Global Navigation Satellite System Multipath Research Articles

Integrated study of water levels and water storage variations using GNSS-MR and remote Sensing: A case study of Sarez Lake, the world's Highest-Altitude dammed lake

Sarez Lake, recognized as the world's highest-altitude dammed lake, necessitates meticulous monitoring of dam deformation, lake water levels, and water storage fluctuations to ensure its safety. In pursuit of this critical objective, a Global Navigation Satellite System (GNSS) monitoring network has been established around the lake to compute real-time station coordinates for deformation monitoring. GNSS Multipath Reflectometry (GNSS-MR) technology has been introduced as an innovative approach, enabling water level retrieval through conventional GNSS geodetic receivers. However, the complex and rugged terrain surrounding Sarez Lake poses challenges to the application of GNSS-MR in this region. This research is dedicated to addressing the challenges posed by the limited available elevation range selection and the retrieval of inter-site water level combinations in such demanding terrain. It proposes a novel method for effectively discerning valid Signal-to-Noise Ratio (SNR) arcs and an inter-site inter-signal water level combination retrieval approach, resulting in a continuous sequence of water level retrievals for this region. The incorporation of remote sensing techniques further facilitates the estimation of water storage fluctuations in the area. The outcomes of this study demonstrate the efficacy of GNSS-MR in capturing the lake's seasonal water-level variations, with retrieval uncertainties ranging from centimeters to low decimeters. The fusion of GNSS-MR with remote sensing data offers a comprehensive approach for monitoring the water levels and water storage fluctuations of Sarez Lake within its challenging environmental conditions. This research provides a valuable methodology applicable to the study and monitoring of other dammed lakes.

Flying Target Detection Technology Based on GNSS Multipath Signals.

In this study, a passive radar system that detects flying targets is developed in order to solve the problems associated with traditional flying target detection systems (i.e., their large size, high power consumption, complex systems, and poor battlefield survivability). On the basis of target detection, the system uses the multipath signal (which is usually eliminated as an error term in navigation and positioning), enhances it by supporting information, and utilizes the multi-source characteristics of ordinary omnidirectional global navigation satellite system (GNSS) signals. The results of a validation experiment showed that the system is able to locate a passenger airplane and obtain its flight trajectory using only one GNSS receiving antenna. The system is characterized by its light weight (less than 5 kg), low power consumption, simple system, good portability, low cost, and 24/7 and all-weather work. It can be installed in large quantities and has good prospects for development.

Resilient Multi-Sensor UAV Navigation with a Hybrid Federated Fusion Architecture

Future UAV (unmanned aerial vehicle) operations in urban environments demand a PNT (position, navigation, and timing) solution that is both robust and resilient. While a GNSS (global navigation satellite system) can provide an accurate position under open-sky assumptions, the complexity of urban operations leads to NLOS (non-line-of-sight) and multipath effects, which in turn impact the accuracy of the PNT data. A key research question within the research community pertains to determining the appropriate hybrid fusion architecture that can ensure the resilience and continuity of UAV operations in urban environments, minimizing significant degradations of PNT data. In this context, we present a novel federated fusion architecture that integrates data from the GNSS, the IMU (inertial measurement unit), a monocular camera, and a barometer to cope with the GNSS multipath and positioning performance degradation. Within the federated fusion architecture, local filters are implemented using EKFs (extended Kalman filters), while a master filter is used in the form of a GRU (gated recurrent unit) block. Data collection is performed by setting up a virtual environment in AirSim for the visual odometry aid and barometer data, while Spirent GSS7000 hardware is used to collect the GNSS and IMU data. The hybrid fusion architecture is compared to a classic federated architecture (formed only by EKFs) and tested under different light and weather conditions to assess its resilience, including multipath and GNSS outages. The proposed solution demonstrates improved resilience and robustness in a range of degraded conditions while maintaining a good level of positioning performance with a 95th percentile error of 0.54 m for the square scenario and 1.72 m for the survey scenario.

