Galileo real-time orbit determination with multi-frequency raw observations

Real-time GNSS-based applications require corresponding real-time orbit products. While traditional GNSS orbits are generated with the dual-frequency IF (Ionosphere-Free) model, the increase of multi-frequency signal satellites brings new challenges for the data processing. Therefore, real-time orbit determination with the multi-frequency UC (Uncombined) model is introduced in this study considering its flexibility. With the derived mathematical model conforming to IGS (International GNSS Service) dual-frequency clock definition and one-week triple-frequency Galileo observation data from 90 IGS network stations, the convergence and accuracy of real-time orbits is assessed and the characteristics of satellite IFCB (Inter-Frequency Clock Bias) are analyzed. Results indicate that the model differences, including dual-frequency IF model, dual-frequency UC model and triple-frequency UC model, contribute to only cm-level differences with CODE (Center for Orbit Determination in Europe) final orbits after a convergence time of around 12 h. The constellation-mean RMS (Root Mean Square) differences of the converged real-time orbits with the CODE final orbits reaches about 5.0 cm, 7.0 cm and 5.0 cm for the radial, tangential and normal directions. The convergence of satellite IFCB is much faster than that of satellite orbit, which reflects a loose correlation between these two parameters. While the Galileo satellite IFCB are temporally stable, the modeling of satellite IFCB may be unreliable when over constrained and becomes even more unstable with commonly encountered datum changes. In summary, real-time GNSS orbit determination with multi-frequency raw observations is feasible and extendable with proper treatment of IFCB.     

多频GNSS电离层折射误差修正方法CSCD

针对电离层折射误差较大的特点,分别对GPS(Global Positioning System)和BDS(Bei Dou Navigation Satellite System)的单一频率的电离层折射误差进行了分析,并将不同频率进行线性组合,计算出组合后的电离层折射误差。此方法修正了双频一阶项、三频一阶项和三频二阶项电离层折射误差。由于电离层延迟修正的同时会放大观测噪声,为此分析比较了不同频率组合修正后的观测噪声,为最佳频率组合的选取提供了理论方法。     

Cycle slip detection using multi-frequency GPS carrier phase observations: A simulation study

The detection and repair of the cycle slip or gross error is a key step for high precision global positioning system (GPS) carrier phase navigation and positioning due to interruption or unlocking of GPS signal. A number of methods have been developed to detect and repair cycle slips in the last two decades through cycle slip linear combinations of available GPS observations, but such approaches are subject to the changing GPS sampling and complex algorithms. Furthermore, the small cycle slip and gross error cannot be completely repaired or detected if the sampling is quite longer under some special observation conditions, such as Real Time Kinematic (RTK) positioning. With the development of the GPS modernization or Galileo system with three frequencies signals, it may be able to better detect and repair the cycle slip and gross error in the future. In this paper, the cycle slip and gross error of GPS carrier phase data are detected and repaired by using a new combination of the simulated multi-frequency GPS carrier phase data in different conditions. Results show that various real-time cycle slips are completely repaired with a gross error of up to 0.2 cycles.     

