BeiDou Navigation Satellite System Data Research Articles

A novel mode of INS-aided BDS real-time high-rate and precise kinematic relative positioning between two moving platforms

ABSTRACT For kinematic relative positioning users between two moving platforms, limited communication bandwidth and computation ability usually cannot support real-time transmission of high-rate (≥10 Hz) BeiDou Navigation Satellite System (BDS) data. The performance of Ambiguity Resolution (AR) is also a major challenge in signal blocked and loss of lock environments. Based on BDS and Inertial Navigation System (INS) data, we develop a novel mode of INS-aided BDS kinematic relative positioning between two moving platforms, aiming to realize real-time, high-rate and precise positioning with low-cost communication modules in challenge environments. To achieve this goal, the INS-aided high-rate relative kinematic positioning and INS-aided BDS AR re-initialization methods are proposed. In this mode, the baseline bias caused by the different position datum is first defined and resolved. Then, high-rate INS data are assisted to obtain kinematic relative position when real-time kinematic positioning results are unavailable within 1 second. Once the BDS data are available, the predicted relative position is used as additional constraint to facilitate AR re-initialization and improve the kinematic positioning performance. The performance of these methods is discussed in a set of experiments with 1 Hz BDS data and 100 Hz INS data, and compared with the conventional method by sending raw BDS/INS measurements. The results show that the proposed methods can achieve an accuracy of about 5 cm for the INS-aided 100 Hz relative positioning in baseline components and lengths, which is equal to the conventional method, but the transmitted data have been sharply reduced by an average of nearly 80%. With the assistance of INS-predicted baseline constraint, the relative positioning performance has been further improved. The accuracy of baseline length errors is less than 4 cm, and the AR fixing rates keep larger than 95% during the experiment, while the wrongly fixed rates are reduced to less than 0.5%.

Load identification of a 2.5 MW wind turbine tower using Kalman filtering techniques and BDS data

The rapid increase in the number of wind turbine installations and operations, is increasing the importance of the health monitoring of these wind turbines. To assess the remaining service life of a wind turbine, continuous monitoring of the internal forces acting on the critical locations of fatigue in the structure is required. However, a large number of sensors are usually required for the comprehensive determination of the internal force at a site-specific location; additionally, these sensors cannot be placed in locations with strong stress or strain gradients. Therefore, in this paper, a strategy for estimating the thrust at the tower top and the bending moment at any position of the wind turbine tower is proposed, which only requires a limited number of acceleration sensors and the BeiDou Navigation Satellite System (BDS). The estimated load includes static and dynamic components. The former is calculated by fitting the derived function and the BDS data, and the latter is estimated by the time-domain inverse method using the Kalman filter and with acceleration sensors. The performance of the proposed strategy is validated in two case studies, including simulated data and recorded data from a 2.5 MW onshore wind turbine located in China. The results show that the strategy can produce an estimation of thrust and bending moment, with good accuracy.

Evaluation of BDS and GPS RAIM availability based on data collected in June 2020

The satellite pseudo-range fault detection with the Receiver Autonomous Integrity Monitoring (RAIM) method is affected by several satellite observations and the geometric distribution of satellites. The poor geometry distribution of satellites will conceal the positioning error caused by the satellite pseudo-range fault, resulting in unreliable detection results. Therefore, the availability evaluation must be made before RAIM to ensure that the fault detection performance will not be affected. On June 23, 2020, China successfully launched the 30th (last) navigation satellite of BeiDou's third-generation navigation satellite system (BDS-3), which is also the 55th BeiDou navigation satellite. Combining all the available satellites of BDS-1, BDS-2 and BDS-3, the positioning performance of BDS can be greatly improved. In order to evaluate the RAIM availability of BeiDou Navigation Satellite System (BDS) and Global Positioning System (GPS) in China, this paper first deduces the mathematical models and their characteristics of the three RAIM availability evaluation methods. Then, the study area (N10°–70°, E60°–150°) is divided into 4536 grid points at intervals of 1 ° × 1 ° in latitude and longitude, and the elevations of these grid points are taken from the global terrain data file. The Horizontal Protection Level (HPL) values of these grid points are calculated during 8–15 June 2020 using BDS and GPS ephemeris data. The RAIM availability differences between the two systems are compared and analysed. The analysis shows the Horizontal Protection Level method (HPLM) based on single-satellite pseudo-range fault is the most practical and convenient. During the 8-day observation period, the HPL values of BDS are significantly smaller than those of GPS in terms of geographic location and observation time, and the variation of HPL time series of BDS is also smaller than that of GPS, which indicates that the RAIM availability of GPS in China is not as good as that of BDS. Most importantly, in the four flight stages of the aircraft's Oceanic/Continental low-density En-route, Continental En-route, Terminal En-route and Non-precision approach (NPA), BDS can completely satisfy its RAIM availability requirement, while GPS can only meet the availability requirement of the En-route (Oceanic/Continental low density) phase, and the availability of the other three phases can at least reach 99.714%.