ConvGRU-MHM: a CNN GRU-enhanced MHM for mitigating GNSS multipath

In high-precision global navigation satellite system (GNSS) short-baseline positioning, multipath is the main source of errors. If the station environment is quasi-static, repeat periods of satellites can be utilized to generate time- or space-dependent multipath models to mitigate multipaths. However, two general problems are associated with the multipath models constructed based on satellite mechanics: (1) an accuracy decrease occurs when the above models are applied to multipath mitigation over a long time-span; (2) when constructing the spatial and temporal grids of the satellite-based spatially dependent multipath model, it is challenging to balance computational efficiency and spatial resolution. We propose a convolutional neural network-gated recurrent unit enhanced multipath hemispherical map (ConvGRU-MHM) in the observational domain to address these problems. The proposed method directly mines the deep features of elevation, azimuth angle, and multipath and the mapping relationship between these to establish a real-time prediction model. The predicted multipath is obtained and returned to the observation equation for multipath mitigation when the real-time position of the satellite is placed in the pre-trained model. We compared the multipath mitigation performance of sidereal filtering and a MHM with that of the ConvGRU-MHM to demonstrate the advantages of the proposed method. The experimental results are as follows: (1) in the short time-span (first 20 d), the mean accuracy improvements of the ConvGRU-MHM in the E/N/U direction performed better than those of the SF and MHM; and (2) in the long-term time (after 50 d), the mean accuracy improvements of the ConvGRU-MHM in the E/N/U direction are higher than that of the SF and MHM by 10%–20%. As a lightweight model, the ConvGRU-MHM can effectively improve the measurement accuracy of GNSS real-time monitoring in fields, such as deformation monitoring and seismic research.

Using convolutional neural networks to detect GNSS multipath.

Global Navigation Satellite System (GNSS) multipath has always been extensively researched as it is one of the hardest error sources to predict and model. External sensors are often used to remove or detect it, which transforms the process into a cumbersome data set-up. Thus, we decided to only use GNSS correlator outputs to detect a large-amplitude multipath, on Galileo E1-B and GPS L1 C/A, using a convolutional neural network (CNN). This network was trained using 101 correlator outputs being used as a theoretical classifier. To take advantage of the strengths of convolutional neural networks for image detection, images representing the correlator output values as a function of delay and time were generated. The presented model has an F score of 94.7% on Galileo E1-B and 91.6% on GPS L1 C/A. To reduce the computational load, the number of correlator outputs and correlator sampling frequency was then decreased by a factor of 4, and the convolutional neural network still has an F score of 91.8% on Galileo E1-B and 90.5% on GPS L1 C/A.

Mitigating GNSS Multipath Effects Using XGBoost Integrated Classifier Based on Consistency Checks

Under the influence of urban building roads, especially interference from multipath effects, global navigation satellite system (GNSS) receiver-related output signal distortion can affect the robustness of the positioning system and the final positioning accuracy. To deal with the above problems, this paper proposes a two-layer consistency-checks (CC) positioning model based on eXtreme Gradient Boosting (XGBoost) integrated learner. First, the model excludes the abnormal values from the correlated output of the first layer by the classical statistical distribution test method. Then, the remaining available measurements are used as the second-layer input, and the measurements are used as learning data using an integrated machine learning method, XGBoost, to efficiently detect and identify non-line-of-sight (NLOS), LOS, and other reflective multipath signals. In order to better mitigate errors in the dynamic relative positioning process, the second-layer checking process uses dynamic pseudorange differencing technique (DPDT) and weighted least squares method (WLS) to smooth the output outcome of the receiver. In the experimental part, we compare and analyze the proposed method with the existing methods from different perspectives in this paper, respectively. The results show that the performance of the model is significantly improved after applying the CC method, in which the average classification accuracy of the multipath signals in the target feature set can reach 91.6%. According to the final positioning results, the proposed method shows a significant accuracy improvement compared to the existing research methods.

