Search Results (17)

The combination of GNSS RTK and INS offers complementary advantages but faces significant challenges in urban canyons. Frequent cycle slips in carrier phase measurements and ambiguity resolution algorithms increase computational burden without improving positioning accuracy. Additionally, environmental interference introduces noise into observations, potentially leading to complete signal loss. To address these issues, this paper proposes a factor graph optimization (FGO) positioning algorithm incorporating predictive observation factors. First, a penalized spline (P-spline) is constructed to predict and smooth Doppler measurements. The predicted Doppler is then fused with the dynamics model predictions to enhance robustness. Using predictive Doppler, carrier phase and pseudorange observations are reconstructed, generating predictive constraint factors to improve positioning accuracy. Real-world tests conducted in urban canyons, including Shanghai, demonstrate that the proposed method maintains stable positioning performance even under short-term signal outages, effectively mitigating cumulative positioning errors caused by data loss. Compared to traditional methods that rely solely on available observations, the proposed algorithm improves northward and dynamic positioning accuracy by 35% and 29%, respectively, providing a highly robust navigation solution for complex urban environments. Full article

Smartphones, due to the integration of low-cost GNSS chips and linearly polarized antennas, frequently experience abnormal errors in their observations, particularly during positioning on water surfaces. In response to this issue, this paper proposes a method for detecting and correcting abnormal errors in GNSS observations on smartphones. Firstly, the state and observation equations of the Kalman filter are formulated based on the continuous and smooth characteristics of pseudorange and carrier observations. Secondly, real-time detection of abnormal error occurrence in observations is performed by assessing whether the difference between the predicted and observed values computed by the Kalman filter exceeds a specified threshold. Finally, depending on abnormal errors within the epoch, different strategies are applied for real-time reparation of observations containing anomalies. Two smartphones have been used for static tests on land and kinematic tests on water. Results show that under various environmental conditions, the proposed method effectively enhances the quality of observations on smartphones. Specifically, the method achieved a maximum improvement of 86.03% in pseudorange quality and 84.31% in carrier phase quality. The method proposed in this paper outperformed the State-Based method by approximately 10% on land and by 10–35% on water. It also shows high stability and reliability, particularly in complex environments such as navigation on water. Full article

The BeiDou Navigation Satellite System (BDS) has developed rapidly, and the combination of BDS Phase II (BDS-2) and BDS Phase III (BDS-3) has attracted wide attention. It is found that there are code ISBs between BDS-2 and BDS-3, which may have a certain impact on the BDS-2 and BDS-3 combined positioning. This paper focuses on the performance of BDS-2/BDS-3 combined B1I single-frequency pseudorange positioning and investigates the positioning performance with and without code ISBs correction for different types of receivers, include geodetic GNSS receivers and low-cost receivers. The results show the following: (1) For geodetic GNSS receivers, the code ISBs of each receiver is about −0.3 m to −0.8 m, and the position deviation is reduced by 7% after correcting code ISBs. The code ISBs in the baseline with homogeneous receivers has a little influence on the positioning result, which can be ignored. The code ISBs in the baseline with heterogeneous receivers is about −0.5 m, and the position deviation is reduced by 4% after correcting code ISBs. (2) The code ISBs in the low-cost receivers are significantly larger than those in the geodetic GNSS receivers, and the impact on the positioning performance of the low-cost receivers is significantly greater than that on the geodetic GNSS receivers. After correcting the code ISBs, the position deviation of low-cost receivers can be reduced by around 12% for both undifferenced and differenced modes. (3) For low-cost receivers, correcting the code ISBs can increase the number of epochs successfully solved, which effectively improves the low-cost navigation and positioning performance. (4) The carrier-phase-smoothing method can effectively reduce the distribution dispersion of code ISBs and make the estimation of ISBs more accurate. The STD values of estimated code ISBs in geodetic GNSS receivers are reduced by about 40% after carrier-phase smoothing, while the corresponding values are reduced by about 7% in low-cost receivers due to their poor carrier-phase observation quality. Full article

