Impact of loading effects on determination of the International Terrestrial Reference Frame

The International Terrestrial Reference Frame (ITRF), as a realization of the International Terrestrial Reference System (ITRS), is represented by a set of station positions and linear velocities. They are intended to be used as regularized coordinates to which some corrections should be added to access instantaneous coordinates. The latest ITRS realization is the ITRF2005, which has integrated time series of station positions to form long-term solutions for the four space geodetic techniques. Currently, a purely linear model is used to parameterize station displacements in the estimation process, plus occasional discontinuities in case of earthquakes or equipment changes. However the input data have been derived without applying surface loading models and so surface loading effects are supposed to be embedded in the coordinates as measured quantities. We evaluate the effect of applying a posteriori loading corrections, which include the effect of atmospheric, non-tidal ocean, and continental water loading, to time series of positions estimated from Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), and Global Positioning System (GPS) data. We notice that they reduce about 50% or more of the annual signals in the translation and scale parameter time series of the SLR and VLBI techniques, except in SLR Z translation. In general, the estimated secular frame definition is negligibly affected and estimated positions and velocities are not significantly modified for stations that have accumulated a large number of observations. A multi-technique combination of such derived frames allows concluding that, for some cases, loading model corrections might degrade co-located station coordinates almost as much as they benefit them. However, most significant improvement of the estimated secular coordinates is observed for stations with less than 100 estimated positions as demonstrated with a multi-technique combination.     

Impact of ITRS 2014 realizations on altimeter satellite precise orbit determination

This paper evaluates orbit accuracy and systematic error for altimeter satellite precise orbit determination on TOPEX, Jason-1, Jason-2 and Jason-3 by comparing the use of four SLR/DORIS station complements from the International Terrestrial Reference System (ITRS) 2014 realizations with those based on ITRF2008. The new Terrestrial Reference Frame 2014 (TRF2014) station complements include ITRS realizations from the Institut National de l’Information Géographique et Forestière (IGN) ITRF2014, the Jet Propulsion Laboratory (JPL) JTRF2014, the Deutsche Geodätisches Forschungsinstitut (DGFI) DTRF2014, and the DORIS extension to ITRF2014 for Precise Orbit Determination, DPOD2014. The largest source of error stems from ITRF2008 station position extrapolation past the 2009 solution end time. The TRF2014 SLR/DORIS complement impact on the ITRF2008 orbit is only 1–2 mm RMS radial difference between 1992–2009, and increases after 2009, up to 5 mm RMS radial difference in 2016. Residual analysis shows that station position extrapolation error past the solution span becomes evident even after two years, and will contribute to about 3–4 mm radial orbit error after seven years. Crossover data show the DTRF2014 orbits are the most accurate for the TOPEX and Jason-2 test periods, and the JTRF2014 orbits for the Jason-1 period. However for the 2016 Jason-3 test period only the DPOD2014-based orbits show a strong and statistically significant margin of improvement. The positive results with DTRF2014 suggest the new approach to correct station positions or normal equations for non-tidal loading before combination is beneficial. We did not find any compelling POD advantage in using non-linear over linear station velocity models in our SLR & DORIS orbit tests on the Jason satellites. The JTRF2014 proof-of-concept ITRS realization demonstrates the need for improved SLR+DORIS orbit centering when compared to the Ries (2013) CM annual model. Orbit centering error is seen as an annual radial signal of 0.4 mm amplitude with the CM model. The unmodeled CM signals show roughly a 1.8 mm peak-to-peak annual variation in the orbit radial component. We find the TRF network stability pertinent to POD can be defined only by examination of the orbit-specific tracking network time series. Drift stability between the ITRF2008 and the other TRF2014-based orbits is very high, the relative mean radial drift error over water is no larger than 0.04 mm/year over 1993–2015. Analyses also show TRF induced orbit error meets current altimeter rate accuracy goals for global and regional sea level estimation.     

