Performance of GPS-based accelerometry: A simulation experiment

Recent studies have shown that with the availability of high-quality CHAMP and GRACE gravity field models, it is feasible to determine accurate non-gravitational accelerations for low Earth orbiting satellites indirectly from precise GPS satellite-to-satellite observations. Possible applications of this so-called GPS-based accelerometry approach consist of accelerometer calibration and atmospheric density and wind computations. With the growing number of high-quality space-borne GPS receivers, this method could be applied to a large range of satellites. In this paper an extensive simulation study has been carried out, based on real accelerometer data from the GRACE mission, in order to determine the optimal processing strategy and the resulting accuracy of the estimated non-gravitational accelerations. It is shown that the optimal processing strategy consists of a piecewise linear parameterization of the estimated empirical accelerations, together with short 6-h orbit arcs. The GPS-based accelerometry approach makes use of triple-differenced GPS observations and the impact of considering the correlated observation noise was found to be marginal in the presence of other error sources such as GPS ephemeris errors. Using a priori non-gravitational force models improves the recovery of low temporal resolution accelerations, except during huge geomagnetic storms. With this strategy, non-gravitational accelerations can be recovered during high solar activity with an accuracy of better than 10% of the total signal in along-track direction and around 25–40% in cross-track direction, at time resolutions of around 8–20 min. During solar minimum conditions, the relative recovery error will increase to approximately 50% in along-track direction and around 60–70% in cross-track direction, due to the reduced atmospheric drag signal. Unfortunately, GPS-based accelerometry is hardly sensitive in the radial direction.     

Horizontal and vertical thermospheric cross-wind from GOCE linear and angular accelerations

Thermospheric wind measurements obtained from linear non-gravitational accelerations of the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite show discrepancies when compared to ground-based measurements. In this paper the cross-wind is derived from both the linear and the angular accelerations using a newly developed iterative algorithm. The two resulting data sets are compared to test the validity of wind derived from angular accelerations and quantify the uncertainty in accelerometer-derived wind data. In general the difference is found to be less than 50?m/s vertically after high-pass filtering, and 100?m/s horizontally. A sensitivity analysis reveals that continuous thrusting is a major source of uncertainty in the torque-derived wind, as are the magnetic properties of the satellite. The energy accommodation coefficient is identified as a particularly promising parameter for improving the consistency of thermospheric cross-wind data sets in the future. The algorithm may be applied to obtain density and cross-wind from other satellite missions that lack accelerometer data, provided the attitude and orbit are known with sufficient accuracy.     

High-fidelity geometry models for improving the consistency of CHAMP,GRACE, GOCE and Swarm thermospheric density data sets

During the last two decades, accelerometers on board of the CHAMP, GRACE, GOCE and Swarm satellites have provided high-resolution thermosphere density data to improve our knowledge on atmospheric dynamics and coupling processes in the thermosphere-ionosphere region. Most users of the data have focused on relative density variations. Scale differences between datasets and models have been largely neglected or removed using ad hoc scale factors. The origin of these scale differences arises from errors in the aerodynamic modelling, specifically in the modelling of the satellite outer surface geometry and of the gas-surface interactions. Therefore, the first step to remove the scale differences is to enhance the geometry modelling. This work forms the foundation for the future improvement of characterization of satellite aerodynamics and gas-surface interactions models at TU Delft, as well as for extending the use of sideways and angular accelerations in the aerodynamic analysis of accelerations and derivation of thermosphere datasets. Although work to improve geometry and aerodynamic force models by other authors has focused on CHAMP and GRACE, this paper includes the GOCE and Swarm satellites as well. In addition, it uses a density determination algorithm that is valid for arbitrary attitude orientations, enabling a validation making use of attitude manoeuvres. The results show an improvement in the consistency of density data between these four missions, and of data obtained before, during and after attitude manoeuvres of CHAMP and Swarm. The new models result in larger densities, compared to the previously used panel method. The largest average rescaling of density, by switching to the new geometry models is reached for Swarm at 32%, the smallest for GRACE at 5%. For CHAMP and GOCE, mean differences of 11% and 9% are obtained respectively. In this paper, an overview of the improvements and comparisons of data sets is provided together with an introduction to the next research phase on the gas-surface interactions.     