The continuously improving performance of mass-market global navigation satellite system (GNSS) chipsets is enabling the prospect of high-precision GNSS positioning for smartphones. Nevertheless, a substantial portion of Android smartphones lack the capability to access raw carrier phase observations. Therefore, this paper introduces a precise code positioning (PCP) method, which utilizes Doppler-smoothed pseudo-range and inter-satellite single-difference methods. For the first time, the results of a quality investigation involving BDS-3 B1C/B2a/B1I, GPS L1/L5, and Galileo E1/E5a observed using smartphones are presented. The results indicated that Xiaomi 11 Lite (Mi11) exhibited a superior satellite data decoding performance compared to Huawei P40 (HP40), but it lagged behind HP40 in terms of satellite tracking. In the static open-sky scenario, the carrier-to-noise ratio (CNR) values were mostly above 25 dB-Hz. Additionally, for B1C/B1I/L1/E1, they were approximately 8 dB-Hz higher than those for B2a/L5/E5a. Second, various PCP models were developed to address ionospheric delay. These models include the IF-P models, which combine traditional dual-frequency IF pseudo-ranges with single-frequency ionosphere-corrected pseudo-ranges using precise ionospheric products, and IFUC models, which rely solely on single-frequency ionosphere-corrected pseudo-ranges. Finally, static and dynamic tests were conducted using datasets collected from various real-world scenarios. The static tests demonstrated that the PCP models could achieve sub-meter-level accuracy in the east (E) and north (N) directions, while achieving meter-level accuracy in the upward (U) direction. Numerically, the root mean square error (RMSE) improvement percentages were approximately 93.8%, 75%, and 82.8% for HP40 in the E, N, and U directions, respectively, in both open-sky and complex scenarios compared to single-point positioning (SPP). In the open-sky scenario, Mi11 showed an average increase of about 85.6%, 87%, and 16% in the E, N, and U directions, respectively, compared to SPP. In complex scenarios, Mi11 exhibited an average increase of roughly 68%, 75.9%, and 90% in the E, N, and U directions, respectively, compared to SPP. Dynamic tests showed that the PCP models only provided an improvement of approximately 10% in the horizontal plane or U direction compared to SPP. The triple-frequency IFUC (IFUC123) model outperforms others due to its lower noise and utilization of multi-frequency pseudo-ranges. The PCP models can enhance smartphone positioning accuracy. Full article

Carrier Smoothing Code (CSC), as a low-pass filter, has been widely used in GNSS positioning processing to reduce pseudorange noise via carrier phases. However, current CSC methods do not consider the systematic bias between the code and carrier phase observation, also known as Satellite-induced Code Bias (SICB). SICB has been identified in the BDS-2 and the bias will reduce the accuracy or reliability of the CSC. To confront bias, an improved CSC algorithm is proposed by considering SICB for GEO, IGSO, and MEO satellites in BDS constellations. The correction model of SICB for IGSO/MEO satellites is established by using a 0.1-degree interval piecewise weighted least squares Third-order Curve Fitting Method (TOCFM). The Variational Mode Decomposition combined with Wavelet Transform (VMD-WT) is proposed to establish the correction model of SICB for the GEO satellite. To verify the proposed method, the SICB model was established by collecting 30 Multi-GNSS Experiment (MGEX) BDS stations in different seasons of a year, in which the BDS data of ALIC, KRGG, KOUR, GCGO, GAMG, and SGOC stations were selected for 11 consecutive days to verify the effectiveness of the algorithm. The results show that there is obvious SICB in the BDS-2 Multipath (MP) combination, but the SICB in the BDS-3 MP is smaller and can be ignored. Compared with the modeling in the references, TOCFM is more suitable for IGSO/MEO SICB modeling, especially for the SICB correction at low elevation angles. After the VMD-WT correction, the Root Mean Square Error (RMSE) of SICB of B1I, B2I, and B3I in GEO satellites is reduced by 53.35%, 63.50%, and 64.71% respectively. Moreover, we carried out ionosphere-free Single Point Positioning (IF SPP), Ionosphere-free CSC SPP (IF CSC SPP), CSC single point positioning with the IGSO/MEO SICB Correction based on the TOCFA Method (IGSO/MEO SICB CSC), and CSC single point positioning with the IGSO/MEO/GEO SICB correction based on VMD-WT and TOCFA (IGSO/MEO/GEO SICB CSC), respectively. Compared to IF SPP, the average improvement of the IGSO/MEO/GEO SICB CSC algorithm in the north, east, and up directions was 24.42%, 27.94%, and 24.98%, respectively, and the average reduction in 3D RMSE is 24.54%. Compared with IF CSC SPP, the average improvement of IGSO/MEO/GEO SICB CSC is 7.03%, 6.50%, and 10.48% in the north, east, and up directions, respectively, while the average reduction in 3D RMSE was 9.86%. IGSO/MEO SICB mainly improves the U direction positioning accuracy, and GEO SICB mainly improves the E and U direction positioning accuracy. After the IGSO/MEO/GEO SICB correction, the overall improvement was about 10% and positioning improved to a certain extent. Full article

