Pseudorange Error Research Articles

FGO-MFI: factor graph optimization-based multi-sensor fusion and integration for reliable localization

Reliable and precise information pertaining to the position, velocity, and attitude is essential for automated driving. This paper proposes FGO-MFI, a cost-effective and robust multi-sensor fusion and integration localization framework that utilizes factor graph optimization. Firstly, a tightly coupled Global Navigation Satellite Systems (GNSS)/on-board sensor fusion localization framework is established to estimate vehicle states, including position, velocity, and attitude. To address the large drift rate of the Inertial Measurement Unit (IMU), this study introduces a novel IMU/Dynamics pre-integration method based on the vehicle dynamics model. We establish a two-degree-of-freedom vehicle dynamics model utilizing measurements from the wheel speed sensor and steering wheel angle sensor. The IMU/Dynamics factor is devised through a close integration of the model output and IMU pre-integration, enabling the construction of precise odometry with low-cost on-board sensors. Then, to address the issue of the non-Gaussian distribution of GNSS pseudorange error, this paper employs a Gaussian Mixture Model (GMM) to characterize the pseudorange noise, which is then applied to further sensor fusion. Given the time-varying nature of pseudorange noise, the expectation maximization algorithm is utilized to estimate GMM parameters online, leveraging the pseudorange residuals within a sliding window. Comprehensive experiments, inclusive of challenging scenarios such as urban canyons, tunnels, and wooded areas, have been carried out. They affirm the superior performance of the proposed method. Experiments have shown that our method demonstrates reliable localization across different statuses of GNSS signal, exhibiting a 39.4% improvement in the root mean square error of position error when compared to the state-of-the-art. Additionally, this FGO-MFI is a general sensor data fusion framework and is able to incorporate diverse sensor measurements, for example, from cameras and LiDARs to provide more reliable and accurate localization information.

A robust GNSS sensors in presence of signal blockage for USV application

Unmanned surface vehicle (USV) can navigate autonomously via the global navigation satellite system (GNSS). However, the traditional GNSS scalar tracking loop easily loses lock in low carrier-to-noise ratio (CNR) situations, such as signal occlusion and weak signals. Meanwhile, an increase in the carrier/code phase error leads to an increase in the measurement error of the navigation filter, which decreases the accuracy of the position estimation. To solve this problem, this paper proposes a carrier and code tracking structure based on a forward and backward Kalman filter to dynamically adjust the gain of the vector tracking loop. The carrier and code phase errors calculated by the loop discriminators were linearly transformed into pseudo-range rate and pseudo-range errors after filtering and smoothing, which were used as the measurements of the navigation filter. The signal CNR was used to adaptively adjust the measurement noise covariance matrix of the loop filters. The field tests used a commercial receiver’s navigation solution as the reference. In the stationary test, the proposed structure reduced the localization error by 44.3% compared with the traditional methods. In kinematic experiments, the proposed structure reduced the carrier and code phase errors in a harsh signal environment and improved the positioning accuracy at the source. The test results demonstrate that the proposed GNSS tracking method can provide a possible solution for the development of navigation systems for USV.

A muon high-resolution pseudorange measurement method: Application to muon navigation in confined spaces

Confined spaces such as polar regions, deep earth and deep ocean are crucial navigation scenarios where traditional navigation techniques have difficulty in obtaining external signals for positioning. The cosmic ray muons, which carry the spatial and energetic information, are easy to penetrate these confined spaces. Therefore, the unique muon characteristic provides a new perspective to estimate detector position, which can be considered using in confined spaces navigation. In this paper, a well-developed theory of muon navigation is established by combining a muon pseudorange measurement method. Moreover, an Equivalent Velocity Calculation Model (EVCM) and a Muon Sequence Matching Technology (MSMT) are proposed. The first model corrects flight pseudorange error caused by the relativistic energy loss and the second technology compensates the random error in pseudorange measurement. Further, a series of simulations are performed to analyze the muon events number which can be received by detector in different scenarios with the variations of zenith angle, detector area, varied detector plates gap, and muon flight distance. Meanwhile, the simulation results demonstrate that the muon navigation update rate every 10 minutes can reach 5.989 in confined spaces at 100 m, and further pseudorange error analysis indicates that the meter-level positioning accuracy can be acquired. Finally, we construct a muon coincidence measurement scheme and verify that the laws of the muon positioning system for high-energy muons are consistent with the simulation results.

