Multiple Reference Stations Research Articles

Risk overbounding for ionospheric gradient monitor using geometry-free double differenced carrier phase measurements

Ionosphere anomaly can cause large spatial gradients in the double-differenced carrier phase (DDCP) measurements. Taking advantage of this characteristic, the ionospheric gradient monitor (IGM) is designed with multiple ground reference stations to detect threatening ionospheric gradients for safety of life applications. An optimal IGM should be most sensitive to ionospheric gradients and least sensitive to other errors. However, current IGM suffers from the influence of tropospheric error, which can degrade monitor performance under extreme weather conditions by causing risks of false alarms and missed detections. To address this issue, an alternative IGM is proposed using the geometry-free combination of DDCP as the test statistic. Ambiguity resolution procedure is designed for estimating the ambiguity term in the test statistic. The risk induced by the wrong ambiguity fix and tropospheric error are analyzed and bounded with required averaging period and minimum baseline length. The results show that the proposed theoretical IGM is capable of achieving probability of false alarm of 10–8 and probability of missed detection of 10–6 with a filtering period of 612 s and baseline length of 371.7 m or a filtering period of 544 s and baseline length of 384.4 m. The experimental results using data collected from Hong Kong Satellite Positioning Reference Station Network demonstrate that the performance of the proposed theoretical IGM is comparable to that of the existing detection algorithm.

Design of a 3D space early warning system for high precision positioning technology of Beidou and analysis of differential positioning accuracy

The Beidou satellite navigation system has achieved certain results in positioning accuracy, but due to factors such as system errors, its accuracy still does not fully meet the requirements of high-precision measurement. Therefore, this study proposes a design method for a three-dimensional space early warning system, aiming to combine the positioning function of the BeiDou satellite navigation system and differential positioning technology to improve positioning accuracy. By utilizing differential positioning technology, multiple reference stations are arranged around the receiving device, and the positioning information received by these stations is used for accuracy correction. This method can effectively offset errors such as atmospheric errors, clock errors, and multipath effects between receivers, making the obtained positioning results more accurate. Through the design and implementation of a three-dimensional space early warning system, positioning errors can be predicted and monitored, and abnormal positioning situations can be detected and corrected in a timely manner, thereby improving the overall reliability of positioning. The system designed in this article can effectively improve positioning accuracy, meet the requirements of modern measurement technology for positioning accuracy, and demonstrate the superiority of the system through experimental verification and differential positioning accuracy analysis.

BDS/GPS Multi-Baseline Relative Positioning for Deformation Monitoring

The single-baseline solution (SBS) model has been widely adopted by the existing global navigation satellite system (GNSS) deformation monitoring systems due to its theoretical simplicity and ease of implementation. However, the SBS model neglects the mathematical correlation between baselines, and the accuracy and reliability can be degraded for baselines with long length, large height difference or frequent satellite signal occlusion. When monitoring large-area ground settlement or long-spanned linear objects such as bridges and railroads, multiple reference stations are frequently utilized, which can be exploited to improve the monitoring performance. Therefore, this paper evaluates the multi-baseline solution (MBS) model, and constrained-MBS (CMBS) model that has a prior constraint of the spatial-correlated tropospheric delay. The reliability and validity of the MBS model are verified using GPS/BDS datasets from ground settlement deformation monitoring with a baseline length of about 20 km and a height difference of about 200 m. Numerical results show that, compared with the SBS model, the MBS model can reduce the positioning standard deviation (STD) and root-mean-squared (RMS) errors by up to (47.4/51.3/66.2%) and (56.9/60.4/58.4%) in the north/east/up components, respectively. Moreover, the combined GPS/BDS positioning performance for the MBS model outperforms the GPS-only and BDS-only positioning models, with an average accuracy improvement of about 13.8 and 25.8%, with the highest accuracy improvement of about 41.6 and 43.8%, respectively. With the additional tropospheric delay constraint, the CMBS model improves the monitoring precision in the up direction by about 45.0%.