Inertial aided BDS triple-frequency integer ambiguity rounding method

The integer ambiguity resolution (AR) of carrier phase is significant for Global Navigation Satellite System (GNSS) precise positioning. However, in kinematic case, single-epoch AR methods based on alone GNSS are usually not reliable due to the instable pseudorange accuracy. Moreover, the computation of classical AR method Least Squares Ambiguity Decorrelation Adjustment (LAMBDA) is large. Thus, the inertial measurement unit (IMU) is introduced, a new inertial-aided AR method that directly rounds the float ambiguity of BeiDou triple-frequency combined observations, which is characterized by long wavelength, low carrier-phase noise and ionospheric delay, is proposed. The mathematical model of the new method is derived first. Then the impacts of the carrier-phase noise, ionospheric delay and inertial navigation system (INS) position error on the AR success ratio of combined observation are analyzed through probabilistic approach. Based on above investigation, the combinations (0, ?1, 1), (1, 4, ?5) and (4, ?2, ?3) are selected to resolve the original ambiguity. A vehicular integrated navigation test is performed to demonstrate the proposed method. The results show that the average AR success ratios of the three selected combinations, whose float ambiguity errors are 0.041, 0.146, 0.279 cycle respectively, are above 97.25% without regard to low-elevation C05. With respect to positioning accuracy based on our AR method when compared with IE software, the east, north, up error RMS of position are 0.042, 0.024, 0.069 m, respectively. In terms of the AR recover after the BeiDou signals outage, as long as 62 s BeiDou signal complete outage, all the ambiguities of all satellites could be re-fixed immediately. Besides, during the 90 s signals partial outage, the AR is not influenced by the position error, since the float ambiguity errors are all below half-cycle. The research of this contribution demonstrates the effectiveness of the proposed new method, which indicates it is applicable to kinematic positioning, even in BDS degraded and denied environments.     

Analysis of the code and phase between-receiver inter-system biases of the overlapping frequencies for GPS/Galileo/BDS

The overlapping-frequency signals from different GNSS constellations are interoperable and can be integrated as one constellation in multi-GNSS positioning when inter-system bias (ISB) is properly disposed. The look-up table method for ISB calibration can enhance the model strength, maximize the number of integer-estimable ambiguities, and thus is preferred. However, the characteristics and magnitudes of the receiver code ISB and phase fractional ISB (F-ISB) are not well known and the wrong values of the biases can seriously degrade the positioning results. In this contribution, we first estimate the between-receiver code ISB and phase F-ISB of hundreds of the baselines up to around 25km in the European Permanent GNSS Network (EPN) and the Multi-GNSS Experiment (MGEX) for the overlapping frequencies L1-E1 (L1), L5-E5a (L5) and E5b-B2b (L7). The data collected from 1st January 2016 to 1st January 2019. Second, the receiver-type and firmware-version combinations for the receivers of Trimble, Leica, Javad, Septentrio and NovAtel are carefully classified. Results show that the Septentrio receivers have consistent code and phase ISB values for the three overlapping frequencies i.e. only one value for each frequency and no receivers are different. The Leica, Trimble and Javad receivers have two or more ISB values for at least one of the three frequencies. A few receivers with biases to the groups are also found and listed. Third, the code ISB and phase F-ISB of the groups are adjusted by the least-squares method. The root mean square errors (RMSE) of the least square adjustment are 0.240 m, 0.250 m and 0.200 m for code of L1, L5 and L7 frequencies, respectively, and are 0.0009 m, 0.0015 m and 0.0031 m for phase of L1, L5 and L7 frequencies, respectively. Finally, the effects of code ISB errors on code positing are investigated with the zero-baseline MAT1_MATZ. The distance root mean square error (DRMS) of L1-E1 code positioning can be reduced by 48.2% with 5 GPS and Galileo satellites and the DRMS degrades quickly when the code ISB error is larger.     

Testing a new multivariate GNSS carrier phase attitude determination method for remote sensing platforms

GNSS (Global Navigation Satellite Systems)-based attitude determination is an important field of study, since it is a valuable technique for the orientation estimation of remote sensing platforms. To achieve highly accurate angular estimates, the precise GNSS carrier phase observables must be employed. However, in order to take full advantage of the high precision, the unknown integer ambiguities of the carrier phase observables need to be resolved. This contribution presents a GNSS carrier phase-based attitude determination method that determines the integer ambiguities and attitude in an integral manner, thereby fully exploiting the known body geometry of the multi-antennae configuration. It is shown that this integral approach aids the ambiguity resolution process tremendously and strongly improves the capacity of fixing the correct set of integer ambiguities. In this contribution, the challenging scenario of single-epoch, single-frequency attitude determination is addressed. This guarantees a total independence from carrier phase slips and losses of lock, and it also does not require any a priori motion model for the platform. The method presented is a multivariate constrained version of the popular LAMBDA method and it is tested on data collected during an airborne remote sensing campaign.     

