Snow depth retrieval by using robust estimation algorithm to perform multi-SNR and multi-system fusion in GNSS-IR

Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) technology provides a new means of snow depth detection. Multi-satellite and multi-Signal-to-Noise Ratio (SNR) provide more data for daily high-precision snow depth retrieval, but also face the problem of data fusion and effective utilization. Therefore, this study proposes a robust estimation algorithm based on multi-satellite and multi-SNR fusion applied to the observations of a GNSS station in Alaska. This study uses four solutions (S_avg, S_med, S_{RE_avg} and S_{RE_med}) to carry out multi-system fusion snow depth inversion and precision comparison research. The S_avg has more obvious disadvantages, which is not suitable for snow depth assessment. The S_{RE_avg} and S_{RE_med} have better snow depth retrieval effects in the snowy periods. The correlation coefficient (R), root mean square error (RMSE) and mean error (ME) of the calculated snow depth using the robust estimation algorithm with respect to the nearest in-situ measurements reached 0.759, 3.7 cm and ?1.4 cm, respectively. Compared with the S_med, the R is increased by 2.0 %, the RMSE corresponds to an improvement of 2.6 %. Moreover, the ME of the snow depth retrievals, as an indicator of the measurement bias, has significantly decreased by 6.7 %. The result also shows that the snow depth inversion by the robust estimation algorithm is more consistent with the in-situ measurements, further extending and advancing the optimal algorithm for snow depth retrieval.     

基于GA-SVM的GNSS-IR土壤湿度反演方法

针对提高大范围土壤湿度测量精度的问题,研究了土壤湿度的全球卫星导航系统干涉测量法（GNSS-IR）,提出了一种基于支持向量机（SVM）的土壤湿度反演模型,利用遗传算法（GA）的自动寻优功能寻找SVM的最佳参数。结果表明,GA-SVM模型在测试集上得到的土壤湿度反演值与实测值的平均绝对百分比误差（MAPE）仅为0.69%,最大相对误差（MRE）为1.22%,线性回归方程决定系数达到了0.956 9。进一步与统计回归、粒子群优化的SVM模型（PSO-SVM）及反向传播（BP）神经网络方法进行对比,结果说明:在样本数目有限的情况下,GA-SVM方法更适用于土壤湿度的GNSS-IR技术反演,且反演精度较高,泛化性能良好。      

基于GPS多星三频数据融合的GNSS-IR土壤湿度反演方法

土壤湿度的监测是全球卫星导航系统干涉测量法（GNSS-IR）的关键应用之一。传统的GNSS-IR土壤湿度反演方法一般只针对单颗卫星的单一频段，未充分利用不同轨道、不同频率卫星信号的差异性与互补性。针对此问题，提出了一种将GPS多星的L1、L2和L5频段数据加权融合进行联合反演的方法，该方法利用基于最小方差的自适应融合算法得到加权因子，并通过现场实验进行了方法验证。结果表明:在测试集上所提出的反演方法相比于传统的Larson方法，相关系数提高了24.69%，均方根误差下降了22.28%，与均值融合法相比，相关系数提高了26.77%，均方根误差下降了23.26%，证明了所提方法能有效提高反演精度。      

Evaluation and improvement of coastal GNSS reflectometry sea level variations from existing GNSS stations in Taiwan

Global sea level rise due to an increasingly warmer climate has begun to induce hazards, adversely affecting the lives and properties of people residing in low-lying coastal regions and islands. Therefore, it is important to monitor and understand variations in coastal sea level covering offshore regions. Signal-to-noise ratio (SNR) data of Global Navigation Satellite System (GNSS) have been successfully used to robustly derive sea level heights (SLHs). In Taiwan, there are a number of continuously operating GNSS stations, not originally installed for sea level monitoring. They were established in harbors or near coastal regions for monitoring land motion. This study utilizes existing SNR data from three GNSS stations (Kaohsiung, Suao, and TaiCOAST) in Taiwan to compute SLHs with two methods, namely, Lomb–Scargle Periodogram (LSP)-only, and LSP aided with tidal harmonic analysis developed in this study. The results of both methods are compared with co-located or nearby tide gauge records. Due to the poor quality of SNR data, the worst accuracy of SLHs derived from traditional LSP-only method exceeds 1?m at the TaiCOAST station. With our procedure, the standard deviations (STDs) of difference between GNSS-derived SLHs and tide gauge records in Kaohsiung and Suao stations decreased to 10?cm and the results show excellent agreement with tide gauge derived relative sea level records, with STD of differences of 7?cm and correlation coefficient of 0.96. In addition, the absolute GNSS-R sea level trend in Kaohsiung during 2006–2011 agrees well with that derived from satellite altimetry. We conclude that the coastal GNSS stations in Taiwan have the potential of monitoring absolute coastal sea level change accurately when our proposed methodology is used.     