A New Cycle-Slip Repair Method for Dual-Frequency BDS Against the Disturbances of Severe Ionospheric Variations and Pseudoranges with Large Errors

Many Beidou navigation satellite system (BDS) receivers or boards provide dual-frequency measurements to conduct precise positioning and navigation for low-power consumption. Cycle-slip processing is a primary work to guarantee consistent, precise positioning with the phase data. However, the cycle-slip processing of BDS dual-frequency phases still follows with those of existing GPS methods. For single-satellite data, cycle-slip detection (CSD) with the geometry-free phase (GF) is disturbed by severe ionospheric delay variations, while CSD or cycle-slip repair (CSR) with the Melbourne–Wubbena combination (MW) must face the risk of the tremendous disturbance from large pseudorange errors. To overcome the above limitations, a new cycle-slip repair method for BDS dual-frequency phases (BDCSR) is proposed: (1) An optimal model to minimize the variance of the cycle-slip calculation was established to the dual-frequency BDS, after correcting the ionospheric variation with a reasonable and feasible way. (2) Under the BDS dual-frequency condition, a discrimination function was built to exclude the adverse disturbance from the pseudorange errors on the CSR, according to the rankings of the absolute epoch-difference GFs calculated by the searched cycle-slip candidates after correcting the ionospheric variation. Subsequently, many compared CSR tests were implemented in conditions of low and medium elevations during strong geomagnetic storms. Comparisons from the results of different methods show that: (1) The variations of ionospheric delays are intolerable in the cycle-slip calculation during the geomagnetic storm, and the tremendous influence from the ionospheric variation should be corrected before calculating the cycle-slip combination with the BDS dual-frequency data. (2) Under the condition of real dual-frequency BDS data during the geomagnetic storm, the actual success rate of the conventional dual-frequency CSR (CDCSR) by employing the optimized combinations, but absenting from the discrimination function, is lower than that of BDCSR by about 2%; The actual success rate of the CSD with MW (MWCSD), is lower than that of BDCSR by about 2%. (3) After adding gross errors of 0.7 m to all real epoch-difference pseudoranges epoch-by-epoch, results of CDCSR and MWCSD showed many errors. However, BDCSR achieved a higher actual success rate than those of CDCSR and MWCSD, about 43% and 16%, respectively, and better performance of refraining the disturbance of large pseudorange error on the cycle-slip determination was achieved in the BDCSR methodology.

Prediction of BeiDou Satellite Orbit Maneuvers to Improve the Reliability of Real-Time Navigation Products

