Multipath Error Research Articles

Phase Residuals Analysis in Kinematic Orbit Determination of GRACE-FO

The GRACE-FO based scientific research will benefit from the improvement of the kinematic orbit quality. This study investigated the errors that could potentially impact the accuracy of orbit determination and applied error corrections to the observations, including phase center variation (PCV) and multipath error, with a specific focus on enhancing the performance of GRACE-FO kinematic precise orbit determination based on the zero-difference method. When the observation model for precise orbit determination is highly consistent with the actual situation, the phase residuals should only consist of observation noise. However, the phase residuals encompass both modeled errors and unmodeled errors, such as PCV and multipath errors. The study utilized the GPS observation data of the GRACE-FO satellites in January 2022 to derive the fixed ambiguity solutions based on the zero-difference ionosphere-free linear combination, thereby obtaining the phase residuals. Subsequently, the antenna PCV was estimated based on the residual method, resulting in a substantial reduction in carrier phase residuals through PCV correction. A comparison with the reference orbits revealed that the root mean square (RMS) of the fixed solutions with PCV correction improved by 2.8 to 4.3 mm in three directions. Furthermore, the wavelet decomposition was performed on the phase residuals to extract the multipath errors and reconstruct the carrier phase observations. The RMS of the kinematic orbits improved by 4.3 to 5.9 mm with the incorporation of both the PCV and multipath error corrections. The RMS of the satellite laser ranging (SLR) residuals of the two GRACE-FO (GRACE-C and GRACE-D) satellites were 1.43 cm and 1.48 cm, respectively. The results indicate that these methods have the potential to enhance the kinematic orbit accuracy of the GRACE-FO satellites, bringing it closer to the a posteriori scientific orbit accuracy.

Evaluating antenna phase center variation effects on tropospheric delay retrieval using a low-cost dual-frequency GNSS receiver

Abstract This study examines the impact of Phase Center Variation (PCV) corrections on Zenith Wet Delay (ZWD) accuracy using a low-cost U-blox ZED-F9P receiver paired with three different antenna configurations: the high-grade TRM57971 antenna, the moderate-grade AS-ANT3BCAL antenna, and the low-cost ANN-MB-00 antenna. Among the three antennas evaluated, the low-cost antenna exhibited the largest PCV magnitude and a pronounced elevation angle dependence. In contrast, the other two antennas demonstrated lower levels of PCV variation. Without PCV corrections, the low-cost antenna showed significant ZWD biases compared to reference values. Applying PCV corrections significantly improved its accuracy, reducing bias and RMS by 88% and 79%, respectively. Moderate- and high-grade antennas experienced minimal improvement with correction. All antennas exhibited remarkable day-to-day repeatability in their residual patterns, despite variations observed in the RMS of phase residuals. This observed repeatability is likely attributable to the presence of unmodeled multipath contributions. The variations in RMS, in turn, can be primarily ascribed to inherent differences in multipath resistance among the antenna designs. This study highlights the critical role of PCV corrections for accurate ZWD estimation with low-cost GNSS receivers. Future research should prioritize the acquisition of manufacturer-provided calibration data for low-cost antennas to streamline and enhance the accuracy of PCV correction applications. Moreover, efforts should be directed toward developing innovative solutions, such as low-cost, multipath-resistant antennas or advanced signal processing algorithms, to mitigate the impact of multipath errors. By addressing these areas, low-cost GNSS solutions can become more reliable and cost-effective tools for tropospheric delay estimation.