Low-Profile Substrate Integrated Choke Rings for GNSS Multipath Mitigation

In this article, a novel technique for the miniaturization of corrugated structures is presented, and multifolded corrugations (MFCs) are introduced. The miniaturization is achieved by implementing multiple folds or slits inside corrugations. The proposed miniaturization technique is modeled using the modal expansion method. An equivalent circuit is extracted, which precisely models the surface impedance of the proposed MFCs. A time-efficient design procedure is presented based on the equivalent circuit model, and a dual-band double-folded substrate integrated choke ring (DFSICR) structure is designed to suppress the propagation of surface waves over the main global navigation satellite system (GNSS) frequency bands: L1 (1573–1587 MHz) and L2 (1215–1240 MHz). The DFSICR demonstrates significant multipath mitigation capabilities, close to that of a classic choke ring, while it eliminates the drawbacks of a conventional choke ring, such as large size, heaviness, costly fabrication, and inability to integrate with printed circuit board (PCB) structures. An example design shows miniaturization of 85% in height and 38% in diameter compared to the conventional choke ring. A prototype is fabricated using FR4 laminates, which demonstrates a weight reduction of more than 90% compared to the classic choke ring. The measurement results confirm the validity of the proposed technique.

Sea-Level Monitoring and Ocean Tide Analysis Based on Multipath Reflectometry Using Received Strength Indicator Data From Multi-GNSS Signals

Compared with tide gauges, Global Navigation Satellite System Multipath Reflectometry (GNSS-MR) can provide low-cost, long-term sea-level data that are not susceptible to crustal loading. Signal-to-noise ratio (SNR) observables in GNSS files are commonly used for GNSS-MR; however, these observables are not always present, especially in early GNSS files. Several different combinations of codes and carrier-phases for GNSS-MR as substitutes to extract sea level have been proposed; however, the requirement of these methods for application of cycle slip detection or multi-frequency observations to isolate multipath signals reduces their applicability. Here, we propose a new method for sea-level estimation using Signal Strength Indicator (SSI) data in GNSS observation files, which is an alternative to existing methods because SSI data always exist. To verify the proposed method, we used four multi-GNSS data from three stations to monitor sea level. Sea-level estimations with root-mean-square errors of 7–8, 5–9, 12–15 and 9–13 cm relative to in-situ data were retrieved, and the correlation coefficients for these stations were bigger than 0.98, 0.98, 0.93 and 0.96, respectively. Moreover, the proposed method measures sea levels with precision similar with the traditional SNR method. In addition, sea-level results derived from the proposed method at these stations were further applied to estimate ocean tides. Ocean-tide coefficients for several main tides determined by different data were in good agreement.

Ten-Minute Sea-Level Variations From Combined Multi-GNSS Multipath Reflectometry Based on a Weighted Iterative Least-Square Method

Accurate and high-frequency sea level monitoring is of great importance in ocean environments and global climatic studies, but traditional techniques have their respective limitations. In the last decades, the application of Global Navigation Satellite System Multipath Reflectometry (GNSS-MR) in sea level monitoring has developed rapidly. Recently, more available GNSS signals are expected to bring new opportunities to improve its performance and achieve high spatial-temporal resolution. In this paper, a new algorithm is developed to optimize the method of multi-GNSS multipath reflectometry and improve the precision and sampling rate for GNSS-MR sea level monitoring. In order to make full use of the short-term multipath oscillation information, a sliding window is used to collect the SNR sequences. A weighted iterative least-square method is introduced to combine the selected SNR observations of GPS, GLONASS, Galileo, and BDS systems, and retrieve sea level with 10-minute intervals at BRST station for one year. A novel index called Local Kurtosis (LK) is proposed, which can be used to evaluate the quality of the Lomb-Scargle periodogram (LSP) and design the weight matrix in the least-square combinatorial process. Compared to using individual signals, the optimized combination algorithm decreased the root mean square error (RMSE) by 78%, from 0.610 m to 0.134 m, and increased the correlation coefficient R² from 0.851 to 0.992. In addition, the tidal constituents monitored by multi-GNSS-MR and tide gauge are highly consistent, demonstrating that the multi-GNSS-MR can accurately retrieve daily and subdaily tidal constituents of periods longer than 10 min.