一种高动态环境下卫星扩频信号的快速捕获方法研究

现代卫星导航及测控应用对接收机在高动态环境下实现测量通信提出了迫切需求。为了解决大多普勒频偏扩频信号的快速捕获问题,提出了一种在频域并行搜索码相位及多普勒频偏的双频域快速捕获方法。采用双块补零算法将长的相关积分操作分割为多个短的相关积分操作,然后采用快速傅里叶变换进行圆周相关,大大节约了处理时间,利用频域圆周移位与时域载波剥离等价的原理,大幅提高了频率搜索效率。与时域相关算法和单频域计算方法相比,在捕获灵敏度不变的条件下,该方法将计算量减少90%,显著提高了运算速度,适合高动态环境下扩频信号的快速捕获。该方案应用于星载接收机平台FPGA实现,测试结果表明该方案可以在0.1s内完成±500kHz频偏下扩频信号捕获。     

一种地基GNSS接收机差分码偏差估算方法

GNSS不同频点间的码伪距作差会引入信号的差分码偏差(DCB),包括GNSS卫星及地面接收机的DCB.本文提出一种地基GNSS接收机差分码偏差参数估算方法,首先由电离层文件参数作线性插值,计算出电离层延迟误差.之后对IGS站观测文件进行加权最小二乘法估计,得到GPS卫星和地面GNSS接收机的L1C频点和L2P频点间码偏...     

Dual-frequency carrier smoothed code filtering with dynamical ionospheric delay modeling

In GNSS applications, carrier-smoothed-code is a widely used technique to combine code pseudo-range and carrier phase measurements. A dynamical ionospheric delay modeling method is proposed based on Kalman filter and least-squares theory. The level of the process noise is adaptively tuned along with the real-time KF state estimation, based on the online variance component estimation method. Meanwhile, the correlations of the time differenced carrier phase measurements are considered. This approach avoids overly optimistically evaluating the estimate and improves the transient accuracy of the estimates. A real GPS dataset is employed to check the performance of the proposed method under different conditions. The results show that the new algorithm can model the ionospheric delay variation well with different sampling intervals or even in ionospheric abnormal environment. The positioning accuracy can be confirmed, about 21%, 35% and 16% better are obtained in the N, E, and U direction than raw dataset.     

Accuracy assessment of single and double difference models for the single epoch GPS compass

The single epoch GPS compass is an important field of study, since it is a valuable technique for the orientation estimation of vehicles and it can guarantee a total independence from carrier phase slips in practical applications. To achieve highly accurate angular estimates, the unknown integer ambiguities of the carrier phase observables need to be resolved. Past researches focus on the ambiguity resolution for single epoch; however, accuracy is another significant problem for many challenging applications. In this contribution, the accuracy is evaluated for the non-common clock scheme of the receivers and the common clock scheme of the receivers, respectively. We focus on three scenarios for either scheme: single difference model vs. double difference model, single frequency model vs. multiple frequency model and optimal linear combinations vs. traditional triple-frequency least squares. We deduce the short baseline precision for a number of different available models and analyze the difference in accuracy for those models. Compared with the single or double difference model of the non-common clock scheme, the single difference model of the common clock scheme can greatly reduce the vertical component error of baseline vector, which results in higher elevation accuracy. The least squares estimator can also reduce the error of fixed baseline vector with the aid of the multi-frequency observation, thereby improving the attitude accuracy. In essence, the “accuracy improvement” is attributed to the difference in accuracy for different models, not a real improvement for any specific model. If all noise levels of GPS triple frequency carrier phase are assumed the same in unit of cycles, it can be proved that the optimal linear combination approach is equivalent to the traditional triple-frequency least squares, no matter which scheme is utilized. Both simulations and actual experiments have been performed to verify the correctness of theoretical analysis.     