Extraction and analysis of short-term variation characteristics of code multipath error

Multipath errors (MP) can seriously affect positioning accuracy. Extracting and analyzing the variation characteristics of MP can provide a basis for mitigating it, but the current studies primarily focus on the characteristics of long-term variation of multipath errors while ignoring its short-term variation, which leads to incomplete understanding of the MP. Code and carrier phase dual-frequency observation combination and moving average method are combined to achieve accurate extraction of short-term code multipath error variation (MPvar), and different moving average strategies are adopted to satisfy the needs of real-time and after-the-fact extraction. The variation characteristics of MPvar between sea and land, among different GNSS systems, among different orbits of the BDS system are compared and analyzed. Study indicates that the carrier-to-noise ratio (C/N0) at sea is low and fluctuates greatly compared with the C/N0 at land, but the MPvar at sea is much smoother. There are differences in the magnitude of MPvar for each GNSS system, but they are all correlated with the elevation angle. For BDS GEO satellites, although the elevation angle variations are minimal, the MPvar has significant variations. Therefore, this study suggests that the MP variations of the BDS GEO satellites cannot be regarded as a smooth process when MP sources exist in the vicinity of the static observation stations. The extraction method and analysis results in this study helps to provide ideas for mitigating MP from a perspective of short-term variation.

Selected applications of satellite technologies in rail transport

Global Navigation Satellite Systems (GNSS) are increasingly being used in various modes of transport, including rail transport. When this technology is applied to railway traffic control, it is essential to ensure a high level of safety and reliability. The approval of a railway traffic control system requires a safety analysis, which includes hazard analysis and risk analysis. This also includes GNSS-based solutions in terms of their compliance with safety integrity requirements, i.e. THR (Tolerable Hazard Rate) and SIL (Safety Integrity Level) parameters, as defined in normative documents. In the case of railway traffic control systems, the level of dependability of the determined train position, referred to as position integrity, is very important in ensuring safety. Position integrity is affected by many factors, including: errors due to SIS (Signal-In-Space) propagation, multipath errors, signal interference or GNSS receiver errors. In order to improve position integrity, among other things, new data processing methods can be used to improve the accuracy and reliability of measurements. The paper presents the concept of satellite signal processing for precise determination of the position of objects in selected railway systems. The Kalman filter based model of satellite signal filtration and its selected applications, which were tested in the real condition, was presented. The application of Kalman filtration indicated in the paper is a universal method that improves the estimated measurement parameters and can be used in many applications of satellite systems for railway tasks. The applicability of satellite systems to automatic train operation, defect positioning in automatic and manual flaw detection tests, determining track spatial orientation and train integrity control have been considered. The conducted tests confirmed the correctness of the adopted concept and the model of satellite signals filtration developed for this purpose. According to the authors, the described methods can also be used in many other tasks related to rail transport.

Research on multipath error detection model in forest based on Signal-to-noise ratio

Research on multipath error detection model in forest based on Signal-to-noise ratio

Overbounding Multipath Error in Urban Canyon With LSTM Using Multi-Sensor Features

Overbounding Multipath Error in Urban Canyon With LSTM Using Multi-Sensor Features

Research on an Autonomous Localization Method for Trains Based on Pulse Observation in a Tunnel Environment.

China's rail transit system is developing rapidly, but achieving seamless high-precision localization of trains throughout the entire route in closed environments such as tunnels and culverts still faces significant challenges. Traditional localization technologies cannot meet current demands, and the present paper proposes an autonomous localization method for trains based on pulse observation in a tunnel environment. First, the Letts criterion is used to eliminate abnormal gyro data, the CEEMDAN method is employed for signal decomposition, and the decomposed signals are classified using the continuous mean square error and norm method. Noise reduction is performed using forward linear filtering and dynamic threshold filtering, respectively, maximizing the retention of its effective signal components. A SINS/OD integrated localization model is established, and an observation equation is constructed based on velocity matching, resulting in an 18-dimensional complex state space model. Finally, the EM algorithm is used to address Non-Line-Of-Sight and multipath effect errors. The optimized model is then applied in the Kalman filter to better adapt to the system's observation conditions. By dynamically adjusting the noise covariance, the localization system can continue to maintain continuous high-precision position information output in a tunnel environment.