A NOVEL GPS FAULT DETECTION AND EXCLUSION ALGORITHM AIDED BY IMU AND VO DATA FOR VEHICLE INTEGRATED NAVIGATION IN URBAN ENVIRONMENTS

Abstract. High accuracy positioning is crucial for various applications that require accurate and reliable positioning data, such as autonomous vehicles (AVs), agriculture, and intelligent transportation. Global Positioning System (GPS) is widely used in integration with Inertial Measurement Unit (IMU) and Visual Odometry (VO) to implement an accurate and robust navigation system. However, the performance of the integrated system can be severely degraded in urban environments due to non-line-of-sight (NLOS) reception and multipath interference. To overcome these challenges, a novel Fault Detection and Exclusion (FDE) algorithm aided with IMU and VO measurements is proposed to identify and isolate the contaminated satellite signals. The algorithm utilizes instantaneous measurements from IMU and VO to predict the current vehicle position, enabling the estimation of pseudorange errors in GPS measurements. A FDE algorithm based on Hierarchical clustering is then developed to identify GPS signals with significant errors based on the predicted pseudorange error. An experimental field test was conducted using a land vehicle to evaluate the effectiveness of the proposed algorithm. The results show that the GPS/IMU/VO integrated navigation system with the proposed FDE algorithm has significantly improved the positioning accuracy and reliability compared to the traditional system. The proposed algorithm achieves a positioning accuracy with a 3D Root Mean Square Error (RMSE) of 11.18m in urban environment, making an improvement of 68.2% over the traditional GPS/IMU/VO integrated navigation system.

A Modified Cycle Slip Detection Method with GNSS Doppler Assistance and Optimizing by Adaptive Threshold and Sliding Polynomial Fitting

Cycle slip determination plays an important role in high-precision data processing and application of global navigation satellite systems (GNSS). The TurboEdit method consists of the Melbourne-Wubbena (MW) and the geometry-free phase (GF) combination. It can correctly detect and repair cycle slip in most cases. Cycle slip detection (CSD) with GF is disturbed by severe ionospheric delay variations; moreover, CSD or cycle slip repair (CSR) with the MW faces the risk of the disturbance from large pseudorange errors. Hence, cycle slip determination would be difficult under some extreme conditions, e.g., cycle slips occur in low altitude satellite, low sampling rate of dual-frequency observations. To overcome the limitations, a new dual-frequency CSD and CSR method is proposed. The main contents are as follows: (1) compared with the MW method, the Doppler-assisted phase subtraction pseudorange (DAPSP) method that we proposed has no detection blind spot and can effectively reduce the influence of pseudorange noise at high sampling rates; thus, we replace MW by the DAPSP method to improve the detection accuracy. (2) An adaptive threshold model with root mean square (RMS) is established to effectively reduce the missing and false range detection of cycle slip. (3) The sliding polynomial fitting-assisted GF (SPFAGF) is carried out according to the satellite altitude angle. The trend of ionospheric delay and residual multipath effect error between adjacent epochs is extracted and suppressed by SPFAGF. The method combined with DAPSP and SPFAGF (DAPSP-SPFAGF) overcomes the situation that the TurboEdit method cannot effectively detect under extreme conditions. The experimental results of Beidou dual-frequency observation data show that the TurboEdit method and the DAPSP-SPFAGF method can perform CSD and CSR in most cases. At the sampling rate of 1 s, the detection speed of DAPSP-SPFAGF method is significantly faster than TurboEdit method. The number of false positives about CSD is reduced from 68 to 0. At the sampling rate of 30 s and under the condition of the observed satellite altitude angle below 30°, the false alarm rate of the DAPSP-SPFAGF method is 0, but the TurboEdit method’s false alarm rate is 71.2%. So DAPSP-SPFAGF method is prior to the TurboEdit method at the high sampling rates or under extreme conditions, especially it can accurately detect and repair cycle slip and reduce the false positives and false alarm rate.