Mitigation of receiver biases in ionospheric observables from PPP with ambiguity resolution

PPP (Precise Point Positioning) is a GNSS (Global Navigation Satellite Systems) positioning method that requires SSR (State Space Representation) corrections in order to provide solutions with an accuracy of centimetric level. The so-called RT-PPP (Real-time PPP) is possible thanks to real-time precise SSR products, for orbits and clocks, provided by IGS (International GNSS Service) and its associate analysis centers such as CNES (Centre National d'Etudes Spatiales). CNES SSR products also enable RT-PPP with integer ambiguity resolution. In GNSS related literature, PPP with ambiguity resolution (PPP-AR) in real-time is often referred as PPP-RTK (PPP – Real Time Kinematic). PPP-WIZARD (PPP - With Integer and Zero-difference Ambiguity Resolution Demonstrator) is a software that is made available by CNES. This software is capable of performing PPP-RTK. It estimates slant ionospheric delays and other GNSS positioning parameters. Since ionospheric effects are spatially correlated by GNSS data from active networks, it is possible to model and provide ionospheric delays for any position in the network coverage area. The prior knowledge ionospheric delays can reduce positioning convergence for PPP-RTK users. Real-time ionospheric models could benefit from highly precise ionospheric delays estimated in PPP-AR. In this study, we demonstrate that ionospheric delays obtained throughout PPP-AR estimation are actu ally ionospheric observables. Ionospheric observables are biased by an order of few meters caused by the receiver hardware biases. These biases prohibit the use of PPP-WIZARD ionospheric delays to produce ionospheric models. Receiver biases correction is essential to provide ionospheric delays while using PPP-AR based ionospheric observables. In this contribution, a method was implemented to estimate and mitigate receiver hardware biases influence on slant ionospheric observables from PPP-AR. In order to assess the proposed approach, PPP-AR data from 12 GNSS stations were processed over a two-month period (March and April 2018). A comparison between IGS ionospheric products and PPP-AR based ionospheric observables corrected for receiver biases, resulted in a mean of differences of −39 cm and 51 cm standard deviation. The results are consistent with the accuracy of the IGS ionospheric products, 2–8 TECU, considering that 1 TECU is ~16 cm in L1. In another analysis, a comparison of ionospheric delays from 5 pairs of short baselines GNSS stations found an agreement of 0.001 m in mean differences with 22 cm standard deviation after receiver biases were corrected. Therefore, the proposed solution is promising and could produce high quality (1–2 TECU) slant ionospheric delays. This product can be used in a large variety of modeling approaches, since ionospheric delays after correction are unbiased. These results indicate that the proposed strategy is promising, and could benefit applications that require accuracy of 1–2 TECU (~16–32 cm in L1).     

A real-time combined quality control method for GNSS precise positioning in harsh environments

Global Navigation Satellite System (GNSS) precise positioning can be significantly affected by severe multipath effects and outliers in harsh environments, and highly relies on quality control strategies. Previous studies mainly focus on the posterior residuals to check and exclude the outliers in GNSS observations, limited work emphasizes the combined quality control method considering both the prior and posterior knowledge simultaneously. This paper proposed a real-time combined quality control method to process the multipath effects and outliers in harsh environments simultaneously. Specifically, in the prior stage, a modified multipath processing strategy is proposed for both phase and code observations, then a modified detection, identification, and adaptation (DIA) method considering the maximum times of data snooping is studied in the posterior stage. Two dedicated experiments in real harsh environments were carried out to evaluate the performance of the proposed combined quality control method. For the static experiment, the proposed method exhibits smaller positioning errors, the best positioning accuracy, and the highest availability in this study. Specifically, the proposed method exhibits an improved percentage of 55.4 %, 56.3 %, and 59.7 % for positioning accuracy compared to those without the quality control method in the E, N, and U directions, respectively. Besides, the proposed method can further improve the performance of ambiguity resolution with an improved percentage of 32.2 %. For the kinematic experiment, the three-dimensional positioning accuracy of the proposed method is 0.577 m, which exhibits a 40.0 % improvement compared to those without the quality control method. Also, the proposed method exhibits better performance under relatively strong multipath effects. In this sense, the proposed real-time combined quality control method is highly appreciated in terms of positioning availability, accuracy, and ambiguity resolution for GNSS precise positioning, especially in harsh environments.     