利用卫星两行轨道根数反演热层密度

两行轨道根数（TLEs）是基于一般摄动理论产生的用于预报地球轨道飞行器位置和速度的一组轨道参数,通过求解大气阻力微分方程,可反演出热层大气密度. 本文选取近圆轨道CHAMP卫星和椭圆轨道Explorer8卫星,以两行轨道根数数据为基础,计算反弹道系数,并根据不同轨道特征采用两种不同反演方法对热层大气密度进行研究. 结果表明,这两种方法反演得到的大气密度与实测值均符合较好,其中CHAMP卫星的反演结果和经验模式值相对于实测值的误差分别为7.94%和13.94%,Explorer8卫星的误差分别为9.04%和14.32%. 相比模式值,利用两行轨道根数数据反演的热层大气密度更接近于实测值,说明该方法可以作为获取大量可靠大气密度数据的一种有效途径.      

Measuring atmospheric density using GPS–LEO tracking data

We present a method to estimate the total neutral atmospheric density from precise orbit determination of Low Earth Orbit (LEO) satellites. We derive the total atmospheric density by determining the drag force acting on the LEOs through centimeter-level reduced-dynamic precise orbit determination (POD) using onboard Global Positioning System (GPS) tracking data. The precision of the estimated drag accelerations is assessed using various metrics, including differences between estimated along-track accelerations from consecutive 30-h POD solutions which overlap by 6 h, comparison of the resulting accelerations with accelerometer measurements, and comparison against an existing atmospheric density model, DTM-2000. We apply the method to GPS tracking data from CHAMP, GRACE, SAC-C, Jason-2, TerraSAR-X and COSMIC satellites, spanning 12 years (2001–2012) and covering orbital heights from 400 km to 1300 km. Errors in the estimates, including those introduced by deficiencies in other modeled forces (such as solar radiation pressure and Earth radiation pressure), are evaluated and the signal and noise levels for each satellite are analyzed. The estimated density data from CHAMP, GRACE, SAC-C and TerraSAR-X are identified as having high signal and low noise levels. These data all have high correlations with anominal atmospheric density model and show common features in relative residuals with respect to the nominal model in related parameter space. On the contrary, the estimated density data from COSMIC and Jason-2 show errors larger than the actual signal at corresponding altitudes thus having little practical value for this study. The results demonstrate that this method is applicable to data from a variety of missions and can provide useful total neutral density measurements for atmospheric study up to altitude as high as 715 km, with precision and resolution between those derived from traditional special orbital perturbation analysis and those obtained from onboard accelerometers.     

High accuracy satellite drag model (HASDM)

The dominant error source in force models used to predict low-perigee satellite trajectories is atmospheric drag. Errors in operational thermospheric density models cause significant errors in predicted satellite positions, since these models do not account for dynamic changes in atmospheric drag for orbit predictions. The Air Force Space Battlelab’s High Accuracy Satellite Drag Model (HASDM) estimates and predicts (out three days) a dynamically varying global density field. HASDM includes the Dynamic Calibration Atmosphere (DCA) algorithm that solves for the phases and amplitudes of the diurnal and semidiurnal variations of thermospheric density near real-time from the observed drag effects on a set of Low Earth Orbit (LEO) calibration satellites. The density correction is expressed as a function of latitude, local solar time and altitude. In HASDM, a time series prediction filter relates the extreme ultraviolet (EUV) energy index E_10.7 and the geomagnetic storm index a_p, to the DCA density correction parameters. The E_10.7 index is generated by the SOLAR2000 model, the first full spectrum model of solar irradiance. The estimated and predicted density fields will be used operationally to significantly improve the accuracy of predicted trajectories for all low-perigee satellites.     

A shadow function model based on perspective projection and atmospheric effect for satellites in eclipse

Accurate Solar Radiation Pressure (SRP) modelling is critical for correctly describing the dynamics of satellites. A shadow function is a unitless quantity varying between 0 and 1 to scale the solar radiation flux at a satellite’s location during eclipses. Errors in modelling shadow function lead to inaccuracy in SRP that degrades the orbit quality. Shadow function modelling requires solutions to a geometrical problem (Earth’s oblateness) and a physical problem (atmospheric effects). This study presents a new shadow function model (PPM_atm) which uses a perspective projection based approach to solve the geometrical problem rigorously and a linear function to describe the reduction of solar radiation flux due to atmospheric effects. GRACE (Gravity Recovery And Climate Experiment) satellites carry accelerometers that record variations of non-conservative forces, which reveal the variations of shadow function during eclipses. In this study, the PPM_atm is validated using accelerometer observations of the GRACE-A satellite. Test results show that the PPM_atm is closer to the variations in accelerometer observations than the widely used SECM (Spherical Earth Conical Model). Taking the accelerometer observations derived shadow function as the “truth”, the relative error in PPM_atm is ?0.79% while the SECM 11.07%. The influence of the PPM_atm is also shown in orbit prediction for Galileo satellites. Compared with the SECM, the PPM_atm can reduce the radial orbit error RMS by 5.6?cm over a 7-day prediction. The impacts of the errors in shadow function modelling on the orbit remain to be systematic and should be mitigated in long-term orbit prediction.     