Noise analysis of continuous GPS coordinate time series for CMONOC

The Crustal Movement Observation Network of China (CMONOC) is one of the major scientific infrastructures, mainly using Global Positioning System (GPS) measurements, to monitor crustal deformation in the Chinese mainland. In this paper, decade-long coordinate time series of 26 continuous GPS sites of CMONOC are analyzed for their noise content using maximum likelihood estimation (MLE). We study the noise properties of continuous GPS time series of CMONOC for the unfiltered, filtered solutions and also the common mode signals in terms of power law plus white noise model. In the spatial filtering, we remove for every time series a common mode error that was estimated from a modified stacking of position residuals from other sites within ∼1000 km of the selected site. We find that the common mode signal in our network has a combination of spatially correlated flicker noise and a common white noise with large spatial extent. We demonstrate that for the unfiltered solutions of CMONOC continuous GPS sites the main colored noise is a flicker process, with a mean spectral index of ∼1. For the filtered solutions, the main colored noise is a general power law process, indicating that a major number of the filtered regional solutions have a combination of noise sources or local effects. The velocity uncertainties from CMONOC continuous GPS coordinate time series may be underestimated by factors of 8–16 if a pure white noise model is assumed. In addition, using a white plus flicker noise model, the median values of velocity errors for the unfiltered solutions are 0.16 (north), 0.17 (east) and 0.58 (vertical) mm/yr, and the median values for the filtered solutions are 0.09 (north), 0.10 (east) and 0.40 (vertical) mm/yr.     

CNES/GRGS 10-day gravity field models (release 2) and their evaluation

GRACE, designed to monitor temporal variations in the fluid mass at the surface of the Earth, is still operating and providing invaluable data 7 years after launch. One hundred and ninety-nine satellite-only geopotential solutions to degree and order 50 were recomputed per 10-day interval for the period 29 July 2002–27 May 2008 using an improved data editing and solution regularization procedure. These release 2 solutions are significantly improved compared to release 1 solutions, the noise over deserts and oceans in the form of North–South striping being reduced by 20–40%. This is thanks to the tailored regularization of each individual Stokes coefficient applied in the solution procedure, and to a time-variable reference model containing mean annual, semiannual and secular variations for degrees 2–50 towards which the variations per 10-day solution are constrained. It may attenuate signals of the order of a few percent, whereas this always occurs when applying a Gaussian smoother even with a half-width smoothing radius as small as 300 km. The uncertainty of an individual point in the time series of a basin expressed in equivalent water height inferred from the 10-day solutions is approximately 20 mm. Comparison of these 10-day solutions to monthly GRACE project solutions (CSR, GFZ and JPL) shows substantial differences. Even for the largest basin, the Amazon, a 15% difference in annual amplitude is found between CNES release 2 and CSR versus GFZ and JPL. The mass-loss estimates for East and West Greenland vary by 100%. Sometimes clear outliers are detected in the GFZ and JPL solutions when a particular basin is studied, which have to be eliminated. In view of the large differences detected between the time series for specific basins, it is hazardous to draw conclusions based on a single solution.     

Effects on noise properties of GPS time series caused by higher-order ionospheric corrections

Higher-order ionospheric (HOI) effects are one of the principal technique-specific error sources in precise global positioning system (GPS) analysis. These effects also influence the non-linear characteristics of GPS coordinate time series. In this paper, we investigate these effects on coordinate time series in terms of seasonal variations and noise amplitudes. Both power spectral techniques and maximum likelihood estimators (MLE) are used to evaluate these effects quantitatively and qualitatively. Our results show an overall improvement for the analysis of global sites if HOI effects are considered. We note that the noise spectral index that is used for the determination of the optimal noise models in our analysis ranged between −1 and 0 both with and without HOI corrections, implying that the coloured noise cannot be removed by these corrections. However, the corrections were found to have improved noise properties for global sites. After the corrections were applied, the noise amplitudes at most sites decreased, among which the white noise amplitudes decreased remarkably. The white noise amplitudes of up to 81.8% of the selected sites decreased in the up component, and the flicker noise of 67.5% of the sites decreased in the north component. Stacked periodogram results show that, no matter whether the HOI effects are considered or not, a common fundamental period of 1.04 cycles per year (cpy), together with the expected annual and semi-annual signals, can explain all peaks of the north and up components well. For the east component, however, reasonable results can be obtained only based on HOI corrections. HOI corrections are useful for better detecting the periodic signals in GPS coordinate time series. Moreover, the corrections contributed partly to the seasonal variations of the selected sites, especially for the up component. Statistically, HOI corrections reduced more than 50% and more than 65% of the annual and semi-annual amplitudes respectively at the selected sites.     

