Besides high accuracy, integrity monitoring (IM) is indispensable for safety–critical real-time land vehicle and aviation applications. As the traditional advanced receiver autonomous integrity monitoring (ARAIM) method is designed for (smoothed) pseudorange-based positioning, the complexity of multi-frequency multi-constellation PPP-RTK using carrier phase measurements has not been given sufficient consideration. This study proposes an IM scheme for multi-frequency multi-constellation uncombined PPP-RTK applying the ARAIM theory, with a new comprehensive threat model to accommodate not only pseudorange measurements, but also carrier phase measurements, and other fault events arising from the network corrections that support PPP-RTK. Characteristics of different types of faults are analyzed with the aid of numerical experiments. In addition, the impact of ambiguity-fixed solutions on PPP-RTK integrity performance is investigated. The authors have also conducted case studies, including static and real-kinematic positioning experiments. Experiments have demonstrated that fast convergence in accuracy and the position error bounds, or protection levels, with a given integrity risk, in horizontal position components of PPP-RTK could be achieved. For the open sky environments on a highway, the protection levels estimated by PPP-RTK solutions have the potential to meet the alert limit requirement for road transportation using ambiguity-fixed PPP-RTK positioning under the assumption that the risks of wrong ambiguity fixing are very small and can be ignored.

Global Navigation Satellite System raw measurements from Android smart devices make accurate positioning possible with advanced techniques, e.g., precise point positioning (PPP). To achieve the sub-meter-level positioning accuracy with low-cost smart devices, the PPP algorithm developed for geodetic receivers is adapted and an approach named Smart-PPP is proposed in this contribution. In Smart-PPP, the uncombined PPP model is applied for the unified processing of single- and dual-frequency measurements from tracked satellites. The receiver clock terms are parameterized independently for the code and carrier phase measurements of each tracking signal for handling the inconsistency between the code and carrier phases measured by smart devices. The ionospheric pseudo-observations are adopted to provide absolute constraints on the estimation of slant ionospheric delays and to strengthen the uncombined PPP model. A modified stochastic model is employed to weight code and carrier phase measurements by considering the high correlation between the measurement errors and the signal strengths for smart devices. Additionally, an application software based on the Android platform is developed for realizing Smart-PPP in smart devices. The positioning performance of Smart-PPP is validated in both static and kinematic cases. Results show that the positioning errors of Smart-PPP solutions can converge to below 1.0 m within a few minutes in static mode and the converged solutions can achieve an accuracy of about 0.2 m of root mean square (RMS) both for the east, north and up components. For the kinematic test, the RMS values of Smart-PPP positioning errors are 0.65, 0.54 and 1.09 m in the east, north and up components, respectively. Static and kinematic tests both show that the Smart-PPP solutions outperform the internal results provided by the experimental smart devices.

Global navigation satellite system (GNSS) plays a crucial role in providing the globally referenced positioning for self-driving systems. Unfortunately, the numerous multipath or non-line-of-sight (NLOS) receptions (known as outlier observations) caused by the signal reflections from buildings reduce the positioning accuracy of GNSS in dense urban environments. The recently investigated factor graph- based GNSS positioning formulation simultaneously considers the historical information, which significantly increases the measurement redundancy of state estimation. Taking this advantage, this paper proposes an outlier mitigation method where the bias involved in the outliers is estimated simultaneously with the position of the receiver. Specifically, the outliers are firstly detected using a pre-trained deep learning network. Secondly, an unknown variable associated with the bias is assigned to each identified outlier measurement. Then the position of the GNSS receiver, together with the bias of outlier measurements, is estimated simultaneously via the factor graph optimization (FGO) based on the pseudorange measurements and Doppler frequency shift. Finally, the effectiveness of the proposed method is validated using a dataset collected in the urban canyon by a low-cost automobile- level GNSS receiver.

Carrier phase-based ionospheric observables using PPP models