Optimized multi-point hemispherical grid model with adaptive grid division based on the prior information of multipath error

The multi-point hemispherical grid model (MHGM) utilizes residual of double-differenced observations to extract precise multipath error information. It models the entire network of multipath error effects across different stations to achieve effective error correction. However, because all the parameters are estimated collectively using the least squares method, the increased number of grid point parameters can significantly consume memory, CPU, and other computing resources required for modeling. In response to the computational resource consumption challenge associated with fixed-resolution MHGM in multi-station applications, a space domain adaptive grid division method is proposed to optimize the modeling of multipath errors. This approach utilizes prior distribution information of multipath errors to optimize the grid structure. It reduces the number of grids in areas where multipath errors exhibit minimal changes, and provides detailed parameterization for areas with significant variations. Experimental results demonstrate the effectiveness of this method in significantly reducing the number of estimated parameters using MHGM. In statistical analysis of double-differenced phase observation residuals with fixed ambiguities, as the number of estimated parameters in the MHGM decreases to only 24.6 % of the fixed-resolution approach, memory usage during parameter estimation remains a mere 6 % of that required in the fixed-resolution approach. This highlights its potential value in mitigating multipath errors when modeling GNSS large-scale network data.

GNSS location error reduction method for microtremor survey system based on EMD-CNN-LSTM

Abstract Large errors exist when the microtremor survey system uses the global navigation satellite system (GNSS) for static localization. Aiming at the problem that the existing methods cannot effectively weaken the random error and multipath error, an error weakening method based on Empirical Mode Decomposition (EMD), Convolutional Neural Networks (CNN), and Long Short-term Memory Networks (LSTM) is proposed. The model first uses EMD to decompose the high-frequency random error, then reconstructs the low-frequency component and extracts the local features using CNN, and finally learns the change rule of multipath error using LSTM and weakens it. The model can remove random errors in the early stage while reducing the interference of noise on the neural network in the later stage and then improve the accuracy of localization. The experimental results show that the model can effectively improve the localization accuracy in the case of short-time measurements so that the localization accuracy in the E, N, and U directions can be improved by 74.57%, 74.76%, and 71.86%, respectively, which is more than 10% higher than the localization accuracy improvement rate of the existing CNN-LSTM model.

Multipath error extraction and mitigation based on refined wavelet level and threshold selection

Multipath error extraction and mitigation based on refined wavelet level and threshold selection

Ranging Offset Calibration and Moving Average Filter Enhanced Reliable UWB Positioning in Classic User Environments

With the rapid development of the Internet of Things (IoT), the positioning accuracy requirement of the IoT is increasing, especially for those applications without Global Navigation Satellite System (GNSS) signals. Ultra-Wideband (UWB) is treated as a high-accuracy positioning method that can be utilized in GNSS-blocked environments. However, UWB’s performance is still limited when it is applied in practical applications due to errors such as Non-Line-of-Sight (NLOS) errors, multipath errors, and systematic errors in UWB range values. To constrain the impacts of these mentioned errors on UWB positioning accuracy, this work proposes a novel UWB positioning model by introducing a UWB ranging offset calibration algorithm and a moving average filter into a robust extended Kalman filter. In such a UWB positioning model, the ranging offset calibration algorithm is employed to limit the infuence of UWB systematic errors, and the prior residual-based IGG-III weighting model is used to restrain the impacts of NLOS and multipath errors. The moving average filter is to further decrease the impact of the measuring noise on UWB positioning parameter estimation. To investigate the effectiveness of this proposed method, three sets of UWB experiments are arranged in three classic user environments. The experimental results show that (1) after applying the UWB ranging offset calibration algorithm, UWB positioning accuracies in classic environments, namely indoor condition, outdoor condition, and transition area are increased by 50.3%, 20.2%, and 46.9%, respectively; (2) the moving average filter can effectively improve the smoothness of UWB positioning results in terms of standard deviation; (3) the prior residual-based robust theory brings about 49.4% and 25.2% positioning improvements to horizontal and vertical components under poor measurement quality conditions, but such improvements are rather slight when there are good-quality measurements; and (4) after applying the ranging offset calibration algorithm and moving average filter to the robust EKF together, the elevation accuracy of UWB positioning is increased by 67.1%, 22.2%, and 50.5%, respectively, in the three classic user environments.