Extended Double-delta Correlator Technique for GNSS Multipath Mitigation

Multipath is one of the main error sources in global navigation satellite system (GNSS). Many multipath mitigation methods have been proposed, such as the narrow correlator technique and the double-delta (DD) correlator technique. In light of the BPSK modulated signals used in many GNSS, an extended DD (EDD) correlator technique expanding from the DD correlator, which uses multiple pairs of correlators with more general spacing and weight, is proposed in this paper. Furthermore, the paper provides the discriminator structure, the closed-form expressions for multipath error envelope under infinite bandwidth and the closed-form expressions for the relationship between multipath error, thermal noise performance and design parameters of the discriminator. Based on the explicit performance expressions, the appropriate selection principles of parameters are given and verified by theoretical analysis and simulation. The results show that the proposed method can improve the performance optimization freedom of the DD technique without significantly increasing the design complexity. Moreover, the multipath performance is better than DD under infinite bandwidth and has great adaptability to limited bandwidth and the next generation GNSS signals, such as BOC and MBOC. The EDD technique can also be utilized as a noncoherent discriminator and has better anti-multipath performance. Furthermore, the EDD technique can achieve balance between multipath mitigation performance and thermal noise performance by adjusting correlator spacing and weight and can be self-adaptive to multipath relative amplitude in the environment.

Performance Analysis of a GNSS Multipath Detection and Mitigation Method With Two Low-Cost Antennas in RTK Positioning

Global navigation satellite system (GNSS) plays a vital role in high-precision positioning whereas detecting and mitigating carrier phase multipath error is still a significant challenge. Multipath error is closely related to the users’ environment, so it is difficult to mitigate by traditional differencing techniques. In this paper, we discuss the possibility and potential performance of multipath detection and mitigation with low-cost antennas in real-time kinematic (RTK) positioning. We employ two low-cost antennas and assume that the baseline length is known. We employ the carrier phase, ephemeris, and baseline length to detect the observed and estimated baseline vectors’ consistency in real-time. A reasonable threshold is proposed to detect the satellite signals with the multipath effect, then we eliminate these signals and use the remaining satellite signals for RTK positioning to mitigate multipath. The experiments are carried out in the open environment without multipath and the environment with specular multipath. Experimental results show that the false alarm rate of this method is entirely consistent with the theoretical value. When the number of satellites is six and eight, this method can reduce the RMS (root mean square) of positioning error by approximately 64% and 49%, respectively. At the same time, this method can improve the ambiguity success rate to above 99%.

3D Mapping Database Aided GNSS Based Collaborative Positioning Using Factor Graph Optimization

The recent development in vehicle-to-everything (V2X) communication opens a new opportunity to improve the positioning performance of the road users. We explore the benefit of connecting the raw data of the global navigation satellite system (GNSS) from the agents. In urban areas, GNSS positioning is highly degraded due to signal blockage and reflection. 3D building model can play a major role in mitigating the GNSS multipath and non-line-of-sight (NLOS) effects. To combine the benefits of 3D models and V2X, we propose a novel 3D mapping aided (3DMA) GNSS-based collaborative positioning method that makes use of the available surrounding GNSS receivers’ measurements. By complementarily integrating the ray-tracing based 3DMA GNSS and the double difference technique, the random errors (such as multipath and NLOS) are mitigated while eliminating the systematic errors (such as atmospheric delay and satellite clock/orbit biases) between road user. To improve the accuracy and robustness of the collaborative algorithm, factor graph optimization (FGO) is employed to optimize the positioning solutions among agents. Multiple low-cost GNSS receivers are used to collect both static and dynamic data in Hong Kong and to evaluate the proposed algorithm by post-processing. We reduce the GNSS positioning error from over 30 meters to less than 10 meters for road users in a deep urban canyon.