Indoor and Outdoor Fusion Positioning Technology Based on BeiDou Satellite Navigation

In order to solve the inaccuracy and discontinuity of BeiDou differential indoor and outdoor navigation and positioning, this article highlights an indoor and outdoor fusion positioning method based on BeiDou differential and WIFI. This positioning method combines the micro-inertial navigation positioning technology with a single positioning method such as Bluetooth, WIFI fingerprint, ZigBee, ultra-wideband UWB, etc., to correct the BeiDou pseudo range equation to reduce the spatial pseudo range error. And it can integrate BeiDou differential pseudo range equation and linear filtering algorithm to achieve precise positioning of navigation. The research results show that the method realizes the positioning of the indoor and outdoor interactive area by fusing the satellite pseudo-range equation and the base station pseudo-range equation. And it realizes the seamless integration of indoor and outdoor precise positioning, which improves the positioning accuracy and reliability.

Resilient Pseudorange Error Prediction and Correction for GNSS Positioning in Urban Areas

Positioning, navigation and timing (PNT) is essential for internet of things (IoT) communications and location-based services. Although GNSS can provide accurate PNT in open areas, obtaining reliable PNT is still a considerable technical challenge in complex urban environments. This is because the GNSS signals are more likely to be affected by multipath interference and non-line of sight (NLOS) reception issues arising from the obstructions and reflections in built environments. These introduce range measurement errors that degrade the GNSS positioning accuracy. This paper proposes two resilient pseudorange error prediction and correction strategies to improve the GNSS positioning accuracy in urban environments. In particular, considering the carrier-to-noise density (C/N0), satellite elevation angle and local positional information, the random forest based pseudorange error prediction and correction models are constructed in two variations, including: 1) the point-based correction (PBC), and 2) the grid-based correction (GBC). The final improved positioning solution is then calculated by using the least square method (LSM) of the corrected pseudoranges. Kinematic test results in urban environments show that both variations of the proposed model can improve the positioning accuracy by 42.9% and 40.8% in horizontal, and by 60.1% and 63.3% in 3D, respectively, compared to the positioning results obtained by traditional method without pseudorange error corrections. The improvements are 41.1% and 38.9% in horizontal, and 45.7% and 50.0% in 3D, respectively, compared with traditional elevation angle weighting method.

Data + pilot biases in modern GNSS signals

While traditional GNSS signals are always modulated with navigation data, various modern signals provide a distinct pilot channel without data modulation to support long coherent integration times. Intra-signal biases between the data and pilot components of such signals are evaluated for satellites of the GPS, Galileo, BeiDou-3, and QZSS constellations using measurements from a dedicated set of receivers. Peak values of about 2 ns are obtained for the GPS L5 signal, while slightly smaller values of up to 1 ns apply for the B1C and B2a signals of BeiDou-3 as well as the QZSS L1C signal. For Galileo E1 and E5a/b, data + pilot biases are confined to less than 0.1–0.3 ns, which is typically less than other pseudorange errors for these signals. Fully negligible values of < 0.05 ns are obtained for the L1C and L2C signals of GPS as well as the L2C signal of QZSS in accord with expectations for time-multiplexed or interlaced modulations. To support consistent processing of multi-GNSS data in heterogeneous networks, biases between combined data + pilot tracking and pilot-only tracking are derived in a dedicated zero-baseline receiver test bed. The analysis confirms the general understanding that biases between combined and pilot-only pseudoranges amount to a fixed fraction of the corresponding data + pilot biases. This fraction depends on the power sharing of the data and pilot component in the respective signals and amounts to 50% in most cases. The results of this study are expected to remove the prevailing problem of two distinct receiver groups in the generation of satellite clock and bias products by the International GNSS Service and to enable a rigorous and consistent use of these products by multi-GNSS users.

