Tightly combined GPS/Galileo RTK for short and long baselines: Model and performance analysis

To ensure the compatibility and interoperability with modernized GPS, Galileo satellites are capable of broadcasting navigation signals on carrier phase frequencies that overlap with GPS, i.e., GPS/Galileo L1-E1/L5-E5a. Moreover, the GPS/Galileo L2-E5b signals have different frequencies with wavelength differences smaller than 4.2?mm. Such overlapping and narrowly spaced signals between GPS and Galileo bring the opportunity to use the tightly combined double-differenced (DD) model for precise real-time kinematic (RTK) positioning, resulting in improved performance of ambiguity resolution and positioning with respect to the classical standard or loosely combined DD model. In this paper, we focus on the model and performance assessment of tightly combined GPS/Galileo L1-E1/L2-E5b/L5-E5a RTK for short and long baselines. We first investigate the tightly combined GPS/Galileo DD observational model for both short and long baselines with simultaneously considering the GPS/Galileo overlapping and non-overlapping frequencies. Particularly, we introduce a reparameterization approach to solve the rank deficiency that caused by the correlation between the DISB parameters and the DD ionospheric parameters for both overlapping and non-overlapping frequencies. Then we present performance assessment for the tightly combined GPS/Galileo RTK model with real-time estimation of the differential inter-system bias (DISB) parameters for short and long baselines in terms of ratio value, ambiguity dilution of precision (ADOP), ambiguity conditional number, decorrelation number, search count, empirical success rate, time-to-first-fix (TTFF), and positioning accuracy. Results from both static and kinematic experiments demonstrated that compared to the loosely combined model, the tightly combined model can deliver improved performance of ambiguity resolution and precise positioning with different satellite visibility. For the car-driven short baseline experiment with 10° elevation cut-off angle, the tightly combined model can not only significantly increase the ratio value by approximately 27.5% (from 16.0 to 20.4), but also reduce the ambiguity ADOP, the conditional number, and the search count in LAMBDA by approximately 22.2% (from 0.027 to 0.021 cycles), 14.9% (from 199.2 to 169.6), and 25.4% (from 150.1 to 112.0), respectively. Comparable decorrelation number, empirical success rate, and positioning accuracy are also obtained. For the car-driven long baseline experiment, it is also observed that the ambiguity resolution performance in terms of the ratio value, the decorrelation number, the condition number, and the search count are significantly improved by approximately 18.5% (from 2.7 to 3.2), 22.0% (from 0.186 to 0.227), 55.9% (from 937.6 to 413.7), and 10.3% (from 43.8 to 39.3), respectively. Moreover, comparable ADOP, empirical success rate, and positioning accuracy are obtained as well. Additionally, the TTFF can be reduced (from 54.1 to 51.8 epochs with 10° elevation cut-off angle) as well from the results of static experiments.     

新的GPS单频单历元定姿算法

LAMBDA算法依赖于初始的模糊度浮点解,但仅用载波相位观测方程需要多个历元才能获得浮点解,将导致初始化时间过长.针对这一问题,对GPS(Global Positioning System)单历元的载波相位单差方程进行特殊变换,将未知的整周模糊度看成噪声,从而构造出新的观测方程,和原始的观测方程进行组合求解,克服了仅用载波相位双差观测方程因为亏秩而无法在单历元获得浮点解的缺点,解决了初始化时间的问题.通过深入研究浮点解和固定解之间的关系,提出一种将低精度浮点解映射到固定解的方法,降低了LAMBDA算法对高精度浮点解的依赖性,避免了用多个历元获取浮点解的高精度,从而实现了单频、单历元的整周模糊度估计.通过实际测试,该算法成功率高于97%,能够有效地用于实时动态姿态解算.      