Antenna Array-Aided Real-Time Kinematic Using Moving Base Stations

A global navigation satellite systems (GNSS) real-time kinematic (RTK) using multiple base stations is referred as an antenna array-aided RTK. This positioning method more reliably resolves carrier phase integer ambiguities by processing additional measurements provided from multiple GNSS reference stations whose antenna locations are accurately surveyed. In this study, a conventional antenna array-aided RTK is extended to improve RTK performance with multiple moving base stations. Because accurately surveyed antenna coordinates are not available, we propose an antenna array-aided Kalman filter approach to first check the sanity of the fixed integer ambiguities and baselines estimated by moving reference stations and use them as a-priori information in RTK measurement formulations. Our flight test results with three unmanned aerial vehicles confirmed that the proposed Kalman filter formulation outperformed the conventional RTK and a priori antenna array-aided RTK approaches in the aspects of positioning accuracy, time to first fix, and success probability of integer ambiguity fixes.

Single Epoch Ambiguity Resolution of Small-Scale CORS with Multi-Frequency GNSS

The network real-time kinematic (RTK) technique uses continuously operating reference stations (CORS) within a geographic area to model the distance dependent errors, allowing users in the area to solve ambiguities. A key step in network RTK is to fix ambiguities between multiple reference stations. When a new satellite rises or when maintenance happens, many unknown parameters are involved in the mathematical model, and traditional methods take some time to estimate the integer ambiguities reliably. The purpose of this study is the single-epoch ambiguity resolution on small-scale CORS network with inter-station distance of around 50 km. A new differencing scheme is developed to explore the full potential of multi-frequency Global Navigation Satellite System (GNSS). In this scheme, a differencing operation is formed between satellites with the closest mapping functions. With the new differencing scheme, tropospheric error can be mostly neglected after the correction, as well as the double-differencing operation. Numerical tests based on two baselines of 49 km and 35 km show that the success rate of ambiguity resolution can reach more than 90%. The single-epoch ambiguity resolution for reference stations brings many benefits to the network RTK service, for example, the instantaneous recovery after maintenance or when a new satellite rises.

Optimization analysis for the performance of post-processing kinematic GNSS local multiple reference stations

Optimization analysis for the performance of post-processing kinematic GNSS local multiple reference stations

Research on Virtual Reference Station (VRS) Technology and Differential Correction Information

With the continuous operation of reference stations for various purposes, the system has been built one after another. The network RTK (carrier real-time dynamic positioning technology) composed of multi-base stations has emerged, which solves the limitation of conventional RTK. Although some of these systematic errors can be weakened by the model, their residual can not be ignored. Conventional RTK has some problems in practical application. Differential technology can only eliminate common errors between reference stations and user stations under certain conditions. The emergence of VRS (Virtual Reference Station) technology in network RTK has greatly improved the effective distance of RTK technology. The VRS is characterized by continuous operation of multiple reference station networks and long-distance high-precision real-time positioning. While ensuring that the distance between the base stations cannot be too long and the user’s positioning accuracy is at the same time. Also consider the range of user operations that the system can cover.

A simplified processing algorithm for multi-baseline RTK positioning in urban environments

The real-time kinematic (RTK) positioning with the multi-baseline solution (MBS) can provide high accuracy and availability for emerging applications. When the multi-systems and multi-frequencies observations for multiple stations are adopted, a heavy computational burden can arise to degrade the performance of RTK positioning. In this paper, a simplified multi-baseline solution (SMBS) algorithm based on the equivalence principle is proposed to improve the computational efficiency. Firstly, the classical equivalent observation equations (COE) are introduced and the variance–covariance (VC) matrix for SD observations is presented. Then, the simplified equivalent observation equations (SOE) can be obtained throughthe formuladerivationof transformation matrix. Secondly, the sequential Kalman filter (SKF) with multiple groups is used instead of the classical Kalman filter (CKF) to improve filtering efficiency. Finally, the performance of the proposed algorithm is comprehensively evaluated and analyzed by the static and kinematic experiments. The results demonstrate that the SMBS algorithm adopting SOE and SKF strategies can significantly accelerate the processing procedure of RTK positioning and reduce the processing time for a single epoch. The SOE strategy has an average efficiency improvement by approximately 74.7% for static, and 60.6% for the kinematic experiment, and the improvement of the SKF strategy is 49.6% and 58.0%. Moreover, the SMBS algorithm can provide a higher positioning accuracy and availability than the single-baseline solution (SBS) model. Especially for multiple reference stations, the state parameters of the rover station can be compressed to enhance the geometric strength of the positioning model, which can provide a smaller PDOP and ADOP values and improve the performance of ambiguity resolution (AR).