GNSS-IR双频数据融合的土壤湿度反演方法

目前全球导航卫星系统反射信号干涉测量（GNSS-IR）土壤湿度反演研究仅针对单一频点展开,提出用熵值法将2个频点数据进行融合以改进土壤湿度反演精度。首先,利用频谱分析法分别解析出各频点的信噪比（SNR）序列的振荡频率,计算出对应的等效天线高度,并利用最小二乘法求解各频点信噪比序列相位;然后,通过熵值法进行2个频点的相位观测量融合;最后,利用融合结果与实测土壤湿度建立经验模型,实现土壤湿度反演。利用地基观测实验获得的全球定位系统（GPS）L1和L2信噪比数据对该方法进行了验证,结果表明:L1和L2双频融合反演结果平均标准差为0.6%,比L1单频反演结果提高64.73%,比L2单频反演结果提高32.12%;均方根误差为0.37%,比L1频点降低72.8%,比L2频点降低73.4%。      

基于树模型机器学习方法的GNSS-R海面风速反演

GNSS-R是基于GNSS卫星反射信号的一种新技术.GNSS-R技术可以运用到海面风场反演中，传统的GNSS-R技术反演海面风场主要有波形匹配和经验函数两种方法，风速反演精度约为2m·s-1.波形匹配方法耗时多，计算量大；经验函数方法通常只使用少量物理观测量，会造成信息浪费，损失一定的反演精度.为了提高海面风速的反演精度，引入机器学习领域常用的树模型算法决策树、随机森林、GBDT等对海面风速进行预测.利用GNSS-R与ECMWF数据构成训练集和验证集，训练集用于模型学习，验证集用于检验模型的反演效果.实验结果显示，决策树和随机森林预测误差约为0.6m·s-1，GBDT等算法的预测误差约为2m·s-1，满足风速反演要求.与GNSS-R传统反演方法相比，机器学习树模型算法效果更好，在验证集上表现稳定且误差较小.因此，可以将机器学习树模型算法运用到海面风速反演中.      

基于Krylov子空间的多级维纳抗干扰滤波设计

全球卫星导航系统(GNSS, Global Navigation Satellites System)空时抗干扰要求有较好的实时处理能力,常规矩阵求逆的算法由于计算量太大限制了其在GNSS中的应用.在分析多级维纳滤波(MWF,Multi-stage nested Wiener Filter)原理的基础之上,结合Krylov子空间性质,设计出一种应用于GNSS空时抗干扰的自适应多级维纳滤波器,从而实现了在Krylov子空间中降维滤波,避免了矩阵求逆的大运算量.仿真结果表明,该算法在保证抗干扰性能不受影响的前提下,降低了GNSS空时抗干扰算法的计算量,提高了实时处理能力.     