The positioning, navigation, and timing (PNT) service of the Global Navigation Satellite System (GNSS) is developing in the direction of real time and high precision. However, there are some problems that restrict the development of real-time and high-precision PNT technology. Satellite orbit maneuvering is one of the factors that reduce the reliability of real-time navigation products, especially the high-frequency orbit maneuvering of geostationary earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites. The BeiDou Navigation Satellite System (BDS) constellation is designed to contain GEO, IGSO, and medium earth orbit (MEO). These orbit maneuvers bring certain difficulties for data processing, especially for BeiDou satellites, such as decreased real-time service performance, which results in real-time navigation products including unusable maneuvered satellites. Additionally, the performance of real-time navigation products will decrease because the orbit maneuvers could not be known in advance, which diminishes the real-time PNT service performance of BDS for users. Common users cannot obtain maneuvering times and strategies owing to confidentiality, which can lead to a decline in the BDS real-time service performance. Thus, we propose a method to predict orbit maneuvers. BDS data from the broadcast ephemeris were analyzed to verify the availability of the proposed method. In addition, the results of real-time positioning were analyzed by using ultra-rapid orbit products, demonstrating that their reliability is improved by removing maneuvered satellites in advance. This is vital to improve the reliability of real-time navigation products and BDS service performance.

BDS signal-in-space anomaly probability analysis over the last 6 years

Knowledge of the signal-in-space (SIS) anomaly probability is important for the integrity monitoring of satellite navigation. An efficient SIS anomaly detection method is indispensable for characterizing the probability of SIS anomalies with sufficient confidence. The traditional GPS anomaly detection method based on the zero-mean Gaussian distribution assumption of the instantaneous signal-in-space user range error (IURE) is not suitable for the emerging BeiDou navigation satellite system (BDS) because of the nonzero-mean, asymmetric distribution of the BDS IURE. By deliberately extracting the time series trend terms of the satellite orbit and clock errors, an SIS anomaly detection method with the worst user location protection principle is proposed based on 6 years of BDS data from March 2013 to March 2019. The detection results have shown that the probability of single-satellite SIS anomalies is at the 10−3 level and the probability of multiple-satellite SIS concurrent anomalies is at the 10−4 level. Meanwhile, the operational service performance provided by the BDS gradually improves over time.

A Closed-Form Localization Method Utilizing Pseudorange Measurements From Two Nonsynchronized Positioning Systems

In a time-of-arrival (TOA) or pseudorange based positioning system, user location is obtained by observing multiple anchor nodes (AN) at known positions. Utilizing more than one positioning systems, e.g., combining Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS), brings better positioning accuracy. However, ANs from two systems are usually synchronized to two different clock sources. Different from single-system localization, an extra user-to-system clock offset needs to be handled. Existing dual-system methods either have high computational complexity or sub-optimal positioning accuracy. In this paper, we propose a new closed-form dual-system localization (CDL) approach that has low complexity and optimal localization accuracy. We first convert the nonlinear problem into a linear one by squaring the distance equations and employing intermediate variables. Then, a weighted least squares (WLS) method is used to optimize the positioning accuracy. We prove that the positioning error of the new method reaches Cramer-Rao Lower Bound (CRLB) in far field conditions with small measurement noise. Simulations on 2D and 3D positioning scenes are conducted. Results show that, compared with the iterative approach, which has high complexity and requires a good initialization, the new CDL method does not require initialization and has lower computational complexity with comparable positioning accuracy. Numerical results verify the theoretical analysis on positioning accuracy, and show that the new CDL method has superior performance over the state-of-the-art closed-form method. Experiments using real GPS and BDS data verify the applicability of the new CDL method and the superiority of its performance in the real world.

A Real-Time Cycle Slip Detection and Repair Method Based on Ionospheric Delay Prediction for Undifferenced Triple-Frequency BDS Signals