High-precision Positioning Method for BD3 System Based on Adaptive Optimization

It is of great significance to locate faults quickly and accurately in power distribution system to improve system reliability and recover quickly. With high positioning accuracy, strong anti-interference ability in mountainous areas and cities, and the ability to provide all-weather and all-round services, the BeiDou-3 (BD3) navigation satellite system has broad application prospects in power systems. Using the filtering principle of normalized least mean square (NLMS) filter, a high-precision positioning method for BD3 system based on adaptive optimization is propose to eliminate the pseudo-range error caused by electromagnetic interference. Simulation results show that NLMS-based adaptive pseudo-range filtering method can availably decrease the pseudo-range error caused by high proportional electromagnetic interference in the power system, achieve adaptive optimization of power system device positioning, and improve positioning accuracy.

Improving GNSS positioning performance of Android smart devices by a novel pseudorange correction method

To achieve high-precision global navigation satellite system (GNSS) positioning of smart devices, it is necessary to correct the pseudorange measurements, especially to reduce time-related errors. Traditional pseudorange smoothing methods fail to cope with measurement anomalies and do not consider the time correlation. Therefore, a time-correlated pseudorange correction (TCPC) method is proposed. The Mann-Kendall trend test and breakpoint detection are used to address data anomalies and pseudorange errors are estimated with an adaptive smoothing method. Using the proposed method, the GNSS receivers can improve the pseudorange accuracy and availability for better single-point positioning performance. The positioning errors are reduced by 10%–45% for different GNSS receivers. Moreover, the circular antenna motion mechanism is used to reduce the measurement correlation and enhance observability. Using the TCPC method in the smartphone antenna motion case, the improvement rates of positioning accuracies are 43%–76% and the horizontal positioning accuracy is improved from meter level to decimeter level.

Detection of GPS C/A Code Self-Interference: Monitor Overview and Applicability

<h3>Abstract</h3> Self-interference can cause large errors of up to tens of meters on the GPS C/A code pseudorange measurement. Although the probability of an occurrence of large self-interference errors is small, to enable the use of C/A code phase measurements in high accuracy or safety-of-life applications, a detection or mitigation method is needed. A stressful case of self-interference is modeled on a GPS hardware simulator to investigate monitor performance using real signal results. A summary of contributions in this paper follows. Self-interference pseudorange error characteristics within and mitigation requirements for the Ground Based Augmentation System (GBAS) Approach Service Type D (GAST-D) environment are identified. Existing monitors are evaluated for their response to self-interference and their ability to detect the error based on the GAST-D environment. This includes the potential for misidentification of the error. A novel Frequency Domain Cross-Correlation (FDCC) detector is proposed that can uniquely identify self-interference error with no siting constraints.

A Positioning System in an Urban Vertical Heterogeneous Network (VHetNet)

Global navigation satellite systems (GNSSs) are essential in providing localization and navigation services to most of the world due to their superior coverage. However, due to high pathloss and inevitable atmospheric effect, the positioning performance of any standalone GNSS is still poor in urban areas. To enhance the positioning performance of legacy GNSSs in urban areas, a positioning system, which utilizes high altitude platform station (HAPS) and 5G gNodeBs (gNBs), in a futuristic urban vertical heterogeneous network (VHetNet) is proposed. In this paper, we demonstrate the effectiveness of gNBs in improving the vertical positioning performance for both the GPS-only system and the HAPS-aided GPS system by analyzing the impact of the density of gNBs and the pseudorange error of gNB on the positioning performance of the gNB augmented positioning systems. We also demonstrate the effectiveness of receiver autonomous integrity monitoring (RAIM) algorithms on the HAPS and/or gNB aided GPS systems in urban areas.