Magnetotelluric multi-reference array data processing algorithm

Rational use of multiple remote reference data is an important way to improve the data quality of MT method. Based on the electromagnetic array data processing model, a data processing algorithm with multiple reference stations is proposed. Firstly, reference channels are selected from multiple remote stations to construct the natural field dominated reference data array; then the polarization parameters of natural sources are extracted from the reference data array by robust principal component analysis method; the parameters are then applied to the target array, which constructed by data from the stations to be processed, to estimate the target tensor impedances by robust estimation method. Finally, the effectiveness of the proposed algorithm is discussed by comparing it with the robust least squares and conventional remote reference methods, using a case study in east China. The results show that the new scheme is an effective strategy by using the multiple reference channel data, which can improve the quality of MT data processing in noisy environment and provide a reasonable correction for MT “dead band” distortions.

Comprehensive outage compensation of real-time orbit and clock corrections with broadcast ephemeris for ambiguity-fixed precise point positioning

The main challenge in real-time precise point positioning (PPP) is that the data outages or large time lags in receiving precise orbit and clock corrections greatly degrade the continuity and real-time performance of PPP positioning. To solve this problem, instead of directly predicting orbit and clock corrections in previous researches, this paper presents an alternative approach of generating combined corrections including orbit error, satellite clock and receiver-related error with broadcast ephemeris. Using ambiguities and satellite fractional-cycle biases (FCBs) of previous epoch and the short-term predicted tropospheric delay through linear extrapolation model (LEM), combined corrections at current epoch are retrieved and weighted with multiple reference stations, and further broadcast to user for continuous enhanced positioning during outages of orbit and clock corrections. To validate the proposed method, two reference station network with different inter-station distance from National Geodetic Survey (NGS) network are used for experiments with six different time lags (i.e., 5 s, 10 s, 15 s, 30 s, 45 s and 60 s), and one set of data collected by unmanned aerial vehicle (UAV) is also used. The performance of LEM is investigated, and the troposphere prediction accuracy of low elevation (e.g., 10–20degrees) satellites has been improved by 44.1% to 79.0%. The average accuracy of combined corrections before and after LEM is used is improved by 12.5% to 77.3%. Without LEM, an accuracy of 2–3 cm can be maintained only in case of small time lags, while the accuracies with LEM are all better than 2 cm in case of different time lags. The performance of simulated kinematic PPP at user end is assessed in terms of positioning accuracy and epoch fix rate. In case of different time lags, after LEM is used, the average accuracy in horizontal direction is better than 3 cm, and the accuracy in up direction is better than 5 cm. At the same time, the epoch fix rate has also increased to varying degrees. The results of the UAV data show that in real kinematic environment, the proposed method can still maintain a positioning accuracy of several centimeters in case of 20 s time lag.