Soil Moisture Estimation by GNSS Multipath Signal

Global navigation satellite system (GNSS) multipath signals received by a geodetic-quality GNSS receiver can be used to estimate the water content of soil around the antenna. The direct signals from satellite to GNSS antenna are the most valuable signals in geodetic measurement, such as positioning, navigation, GNSS control network, deformation monitoring, and so on. However, the GNSS antenna also captures the reflected signals from the ground, which contain information of surrounding environment, so that useful information about the reflection surface can be inferred by analyzing the reflected signal. This technique is termed as GNSS-interferometric reflectometry. The signal-to-noise ratio (SNR) data recorded by a receiver contains SNR component of reflected signals, which is related to the soil moisture of the ground. The changes of soil moisture content will cause the change of soil permittivity and reflectivity which are the key factors that make further change of the SNR of reflected signals. We used the measured data to evaluate the correlation between amplitude of multipath induced SNR time series and real soil moisture. An improved soil moisture estimation algorithm based on multipath induced SNR amplitude data is proposed in this paper. The performance of the proposed soil moisture estimation method is evaluated using the 15-month data recorded by PBO H2O GNSS station and a 14-day experiment in Wuhan, China. The experimental results show that the estimated soil moisture has a strong correlation with the real soil moisture and the estimation accuracy in terms of root-mean-square error (RMSE) is 0.0345 cm3cm−3 and 0.0339 cm3cm−3, respectively. Meanwhile, the application scope of the method is given.

GNSS Multipath Error Modeling and Mitigation by Using Sparsity-Promoting Regularization

In high-accuracy global navigation satellite system (GNSS) positioning applications, the multipath is one of the primary error sources because it is hard to parameterize. Being somewhat systematic rather than purely random, the multipath should be viewed more as a signal rather than a noise. On this basis, empirically modeling the multipath is realizable. A new sidereal filtering approach based on sparsity-promoting regularization is proposed to mitigate multipath errors for static short baseline GNSS applications. The key idea of the proposed method emphasizes the use of the $L_{1} $ norm to extract multipaths from noisy carrier phase residuals. Two regularization schemes with the first- and second-order differences are considered. For each scheme, efficient numerical algorithms are developed to find solutions by using the Thomas algorithm and the Cholesky rank-one update algorithm as the core of the iteration for the first- and second-order differences, respectively. Regularization parameters or Lagrange multipliers are optimized by using the bootstrap method. By applying the proposed multipath modeling method, the average improvement ratio of the root-mean-square values of double-difference residuals can reach approximately 66.7% compared with the result without multipath mitigation in the two different datasets. Moreover, positioning precision is improved by approximately 20.8%, 26.3%, and 37.8% in the East, North, and Up directions, respectively. Moreover, the fixed rate of ambiguities is improved by 3.7% on average under the kinematic mode.

Tikhonov Regularization Based Modeling and Sidereal Filtering Mitigation of GNSS Multipath Errors

In Global Navigation Satellite System (GNSS) relative positioning applications, multipath errors are non-negligible. Mitigation of the multipath error is an important task for precise positioning and it is possible due to the repeatability, even without any rigorous mathematical model. Empirical modeling is required for this mitigation. In this work, the multipath error modeling using carrier phase measurement residuals is realized by solving a regularization problem. Two Tikhonov regularization schemes, namely with the first and the second order differences, are considered. For each scheme, efficient numerical algorithms are developed to find the solutions, namely the Thomas algorithm and Cholesky rank-one update algorithm for the first and the second differences, respectively. Regularization parameters or Lagrange multipliers are optimized using the bootstrap method. In experiment, data on the first day are processed to construct a multipath model for each satellite (except the reference one), and then the model is used to correct the measurement on the second day, namely following the sidereal filtering approach. The smoothness of the coordinates calculated using the corrected measurements is improved significantly compared to those using the raw measurement. The efficacy of the proposed method is illustrated by the actual calculation.