An adaptive frequency-based C/N0-constrained multipath extraction and mitigation method for GNSS pseudorange measurements

Abstract The multipath effect poses an inevitable challenge for Global Navigation Satellite System (GNSS) receivers, particularly pronounced in smart devices, which are nevertheless the most common means through which the general public accesses GNSS positioning. Therefore, we propose a novel adaptive method for extracting multipath errors, which fully exploits the multipath frequency characteristics, multipath repeatability, and the correlation between multipath errors and carrier-to-noise ratio (C/N0). This approach aims to enhance the susceptibility of smart devices to multipath influences. Specifically, this method uses the code minus carrier method to calculate the noisy multipath error, exploits the correlation between C/N0 and multipath to constrain the frequency range, employs the ensemble empirical mode decomposition method to decompose the error signal, and utilizes the Hilbert–Huang transform method to obtain the frequency information of the signal component. In multipath repeatability, the proposed method can effectively improve the correlation of multipath signals by up to 0.79. By applying the extraction method, the positioning performance of smart devices can be improved by 13.9%. Therefore, the proposed method extracts multipath error more accurately and is highly usable in low-cost devices.

Analysis of Multipath Changes in the Polish Permanent GNSS Stations Network

This study examines the influence of multipath errors on Global Navigation Satellite System (GNSS) measurements collected at ASG-EUPOS reference stations between 2010 and 2021. Multipath occurs when GNSS signals reflect off surrounding objects before reaching the receiver antenna, leading to positioning errors. In the case of reference stations, all available mitigation techniques were used to minimize the impact of multipath. However, it is still detectable and affects the measurement results. For carrier phase differential positioning, it increases the ambiguous search space, which results in a decrease in determining rover—reference station vector accuracy. The study employs two linear combinations (Code-Minus-Carrier and Multipath Pseudorange Observable) to quantify the multipath effect on both pseudorange and carrier phase measurements. Based on the research, it was found that the multipath values changed depending on the change of the receiver and the terrain around the reference stations. The study observed a gradual decrease in multipath errors from 2010 to 2021, likely due to technological advancements in receiver design. No significant increase in multipath errors was observed due to environmental changes around the stations, suggesting a minimal influence from new reflecting objects nearby. Based on the analyses conducted, it is also recommended to perform periodic tests to detect incorrect receiver configuration or operation.

A Hopular based weighting scheme for improving kinematic GNSS positioning in deep urban canyon

Global navigation satellite system (GNSS) positioning performance in the urban dense environment experiences significant deterioration due to frequent non-line-of-sight (NLOS) and multipath errors. An accurate weighting scheme is critical for positioning, especially in urban environment. Traditional methods for determining the weights of observations typically rely on the carrier-to-noise density ratio (C/N0) and the elevations from satellites to receivers. Nevertheless, the performance of these methods is degraded in the dense urban settings, as C/N0 and elevation measurements fail to fully capture the intricacies of NLOS and multipath errors. In this paper, a novel GNSS observations weighting scheme based on Hopular GNSS signal classifier, which can accurately identify the LOS/NLOS signals using medium-sized training dataset, is proposed to improve the urban kinematic navigation solution in real-time kinematic positioning mode. Four GNSS features: C/N0, time-differenced code-minus-carrier, loss of lock indicator and satellite’s elevation, are employed in the training of the Hopular based signal classifier. The performance of the new method is validated using two urban kinematic datasets collected by a U-blox F9P receiver with a low-cost antenna, in downtown Calgary. For the first testing dataset, the results show that the Hopular based weighting scheme outperforms the three most commonly used GNSS observations weighting schemes: C/N0, elevation, and a combined C/N0-elevation approach. Approximately 10.089 m of horizontal root-mean-squared (RMS) positioning error and 12.592 m of vertical RMS error are achieved using the proposed method; with improvements of 78.83%, 46.82% and 43.27% on horizontal positioning accuracy and 54.00%, 47.51% and 49.69% on vertical positioning accuracy, compared to using C/N0, elevation and C/N0-elevation combined weighting schemes, respectively. For the second testing dataset, a similar performance is achieved with nearly 11.631 m of horizontal RMS error and 10.158 m of vertical RMS error; improvements of 64.58%, 32.90% and 22.40% on horizontal positioning accuracy and 71.99%, 65.24% and 55.88% on vertical positioning accuracy are achieved, compared to using C/N0, elevation and C/N0-elevation combined weighting schemes, respectively.