GPS/BDS RTK Positioning Based on Equivalence Principle Using Multiple Reference Stations

Reliable real-time kinematic (RTK) is crucially important for emerging global navigation satellite systems (GNSSs) applications, such as drones and unmanned vehicles. The performance of conventional single baseline RTK (SBRTK) with one reference station degrades greatly in dense, urban environments, due to signal blockage and multipath error. The increasing use of multiple reference stations for kinematic positioning can improve RTK positioning accuracy and availability in urban areas. This paper proposes a new algorithm for multi-baseline RTK (MBRTK) positioning based on the equivalence principle. The advantages of the solution are to keep observation independent and increase the redundancy to estimate the unknown parameters. The equivalent double-differenced (DD) observation equations for multiple reference stations are firstly developed through the equivalent transform. A modified Kalman filter with parameter constraints is proposed, as well as a partial ambiguity resolution (PAR) strategy is developed to determine an ambiguity subset. Finally, the static and kinematic experiments are carried out to validate the proposed algorithm. The results demonstrate that, compared with single global positioning system (GPS) and Beidou navigation system (BDS) RTK positioning, the GPS/BDS positioning for MBRTK can enhance the positioning accuracy with improvement by approximately (45%, 35%, and 27%) and (12%, 6%, and 19%) in the North (N), East (E), and Up (U) components, as well as the availability with improvement by about 33% and 10%, respectively. Moreover, the MBRTK model with two and three reference receivers can significantly increase the redundancy and provide smaller ambiguity dilution of precision (ADOP) values. Compared with the scheme-one and scheme-two for SBRTK, the MBRTK with multiple reference receivers have a positioning accuracy improvement by about (9%, 0%, and 6%) and (9%, 16%, and 16%) in N, E, and U components, as well as the availability improvement by approximately 10%. Therefore, compared with the conventional SBRTK, the MBRTK can enhance the strength of the kinematic positioning model as well as improve the positioning accuracy and availability.

Stochastic modeling for VRS network-based GNSS RTK with residual interpolation uncertainty

Abstract The key concept of the virtual reference station (VRS) network-based technique is to use the observables of multiple reference stations to generate the network corrections in the form of a virtual reference station at a nearby user’s location. Regarding the expected positioning accuracy, the novice GNSS data processing strategies have been adopted in the server-side functional model for mitigating distance-dependent errors including atmospheric effects and orbital uncertainty in order to generate high-quality virtual reference stations. In addition, the realistic stochastic model also plays an important role to take account of the unmodelled error in the rover-side processing. The results of our previous study revealed that the minimum norm quadratic unbiased estimation (MINQUE) stochastic model procedure can improve baseline component accuracy and integer ambiguity reliability, however, it requires adequate epoch length in a solution to calculate the elements of the variance-covariance matrix. As a result, it may not be suitable for urban environment where the satellite signal interruptions take place frequently, therefore, the ambiguity resolution needs to be resolved within the limited epochs. In order to address this limitation, this study proposed the stochastic model based on using the residual interpolation uncertainty (RIU) as the weighting schemes. This indicator reflects the quality of network corrections for any satellite pair at a specific rover position and can be calculated on the epoch-by-epoch basis. The comparison results with the standard stochastic model indicated that the RIU-weight model produced slightly better positioning accuracy but increased significant level of the ambiguity resolution successful rate.

Improving the Accuracy of Regional Ionospheric Mapping with Double-Difference Carrier Phase Measurement

Regional augmentation systems for a global navigation satellite system (GNSS) provide an ionospheric map correction to the user in order to remove the ionospheric delay error. Measurements are collected from multiple reference stations to estimate the ionospheric map. During this process, the pseudorange measurement error of a reference station causes an error in the correction, which is more evident at edge areas and causes a large error for low-elevation satellites. In this study, an ionospheric modeling algorithm was developed that uses the carrier phase with the pseudorange to greatly reduce the error. The integer-resolved double-difference carrier phase can be obtained through ambiguity resolution method, and the measurement is directly utilized in ionospheric modeling. The performance of the developed method was tested in simulations and with real data for validation. The results of users at various locations showed that the method effectively improved the accuracy of the correction.