载波相位/捷联惯导组合对高轨飞行器的导航

高轨飞行器可用卫星数目较少,信号空间链路损耗大,使用伪距进行测量的精度较低.提出基于GNSS(Global Navigation Satellite System)卫星载波相位与捷联惯导紧组合方法对高轨机动飞行器进行自主导航.该方法将连续跟踪的卫星初次可用时的整周模糊度的浮点解作为状态变量,通过平方根UKF建立了组合导航非线性滤波模型,提出了基于整周浮点解交集的滤波器故障检测方法.研究表明,提出的组合导航方法充分利用了载波相位高测量精度和系统性误差缓变的特点,提高了系统的可靠性和精度.     

第24太阳活动周中国地区电离层闪烁统计特性研究

利用第24太阳活动周中国多个地区GNSS电离层闪烁监测站数据，统计分析中国中低纬地区电离层闪烁特性.结果显示:电离层闪烁主要发生在春秋分及夜间20:00—02:00LT时段；在28°N以南地区，纬度越低电离层闪烁强度和发生概率越高；电离层闪烁发生概率与太阳活动呈正相关，太阳活动上升年电离层闪烁发生概率高于下降年；不同强度地磁活动条件下，电离层闪烁均可能发生，且与地磁活动强度整体呈负相关.通过研究电离层闪烁统计特性，可以为电离层闪烁机理的深入研究、预报及工程应用提供参考.      

基于码片幅度调制的导航信号扩频码认证方法

信号认证是满足全球卫星导航系统(GNSS)民用信号安全性需求的关键，相比于导航电文认证(NMA),扩频码认证(SCA)具有更强的安全性。为了在实现SCA的同时不对非认证用户造成影响，提出了一种基于码片幅度调制(CAM)的导航信号SCA方法，对民用信号的扩频码的码片幅度进行了调制，实现了在扩频码层面的认证特征的引入。为了验证所提方法的有效性，采用理论和仿真分析，与GPS L1C采用的Chimera SCA方法进行了比较。结果表明，所提方法在检测性能方面提升了2.55～2.78 dB。研究成果可为下一代高安全卫星导航信号的设计提供支持。     

A study on cycle slip detection and correction in case of ionospheric scintillation

This research is aiming for cycle slip detection and correction in case of ionospheric scintillation. Different from the normally discussed situation without ionospheric scintillation, ionospheric delay cannot be neglected due to abrupt ionosphere change. In this case, ionosphere-free testing quantities for cycle slip detection and correction have to be used.     

An improved cyclic multi model-eXtreme gradient boosting (CMM-XGBoost) forecasting algorithm on the GNSS vertical time series

The study of GNSS vertical coordinate time series forecasting is helpful for monitoring the crustal plate movement, dam or bridge deformation monitoring, and global or regional coordinate system maintenance. The eXtreme Gradient Boosting (XGBoost) algorithm is a machine learning algorithm that can evaluate features, and it has a great potential and stability for long-span time series forecasting. This study proposes a multi-model combined forecasting method based on the XGBoost algorithm. The method constitutes a new time series as features through the fitting and forecasting results of the forecasting model. The XGBoost model is then used for forecasting. In addition, this method can obtain higher precision forecasting results through circulation. To verify the performance of the forecasting method, 1095 epochs of data in the Up coordinate of 16 GNSS stations are selected for the forecasting test. Compared with the CNN-LSTM model, the experimental results of our forecasting method show that the mean absolute error (MAE) values are reduced by 30.23 %～52.50 % and the root mean square error (RMSE) values are reduced by 31.92 %～54.33 %. The forecasting results have higher accuracy and are highly correlated to the original time series, which can better forecast the vertical movement of the GNSS stations. Therefore, the forecasting method can be applied to the up component of the GNSS coordinate time series.     