Intercomparison of multi-GNSS signals characteristics acquired by a low-cost receiver connected to various low-cost antennas

With the increasing number of low-cost GNSS antennas available on the market, there is a lack of comprehensive analysis and intercomparison of their performance. Moreover, multi-GNSS observation noises are not well recognized for low-cost receivers. This study characterizes the quality of GNSS signals acquired by low-cost GNSS receivers equipped with eight types of antennas in terms of signal acquisition, multipath error and receiver noise. The differences between various types of low-cost antennas are non-negligible, with helical antennas underperforming in every respect. Compared with a geodetic-grade station, GPS and Galileo signals acquired by low-cost receivers are typically weaker by 3–9 dB-Hz. While the L1, E1 and E5b signals are well-tracked, only 72% and 86% of L2 signals are acquired for GPS and GLONASS, respectively. The signal noise for pseudoranges varies from 0.12 m for Galileo E5b to over 0.30 m for GLONASS L1 and L2, whereas for carrier-phase observations it oscillates around 1 mm for both GPS and Galileo frequencies, but exceeds 3 mm for both GLONASS frequencies. Antenna phase center offsets (PCOs) vary significantly between frequencies and constellations, and do not agree between two antennas of the same type by up to 25 mm in the vertical component. After a field calibration a of low-cost antenna and consistent application of PCOs, the horizontal and vertical accuracy is improved to a few millimeter and a few centimeter level for the multi-GNSS processing with double-differenced and undifferenced approach, respectively. Last but not least, we demonstrate that PPP-AR is possible also with low-cost GNSS receivers and antennas, and improves the precision and convergence time. The results prove that selection of low-cost antenna for a low-cost GNSS receiver is of great importance in precise positioning applications.

GNSS multipath error in the context of companion robots’ reliability

A companion robot is capable of performing a variety of activities and thus supporting the elderly and people withdisabilities. It should be able to overcome obstacles on its own, respond to what is happening around it in real-time, andcommunicate with its surroundings. It is particularly important to pay attention to these issues, as a companion robot is likely tobecome a participant in traffic. The aim of the research is to develop a mathematical model that takes into account the use of twonavigation solutions in the companion robot. Thanks to this, it will be possible to use the obtained mathematical relationships tocompare various types of navigation and make a rational choice, enabling the implementation of the assumed activities in aspecific external environment. What is new in this article is the analysis of several navigation methods and the presentation ofresearch carried out in real time using an actual robot.

GNSS multipath error in the context of companion robots’ reliability

GNSS multipath error in the context of companion robots’ reliability

Contribution of BDS-3 observations to the precise orbit determination of LEO satellites: a case study of TJU-01