CARIB18: A Stable Geodetic Reference Frame for Geological Hazard Monitoring in the Caribbean Region

We have developed a Stable Caribbean Reference Frame 2018 (CARIB18) using long-term continuous observations from 18 continuously operating Global Positioning System (GPS) stations fixed on the margins of the stable portion of the Caribbean plate. The frame stability of CARIB18 is approximately 0.7 mm/year in the horizontal direction and 0.9 mm/year in the vertical direction. A method that employs a total of seven parameters for transforming positional time series from a global reference frame (IGS14) to a regional reference frame is introduced. The major products from this study include the seven parameters for realizing CARIB18 coordinates and three-component site velocities of 250 continuous GPS stations (>3 years) with respect to CARIB18. Geological hazard monitoring using GPS has traditionally been performed using the carrier-phase differential method that requires single or multiple reference stations to be simultaneously operated in the field. CARIB18 allows for precise geological hazard monitoring using stand-alone GPS, which substantially reduces field costs and simplifies logistics for long-term geological hazard monitoring. Applications of CARIB18 in plate motion, post-seismic, and volcano monitoring and research are demonstrated in this article. The regional reference frame will be periodically updated every few years with more reference stations and longer periods of observations to mitigate the degradation of the frame over time and will be synchronized with the updates of the International GNSS Service (IGS) IGS reference frame.

Improving the Stochastic Model for VRS Network-Based GNSS Surveying

Abstract The VRS network-based technique has become the main precise GNSS surveying method especially for medium-range baselines (approximately 20-70 km). The key concept of this approach is to use the observables of multiple reference stations to generate the network correction in the form of a virtual reference station for mitigating distance-dependent errors including atmospheric effects and orbital uncertainty at the user’s location. Numerous GNSS data processing strategies have been adopted in the functional model in order to improve both the positioning accuracy and the success of ambiguity resolution. However, it is impossible to completely model the aforementioned errors. As a result, the unmodelled residuals still remain in the virtual reference station observables when the least squares estimation is employed. An alternative approach to deal with these residuals is to construct a more realistic stochastic model whereby the variance-covariance matrix is assumed to be homoscedastic. This research aims to investigate a suitable stochastic model used for the VRS technique. The rigorous statistical method, MINQUE has been applied to estimate the variance-covariance matrix of the double-difference observables for a virtual reference station to rover baseline determination. The findings of the comparison to the equal-weight model and the satellite elevation-based model indicated that the MINQUE procedure could enhance the positioning accuracy. In addition, the reliability of ambiguity resolution is also improved.

협역 전리층의 일관성을 이용한 다중 기준국 기반 전리층 이상 현상 감시 기법

GNSS 측위 정확도에 영향을 주는 전리층 오차는 전리층에 존재하는 전자로 인해 위성의 전파가 굴절됨에 따라 발생하는데 태양활동 정도, 지역, 시간에 따라 그 값이 변한다. 정밀한 전리층 오차 추정이 가능한 이중주파수 수신기와 달리 단일 주파수 수신기의 경우에는 전리층 오차 모델이나 인근 고정기준국을 통해 제공 받는 의사거리 보정정보에 의존해야 한다. 하지만 일반적인 전리층 오차 경향과 달리, 국지적으로 전리층 총 전자수의 급격한 변화가 발생하는 경우 전리층 오차모델을 통한 오차 보정이 어려우며 만약 전리층의 변화가 고정기준국 상공의 전리층과 상이하다면, 의사거리 보정정보를 이용하여도 전리층 오차를 보정하지 못한다. 본 논문에서는, 이런 위험에 대처하기 위한 국지적 전리층 이상 현상에 대한 감시 기법에 대해 제안하고 실제 전리층 이상 현상이 발생한 데이터를 이용해 이를 검증하였다. 제시된 기법을 통해 전리층 이상 현상 발생 여부를 파악하고 단일 주파수 수신기 사용자의 항법해에 대한 신뢰도를 증가시킬 수 있을 것이다.