Magnetic torquer induced disturbing signals within GRACE accelerometer data

The GRACE (Gravity Recovery And Climate Experiment) gravity field satellite mission was launched in 2002. Although many investigations have been carried out, not all disturbances and perturbations upon satellite instruments and sensors are resolved yet. In this work the issue of acceleration disturbances onboard of GRACE due to magnetic torquers is investigated and discussed. Each of the GRACE satellites is equipped with a three-axes capacitive accelerometer to measure non-gravitational forces acting on the spacecraft. We used 10 Hz Level 1a raw accelerometer data in order to determine the impact of electric current changes on the accelerometer. After reducing signals which are induced by highly dominating processes in the low frequency range, such as thermospheric drag and solar radiation pressure, which can easily be done by applying a high-pass filter, disturbing signals from onboard instruments such as thruster firing events or heater switch events need to be removed from the previously filtered data. Afterwards the spikes which are induced by the torquers can be very well observed. Spikes vary in amplitude with respect to an increasing or decreasing current used for magnetic torquers, and can be as large as 20 nm/s². Furthermore, we were able to set up a model for the spikes of each scenario with which we were able to compute model spike time series. With these time series the spikes can successfully be removed from the 10 Hz raw accelerometer data. Spectral analysis of the time series reveal that an influence onto gravity field determination due to these effects is very unlikely, but can theoretically not be excluded.     

Differential code bias estimation based on uncombined PPP with LEO onboard GPS observations

Differential Code Bias (DCB) is an essential correction that must be provided to the Global Navigation Satellite System (GNSS) users for precise position determination. With the continuous deployment of Low Earth Orbit (LEO) satellites, DCB estimation using observations from GNSS receivers onboard the LEO satellites is drawing increasing interests in order to meet the growing demands on high-quality DCB products from LEO-based applications, such as LEO-based GNSS signal augmentation and space weather research. Previous studies on LEO-based DCB estimation are usually using the geometry-free combination of GNSS observations, and it may suffer from significant leveling errors due to non-zero mean of multipath errors and short-term variations of receiver code and phase biases. In this study, we utilize the uncombined Precise Point Positioning (PPP) model for LEO DCB estimation. The models for uncombined PPP-based LEO DCB estimation are presented and GPS observations acquired from receivers onboard three identical Swarm satellites from February 1 to 28, 2019 are used for the validation. The results show that the average Root Mean Square errors (RMS) of the GPS satellite DCBs estimated with onboard data from each of the three Swarm satellites using the uncombined PPP model are less than 0.18 ns when compared to the GPS satellite DCBs obtained from IGS final daily Global Ionospheric Map (GIM) products. Meanwhile, the corresponding average RMS of GPS satellite DCBs estimated with the conventional geometry-free model are 0.290, 0.210, 0.281 ns, respectively, which are significantly larger than those obtained with the uncombined PPP model. It is also noted that the estimated GPS satellite DCBs by Swarm A and C satellites are highly correlated, likely attributed to their similar orbit type and space environment. On the other hand, the Swarm receiver DCBs estimated with uncombined PPP model, with Standard Deviation (STD) of 0.065, 0.037 and 0.071 ns, are more stable than those obtained from the official Swarm Level 2 products with corresponding STD values of 0.115, 0.101, and 0.109 ns, respectively. The above indicates that high-quality DCB products can be estimated based on uncombined PPP with LEO onboard observations.     