High-performance altimeter Doppler processing for measuring sea level height under varying sea state conditions

This paper describes an innovative method for processing nadir altimeter data acquired in Synthetic Aperture Radar (SAR) mode, enhancing the system performances over open ocean. Similarly to the current SAR data processing scheme, the so-called LR-RMC (Low Resolution with Range Migration Correction) method, originally designed by Phalippou and Demeester (2011), includes Doppler beam forming, Doppler shift correction and range correction. In LR-RMC, however, an alternative and less complex averaging (stacking) operation is used so that all the Doppler beams produced in a radar cycle (4 bursts of 64 beams for the open-burst Sentinel-3-mode altimeter) are incoherently combined to form a multi-beam echo. In that manner, contrarily to the narrow-band SAR technique, the LR-RMC processing enlarges the effective footprint to average out the effects of surface waves and particularly those from small sub-mesoscale structures (<1 km) that are known to impact SAR-mode performances. On the other hand, the number of averaged beams is as high as in current SAR-mode processing, thus providing a noise reduction at least equally good. The LR-RMC method has the added benefit of reducing the incoherent integration time with respect to the SAR-mode processing (50 ms compared to 2.5 s) limiting possible surface movement effects. By processing one year of Sentinel-3A SRAL SAR-mode data using the LR-RMC method, it is shown that the swell impact on the SAR altimeter performances is totally removed and that an improvement of 10–50% is obtained in the measurement noise of the sea surface height and significant wave height with respect to SAR mode. Additionally, observational capabilities over the middle scales are enhanced potentially allowing the ocean mesoscale features to be retrieved and observations assimilated more usefully in ocean models.     

Low-cost precise measurement of oscillator frequency instability based on GNSS carrier observation

Global navigation satellite systems (GNSS) receivers can be used in time and frequency metrology by exploiting stable GNSS time scales. This paper proposes a low-cost method for precise measurement of oscillator frequency instability using a single-frequency software GNSS receiver. The only required hardware is a common radio frequency (RF) data collection device driven by the oscillator under test (OUT). The receiver solves the oscillator frequency error in high time resolution using the carrier Doppler observation and the broadcast ephemeris from one of the available satellites employing the onboard reference atomic frequency standard that is more stable than the OUT. Considering the non-stable and non-Gaussian properties of the frequency error measurement, an unbiased finite impulse response (FIR) filter is employed to obtain robust estimation and filter out measurement noise. The effects of different filter orders and convolution lengths are further discussed. The frequency error of an oven controlled oscillator (OCXO) is measured using live Beidou-2/Compass signals. The results are compared with the synchronous measurement using a specialized phase comparator with the standard coordinated universal time (UTC) signal from the master clock H226 in the national time service center (NTSC) of China as its reference. The Allan deviation (ADEV) estimates using the two methods have a 99.9% correlation coefficient and a 0.6% mean relative difference over 1–1000 s intervals. The experiment demonstrates the effectiveness and high precision of the software receiver method.     

TOPSAR data focusing based on azimuth scaling preprocessing

Both Doppler spectral aliasing and azimuth output time folding simultaneously exist in TOPSAR (Terrain Observation by Progressive Scans) raw data. Resampling in both Doppler frequency and azimuth time domain can resolve the azimuth aliasing problem but with the seriously increased computational complexity and memory consumption. According to the special characteristics of TOPSAR raw data support in the slow time/frequency domain (TFD), the presented azimuth scaling preprocessing step is introduced to not only resolve the Doppler spectral aliasing problem but also reduce the increased azimuth samples. Furthermore, the correction of sawtoothed azimuth antenna pattern (AAP) becomes easy to be implemented. The following conventional stripmap processor can be adopted to focus the residual TOPSAR raw data but with the result of azimuth aliased TOPSAR image. The mosaic approach, which has been presented to unfold azimuth aliased ScanSAR image, is exploited to resolve the problem of azimuth output folding in TOPSAR mode. Simulation results and pulse response parameters are given to validate the presented imaging approach.