Multimodal data fusion for SB-JPALS status prediction under antenna motion fault mode

High positioning accuracy and system integrity are crucial for the Sea-based Joint Precision Approach and Landing System (SB-JPALS) to ensure life safety in carrier landing. The antenna motion of shipboard receivers may introduce large positioning error, which is one of the primary failure modes affecting the SB-JPALS integrity. Multimodal data fusion based on dual-frequency GPS observables and antenna motion information is applied to monitor the failure and enables the system to alarm message once position domain error caused by antenna movement exceeds a threshold. Monitoring algorithm uses multiple reference station architecture, selects integrated translating error of all valid reference antennas as the monitor measurement, and establishes a monitor decision-making model based on fault vertical protection level to evaluate the integrity performance. Multiple antenna motion errors are fused to be the integrated translating error and relevant methodology is described. Firstly the associated equation is built between individual antenna motion error and inter-antenna baseline motion error. The latter is regarded as known variables due to feasibility to capture them on the mobile ship platform. Then each antenna motion error is calculated and projected onto satellite line-of-sight direction. Finally the integrated error is obtained by averaging all antenna motion errors. The experiment data analysis result shows that individual antenna motion error derived from inter-antenna baseline errors is consistent with its real value, and the vertical protection level of the integrated translating error computed by multimodal data fusion processing based on multiple reference antennas is smaller than that by individual antenna information, namely, the system achieves better integrity.

Landslide Monitoring Network Establishment within Unified Datum and Stability Analysis in the Three Gorges Reservoir Area

A landslide monitoring network construction within unified datum which combined fiducial points, working reference points, and monitoring points was intensively studied in the Three Gorges Reservoir area. With special long and narrow geographical location in the area, designing and building monitoring network was vital to the realization of landslide monitoring. To build such a network with high precision, this paper mainly focused on the following four aspects: (1) method of using multiple GPS reference stations to build a unified datum network and subnet adjustment, (2) GPS data processing algorithm with millimeter level, (3) analysis of influence on the adjustment resulting from systematic error of time evolution datum from different GPS observations, and (4) establishment and stability analysis of unified datum. Then, using global test and trial-and-error method to analyze the datum based on the GPS observations (2008~2011) of landslide monitoring network in the area, we concluded that there were moved reference points during the three years of high water impoundment, and the horizontal displacement of moved reference points was more than 4 cm, even up to 79.4 cm. The displacement direction of unstable reference points was inspected with geographical environment at sites, which revealed congruency between them.

Multimodal Data fusion for SRGPS antenna motion error reduction

Antenna motion is a primary fault that degrades the integrity of shipboard relative GPS (SRGPS) systems, so we must investigate how to monitor and mitigate its impacts. Previous work proposed a single-baseline mode, but it had obvious problems, such as large motion errors, error measurement difficulties, and poor reliability. To solve these issues, we propose a multiple reference station architecture that deploys more than one reference station at different positions on ship. The observations are first translated to the ship reference point, and then integrated into a comprehensive measurement that accounts for the overall antenna motion errors. We consider two integrating methods: direct and weighted average methods. The direct average method is simple and intuitive, but the weighted average method more effectively reduced the overall antenna motion error by using the reciprocal standard deviation of historical measurements as weighting factors. All the antennas are mounted on the same ship body, so their correlations should also be considered when determining weighting factors. We used the ranking scores of the antennas derived using a graph-learning algorithm and fused them with the standard deviations to create new weighting factors. Finally, our experimental results demonstrated that the weighting factors based on the standard deviations and ranking scores reduced the overall antenna-motion error variance and improved the system integrity.

Network-Based Stochastic Model for Instantaneous GNSS Real-Time Kinematic Positioning

AbstractThe concept of global navigation satellite system (GNSS) real-time kinematic (RTK) positioning through the use of multiple reference stations (Network RTK) is the most common approach to relative positioning, which makes it possible to achieve centimeter-level accuracy for medium baselines. In this approach, ionospheric and geometric correction terms, generated on the basis of a model of interpolation of the distance-dependent biases, are applied to the functional model of rover positioning. The accuracy and reliability of Network RTK performance depend on the accuracy of the defined correction terms. Especially during storm-level ionospheric activity, the applied spatial interpolation model might not be suitable for the real ionospheric state, causing the ambiguity resolution to be less reliable, or even impossible, because of high residual errors. Thus, the residual errors can substantially degrade the correctness of the functional model and should be accounted for to obtain optimal estimation o...