The detection and repair of cycle slips are key steps in high-accuracy GNSS (Global Navigation Satellite System) data processing using carrier phase observations. BDS (BeiDou Navigation Satellite System) triple-frequency observations provide better combinations for cycle slip detections and repairs compared to dual-frequency observations. Although a number of algorithms have been developed and may correctly detect cycle slips most of the time, the reliability of empirical thresholds methods cannot be guaranteed. In this study, an adaptive threshold is proposed for three sets of triple-frequency Geometry-Free (GF) pseudorange minus phase combinations to improve the cycle slip detection performance and reduce the false alarm rate of the cycle slip detection by combining the predicted epoch-differenced ionospheric delays under active ionospheric conditions. Moreover, in the cycle slip repair, the integral combined cycle slips are determined by directly rounding the estimated float-combined cycle slips, which will lead to a repair error if the between-epoch ionospheric variation is large. In this study, a new rounding method considering the predicted epoch-differenced ionospheric delays is proposed, and it is proven that the new method has a higher success rate for estimating the integer value of a cycle slip than the traditional method. The performance of the newly proposed method is validated by using static BDS triple-frequency observations that contain simulated cycle slips. BDS triple-frequency observations were collected at 30-s sampling intervals under active ionospheric conditions. The results show that this method can successfully detect and repair all slips of more than one cycle. In addition, dynamic BDS data collected with a vehicle-based receiver at a 1-s sampling intervals are processed, and the results show that the proposed method is also effective in the detection and repair of cycle slips in dynamic data.

A method for automatic detection and characterization of plasma bubbles using GPS and BDS data

Detecting and characterizing Total Electron Content (TEC) depletion is important for studying the ionospheric threat due to the Equatorial Plasma Bubble (EPB) when applying the Ground-Based Augmentation System (GBAS) at low latitudes. This paper develops a robust method to automatically identify TEC depletion and derive its parameters. The rolling barrel algorithm is used to automatically identify the TEC depletion candidate and its parameters. Then, the depletion candidates are screened by several improved techniques to distinguish actual depletions from other phenomena such as Traveling Ionospheric Disturbance (TID) or abnormal data. Next, based on the depletion signals from three triangular receivers, the method derives EPB parameters such as velocity, width and gradient. The time lag and front velocity are calculated based on cross-correlation using TEC depletions and the geometrical distribution of three triangular receivers. The width and gradient of slope are then determined by using TEC depletion from a single receiver. By comparison, both the station-pair method and proposed method depend on the assumption that the EPB morphology is frozen during the short time when the plasma bubble moves between the receivers. However, our method relaxes the restriction that the baseline length should be shorter than the width of slope required by the station-pair. This relaxation is favorable for studying small-scale slope of depletions using stations of a longer baseline. In addition, the accuracy of the width and gradient is free of impact from hardware biases and small-scale disturbance, as it is based only on the relative TEC variation. The method is demonstrated by processing Global Positioning System (GPS) and BeiDou Navigation Satellite System (BDS) data on 15 August, 2018, in a solar minimum cycle.

Carrier Phase-Based Ionospheric Gradient Monitor Under the Mixed Gaussian Distribution

Anomalous ionospheric gradient is a critical risk to be monitored by ground-based augmentation systems (GBASs) utilized for safety-of-life navigation applications. A dual-frequency carrier phase-based ionospheric gradient monitoring method is proposed under the mixed Gaussian distribution. The minimum detection error of the proposed method can be greatly reduced by allowing acceptable ambiguity resolution failure modes, given the required averaging length. The real BeiDou navigation satellite system data were utilized to test the proposed method. The experimental results showed that the minimum detection error (MDE) of the proposed dual-frequency ionospheric gradient monitoring method can be reduced by at least 30% in comparison with the maximum acceptable anomalous ionospheric gradient of category III GBAS. This study demonstrated that the proposed method can be used to protect against the ionospheric gradient for a ground-based augmentation system.

Near real-time detecting of atmospheric water vapor content based on BeiDou Navigation Satellite System

With the improvement of Beidou navigation satellite system (BDS), real-time monitoring of atmospheric water vapor content based on BDS has become a research hotspot. BDS and GPS observation data of seven MGEX CORS stations were processed using GAMIT10.71 software and the atmospheric precipitable water vapor (PWV) was estimated. The PWV/BDS using Beidou final precise ephemeris and ultra-rapid precise ephemeris was respectively compared with PWV/GPS using IGS final precise ephemeris. The experiment results showed that the PWV/BDS is in good agreement with the PWV/GPS. The standard deviation (Std) of the PWV/BDS based on Beidou final precise ephemeris and ultra-rapid precise ephemeris are respectively 2.91mm and 3.97mm. And the RMSE of the PWV/BDS based on Beidou final precise ephemeris and ultra-rapid precise ephemeris are respectively 3.97mm and 3.85mm with the PWV/GPS as the reference value.