How the accuracy of mobile objects positioning with GNSS affects the energy characteristics of the communication channel in 5G networks

The analytical relations determining the dependence between the accuracy of positioning objects-subscribers on the GNSS signals and the accuracy of pseudorange measurements were obtained. Based on these relationships, the relationship between positioning accuracy and the distribution of power radiated by the antennas into the space is revealed, which allows us to estimate the error of pointing the antenna beams in space. The correlations are based on the assumption of a Rayleigh channel for GNSS signal propagation. It is shown that the positioning accuracy of objects at the pseudo range error of 1 m and a beam width error of 2 degrees determines the average reduction in signal power in the radio channel, due to errors in positioning objects, not more than 0,25 dB, the normalized value of the standard deviation is equal to 13,5 dB. Due to positioning errors it is possible to reduce the signal strength in the radio channel by up to 1 dB.

Maritime DGPS System Positioning Accuracy as a Function of the HDOP in the Context of Hydrographic Survey Performance

The Differential Global Positioning System (DGPS) is a marine navigation system operating at frequencies of 283.5–325 kHz, which is now the primary method for locating vessels in coastal shipping, as well as hydrography and mapping systems worldwide. Its positioning accuracy is determined by the following: the pseudorange error to Global Positioning System (GPS) satellites, the age of pseudorange corrections, and the value of the Horizontal Dilution of Precision (HDOP), which, in terms of accuracy, is crucial in positioning using GPS satellites. In 2020, the International Hydrographic Organization (IHO) introduced a new (the highest) order of hydrographic surveys, i.e., the Exclusive Order, which requires a positioning system to provide an accuracy of 1 m (p = 0.95). The aim of this article is to provide an answer to the question as to whether the maritime DGPS system, whose positioning accuracy is constantly increasing with that of the GPS system, fulfils the requirements for the hydrographic surveys of harbours. To this end, an extensive experimental study on the maritime DGPS system, involving a total of nearly 3.5 million fixes, was conducted. Statistical analyses showed that when ensuring the HDOP values range from 0.8 to 1.4, the DGPS system can be used in hydrographic surveys of harbours.

A weighted GPS positioning algorithm for urban canyons using dual-polarised antennae

ABSTRACT The positioning performance of the Global Positioning System (GPS) is severely degraded in urban canyons due to buildings blocking or attenuating signals. This paper proposes a weighted GPS positioning method using a dual-polarisation antenna in order to deal with this issue. The GPS signals are first classified and labelled into NLOS signals and LOS/MP signals by considering the right-hand circular polarised (RHCP) and the left-hand circular polarised (LHCP) signal strengths. Then, a Bayesian optimisation-based Gaussian process is used to fit the pseudorange error related to the input of the carrier-to-noise ratio of the RHCP QUOTE() and the elevation angle of the LOS/MP signals. The pseudorange errors of the LOS/MP signals are therefore predicted based on the rules extracted from the fitting results. The positioning solutions are then obtained from the weighted least-squares algorithm, with the weighting strategies being based on the predicted pseudorange errors. Static positioning results in deep urban areas showed that the horizontal root-mean-square error (RMSE) positioning has been improved by 64.6% and 57.3%, respectively, while 3D RMSEwas improved by 74.3% and 48.1%, respectively, compared with traditional single-point positioning results.

Improved GNSS vector tracking loop to enhance the navigation performance of USV

The Global Navigation Satellite System (GNSS) is the most common source of location and heading information for unmanned surface vehicle (USV) in real time. However, in areas such as ports or bridges, the GNSS signal will be occluded or weakened. The carrier frequency and code frequency of scalar tracking (ST) in GNSS receiver fluctuates greatly, and even the tracking loop will lose lock. To enhance the navigation performance of USV's GNSS receiver, this paper proposes a framework that uses fixed-lag smoothing (FLS) to assist vector tracking (VT) and applies unscented Kalman filter in the navigation processor. The pseudo-range error and pseudo-range rate error are used as the measurements of navigation processor. FLS serves as a backward filter to enhance the tracking ability of the code loop. The field experiments show that the positioning error of the proposed method is reduced by 72.1% compared to the traditional VT method in the open-sky environments. When the signal is occluded, the positioning results of the traditional ST are dispersed, and also the traditional VT method displays a large error. Moreover, the proposed method is able to reduce the positioning error by 85.4%. The proposed GNSS loop tracking architecture and method can provide a possible solution for USV's navigation system development.