GNSS Multipath Reduction Using GPS and DGPS in the Real Case

In Global Navigation Satellite System (GNSS) like Global Positioning System (GPS) and future Galileo, space signal reception in urban environment seems to be one of most significant. The urban environment is characterized by the presence of an excessive number of obstacles that produce Multiple Path (MP) in positioning the receiver. Consequently, it is of primary importance to characterize and ameliorate the performances of GNSS receiver for this type of application. In this paper, a method to mitigate MP in GNSS applications was proposed. Its principle is based on the addition, to the geographic map of a city or a neighborhood, of a supplementary information that consists of the correction of error caused by the MPs. The latter one was carried out by the comparison of the measurements, realized by Differential GPS (DGPS) and GPS, between two different sites with the same form. The first one was characterized by the presence of the MPs and the second one was completely clear of any type of obstacle. As a consequence, the measurements comparison has allowed us to deduce the GNSS MPs errors. This information can subsequently be used to make the corrections of the errors caused by MPs and it can be generalized by a measurement company to any entire city in order to identify errors in any neighborhood.

GNSS Multipath Mitigation with a Moving Antenna Array

Besides the size and shape of antenna arrays, the correlation between multipath components and a desired signal restricts the use of array processing techniques for Global Navigation Satellite System (GNSS) multipath mitigation. A new method, based on a moving antenna array, to synthesize a larger array and increase its degree of freedom is proposed. Furthermore, a spatial filter is applied to this synthesized array to prevent the signal cancellation phenomenon and mitigate the multipath components.

Spatial Characterization of GNSS Multipath Channels

There is a growing interest in detecting and processing Global Navigation Satellite System (GNSS) signals in indoors and urban canyons by handheld devices. To overcome the signal attenuation problem in such adverse fading environments, long coherent integration is normally used. Moving the antenna arbitrarily while collecting signals is generally avoided as it temporally decorrelates the signals and limits the coherent integration gain. This decorrelation is a function of the antenna displacement and geometry of reflectors and angle of arrival of the received signal. Hence, to have an optimum receiver processing strategy it is crucial to characterize the multipath fading channel parameters. Herein, Angle of Arrival (AoA) and Angle Spread (AS) along with signal spatial correlation coefficient and fading intensity in GNSS multipath indoor channels are defined and quantified theoretically and practically. A synthetic uniform circular array utilizing a right-hand circular polarized (RHCP) antenna has been used to measure the spatial characteristics of indoor GNSS fading channels. Furthermore, rotating effect of a circular polarized antenna on the synthetic array processing and AoA estimation has been characterized. The performance of the beamforming technique via array gain is also assessed to explore the advantages and limitations of beamforming in fading conditions.

High Fidelity Antenna Model Validation Results of a GNSS Multipath Limiting Antenna

The local area augmentation system (LAAS) is a proposed satellite-based landing system by the Federal Aviation Administration (FAA) to serve as a navigation aid for commercial aircraft during the approach and landing phase of flight. The LAAS utilizes a special ground-based antenna array called the multipath limiting antenna (MLA) to provide differentially corrected global navigation satellite system (GNSS) data to oncoming aircraft as well as to reduce the largest error contributor to pseudo-range estimates; the ground multipath. The performance of the MLA is characterized in terms of its desired-to-undesired (D/U) gain ratio, phase center variation (PCV) and group delay (GD). A high fidelity antenna model (HFAM) of the MLA is presented that estimates the D/U, PCV, and GD as a function of elevation angle. The model consists of two main components: (1) a microwave feed distribution circuit model created using a circuit simulator, and (2) a radiating structure model developed using a full-wave method of moments (MoM) field solver. The performance of the model was assessed against antenna range measurements. The results of the HFAM show good correlation for the D/U and PCV while a significant bias was observed on the results for the GD. The dependence of the GD on the radiating element's impedance, tuning process, and Doppler frequency shift are demonstrated via simulations.