Tide variation monitoring based improved GNSS-MR by empirical mode decomposition

Global Navigation Satellite System multipath reflectometry (GNSS-MR) technology has great potential for monitoring tide level changes. GNSS-MR techniques usually extract signal-to-noise ratio (SNR) residual sequences using quadratic polynomials; however, such algorithms are affected considerably by satellite elevation angles. To improve the stability and accuracy of an SNR residual sequence, this study proposed an SNR signal decomposition method based on empirical mode decomposition (EMD). First, the SNR signal is decomposed by EMD, following which the SNR residual sequence is obtained by combining the corresponding intrinsic mode function with the frequency range of the coherent signal. Second, the Lomb–Scargle spectrum is analyzed to obtain the frequency of the SNR residual sequence. Finally, the SNR frequency is converted into the tide height. To verify the validity of the SNR residual sequence obtained by EMD, the algorithm performance was assessed using multigroup satellite elevation angle intervals with measured data from two station, SC02 in the United States and RSBY in Australia. Experimental results demonstrated that the accuracy of the improved algorithm was improved in the low-elevation range. The improved algorithm demonstrated high monitoring accuracy, and the effective number was not less than 80% of the total in SC02, which means it could effectively describe the trend of the tide with accuracy of approximately 10 cm, meanwhile, the RMS error of RSBY could be reduced by 30 cm, to the maximum extent. The EMD method effectively expands the range of available GNSS-MR elevations, avoids the loss of effective information, enhances considerably the utilization rate of GNSS data, and improves the accuracy of GNSS-MR tide level monitoring.     

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.     

压缩感知在电容层析成像中的应用

压缩感知(CS)理论是在充分利用信号稀疏性或可压缩性的情况下,对信号进行少量采样即可实现信号的精确重建。本文尝试将CS理论应用于电容层析成像(ECT)图像重建中,首先,使用快速傅里叶变换(FFT)基将原始图像灰度信号进行稀疏化处理;其次,将ECT灵敏度矩阵的各行按随机顺序进行排列,得到ECT系统随机观测矩阵;最后,选取当前普遍使用的基于内点法、梯度投影(GPSR)算法以及贪婪算法的CS图像重建算法进行ECT图像重建,并与线性反投影及Landweber迭代算法进行了对比。仿真实验结果表明:基于CS图像理论的ECT图像重建算法,其重建精度有所提高。本文同时分析了3种CS图像重建算法的优缺点及适用范围。     

基于QZSS L1信号的岸基GNSS-R码延迟海面测高

为了探究GNSS L1波段中信号不同调制方式的GNSS-R码相位延迟海面的测高性能，开展了双天线岸基GNSS-R海面测高实验，收集了采样率为40 MHz的原始中频数据。利用自主开发的GNSS-R测高软件接收机和反演软件对实验数据进行了处理分析，同时获得了基于QZSS L1C/A码和L1C码的GNSS-R海面测高结果，并分别与岸基同步观测的雷达高度计的测高值进行对比，以对反演结果进行精度评定。实验结果表明:基于QZSS L1C/A码和L1C码的海面测高精度最优可达0.63 m和0.4 m，L1C码的延迟GNSS-R测高精度明显高于L1C/A码。此外，GNSS-R测高精度会随着卫星高度角的增加而有所增加。      

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.     

Analysis of precipitable water vapour characteristics from GNSS measurements during the snow season in Liaoning Province,China

Global Navigation Satellite System (GNSS) remote sensing precipitable water vapour (PWV) data from November 2015 to March 2019 were combined with snowfall observation data and used to analyse PWV characteristics in Liaoning Province during the snow season (from November to March the following year) and their relationship with snowfall. The potential of using GNSS for PWV measurements was demonstrated using sounding data with a correlation coefficient higher than 0.9 and a mean bias error lower than 0.5 mm. According to the GNSS PWV data gathered at 30-min intervals from 68 GNSS stations in Liaoning during the snow season, the monthly PWV average was highest in November and lowest in January. Negative correlations were found between PWV and altitude. Most of the water vapour was concentrated in the low layer of the atmosphere, and the contribution of this vapour to the PWV was higher during the snow season than in summer. A total of 43 snow cases were identified using the snowfall records from 53 GNSS stations, and the characteristics of PWV during these snowfalls were analysed. An increase in PWV was observed before snowfall events. Moreover, the influence of synoptic systems and air mass origins on PWV was analysed based on National Centers for Environmental Prediction (NCEP) reanalysis data and the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) model. The results show that the water vapour condition was better when the synoptic systems or air masses came from areas south of Liaoning.     