低轨航天器弹道系数估算及热层大气模型误差分析

利用低轨（LEO）航天器在轨期间两行轨道根数（TLEs）数据,结合经验大气密度模型NRLMSISE00,反演计算得到其在轨期间的弹道系数B’,以31年B’的平均值代替弹道系数真值,分别通过标准球形目标卫星对比以及物理参数基本相同的非球形目标卫星对比,对弹道系数真值进行了检验;利用不同外形目标卫星弹道系数在不同太阳活动周内的变化规律,结合太阳和地磁活动变化,估计经验大气密度模型的误差分布. 结果表明,利用反演弹道系数31年的平均值来代替真值,其在理论值的正常误差范围内;大气密度模型误差在210～526km高度范围内存在相同的变化趋势,且模型误差随高度增加而增大;在短周期内B’变化与太阳活动指数F_10.7存在反相关性;密度模型不能有效模拟2008年出现的大气密度异常低. 以上结果表明,经验大气密度模型结果需要修正,尤其是在太阳活动峰年和谷年,此外,磁暴期间模型误差的修正对卫星定轨和轨道预报等也具有重要意义.      

Towards accurate atmospheric mass density determination Using precise positional information of space objects

This paper presents a new method of deriving atmospheric mass densities with a high temporal resolution from precise orbit data of low earth orbiting (LEO) space objects. This method is based on the drag perturbation equation of the semi-major axis of the orbit of LEO space objects which relates the change rate of the semi-major axis to the atmospheric mass density. The effectiveness of the new method is evaluated using the GFZ-ISDC GPS rapid science orbit (RSO) products of the CHAMP satellite over a time period of 3 months. The densities derived using this new method and obtained from accelerometer data are compared and good agreements are achieved. An example of using the derived density to generate good orbit prediction for CHAMP is presented.     

第23太阳活动周热层大气密度对太阳辐射指数F10.7响应的模拟研究

利用NCAR-TIEGCM计算了第23太阳活动周期间（1996—2008年）400km高度上的大气密度，并统计分析大气密度对太阳辐射指数FF_10.7的响应.结果表明，在第23太阳活动周内，大气密度的变化趋势与太阳辐射指数FF_10.7的变化趋势基本一致，但是大气密度在不同年份、不同月份对太阳辐射指数FF_10.7的响应存在差异.第23太阳活动周内太阳辐射极大值和极小值之比大于4，而大气密度的极大值与极小值之比则大于10.太阳辐射低年的年内大气密度变化不到2倍，而太阳辐射高年的年内大气密度变化可达2倍甚至3倍.大气密度与FF_10.7指数在北半球高纬的相关系数比南半球高纬的相关系数大.在低纬地区，太阳辐射高年大气密度与FF_10.7指数的相关系数比低年的大.不同纬度上，大气密度与太阳辐射指数FF_10.7的27天变化值之间的相关系数都大于其与81天变化值之间的相关系数.      

Use of two-line element data for thermosphere neutral density model calibration

Traditional empirical thermospheric density models are widely used in orbit determination and prediction of low-Earth satellites. Unfortunately, these models often exhibit large density errors of up to around 30% RMS. Density errors translate into orbit errors, adversely affecting applications such as re-entry operations, manoeuvre planning, collision avoidance and precise orbit determination for geodetic missions. The extensive database of two-line element (TLE) orbit data contains a wealth of information on satellite drag, at a sufficiently high spatial and temporal resolution to allow a calibration of existing neutral density models with a latency of one to two days. In our calibration software, new TLE data for selected objects is converted to satellite drag data on a daily basis. The resulting drag data is then used in a daily adjustment of density model calibration parameters, which modify the output of an existing empirical density model with the aim of increasing its accuracy. Two different calibration schemes have been tested using TLE data for about 50 objects during the year 2000. The schemes involve either height-dependent scale factors to the density or corrections to CIRA-72 model temperatures, which affect the density output based on a physical model. Both schemes have been applied with different spherical harmonic expansions of the parameters in latitude and local solar time. Five TLE objects, varying in perigee altitude between 280 and 530 km, were deliberately not used during calibration, in order to provide independent validation. Even with a single daily parameter, the RMS density model error along their tracks can already be reduced from the 30% to the 15% level. Adding additional parameters results in RMS errors lower than 12%.     