Analysis of the DORIS contributions to ITRF2008

In its function as an ITRS Combination Centre, DGFI is in charge with the computation of an ITRF2008 solution. The computation methodology of DGFI is based on the combination of datum-free normal equations (weekly or session data sets, respectively) of station positions and Earth orientation parameters (EOP) from the geodetic space techniques DORIS, GPS, SLR and VLBI. In this paper we focus on the DORIS part within the ITRF2008 computations. We present results obtained from the analysis of the DORIS time series for station positions, network translation and scale parameters, as well as for the terrestrial pole coordinates. The submissions to ITRF2008 benefit from improved analysis strategies of the seven contributing IDS analysis centres and from a combination of the weekly solutions of station positions and polar motion. The results show an improvement by a factor of two compared to past DORIS data submitted to ITRF2005, which has been evaluated by investigating the repeatabilities of position time series. The DORIS position time series were analysed w.r.t. discontinuities and other non-linear effects such as seasonal variations. About 40 discontinuities have been identified which have been compared with the results of an earlier study. Within the inter-technique combination we focus on the DORIS contribution to the integration of the different space geodetic observations and on a comparison of the geodetic local ties with the space geodetic solutions. Results are given for the 41 co-location sites between DORIS and GPS.     

基于自适应联邦滤波的卫星姿态确定

卡尔曼滤波采用常值量测噪声协方差阵,当量测噪声统计特性发生变化时,易导致估计误差增大,甚至滤波发散。针对该问题,在联邦卡尔曼滤波子系统中采用自适应卡尔曼滤波,形成自适应联邦卡尔曼滤波算法,新算法采用模糊推理系统实时调整量测噪声协方差阵的加权系数,使模型量测噪声逐渐逼近真实噪声水平。将该算法应用于多传感器卫星姿态确定系统,仿真结果验证了算法的有效性。     

自适应混合信息滤波算法及其在 相对导航中的应用

为解决相对导航模型中线性、非线性并存,及多传感器信息融合时基于Kalman滤波的导航算法计算复杂度较大的问题,提出一种混合信息滤波算法;考虑测量噪声统计特性不准确等工程因素,提出一种自适应混合信息滤波相对导航算法.理论分析及仿真验证表明,与基于Kalman滤波的传统导航算法相比,给出的混合信息滤波算法具有多传感器数据融合时计算复杂度低、便于工程实现的优点,且可以完成线性、非线性并存时的导航滤波任务;除上述特点外,在传感器测量噪声统计特性不准确的情况下,给出的自适应混合信息滤波相对导航算法可以通过自适应调整量测协方差阵的方式,使导航系统仍保持较高的精度.     

Rapid local ionosphere modeling based on Precise Point Positioning over Iran: A case study under 2014 solar maximum

Presently, the ionosphere effect is the main source of the error in the Global Positioning System (GPS) observations. This effect can largely be removed by using the two-frequency measurements, while to obtain the reasonable results in the single-frequency applications, an accurate ionosphere model is required. Since the global ionosphere models do not meet our needs everywhere, the local ionosphere models are developed. In this paper, a rapid local ionosphere model over Iran is presented. For this purpose, the GPS observations obtained from 40 GPS stations of the Iranian Permanent GPS Network (IPGN) and 16 other GPS stations around Iran have been used. The observations have been selected under 2014 solar maximum, from the days 058, 107, 188 and 271 of the year 2014 with different geomagnetic activities. Moreover, ionospheric observables based on the precise point positioning (PPP) have been applied to model the ionosphere. To represent our ionosphere model, the B-spline basis functions have been employed and the variance component estimation (VCE) method has been used to regularize the problem.To show the efficiency our PPP-derived local ionosphere model with respect to the International GNSS Service (IGS) global models, these models are applied on the single point positioning using single-frequency observations and their results are compared with the precise coordinates obtained from the double-differenced solution using dual-frequency observations. The results show that the 95th percentile of horizontal and vertical positioning errors of the single-frequency point positioning are about 3.1 and 13.6?m, respectively, when any ionosphere model are not applied. These values significantly improve when the ionosphere models are applied in the solutions. Applying CODE’s Rapid Global ionosphere map (CORG), improvements of 59% and 81% in horizontal and vertical components are observed. These values for the IGS Global ionosphere map (IGSG) are 70% and 82%, respectively. The best results are obtained from our local ionosphere model, where 84% and 87% improvements in horizontal and vertical components are observed. These results confirm the efficiency of our local ionosphere model over Iran with respect to the global models. As a by-product, the Differential Code Biases (DCBs) of the receivers are also estimated. In this line, we found that the intra-day variations of the receiver DCBs could be significant. Therefore, these variations must be taken into account for the precise ionosphere modeling.     