Precise position information available from smartphones can play an important role in developing new location-based service (LBS) applications. Starting from 2016, and after the release of Nougat version (Version 7) by Google, developers have had access to the GNSS raw measurements through the new application programming interface (API), namely android.location (API level 24). However, the new API does not provide the typical GNSS observations directly (e.g., pseudorange, carrier-phase and Doppler observations) which have to be generated by the users themselves. Although several Apps have been developed for the GNSS observations generation, various data analyses indicate quality concerns, from biases to observation inconsistency in the generated GNSS observations output from those Apps. The quality concerns would subsequently affect GNSS data processing such as cycle slip detection, code smoothing and ultimately positioning performance. In this study, we first investigate algorithms for GNSS observations generation from the android.location API output. We then evaluate the performances of two widely used Apps (Geo++RINEX logger and GnssLogger Apps), as well as our newly developed one (namely UofC CSV2RINEX tool) which converts the CSV file to a Receiver INdependent Exchange (RINEX) file. Positioning performance analysis is also provided which indicates improved positioning accuracy using our newly developed tool. Future work finding out the potential reasons for the identified misbehavior in the generated GNSS observations is recommended; it will require a joint effort with the App developers. Full article

Currently, there are more Global Navigation Satellite System (GNSS) signals available for civilians. Many types of GNSS receivers have been updated and several new receivers have been developed for new signals. To know about the performance of these signals and receivers and their stochastic model for data processing, in this study, the data quality of all GNSS signals, especially the new signals are analyzed, and two modified stochastic models with observation noise statistics (STA) and post-fit residuals (RES) are formed. The results show that for all the new signals, the corresponding carrier phase noise is at the same level as other old signals. The pseudorange noise of B2a, L5, E5a, and E5b is within 4 cm and significantly smaller than other signals for receivers without a smooth algorithm, and the multipath error of these signals is about 0.1 m which is also better than other signals. For B1C, the pseudorange multipath error is about 0.4 m, which is close to L1 and E1. Stochastic models are validated for precise orbit determination (POD). Compared with the empirical stochastic model (EMP), both modified models are helpful to reduce the mean unit weight square error and obtain high accuracy orbits with reduced iteration. The 3D orbit accuracy improvement can reach 0.27 cm (7%) for the STA model, and 0.40 cm (10%) for the RES model when compared with the final products from the international GNSS service (IGS). For BDS-3 POD by using B1C and B2a observations, the improvements in the 3D orbit consistency of two adjacent three-day solutions are 0.21 cm (3%) for the STA model and 0.29 cm (4%) for the RES model. In addition, the STA model based on the observation noise of globally distributed stations is less affected by stations with problematic observations and with reduced computation burden. Full article