基于DSP＋LAMBDA算法的GPS实时定位技术研究

主要分析了GPS载波相位整周模糊度LAMBDA求解算法,通过数据模拟测试来验证该算法在DSP上的工作状况。仿真计算证明,在DSP上实现LAMBDA算法可以满足GPS实时动态定位的要求。     

GPS/Galileo组合导航的模糊度搜索空间

为了组合导航的载波相位模糊度固定,将目前在GPS中常用的模糊度固定方法--最小二乘降相关平差（LAMBDA）法直接应用于GPS/Galileo组合模糊度固定,发现其搜索空间的确定方法并不能很好地适应GPS/Galileo组合中模糊度维数较高的情况。通过对常规LAMBDA搜索空间确定方法的分析比较,在传统方法的基础上提出了一种专门针对高维模糊度固定的搜索空间确定方法--修正法确定模糊度搜索空间。通过对修正法进行仿真试验,证明该方法能保证在GPS/Galileo组合定位模式下实际备选模糊度个数基本与预先设定的备选模糊度个数一致,进而能在不降低模糊度固定成功率的基础上有效提高LAMBDA模糊度固定的搜索效率,其性能优于传统的模糊度搜索空间确定方法。     

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.     

航天器应急姿态捕获中GPS信号的应用

星载全球定位系统（GPS）卫星接收机在测量接收各GPS卫星信号时,可同时得到接收信号的信号强度测量辅助数据E。理论分析表明,接收信号的强度E与信号入射天线的法向夹角α强相关。如建立E与α稳定的先验模型,E就可以作为测量值,计算入射天线的角度α。在同一时刻,通过三个以上GPS卫星信号入射天线的角度α,可计算星载GPS卫星接收机接收天线的空间姿态。确定姿态的精度取决于E与α相关先验模型的稳定性。利用CHAMP卫星星载接收机在轨实测数据检验,估算的初始姿态精度为2°~3°。该方法可作为航天器故障状态下应急姿态捕获的一种辅助手段,也可为携带星载GPS而无高精度定姿要求的简易航天器提供一种新的无附加成本的定姿途径。     

基于GPS的三维姿态确定系统研究

论述了基于GPS姿态确定的原理、方法、步骤。首先，利用最小二乘平差校准基线，得到基线的准确长度及相互间的几何关系；随后，可以利用这些约束条件加速模糊度求解过程，适于实时应用。通过估计基线向量得到姿态粗解，以粗解为初值进行迭代最小二乘平差，最后得到最终的姿态解。通过一个实验系统验证，给出了实验结果。     

Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates

The global positioning system (GPS) has become an essential tool for the high precision navigation and positioning. The quality of GPS positioning results mainly depends on the model’s formulations regarding GPS observations, including both a functional model, which describes the mathematical relationships between the GPS measurements and unknown parameters, and a stochastic model, which reflects the physical properties of the measurements. Over the past two decades, the functional models for GPS measurements have been investigated in considerable detail. However, the stochastic models of GPS observation data are simplified, assuming that all the GPS measurements have the same variance and are statistically independent. Such assumptions are unrealistic. Although a few studies of GPS stochastic models were performed, they are restricted to short baselines and short time session lengths. In this paper, the stochastic modeling for GPS long-baseline and zenith tropospheric delay (ZTD) estimates with a 24-h session is investigated using the residual-based and standard stochastic models. Results show that using the different stochastic modelling methods, the total differences can reach as much as 3–6 mm in the baseline component, especially in the height component, and 10 mm in the ZTD estimation. Any misspecification in the stochastic models will result in unreliable GPS baseline and ZTD estimations. Using the residual-based stochastic model, not only the precision of GPS baseline and ZTD estimation is obviously improved, but also the baseline and ZTD estimations are closer to the reference value.     

Enhancing the kinematic precise orbit determination of low earth orbiters using GPS receiver clock modelling

Clock error estimation has been the focus of a great deal of research because of the extensive usage of clocks in GPS positioning applications. The receiver clock error in the spacecraft orbit determination is commonly estimated on an epoch-by-epoch basis, along with the spacecraft’s position. However, due to the high correlation between the spacecraft orbit altitude and the receiver clock parameters, estimates of the radial component are degraded in the kinematic approach. Using clocks with high stability, the predictable behaviour of the receiver oscillator can be exploited to improve the positioning accuracy, especially for the radial component. This paper introduces two GPS receiver clock models to describe the deterministic and stochastic property of the receiver clock, both of which can improve the accuracy of kinematic orbit determination for spacecraft in low earth orbit. In particular, the clock parameters are estimated as time offset and frequency offset in the two-state model. The frequency drift is also estimated as an unknown parameter in the three-state model. Additionally, residual non-deterministic random errors such as frequency white noise, frequency random walk noise and frequency random run noise are modelled. Test results indicate that the positioning accuracy could be improved significantly using one day of GRACE flight data. In particular, the error of the radial component was reduced by over 40.0% in the real-time scenario.     