利用GPS进行时间传递与频率比对

全面介绍了ＢＩＲＭＭ从１９８６～１９９２年间从事利用时间ＧＰＳ进行时间传递与频率比对技术研究方面的情况，包括所建立的ＣＰＳ定时校频系统、单站定时、ＳＡ对定时精度的影响、ＧＰＳ定时信号噪声模型、卡尔曼滤波、电离层时延估算、ＧＰＳ共视试验、ＣＰＳ校频、接收系统差测量等。     

Kalman滤波估算电离层延迟的一种优化方法

频间偏差（Inter Frequency Bias，IFB）通常会给电离层延迟的解算带来误差.目前从电离层延迟中消除频间偏差的方法是基于GPS双频观测数据建立垂直电离层模型，利用卡尔曼滤波实时估算电离层模型系数和频间偏差.然而滤波过程中的测量噪声协方差矩阵没有考虑系统观测量之间的相关性，这会导致滤波模型不准确，进而影响最后求解的电离层延迟的准确性.本文选取了美国19个参考站的GPS双频观测数据，利用卡尔曼滤波实时估算电离层模型系数以及频间偏差.在滤波过程中，通过将先验频间偏差的估计方差引入测量噪声方差，实现对测量噪声协方差矩阵的优化.计算结果表明，优化后得到的卫星频间偏差与欧洲定轨中心（Center for Orbit Determination in Europe，CODE）得到的频间偏差更接近.将优化后的电离层延迟代入伪距解算，得到的位置误差的标准差在东向和天顶向分别下降了12.5%和15.4%，天顶向误差平均值下降了17.6%，定位精度得到提高.      

基于长短时记忆神经网络(LSTM)的钟差预报算法

原子钟钟差预报在原子时计算和原子钟频率驾驭中发挥着重要的作用。长短时记忆神经网络（LSTM）预报算法能够处理多参数长期依赖关系的时间序列预报，以氢钟和铯钟实测数据为样本，通过构建LSTM钟差预报模型，降低了长期原子钟内部噪声以及原子钟漂移对钟差预报的影响，并以72h，240h和720h为预报时长，分别与线性多项式模型、灰色模型和Kalman模型原子钟钟差预报模型进行预报误差对比。研究表明，在240h以上的预报时长中，LSTM建模长期依赖关系的优势得以体现，相较于其他3类模型可以获得更高的预报精度。     

一种无人机视觉导航方法及其滤波算法改进

设计了一种无人机视觉/惯性组合导航系统,将无人机和地标点的运动模型作为状态方程,视觉信息作为观测量构建了与之对应的滤波模型.在滤波处理上,采用了复杂加性噪声模型对系统噪声进行建模处理;将小波分析引入到UKF(Unscented Kalman Filter)滤波中得到小波-UKF滤波算法,以此克服视觉观测噪声对滤波的影响;采用最大后验概率准则(MAP,Maximum A Posterior)自适应估计观测噪声协方差阵,并将其反馈到滤波过程中克服了小波处理后观测噪声方差阵不易确定的不足.仿真结果证明:对滤波算法的改进可以有效地提高滤波估计的精度.     