Fast calibration of between-receiver GPS/Galileo/BDS differential phase bias with millimeter accuracy based on short baseline mode

The differential code and phase biases induced by the receiver hardware (including receiver, antenna, firmware, etc.) of the Global Navigation Satellite System (GNSS) have significant effects on precise timing and ionosphere sensing, thus deserve careful treatment. In this contribution, we propose an approach to fast fix the single-difference ambiguity to finally obtain the unbiased estimates of between-receiver differential phase bias (BR-DPB) and between-receiver differential code-phase bias (BR-DCPB) based on the short baseline mode. The key to this method is that the error sources can be significantly eliminated due to the length of the baseline is very short. At the same time, the empirical constraints and random characteristics of BR-DPB/BR-DCPB were considered, which is conducive to the resolution of single-difference ambiguity. Several sets of GNSS data (GPS L1/L2, Galileo E1/E5b, and BDS B1/B3), recorded by the short baselines in an interval of 30 s and covered a broad range of receiver/antenna types (JAVA, SEPT, LEIC, and TRIM), were used to verify the effectiveness of the proposed method. The numerical tests show that the proposed method is capable of fast fixing the single-difference ambiguity successfully within a few epochs and then providing the unbiased estimates of BR-DPB and BR-DCPB in an epoch-by-epoch manner. Experiments show that the estimated BR-DPB is in millimeter accuracy, which is of great significance for the millimeter-accuracy phase time transfer and ionospheric delay estimation. Furthermore, the calibrated BR-DPB/BR-DCPB can be treated as the known products for long-distance precise timing and ionosphere sensing based on the inter-station single-difference model.     

新型GNSS信号波形设计

在发射带宽严格受限的约束下连续函数波形信号较传统矩形波形表现出了较高的频谱利用率优势和优良性能,很有可能应用到未来的全球卫星导航系统(GNSS,Global Navigation Satellite System)信号体制中.在建立导航信号波形设计准则的理论模型基础上,研究了7种可能适用于未来GNSS系统的新型信号波形,在典型的宽/窄发射带宽条件下,通过仿真评估了传统GNSS信号和新型GNSS信号的精度、抗多径、抗干扰等性能,优选出BOCc和MSK两种适用于不同环境的信号波形: 在频谱资源充足的情况下,BOCc信号具有最优的导航性能;在频率资源受限的情况下,MSK信号兼容性好,抗干扰能力强,拥有较好的导航性能.最后,结合两类信号波形的优缺点提出了我国新一代卫星导航系统信号波形设计的建议.     

无人机组合导航直接法与间接法滤波方式比较

全球导航卫星系统/惯性导航系统（GNSS/INS）组合导航可以提供连续、高精度的位置、速度、姿态信息，被广泛应用于无人机的状态估计。其中滤波算法的构建是其组合关键。不同组合导航的模式会对导航定位结果产生相应的影响。针对直接法和间接法这2种常见的组合模式，分别构建了基于扩展卡尔曼滤波（EKF）的全球定位系统/惯性导航系统（GPS/INS）松组合模式，并将其运用于不同飞行场景下无人机（UAV）的实时动态状态估计。仿真场景以及实际数据验证结果表明，间接法在精度和稳定性方面优于直接法，直接法在滤波计算速率方面优于间接法。因此，当系统具有较高的计算性能，且面向高精度的应用情况下可选择间接法作为无人机导航的技术方案；对于快速求解但精度要求不高的应用情况下，选择直接法作为无人机导航的技术方案可以在一定程度上降低系统的成本。      

基于CLYC闪烁体的中子能谱测量及反演方法

空间中子是影响航天器和航天员安全的重要辐射要素之一。优化中子探测器，提高测量效率，提升反演精度是中子测量的难点。中国空间站将搭载一种基于新型中子探测材料Cs2LiYCl6:Ce（CLYC）闪烁体的中子探测器，该探测器具有同时测量热中子和快中子，以及探测效率高等特点。针对该新型探测器的中子能谱反演，分析了不同能量中子在该探测器中的响应特点，分析了中子反演常用的概率迭代法和非负最小二乘（NNLS）法的优缺点，考虑到这2种方法在CLYC探测器反演应用中的不足，提出了基于增广矩阵的非负最小二乘（AM-NNLS）法。数值实验结果表明:AM-NNLS法具有反演运算效率高和反演相对误差小的特点，验证了所提方法的有效性。      

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.     

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).