Visual-inertial odometry (VIO) is known to suffer from drifting and can only provide local coordinates. In this paper, we propose a tightly coupled GNSS-VIO system based on point-line features for robust and drift-free state estimation. Feature-based methods are not robust in complex areas such as weak or repeated textures. To deal with this problem, line features with more environmental structure information can be extracted. In addition, to eliminate the accumulated drift of VIO, we tightly fused the GNSS measurement with visual and inertial information. The GNSS pseudorange measurements are real-time and unambiguous but experience large errors. The GNSS carrier phase measurements can achieve centimeter-level positioning accuracy, but the solution to the whole-cycle ambiguity is complex and time-consuming, which degrades the real-time performance of a state estimator. To combine the advantages of the two measurements, we use the carrier phase smoothed pseudorange instead of pseudorange to perform state estimation. Furthermore, the existence of the GNSS receiver and IMU also makes the extrinsic parameter calibration crucial. Our proposed system can calibrate the extrinsic translation parameter between the GNSS receiver and IMU in real-time. Finally, we show that the states represented in the ECEF frame are fully observable, and the tightly coupled GNSS-VIO state estimator is consistent. We conducted experiments on public datasets. The experimental results demonstrate that the positioning precision of our system is improved and the system is robust and real-time. Full article

Meteorological activities in the troposphere would affect electron concentrations and distributions in the ionosphere, thereby exciting ionospheric disturbance. To explore the ionospheric anomalies during severe convective weather, the ionospheric phenomenon during the heavy rainfall in Sichuan Province on 9 July 2013 was analyzed based on GNSS data. The Total Electron Content (TEC) are evaluated by carrier phase smoothed pseudoranges. Then, the dTEC (detrend TEC) sequences are obtained by using the cubic smoothing spline. They show obvious N-shaped ionospheric disturbances and have propagation characteristics, with the maximum of 0.4 TECU. Frequency domain analysis using continuous wavelet transform (CWT) also reached similar conclusions—that there are obvious ionospheric disturbances with different frequencies and intensity. Based on the isotropic assumption and feature points method, the horizontal propagation velocity of the disturbances in the ionosphere is estimated to be approximately 150 m/s. Then, Sichuan Province is divided into 1° × 1° grids, and the disturbance trigger source is determined via the grid searching method to be the central of Sichuan Province. Finally, the mechanisms causing ionospheric disturbance are discussed. During the heavy rainfall, the strong convection may excite gravity waves (GWs), which are driven by terrain and background wind fields to propagate upwards to the ionosphere and release energy, causing ionospheric disturbances. Full article

Aiming at the problem of high-precision positioning of mass-pedestrians with low-cost sensors, a robust single-antenna Global Navigation Satellite System (GNSS)/Pedestrian Dead Reckoning (PDR) integration scheme is proposed with Gate Recurrent Unit (GRU)-based zero-velocity detector. Based on the foot-mounted pedestrian navigation system, the error state extended Kalman filter (EKF) framework is used to fuse GNSS position, zero-velocity state, barometer elevation, and other information. The main algorithms include improved carrier phase smoothing pseudo-range GNSS single-point positioning, GRU-based zero-velocity detection, and adaptive fusion algorithm of GNSS and PDR. Finally, the scheme was tested. The root mean square error (RMSE) of the horizontal error in the open and complex environments is lower than 1 m and 1.5 m respectively. In the indoor elevation experiment where the elevation difference of upstairs and downstairs exceeds 25 m, the elevation error is lower than 1 m. This result can provide technical reference for the accurate and continuous acquisition of public pedestrian location information. Full article