基于增强型单频GPS的高精度星间相对定位样条方法

为了实现高精度的分布式SAR星间相对定位,提出了一种基于增强型单频GPS的相对定位样条方法,即在单频GPS测量信息的基础上,增加星间距离观测信息,并结合相对位置参数的连续特性,建立了相对定位的样条模型,最后利用最小二乘法进行参数估计.仿真结果表明,新方法不仅能大大提高相对定位精度,而且还能有效地减少固定整周模糊度所需的历元.最后的理论分析证明了仿真的正确性.      

InfraRed Astronomy Satellite Swarm Interferometry (IRASSI): Overview and study results

The far-infrared (FIR) regime is one of the few wavelength ranges where no astronomical data with sub-arcsecond spatial resolution exist yet. Neither of the medium-term satellite projects like SPICA, Millimetron or OST will resolve this malady. For many research areas, however, information at high spatial and spectral resolution in the FIR, taken from atomic fine-structure lines, from highly excited carbon monoxide (CO) and especially from water lines would open the door for transformative science. These demands call for interferometric concepts. We present here first results of our feasibility study IRASSI (Infrared Astronomy Satellite Swarm Interferometry) for an FIR space interferometer. Extending on the principal concept of the previous study ESPRIT, it features heterodyne interferometry within a swarm of five satellite elements. The satellites can drift in and out within a range of several hundred meters, thereby achieving spatial resolutions of <0.1 arcsec over the whole wavelength range of 1–6 THz. Precise knowledge on the baselines will be ensured by metrology methods employing laser-based optical frequency combs, for which preliminary ground-based tests have been designed by members of our study team. We first give a motivation on how the science requirements translate into operational and design parameters for IRASSI. Our consortium has put much emphasis on the navigational aspects of such a free-flying swarm of satellites operating in relatively close vicinity. We hence present work on the formation geometry, the relative dynamics of the swarm, and aspects of our investigation towards attitude estimation. Furthermore, we discuss issues regarding the real-time capability of the autonomous relative positioning system, which is an important aspect for IRASSI where, due to the large raw data rates expected, the interferometric correlation has to be done onboard, in quasi-real-time. We also address questions regarding the spacecraft architecture and how a first thermomechanical model is used to study the effect of thermal perturbations on the spacecraft. This will have implications for the necessary internal calibration of the local tie between the laser metrology and the phase centres of the science signals and will ultimately affect the accuracy of the baseline estimations.     

基于RT-LAB的组合导航仿真平台设计

设计了一种基于RT-LAB的SINS/GPS/CNS（Strapdown Inertial Navigation System/Global Positioning System/Celestial Navigation System）组合导航系统仿真平台方案,建立具有故障检测、隔离和系统重构能力的基于联邦卡尔曼滤波器的姿态、位置、速度组合导航系统方案和结构.将SINS与GPS的位置之差和速度之差作为SINS/GPS子滤波器的观测量,通过CNS给出的载体惯性姿态信息获得SINS的姿态误差角测量信息.仿真结果表明,该系统方案具有较强的容错性能、较高的导航精度和很强的实时性能,为组合导航技术的研究提供了有益的参考.     