Estimation of flexible space tether state based on end measurement by finite element Kalman filter state estimator

This paper proposes a novel finite element Kalman filter to estimate the unmeasurable state of space tether systems based on the measured state at its ends only. The finite element method calculates the unmeasurable internal state as the virtual measurement based on the dynamic model of the system by imposing the input of measured state at the boundary to the model using the Lagrange multiplier method in the spatial space. Combining the real and virtual measurement into a hybrid measurement model of the system, the full state is reconstructed and propagated in the temporal space by the extended Kalman filter. Two state-space system models, the dynamics-based and kinematics-based state models, in the Kalman filter are explored. The observability and stability of the newly proposed finite element Kalman filter are examined and proved. The advantages of the proposed state estimator are (i) the singularity in the virtual measurement of state caused by the number of internal state greater than the number of state measured at the boundary is eliminated in the statistic meaning by the Kalman filter, and (ii) the effects of noises of the observation data and the uncertainties of model discretization are considered and minimized. The correctness and effectiveness of the proposed state estimator is demonstrated by the numerical analysis of a space tether system orbiting around the Earth. The results show the proposed state estimator with only measured state at the ends of the tether successfully provides an accurate time history estimation of geometric configuration and motion of the entire tether. Moreover, the results also show the difference caused by the dynamics-based and kinematics-based system models in the state estimator is negligible. The kinematics-based system model should be used in the state estimator due to its significantly low computational load. Finally, the proposed method can be easily applied for the state estimation process for other space tethered spacecraft systems.     

Studies of the geocenter motion using 16-years DORIS data

An accuracy of geocenter motion estimation is strongly dependent on the geodetic network size and stations distribution over the Earth’s surface. From this point of view DORIS system has an advantage, as its ground network of beacons consists of more than 50 sites, equally distributed over the Earth’s surface. Aiming to study variations of the geocenter movements, the results of DORIS data analysis for the time span 1993.0–2009.0 (inawd06.snx series), performed at the Analysis Centre of the Institute of astronomy of the Russian Academy of Sciences, have been used. DORIS data processing was made with GIPSY/OASIS II software, developed by Jet Propulsion Laboratory and modified for DORIS data processing by Institute Géographique National. Standard deviations of stations coordinates are estimated at the level 0.5–4.0 cm (internal consistency), depending on the number of satellites used in the solution. RMS of estimated components of the DORIS satellites orbits, compared with the solutions of other IDS analysis centres, do not exceed 1–2 cm. Weekly solutions for coordinates have been transformed from free network solutions (inawd06.snx series) to a well defined terrestrial reference frame ITRF2005 with the use of seven parameters of Helmert transformation, which were examined with a view to study variations of the geocenter movements (ina05wd01.geoc time series). In order to estimate linear trend, amplitudes, periods and phases of geocenter variation a method of linear regression was applied. The evaluated amplitudes of annual variations are of the order of 5–7 mm for X and Y components and 27–29 mm for Z component. Semi-annual amplitudes are also noticeable in all components (1–34 mm for X, Y and Z components). Secular trends in the DORIS geocenter coordinates are: −1.2, −0.1 and −0.3 mm/year for X, Y and Z directions respectively.     

粗差拟准检定法在星载GPS低轨卫星定轨中的应用

利用自适应卡尔曼滤波进行星载GPS低轨卫星定轨时,必须解决量测方程中经常存在的粗差问题．在分析以往方法的优缺点后,用拟准检定法来探测和修正量测方程中存在的粗差．该法的优点是辨识粗差准确率高,能同时定位多个粗差．另外,为了克服星载GPS低轨卫星定轨的滤波器可能出现的数值不稳定性及发散现象,还采用了UD分解算法及Sage自适应滤波器．最后用一个CHAMP卫星的模拟算例验证本方法的可行性和有效性．     

Quality Assessment of the IDS Contribution to ITRF2008

Doppler Orbitography Radiopositionning Integrated by Satellite (DORIS) is one of the four fundamental techniques contributing to the ITRF. The optimal coverage over the globe of the DORIS observing sites and sites co-located with GPS, allow a strong embedding of DORIS within the ITRF network. DORIS contributes to the access to ITRF through precise orbit determination of altimetric satellites with onboard DORIS receivers. The DORIS contribution to the ITRF2008 is enhanced by the fact that the solutions of seven analysis centers were included in the submitted combined time series of weekly station positions and daily polar motion. We evaluate the quality of the DORIS combined solution in terms of its agreement with the other techniques (VLBI, SLR, GPS) contributing to the ITRF2008 combination. We show in particular that the precisions of the current IDS products range between 1.5 to 2.6 mm for station positions (at the epochs of minimum variances); better than 1 mm/yr in velocities and between 170 and 260 micro-arc-seconds for polar motion, a significant improvement by a factor of three to five, compared to past data used in the ITRF2005 combination. This improvement is certainly due to improved analysis strategies employed by the seven IDS analysis centers that contributed to the combined weekly submitted solutions of station positions and polar motion. A spectral analysis of DORIS station height time series indicates that annual and semi-annual signals are dominant. However, TOPEX draconitic period of about 118 days is still detected in about 20% of the station position power spectra. DORIS height annual signals correlate well with GPS annual signal estimated at some co-located stations, which show that DORIS technique is able to detect loading signals.     