This paper evaluates the performance of an integrity monitoring algorithm of global navigation satellite systems (GNSS) for the Kalman filter (KF), termed KF receiver autonomous integrity monitoring (RAIM). The algorithm checks measurement inconsistencies in the range domain and requires Schmidt KF (SKF) as the navigation processor. First, realistic carrier-smoothed pseudorange measurement error models of GNSS are integrated into KF RAIM, overcoming an important limitation of prior work. More precisely, the error covariance matrix for fault detection is modified to capture the temporal variations of individual errors with different time constants. Uncertainties of the model parameters are also taken into account. Performance of the modified KF RAIM is then analyzed with the simulated signals of the global positioning system and navigation with Indian constellation for different phases of aircraft flight. Weighted least squares (WLS) RAIM used for comparison purposes is shown to have lower protection levels. This work, however, is important because KF-based integrity monitors are required to ensure the reliability of advanced navigation methods, such as multi-sensor integration and vector receivers. A key finding of the performance analyses is as follows. Innovation-based tests with an extended KF navigation processor confuse slow ramp faults with residual measurement errors that the filter estimates, leading to missed detection. RAIM with SKF, on the other hand, can successfully detect such faults. Thus, it offers a promising solution to developing KF integrity monitoring algorithms in the range domain. The modified KF RAIM completes processing in time on a low-end computer. Some salient features are also studied to gain insights into its working principles. Full article

The high noise of pseudorange and the ambiguity of carrier phase observation restrain the GNSS (Global Navigation Satellite System) application in military, industrial, and agricultural, to name a few. Thus, it is crucial for GNSS technology to integrate the pseudorange and carrier phase observations. However, the traditional method proposed by Hatch has obtained only a low convergence speed and precision. For higher convergence speed and precision of the smoothed pseudorange, aiming to improve positioning accuracy and expand the application of GNSS, we introduced a new method named MELS (Multi-Epochs Least-Squares) that considered the cross-correlation of the estimating parameters inspired by DELS (Double-Epochs Least-Square). In this study, the ionospheric delay was compensated, and so its impact was limited to the performance of the filters, and then exploited the various filters to integrate carrier phase observation and pseudorange. We compared the various types of Hatch’s filter and LS (Least-Square) methods using simulation datasets, which confirmed that the types of LS method provided a smaller residual error and a faster convergence speed than Hatch’s method under various precisions of raw pseudorange. The experimental results from the measured GNSS data showed that LS methods provided better performance than Hatch’s methods at E and U directions and a lower accuracy at N direction. Nevertheless, the types of LS method and Hatch’s methods improved about 12% and 9–10% at the 3D direction, respectively, which illustrated the accumulating improvement at the enhanced directions was more than the decreased direction, proving that the types of LS method resulted to better performance than the Hatch’s filters. Additionally, the curve of residual and precision based on various LS methods illustrated that the MELS only provided a millimeter accuracy difference compared with DELS, which was proved by the simulated and measured GNSS datasets. Full article

Achieving continuous and high-precision positioning services via smartphone under a Global Navigation Satellite System (GNSS)-degraded environment is urgently demanded by the mass market. In 2018, Xiaomi launched the world’s first dual-frequency GNSS smartphone, Xiaomi Mi 8. The newly added L5/E5 signals are more precise and less prone to distortions from multipath reflections. This paper discusses the characteristics of raw dual-frequency GNSS observations from Xiaomi Mi 8 in urban environments; they are characterized by high pseudorange noise and frequent signal interruption. The traditional dual-frequency ionosphere-free combination is not suitable for Xiaomi Mi 8 raw GNSS data processing, since the noise of the combined measurements is much larger than the influence of the ionospheric delay. Therefore, in order to reasonably utilize the high precision carrier phase observations, a time differenced positioning filter is presented in this paper to deliver continuous and smooth navigation results in urban environments. The filter first estimates the inter-epoch position variation (IEPV) with time differenced uncombined L1/E1 and L5/E5 carrier phase observations and constructs the state equation with IEPV to accurately describe the user’s movement. Secondly, the observation equations are formed with uncombined L1/E1 and L5/E5 pseudorange observations. Then, kinematic experiments in open-sky and GNSS-degraded environments are carried out, and the proposed filter is assessed in terms of the positioning accuracy and solution availability. The result in an open-sky environment shows that, assisted with L5/E5 observations, the root mean square (RMS) of the stand-alone horizontal and vertical positioning errors are about 1.22 m and 1.94 m, respectively, with a 97.8% navigation availability. Encouragingly, even in a GNSS-degraded environment, smooth navigation services with accuracies of 1.61 m and 2.16 m in the horizontal and vertical directions are obtained by using multi-GNSS and L5/E5 observations. Full article