Traffic Speed Prediction Under Non-Recurrent Congestion: Based on LSTM Method and BeiDou Navigation Satellite System Data

The full utilization of Location-Based Vehicle Sensor Data (LB-VSD) can improve the efficiency of traffic control and management. Currently, LB-VSD is widely applied to the prediction of traffic speed. Like the GPS system, BeiDou satellite navigation system (BDS) can collect LB-VSD. In China, the key operation vehicles on the expressway are equipped with BDS to monitor the travel path. This provides a basis for predicting the traffic speed on expressway accurately. In this paper, considering the abnormal data collected by BDS, the screening and processing rules are made, and then the traffic speed sequence is extracted. Considering the data-missing problem caused by equipment failure or abnormal data elimination and the data sparse problem caused by small size of sample, a filling method based on trend-historical data is proposed. Traffic flow evolution is a complex process. Sudden accidents or bad weather can cause a sudden change in traffic flow and non-recurrent traffic congestion. The prediction accuracy of traditional machine learning methods is low when non-recurrent congestion occurred. In order to solve this problem, this paper adopts a deep learning model?Long Short-Term Memory (LSTM) to predict the traffic speed. Moreover, three-regime algorithm is used while building the prediction model. The prediction method is compared with Support Vector Regression (SVR) method. The results show that the prediction accuracy of the proposed method is higher than that of SVR algorithm, and the robustness is better in the case of non-recurrent traffic congestion.

Triple-Frequency Combining Observation Models and Performance in Precise Point Positioning Using Real BDS Data

Although precise point positioning (PPP) is a well-established and promising technique with the use of precise satellite orbit and clock products, it requires a long convergence time to reach a centimeter-level positioning accuracy. The availability of triple-frequency observations from a modernized global navigation satellite system (GNSS) constellations makes it possible to improve performance by formulating new observation models. The contribution of this paper is to propose two new observation models using triple-frequency data. The first model (UofC3) is the triple-frequency extension of dual-frequency University of Calgary model. The second model (UofB) is a combining observation model with five-dimensional observation equations. Thereafter, by theoretically analyzing the dimension of the triple-frequency observation models, all feasible triple-frequency observation models are systematically found out. Finally, the positioning experiments with 3-h observation period using real data at four BeiDou Navigation Satellite System (BDS) Asia-Pacific distributed reference stations on the day of the year (DOY) 42-48, 2018 are conducted to compare the performance of observation models. The results show that the triple-frequency models have less convergence time than the dual-frequency models. Meanwhile, most of the triple-frequency models have approximate convergence time in an experiment. Furthermore, UofB, which is one of the most stabilized observation models as well as uncombined observation model with the triple-frequency data (UC3), has less processing time than UC3. Compared with UofB, UofC3 has less processing time with sacrificing stability. These results show the significance of the UofB and UofC3 for future PPP applications in modernized GNSS.

Positioning Performance of BDS Observation of the Crustal Movement Observation Network of China and Its Potential Application on Crustal Deformation.

The Crustal Movement Observation Network of China (CMONOC) has begun receiving BeiDou Navigation Satellite System (BDS) observations since 2015, and accumulated more than 2.5 years of data. BDS observations has been widely applied in many fields, and long-term continuous data provide a new strategy for the study of crustal deformation in China. This paper focuses on the evaluation of BDS positioning performance and its potential application on crustal deformation in CMONOC. According to the comparative analysis on multipath delay (MPD) and signal to noise ratio (SNR) between BDS and GPS data, the data quality of BDS is at the same level with GPS measurements in COMONC. The spatial distribution of BDS positioning accuracy evaluated as the root mean square (RMS) of daily residual position time series on horizontal component is latitude-dependent, declining with the increasing of station latitude, while the vertical one is randomly distributed in China. The mean RMS of BDS position residual time series is 7 mm and 22 mm on horizontal and vertical components, respectively, and annual periodicity in position time series can be identified by BDS data. In view of the accuracy of BDS positioning, there are no systematic differences between GPS and BDS results. Based on time series analysis with data volume being 2.5 years, the noise characteristics of BDS daily position time series is time-correlated and corresponding noise is white plus flicker noise model, and the derived mean RMS of the BDS velocities is 1.2, 1.5, and 4.1 mm/year on north, east, and up components, respectively. The imperfect performance of BDS positioning relative to GPS is likely attributed to the relatively low accuracy of BDS ephemeris, and the sparse amount of MEO satellites distribution in the BDS constellation. It is expectable to study crustal deformation in CMONOC by BDS with the gradual maturity of its constellation and the accumulation of observations.