Contribution analysis of QZSS to single-frequency PPP of GPS/BDS/GLONASS/Galileo

The Quasi-Zenith Satellite System (QZSS) established by the Japan Aerospace Exploration Agency mainly serves the Asia-Pacific region and its surrounding areas. Currently, four in-orbit satellites provide services. Most users of GNSS in the mass market use single-frequency (SF) receivers owing to the low cost. Therefore, it is meaningful to analyze and evaluate the contribution of the QZSS to SF precise point positioning (PPP) of GPS/BDS/GLONASS/Galileo systems with the emergence of GNSS and QZSS. This study compares the performances of three SF PPP models, namely the GRoup and PHase Ionospheric Correction (GRAPHIC) model, GRAPHIC with code observation model, and an ionosphere-constrained model, and evaluated the contribution of the QZSS to the SF PPP of GPS/BDS/GLONASS/Galileo systems. Moreover, the influence of code bias on the SF PPP of the BDS system is also analyzed. A two-week dataset (DOY 013–026, 2019) from 10 stations of the MGEX network is selected for validation, and the results show that: (1) For cut-off elevation angles of 15, 20, and 25°, the convergence times for the static SF PPP of GLONASS + QZSS are reduced by 4.3, 30.8, and 12.7%, respectively, and the positioning accuracy is similar compared with that of the GLONASS system. Compared with the BDS single system, the convergence times for the static SF PPP of BDS + QZSS under 15 and 25° are reduced by 37.6 and 39.2%, the horizontal positioning accuracies are improved by 18.6 and 14.1%, and the vertical components are improved by 13.9 and 21.4%, respectively. At cut-off elevation angles of 15, 20, and 25°, the positioning accuracy and precision of GPS/BDS/GLONASS/Galileo + QZSS is similar to that of GPS/BDS/GLONASS/Galileo. And the convergence times are reduced by 7.4 and 4.3% at cut-off elevation angles of 20 and 25°, respectively. In imitating dynamic PPP, the QZSS significantly improves the positioning accuracy of BDS and GLONASS. However, QZSS has little effect on the GPS-only, Galileo-only and GPS/BDS/GLONASS/Galileo. (2) The code bias of BDS IGSO and MEO cannot be ignored in SF PPP. In static SF PPP, taking the frequency band of B1I whose multipath combination is the largest among the frequency bands as an example, the vertical component has a systematic bias of approximately 0.4–1.0 m. After correcting the code bias, the positioning error in the vertical component is lower than 0.2 m, and the positioning accuracy in the horizontal component are improved accordingly. (3) The SF PPP model with ionosphere constraints has a better convergence speed, while the positioning accuracy of the three models is nearly equal. Therefore the GRAPHIC model can be used to get good positioning accuracy in the absence of external ionosphere products, but its convergence speed is slower.     

Estimating inter-system biases for tightly combined Galileo/BDS/GPS RTK

The overlapping carrier frequencies L1/E1, L5/E5a and B2/E5b from GPS/Galileo/BDS allow inter-system double-differencing of observations, which shows a clear advantage over differencing of the observations of each constellation independently. However, the inter-system biases destroy the integer nature of the inter-system double-differencing ambiguities. Two methods of direct rounding and parameter estimation are used to determine the ISB value. By analyzing data collected from Curtin University from 2015 to 2018, the phase and code inter-system bias (ISB) are related to the receiver type, firmware version and the selected overlapping frequency. Upgrade of receiver firmware version results in changes of ISB values. For example, the upgrade of Javad firmware in Dec, 15, 2017 causes the difference of 0.5 cycles ISB between BDS GEO and non-GEO satellites. By comparing the three dynamic models which include white noise process, random walk process, and random constant in the parameter estimation method, the ISB determined by the random constant model is consistent with the value obtained by the direct rounding method. After the calibration of ISBs, the performances of tightly combined positioning are assessed. The success rate of ambiguity resolution and accuracy of positioning for the tight combination (TC) are significantly improved in comparison with that for the loose combination (LC) over short baselines. For L5/E5a, on which only few satellites can be observed, the maximum increase in success rates of ambiguity resolution can reach 31.7%, i.e., from 54.9% of LC to larger than 86.6% of TC, and the positioning accuracies can even be increased by 0.13 m, i.e., from 0.208 of LC to 0.074 m of TC in East direction for the mix-receiver TRIMBLE NETR9-SEPT POLARX4 in 2018.     