The precise orbit determination (POD) of scientific low Earth orbit (LEO) satellites is a prerequisite for the successful implementation of scientific missions. In recent years, global navigation satellite systems have become the main means of determining the orbits of LEO satellites. The global navigation satellite system receiver onboard the Tianjin University No. 1 (TJU-01) satellite receives both GPS and BDS-2/3 signals, with the addition of BDS-2/3 observations playing an important role in improving the POD of LEO satellites. This study comprehensively analyzes the spaceborne GPS/BDS data quality, including BDS-2/3 and GPS code multipath errors. Appreciable code multipath errors are found for the B1I signal of BDS-2 medium Earth orbit (MEO) satellites at elevations higher than 40°, whereas slight near-field relevant multipath errors of both frequencies are found for GPS and BDS-3 MEO satellites. The GPS and BDS-2/3 code multipath errors are estimated through elevation/azimuth-relevant piece-wise modeling and applied in the POD calculations. Several schemes, namely GPS-based, BDS-based, BDS-based without geo-synchronous (GEO) satellites, and GPS/BDS combined schemes, are designed to evaluate the POD performance. Fourteen days of data are calculated and the average three-dimensional (3D) orbital root mean square (RMS) of orbit overlapping differences obtained from GPS-based and BDS-based POD (without GEO satellites) solutions are 37.4 and 27.1 mm, respectively. The BDS-based solutions are obviously better than the GPS-based solutions, mainly owing to better data availability. The GPS/BDS combined solutions have the best accuracy, with a 3D RMS value of 20.6 mm. In addition, when BDS GEO satellites are included, the 3D RMS of the overlapping orbit differences reduces to 32.9 and 27.4 mm for BDS-based and GPS/BDS combined solutions, respectively. Double-difference (DD) and single-difference (SD) integer ambiguity resolution (IAR) are adopted to further improve the POD performance. The fixed orbit of the TJU-01 satellite is solved through DD IAR and SD IAR, and the contribution of the TJU-01 satellite to ambiguity fixing is analyzed. Relative to the float solution, the improvements made using the two ambiguity fixing approaches are equivalent, both being approximately 13%. The importance of this research is not only the precise determination of the orbit of TJU-01 for occultation service but also the demonstration of the contribution of BDS observations to the performance of the POD of LEO satellites.

GNSS Carrier-Phase Multipath Modeling and Correction: A Review and Prospect of Data Processing Methods

A multipath error is one of the main sources of GNSS positioning errors. It cannot be eliminated by forming double-difference and other methods, and it has become an issue in GNSS positioning error processing, because it is mainly related to the surrounding environment of the station. To address multipath errors, three main mitigation strategies are employed: site selection, hardware enhancements, and data processing. Among these, data processing methods have been a focal point of research due to their cost-effectiveness, impressive performance, and widespread applicability. This paper focuses on the review of data processing mitigation methods for GNSS carrier-phase multipath errors. The paper begins by elucidating the origins and mitigation strategies of multipath errors. Subsequently, it reviews the current research status pertaining to data processing methods using stochastic and functional models to counter multipath errors. The paper also provides an overview of filtering techniques for extracting multipath error models from coordinate sequences or observations. Additionally, it introduces the evolution and algorithmic workflow of sidereal filtering (SF) and multipath hemispherical mapping (MHM), from both coordinate and observation domain perspectives. Furthermore, the paper emphasizes the practical significance and research relevance of multipath error processing. It concludes by delineating future research directions in the realm of multipath error mitigation.

Characterization of BDS Multipath Effect Based on AT-Conv-LSTM Network

Multipath effects are the most challenging error sources for the Global Navigation Satellite System receiver, affecting observation quality and positioning accuracy. Due to the non-linear and time-varying nature, multipath error is difficult to process. Previous studies used a homogeneous indicator to characterize multipath effects and only revealed the temporal or spatial correlations of the multipath, resulting in limited correction performance. In this study, we consider the code multipath to be influenced not only by the elevation and azimuth angle of certain stations to satellites but also to be related to satellite characteristics such as nadir angle. Hence, azimuth angle, elevation angle, nadir angle and carrier-to-noise power density ratio are taken as multiple indicators to characterize the multipath significantly. Then, we propose an Attention-based Convolutional Long Short-Term Memory (AT-Conv-LSTM) that fully exploits the spatiotemporal correlations of multipath derived from multiple indicators. The main processing procedures using AT-Conv-LSTM are given. Finally, the AT-Conv-LSTM is applied to a station for 16 consecutive days to verify the multipath mitigation effectiveness. Compared with sidereal filtering, multipath hemispherical map (MHM) and trend-surface analysis-based MHM, the experimental results show that using AT-Conv-LSTM can decrease the root mean square error and mean absolute error values of the multipath error more than 60% and 13%, respectively. The proposed method can correct the code multipath to centimeter level, which is one order of magnitude lower than the uncorrected code multipath. Therefore, the proposed AT-Conv-LSTM network could be used as a powerful alternative tool to realize multipath reduction and will be of wide practical value in the fields of standard and high-precision positioning services.