BeiDou Code Pseudorange Precision Estimation and Time Correlation Analysis from Trimble Net-R9 and ComNav 708 Receivers

Stochastic models describe the observation precisions and their correlations with each other and play an important role in reliable global navigation satellite system ambiguity resolution and precise positioning. However, the characteristics of BeiDou Navigation Satellite System (BDS) observations are still not clear at present. In general, the stochastic model used for BDS is based on empirical models from global positioning system (GPS) knowledge in most cases. In this paper, the zero-baseline dual-frequency GPS and BDS data with different sampling intervals are used to evaluate the precision and time correlation of the BDS code pseudorange observations. The results show that the precisions of BDS and GPS code measurements are almost of the same magnitude. However, the standard deviations of BDS measurements are larger than those of GPS measurements. Inclined geostationary orbit observations suffer from periodic error, which has been confirmed to be unaffected by multipath error in this paper. Traditional elevation-dependent models cannot work well for precise positioning for either GPS or BDS because the elevation dependencies of the two carrier frequencies’ pseudorange observations are not the same. Moreover, BDS observations have a significant time correlation, especially for geostationary orbit satellites. The time correlation coefficients are maintained at ~0.63–0.75 for different receiver types. Consequently, the BDS positioning residuals are significantly larger than those of GPS even if the observations have similar precision.

The Comparison and Analysis of BDS NRTK between DD and UD Models

The BeiDou Navigation Satellite System (BDS) Network Real Time Kinematic (NRTK) position algorithm with both Double-Differenced (DD) model and Un-Differenced (UD) model is investigated in this study. This algorithm is realized and validated with experimental BDS data collected at four regional stations. For the experiment within the regional network, a short convergence time for each model is considered. The results show that the BDS NRTK is able to provide positioning service with accuracy at the cm level. Theoretically, UD-NRTK and DD-NRTK are equivalent to each other. The small differences found between the DD and UD models in this study can be clarified in that the error correction for the DD model is more precise than that for the UD model, resulting in faster solution convergence in the DD model. However, the noise of the DD model is two times of the UD model, which usually leads to larger final RMS of positioning accuracy for the DD model. Copyright © 2018 Institute of Navigation

Investigation of ionospheric scintillation effects on BDS precise point positioning at low-latitude regions

We present a study on the effects of ionospheric scintillation on BeiDou Navigation Satellite System (BDS) precise point positioning (PPP) at low-latitude regions. The analysis was carried out using BDS data collected by a newly installed ionospheric scintillation monitoring receiver located at Sha Tin of Hong Kong and 15 Hong Kong Satellite Positioning Reference Station Network (SatRef) stations from October 6, 2015, to November 17, 2015. The rate of total electron content index (ROTI) derived from BDS data is shown to be a good indicator in observing the ionospheric scintillation. The analysis indicates that the correlation coefficient between ROTI and $$S_{4}$$ / $$\sigma_{\varphi }$$ is about 0.7. Under scintillation activity, the time series of positioning results for BDS static PPP show a stable variation, but the irregularities are reflected in the time series of code and phase residuals with the maximum values as 7.096 and − 0.469 m, respectively. Further, under scintillation condition it is found that positioning results for BDS kinematic PPP vary significantly and the range can reach several meters in the east, north and up directions. The statistical results show that the three-dimensional root-mean-square of BDS PPP is 1.842 m under scintillation condition, which is much larger than that for non-scintillation condition as 0.155 m.