In May 2016, the availability of GNSS raw measurements on smart devices was announced by Google with the release of Android 7. It means that developers can access carrier-phase and pseudorange measurements and decode navigation messages for the first time from mass-market Android-devices. In this paper, an improved Hatch filter algorithm, i.e., Three-Thresholds and Single-Difference Hatch filter (TT-SD Hatch filter), is proposed for sub-meter single point positioning with raw GNSS measurements on Android devices without any augmentation correction input, where the carrier-phase smoothed pseudorange window width adaptively varies according to the three-threshold detection for ionospheric cumulative errors, cycle slips and outliers. In the mean time, it can also eliminate the inconsistency of receiver clock bias between pseudorange and carrier-phase by inter-satellite difference. To eliminate the effects of frequent smoothing window resets, we combine TT-SD Hatch filter and Kalman filter for both time update and measurement update. The feasibility of the improved TT-SD Hatch filter method is then verified using static and kinematic experiments with a Nexus 9 Android tablet. The result of the static experiment demonstrates that the position RMS of TT-SD Hatch filter is about 0.6 and 0.8 m in the horizontal and vertical components, respectively. It is about 2 and 1.6 m less than the GNSS chipset solutions, and about 10 and 10 m less than the classical Hatch filter solution, respectively. Moreover, the TT-SD Hatch filter can accurately detect the cycle slips and outliers, and reset the smoothed window in time. It thus avoids the smoothing failure of Hatch filter when a large cycle-slip or an outlier occurs in the observations. Meanwhile, with the aid of the Kalman filter, TT-SD Hatch filter can keep continuously positioning at the sub-meter level. The result of the kinematic experiment demonstrates that the TT-SD Hatch filter solution can converge after a few minutes, and the 2D error is about 0.9 m, which is about 64%, 89%, and 92% smaller than that of the chipset solution, the traditional Hatch filter solution and standard single point solution, respectively. Finally, the TT-SD Hatch filter solution can recover a continuous driving track in this kinematic test. Full article

The network real-time differential positioning technique is a good choice for meter and sub-meter level’s navigation. More attention has been paid to the Global Positioning System (GPS) and GPS + GLONASS (GLObal NAvigation Satellite System) network real-time differential positioning, but less on the GPS + BDS (BeiDou Navigation Satellite System) combination. This paper focuses on the GPS + BDS network real-time differential positioning. Since the noise of pseudorange observation is large, carrier-phase-smoothed pseudorange is usually used in the network real-time differential positioning to improve the positioning accuracy, while it will be interrupted once the satellite signal is lost or a cycle slip occurs. An improved algorithm in the position domain based on position variation information is proposed. The improved method is immune to the smoothing window and only depends on the number of available satellites. The performance of the network real-time differential positioning using the improved method is evaluated. The performance of GPS + BDS combination is compared with GPS-only solution as well. The results show that the positioning accuracy can be increased by around 10%–40% using the improved method compared with the traditional one. The improved method is less affected by the satellite constellation. The positioning accuracy of GPS + BDS solution is better than that of GPS-only solution, and can reach up to 0.217 m, 0.159 m and 0.330 m in the north, east and up components for the static user station, and 0.122 m, 0.133 m and 0.432 m for the dynamic user station. The positioning accuracy variation does not only depend on whether the user is inside or outside the network, but also on the position relation between the user and network. Full article