Thermospheric heating at high latitudes as observed from intercosmos-Bulgaria-1300 and dynamics explorer-B

This paper reports the results of the first direct comparison of near simultaneous measurements obtained by the INTERCOSMOS-BULGARIA-1300 and the DYNAMICS EXPLORER-B satellites. The ICB-1300 is in a near circular orbit at a mean height of about 850 km. The DE-B satellite in an elliptical orbit is sometimes directly below the ICB-1300 satellite providing an opportunity to investigate the response of the thermosphere to particle fluxes from the magnetosphere. Energy fluxes in the range 0.2–15 keV are obtained from an energetic particle analyzer on board the ICB-1300 satellite. The thermospheric composition and density are obtained by a neutral gas mass spectrometer (NACS) on the DE-B satellite. During the period 20 August–20 November, 1981, observations show tht the times and locations of maxima in magnetospheric energy deposition coincide with regions of maximum thermospheric upwelling characterized by composition changes.     

基于经验加速度的低轨卫星轨道预报新方法

研究将定轨过程中的经验加速度应用于地球低轨卫星轨道预报的新方法. 利用GPS伪距观测数据和简化动力学最小二乘批处理方法对地球低轨卫星定 轨, 其中卫星位置、速度及大气阻力系数和辐射光压系数可以直接用于轨道预报. 作为简化动力学最重要特征的经验加速度呈现准周期、余弦曲线特点, 可通过 傅里叶级数拟合建模. 确定性动力学模型与补偿大气阻力模型误差的切向经验 加速度级数拟合模型组成增强型动力学模型用于提高轨道预报精度. 应用 GRACE-A星载GPS伪距观测数据和IGS超快星历定轨并进行轨道预报, 结果表明 轨道预报初值位置精度达到0.2m, 速度精度达到1×10-4m·s-1, 预报3天位置精度优于60m, 比只利用确定性动力学模型进行预报精度平 均提高2.3倍. 先定轨后预报的模式可用在星上自主精确导航系统中.      

基于卫星加速度数据反演的热层大气密度与NRLMSISE-00模式结果的比较研究

利用CHAMP/STAR加速度数据反演的热层大气密度与NRLMSISE-00模式反演的热层大气密度进行比较, 结果表明, 热层大气密度在春秋季期间高于冬夏季, 并且太阳活动高年比低年更加显著; 日照面和阴影区大气密度的比值在低纬地区由太阳活动高年的4下降到太阳活动低年的2左右, 中纬地区大约由3变化到1.5, 高纬地区变化较小; NRLMSISE-00模式能够较好地模拟热层大气密度的变化趋势, 但是磁暴期间模式精度较差. 统计结果表明, 模式整体比反演结果偏高, 2002-2008年相对偏差分别为16.512%, 20.004%, 18.915%, 18.245%, 25.161%, 33.261%和41.980%; NRLMSISE-00模式在高纬地区的相对偏差为27.337%, 高于中低纬地区的24.047%; 模式在中等太阳活动水平相对偏差较为稳定, 基本在15%左右.      

GRACE accelerometer calibration by high precision non-gravitational force modeling

The precise modeling and knowledge of non-gravitational forces acting on satellites is of big interest to many scientific tasks and missions. Since 2002, the twin GRACE satellites have measured these forces in a low Earth orbit with highly precise accelerometers, for about 15?years. Besides the significance for the GRACE mission, these measurement data allow the evaluation of modeling approaches and the improvement of force models. Unfortunately, before any scientific usage, the accelerometer measurements need to be calibrated, namely scale factor and bias have to be regularly estimated.In this study we demonstrate an accelerometer calibration approach, solely based on high precision non-gravitational force modeling without any use of empirically or stochastically estimated parameters, using our in-house developed satellite simulation tool XHPS. The aim of this work is twofold, first we use the accelerometer data and the residuals resulting from the calibration to quantitatively analyze and validate different non-gravitational force model approaches. In a second step, we compare the calibration results to three different calibration methods from different authors, based on gravity field recovery, GPS-based precise orbit determination, and based on modeled accelerations.We consider atmospheric drag forces and winds, as well as radiation forces due to solar radiation pressure, albedo, Earth infrared and thermal radiation (TRP) of the satellite itself. For TRP, we investigate different transient temperature calculation approaches for the satellite surfaces with absorbed power from the aforementioned radiation sources. A detailed finite element model of the satellite is utilized for every force, considering orientation, material properties and shadowing conditions for each element.For cross-track and radial direction, which are mainly affected by the radiative forces, our calibration residuals are quite small when drag is not super dominant (1–3?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$50?$\text{nm}/{\text{s}}^2$). For these directions the calibration seems to perform better than the other compared methods, where some bigger differences were found. For the drag dominated along-track direction it is vice versa, here our method is not sensitive enough because the difference between modeled and measured drag is bigger (e.g. residuals around 10?$\text{nm}/{\text{s}}^2$ for total accelerations around $\pm$70?$\text{nm}/{\text{s}}^2$ for low solar activity). In along-track direction the orbit determination based methods are more sensitive and produce more reliable results. Results for the complete GRACE mission time span from 2003 to 2017 are shown, covering different seasonal environmental conditions.     