Three-frequency BDS precise point positioning ambiguity resolution based on raw observables

All BeiDou navigation satellite system (BDS) satellites are transmitting signals on three frequencies, which brings new opportunity and challenges for high-accuracy precise point positioning (PPP) with ambiguity resolution (AR). This paper proposes an effective uncalibrated phase delay (UPD) estimation and AR strategy which is based on a raw PPP model. First, triple-frequency raw PPP models are developed. The observation model and stochastic model are designed and extended to accommodate the third frequency. Then, the UPD is parameterized in raw frequency form while estimating with the high-precision and low-noise integer linear combination of float ambiguity which are derived by ambiguity decorrelation. Third, with UPD corrected, the LAMBDA method is used for resolving full or partial ambiguities which can be fixed. This method can be easily and flexibly extended for dual-, triple- or even more frequency. To verify the effectiveness and performance of triple-frequency PPP AR, tests with real BDS data from 90 stations lasting for 21 days were performed in static mode. Data were processed with three strategies: BDS triple-frequency ambiguity-float PPP, BDS triple-frequency PPP with dual-frequency (B1/B2) and three-frequency AR, respectively. Numerous experiment results showed that compared with the ambiguity-float solution, the performance in terms of convergence time and positioning biases can be significantly improved by AR. Among three groups of solutions, the triple-frequency PPP AR achieved the best performance. Compared with dual-frequency AR, additional the third frequency could apparently improve the position estimations during the initialization phase and under constraint environments when the dual-frequency PPP AR is limited by few satellite numbers.

Adaptive Kalman filter based on variance component estimation for the prediction of ionospheric delay in aiding the cycle slip repair of GNSS triple-frequency signals

In order to incorporate the time smoothness of ionospheric delay to aid the cycle slip detection, an adaptive Kalman filter is developed based on variance component estimation. The correlations between measurements at neighboring epochs are fully considered in developing a filtering algorithm for colored measurement noise. Within this filtering framework, epoch-differenced ionospheric delays are predicted. Using this prediction, the potential cycle slips are repaired for triple-frequency signals of global navigation satellite systems. Cycle slips are repaired in a stepwise manner; i.e., for two extra wide lane combinations firstly and then for the third frequency. In the estimation for the third frequency, a stochastic model is followed in which the correlations between the ionospheric delay prediction errors and the errors in the epoch-differenced phase measurements are considered. The implementing details of the proposed method are tabulated. A real BeiDou Navigation Satellite System data set is used to check the performance of the proposed method. Most cycle slips, no matter trivial or nontrivial, can be estimated in float values with satisfactorily high accuracy and their integer values can hence be correctly obtained by simple rounding. To be more specific, all manually introduced nontrivial cycle slips are correctly repaired.

Operational modal analysis of rigid frame bridge with data from navigation satellite system measurements

The Real Time BeiDou Navigation Satellite System (BDS) has evolved into a reliable technique to detect both the three-dimensional magnitudes and frequencies of displacement of structures. BDS technology is exactly what monitoring needs for the bridge deformation. Also, the oscillations and damage severity can be evaluated and classified according to the dynamic bridge characteristics obtained from BDS. The intention of the present work is to demonstrate the use of BDS to provide data for the assessment of existing structures safety. The raw data were collected continuously over a period of 24 h at a minimum rate of 1 Hz. The collected data include traffic flow (for load estimation) and environment factors (such as wind speed, wind direction, relative humidity and temperature). The vibration frequencies are also measured from BDS data and compared with those given in the literature. The results of all the experiments proved to be very encouraging, and showed that the performance of BDS as it has developed in recent years, and that the BDS is reliably in quantifying both environmental induced bridge vibrations and high-frequency transient motion caused by vehicle loading, in particular changes of mass associated with changes in traffic loading are observed, providing the ability for verification and/or improvement of bridge design and modelling.