Epochwise prediction of GPS single differenced ionospheric delays of formation flying spacecraft

Both single and dual frequency GPS relative navigation filters may benefit from proper predictions of single differenced ionospheric delays. In this article, the single differenced ionospheric delays of GPS observations are predicted for the GRACE formation during the switch manoeuvre.Two prediction methods are considered. The first is based on a Taylor expansion to first order of a mapping function that maps slant total electron content measurements to vertical total electron content estimates. The second method fits a shape profile through undifferenced ionospheric data available. It then raytraces through this profile to estimate the difference in total electron content along the path of the GPS signals.Continuously changing ionospheric conditions hamper the assessment of the quality of the predictions. Comparison of both methods shows that the raytracing method performs better. The difference of predictions and measurements generally shows a smaller RMS than the measurements alone. However, both methods suffer from a number of systematically unpredicted observations, which arise from small unaccounted differential variations in electron densities along the path of the GPS signals. These prediction methods perform better when spacecraft separation is small. Baselines considered here range from tens of kilometres down to several hundred metres. When smallest spacecraft separation occurs (0.4 km), the single differenced ionospheric delays exhibit RMS values of 0.0089 m. The first method shows a difference between measurements and predictions with an RMS of 0.0081 m. For the second method the difference RMS is found to be 0.0067 m.     

Galileo/GPS载波相位组合观测值可匹配的研究

详细讨论了Galileo系统的4种载波与GPS L2载波的相位组合观测值的可匹配问题.在模糊度保持为整数的前提下,给出了Galileo/GPS载波相位组合观测值的定义,并对包括系统噪声和观测噪声在内的有关误差影响加以分析,最后给出了组合观测值可匹配的定义和判断可匹配的充要条件.      

Galileo系统与GPS卫星定位系统相位组合观测值的模型研究

在介绍Galileo系统空间信号的基础上,以模糊度保持整数为前提,给出了Galileo系统的4个频率载波与GPS L2载波的组合相位观测值的定义,并对有关误差影响加以分析,最后根据一定的组合标准论述了具有相应特性的组合观测值,并给出一些典型的组合.      

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.     

Preliminary analysis of the quality and positioning performance of BDS-3 global interoperable signal B1C&B2a

BeiDou-3 Navigation Satellite System (BDS-3) satellites are equipped with the new generation GNSS signals B1C and B2a, which support the interoperability with GPS and Galileo systems. In this study, the pseudo-range multipath error and carrier phase observation noise of the BDS-3 B1C and B2a signals were evaluated based on zero baseline measurements from the day of year (DOY) 113 to 116, 2020. Further, the precision and performance of the single point positioning (SPP) and precise point positioning (PPP) are assessed at 9 stations. This assessment manifests that the standard deviations (STDs) of the pseudo-range multipath error are about 0.09 ~ 0.22 m, while STDs of the carrier phase observation noise are about 0.075 mm. For the single-frequency SPP, its positioning precision is about 2.03 ~ 4.85 m and 3.29 ~ 10.73 m at the 99.99% confidence level in horizontal and vertical directions, respectively, while the dual-frequency SPP precision is about 1.92 ~ 8.02 m and 4.81 ~ 12.77 m in horizontal and vertical directions, respectively. For the daily static PPP, the convergence time is about 20 ~ 30 min, while the daily positioning precision can reach 1.38 ~ 4.42 cm and -1.31 ~ 4.34 cm in horizontal and vertical directions, respectively. In general, the quality and the SPP and PPP performance of the BDS-3 B1C&B2a signals are comparable to the GPS and Galileo.     

航天器交会最终逼近段相对姿态估计与控制

对航天器交会对接最终逼近段,给出姿态运动学方程统一形式以及相对姿态动力学方程;除了应用交会航天器的绝对姿态运动方程进行相对姿态估计(间接法)外,还直接应用相对姿态运动方程进行相对姿态估计(直接法);阐述相对姿态控制的相平面法与四元数反馈法的设计方法.相平面控制法应用常值推力,针对小姿态角机动的特点,将相对姿态通道解耦为3个独立的二阶子系统,设计相平面推力方向切换函数;四元数反馈法应用简化的基于本征轴旋转的线性二阶系统,选择相对四元数与角速率反馈增益系数,确定控制力矩.此外,对相对姿态估计与控制方法进行模拟计算与比较.理论分析与模拟计算结果表明:应用扩展Kalman滤波的相对姿态间接估计法与直接估计法是有效的,后者有可能简化估计算法;相平面控制法与四元数反馈法均可有效实现相对姿态控制,前者应用常值推力(推力方向与姿态反馈有关),较易实现,但动力消耗较大,后者按控制力矩随姿态反馈量而变,动力消耗较小.