基于CHAMP卫星观测数据对热层大气密度的经验正交分析

对2003年(太阳活动较高年)至2007年(太阳活动低年) CHAMP卫星的热层大气密度观测数据进行了经验正交函数(EOF)分析, 得到了400 km高度上白天平均大气密度ρ的太阳活动周变化与年度变化等不同变化分量. 研究结果表明, ρ受太阳活动影响较大, 其太阳周变化分量与F10.7指数变化之间的相关系数可高达94.5 %; ρ的太阳周变化分量随纬度增加而减小, 且在中高纬地区, 南半球的值明显大于北半球的值, 在低纬地区则出现基本对称的双峰分布, 即赤道质量密度异常(EMA)结构. 在ρ的年变化中, 呈现出明显的季节变化, 即夏季低冬季高; 同时ρ的年变化幅度随太阳活动增加而增强, 随纬度增加而增强. 将本文结果与经验模式NRLMSISE00在观测条件下的输出数据进行对比, 发现两者的太阳周变化与年变化分量基本一致, 但本文观测数据的太阳周成分随纬度变化略小, 年变化幅度略大, 且NRLMSISE00模式不能再现EMA结构. 研究结果对揭示热层气候学变化特征具有重要意义.      

Characteristics of GOCE orbits based on Satellite Laser Ranging

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first European Space Agency’s (ESA) Earth Explorer core mission. Through its extremely low, about 260?km above the Earth, circular, sun-synchronous orbit, the satellite gained high spatial resolution and accuracy gravity gradient, and ocean circulation data. Global Positioning System (GPS) receivers, mounted on the spacecraft, allowed the determination of reduced-dynamic and kinematic GOCE orbits, whereas Laser Retroreflector Array (LRA) dedicated to Satellite Laser Ranging (SLR) allowed an independent validation of GPS-derived orbits. In this paper, residuals between different GPS-based orbit types and SLR observations are used to investigate the sensitivity and the influence of solar, geomagnetic, and ionospheric activities on the quality of kinematic and reduced-dynamic GOCE orbits. We also analyze the quality of data provided by individual SLR sites, by detecting time biases using ascending and descending sun-synchronous GOCE orbit passes, and the residual analysis of the measurement characteristics, i.e., the dependency of SLR residuals as a function of nadir and horizontal angles. Results show a substantial vulnerability of kinematic orbit solutions to the solar F10.7 index and the ionospheric activity measured by the variations of the Total Electron Content (TEC) values. The sensitivity of kinematic orbits to the three-hour-range KP index is rather minor. The reduced-dynamic orbits are almost insensitive to indices describing ionospheric, solar, and geomagnetic activities. The investigation of individual SLR sites shows that some of them are affected by time bias errors, whereas other demonstrate systematics, such as a dependency between observation residuals and the satellite nadir angle or the horizontal azimuth angle from the SLR station to the direction of the satellite.     

电离层周日变化对解算GPS硬件延迟稳定性的影响

针对电离层周日变化特征分析了其可能对SCORE方法估算的硬件延迟稳定性的影响. 利用BJFS以及XIAM台站的GPS观测数据, 解算了位于太阳活动高年(2001年)和太阳活动低年(2009年)的卫星硬件延迟并分析了估算的硬件延迟的稳定性. 研究发现, 电离层周日变化对估算的硬件延迟稳定性具有一定影响, 但是利用不同台站所得到的卫星硬件延迟稳定性在昼夜不同时间上的解算结果存在一定差异. 电离层周日变化对利用 BJFS台站数据解算的硬件延迟稳定性日夜差异较为明显, 在太阳活动高年利用XIAM 台站数据解算的硬件延迟日夜稳定性差异不很明显, 由于XIAM台站处于电离层赤道异常峰附近, 夜间电离层变化很大, 因此对比中纬度地区, 电离层周日变化对赤道异常峰附近地区硬件延迟稳定性解算结果的影响相对较小, 但在太阳活动低年, 其影响仍较为显著.