太阳辐射对环火段通信链路的影响分析及参数设计

深空探测的上合阶段(superior solar conjunction,SSC)，太阳强辐射成为影响地面站接收噪声温度计算分析的关键性因素之一。针对太阳辐射引起的高传输误码率甚至通信中断问题，以火星探测为例，提出一种定量化计算环火段太阳 地面站 探测器夹角∠SEP的方法，结合角度关系分析了环火段SSC阶段太阳对链路产生影响的原因，重点分析了地面站接收太阳噪声温度与空间链路、空口参数以及天线波束特性之间的关系。研究及仿真试验表明，当天线口径一定时，地面站的接收噪温峰值Tsmax和太阳对地面站的影响时长ti均与通信频率成反比; 在通信频率一定时，Tsmax与天线口径成正比，t_i与天线口径成反比；当天线口径固定为34m时，S频段下的Tsmax高达12830K，是Ka频段下的1.8倍，S频段的ti比Ka频段下的ti表现在∠SEP上延长近0.5°。当通信频率固定为S频段时，70m口径天线与18m口径天线相比，Tsmax高出1920K，但是ti表现在∠SEP上缩短约0.53°。结合太阳辐射对通信链路的影响分析，给出了不同∠SEP下的链路参数设计建议，为火星探测链路中的参数设置提供参考。     

Some comparisons of orbit determination and parameter estimation based on LAGEOS 1 and LAGEOS 2 data

The modelling accuracy of the LAGEOS 1 orbit was continously improved since its launch in 1976. In spite of these experiences the modelling accuracy of LAGEOS 2 is still about 20 per cent worse. Considering e. g. only the influence of different gravity field models it has been shown that the orbital fits for arc lengths of one month is generally about 25 mm for LAGEOS 1 and more than 30 mm for LAGEOS 2. This is mainly due to the fact that LAGEOS 2 has not yet been used for the determination of most gravity field models. The influences of different model parameters on the estimation of station coordinates, Earth rotation parameters, the geogravitational coefficient, the radiation pressure coefficient, and the empirical acceleration has been studied. The differences and peculiarities of both satellites are discussed. Although the analysis of LAGEOS 2 data still does not reach the high level of LAGEOS 1 combination solutions using both satellites allow new insights, higher accuracies, and a higher time resolution for the parameters and phenomena investigated.     

DORIS-based point mascons for the long term stability of precise orbit solutions

In recent years non-tidal Time Varying Gravity (TVG) has emerged as the most important contributor in the error budget of Precision Orbit Determination (POD) solutions for altimeter satellites’ orbits. The Gravity Recovery And Climate Experiment (GRACE) mission has provided POD analysts with static and time-varying gravity models that are very accurate over the 2002–2012 time interval, but whose linear rates cannot be safely extrapolated before and after the GRACE lifespan. One such model based on a combination of data from GRACE and Lageos from 2002–2010, is used in the dynamic POD solutions developed for the Geophysical Data Records (GDRs) of the Jason series of altimeter missions and the equivalent products from lower altitude missions such as Envisat, Cryosat-2, and HY-2A. In order to accommodate long-term time-variable gravity variations not included in the background geopotential model, we assess the feasibility of using DORIS data to observe local mass variations using point mascons. In particular, we show that the point-mascon approach can stabilize the geographically correlated orbit errors which are of fundamental interest for the analysis of regional Mean Sea Level trends based on altimeter data, and can therefore provide an interim solution in the event of GRACE data loss. The time series of point-mass solutions for Greenland and Antarctica show good agreement with independent series derived from GRACE data, indicating a mass loss at rate of 210 Gt/year and 110 Gt/year respectively.