An Approach to Improve the Indoor Positioning Performance of Pseudolite/UWB System with Ambiguity Resolution

Indoor localization is still an open challenge, and some pseudolites have been developed to achieve seamless positioning service based on some commercialized GNSS chips. However, most of these indoor localization technologies often fail in a reasonable solution to the key problems such as low cost and highly accurate and efficient for users. In this paper, we propose an indoor location method based on integrated pseudolite and UWB; the virtual pseudo-range measurements of UWB are used to replace the pseudo-range measurements of pseudolite to solve the indoor multipath problem, which is tightly coupled with the corrected carrier phase measurements of pseudolite. Then, the channel-difference observation equation and UWB-aided ambiguity resolution are proposed for precise positioning. In order to test the proposed method, several experiments are conducted. The results show that the virtual pseudo-range errors from UWB are smaller than that of GNSS, and such a small bias will be better for the fast fixing of ambiguity. In addition, the positioning accuracy of the proposed indoor location method is improved from cm-level for the float solution to mm-level for the fixed solution; these performances would be more convincing to users than that given in the most pseudolite and UWB.

GBAS flight test integrity simulation evaluation

In order to improve the navigation performance of the conventional ground-based augmentation system (GBAS) Category I precision approach phase, the performance ver ification of the integrity technology of the GBAS based on BeiDou satellite navigation system is studied. The integrity and system pseudo-range error models of the CAT I precision approach based on BeiDou are investigated, combined with the provisions in relevant standards and the calculation method of integrity. The experimental results show that the integrity data calculated by the system meets the CAT I precision approach integrity requirements of the Radio Technical Commission for Aeronautics specification and provides a timely warning when anomalies occur in the pseudo-rang error model through changes in the protection level.

The Role of Antennas on GNSS Pseudorange and Multipath Errors and Their Impact on DFMC Multipath Models for Avionics

<h3>Abstract</h3> Current satellite navigation systems are providing more and more dual-frequency capabilities, enabling improved navigation accuracy and a reduction of residual errors (e.g., from ionosphere). Recently, the aviation community has started an effort to achieve new standardized Minimum Operational Performance Specifications (MOPS) for GNSS equipment in order to allow for the use of dual-frequency multi-constellation (DFMC) systems in the future, with clear benefits in terms of obtainable navigation performance. In such conditions, residual errors introduced by the user GNSS antenna become even more relevant and need to be properly identified and bounded, both in antenna specifications and in the models for aircraft multipath. The present work investigates this problem and shows the results of an activity aiming at new airborne multipath models for L1/E1 and L5/E5a frequency bands and for their ionospheric-free combination. The paper outlines a detailed investigation of the physical rationale of such errors.

Building a robust transition matrix using causal matrix for route recommendation

Route recommendation aims to recommend the best future route based on the historical visits. However, the route data contain noise due to the GPS pseudo-range errors. While there are some works on noise removal due to the errors, the previous works handle the errors in the data collection state rather than in the data pre-processing stage. In the field of business process, heuristic miner has been used to handle data noise in the event logs. This study aims to propose a method to build a transition matrix using the causal matrix based on the dependency measure in heuristic miner. The dependency measure resulted from heuristic miner is fed into a collaborative filtering approach, that is matrix factorization, to build a model. In the end, we compare the performance of the causal matrix with a traditional frequency-based approach to see the effect of the proposed method to remove the noise. The result showed that a transition matrix with a causal matrix from heuristic miner can produce a better performance than the transition matrix without the dependency measure with a causal matrix.