The impact of celestial pole offset modelling on VLBI UT1 intensive results

Very Long Baseline Interferometry (VLBI) Intensive sessions are scheduled to provide operational Universal Time (UT1) determinations with low latency. UT1 estimates obtained from these observations heavily depend on the model of the celestial pole motion used during data processing. However, even the most accurate precession- nutation model, IAU 2000/2006, is not accurate enough to realize the full potential of VLBI observations. To achieve the highest possible accuracy in UT1 estimates, a celestial pole offset (CPO), which is the difference between the actual and modelled precession-nutation angles, should be applied. Three CPO models are currently available for users. In this paper, these models have been tested and the differences between UT1 estimates obtained with those models are investigated. It has been shown that neglecting CPO modelling during VLBI UT1 Intensive processing causes systematic errors in UT1 series of up to 20 μas. It has been also found that using different CPO models causes the differences in UT1 estimates reaching 10 μas. Obtained results are applicable to the satellite data processing as well.     

基于RWTLS的Allan方差算法简化

Allan方差是现在应用最广泛的随机误差辨识方法之一。大量的试验表明Allan方差可有效地分离出导航过程中的多项随机误差,但是Allan方差也有自身的局限性。针对Allan方差在处理大数据量时计算效率低下、辨识度受粗差的影响较大的问题,本文提出了简化Allan方差算法的方案。首先,在确保Allan方差计算准确的前提下,以提高Allan方差计算效率为目的,对Allan方差算法进行简化;然后,利用抗差加权整体最小二乘（RWTLS）模型的迭代算法对简化后的Allan方差辨识结果进行抗差拟合处理;最后,以光纤式惯性测量单元（IMU）为分析对象,设计试验方案对简化后的Allan方差进行验证。     

Deriving time-series three-dimensional displacements of mining areas from a single-geometry InSAR dataset

This paper presents a method for deriving time-series three-dimensional (3-D) displacements of mining areas from a single-geometry interferometric synthetic aperture radar (InSAR) dataset (hereafter referred to as the SGI-based method). This is mainly aimed at overcoming the limitation of the traditional multi-temporal InSAR techniques that require SAR data from at least three significantly different imaging geometries to fully retrieve time-series 3-D displacements of mining areas. The SGI-based method first generates the multi-temporal observations of the mining-induced vertical subsidence from the single-geometry InSAR data, using a previously developed method for retrieving 3-D mining-related displacements from a single InSAR pair (SIP). The weighted least-squares solutions of the time series of vertical subsidence are estimated from these generated multi-temporal observations of vertical subsidence. Finally, the time series of horizontal motions in the east and north directions are estimated using the proportional relationship between the horizontal motion and the subsidence gradient of the mining area, on the basis of the SGI-derived time series of vertical subsidence. Seven ascending ALOS PALSAR images from the Datong mining area of China were used to test the proposed SGI-based method. The results suggest that the SGI-based method is effective. The SGI-based method not only extends the SIP-based method to time-series 3-D displacement retrieval from a single-geometry InSAR dataset, but also limits the uncertainty propagation from InSAR-derived deformation to the estimated 3-D displacements.     

原子钟模型和频率稳定度分析方法

首先给出典型的原子钟时差观测量模型,包括确定性部分（时差、频差、线性频漂和周期性波动项）、随机性部分（即原子钟噪声）和观测噪声;分析了各分量对应的Allan偏差的表达式。针对部分文献对Kalman滤波器估计原子钟状态原理描述不清晰的问题,描述了原子钟随机微分方程模型和各物理量的含义,从最优估计和低通滤波器两个角度阐述其原理。针对观测噪声过大、存在周期性波动等原因造成无法准确估计原子钟噪声强度的情况,提出了综合Kalman滤波器状态估计结果和Allan偏差图,估计原子钟噪声和观测噪声强度的方法;提出了3种不同的估计线性频漂幅度的方法,并通过实测数据相互验证;针对周期性波动在时差中不明显的问题,结合原子钟随机微分方程模型,提出了综合Kalman滤波器状态估计的结果和对数Allan偏差图估计周期性波动周期和幅度的方法。对两台国产氢钟的实测数据进行了验证,证明该方法物理原理清晰,操作简便易行,具有实用性。通过该方法可以外推得到所有平滑时间的Allan偏差估计值。     

DORIS Contribution to ITRF2005

We examine the contribution of the Doppler Orbit determination and Radiopositioning Integrated by Satellite (DORIS) technique to the International Terrestrial Reference Frame (ITRF2005) by evaluating the quality of the submitted solutions as well as that of the frame parameters, especially the origin and the scale. Unlike the previous versions of the ITRF, ITRF2005 is constructed with input data in the form of time-series of station positions (weekly for satellite techniques and daily for VLBI) and daily Earth orientation parameters (EOPs), including full variance–covariance information. Analysis of the DORIS station positions’ time-series indicates an internal precision reaching 15 mm or better, at a weekly sampling. A cumulative solution using 12 years of weekly time-series was obtained and compared to a similar International GNSS Service (IGS) GPS solution (at 37 co-located sites) yielding a weighted root mean scatter (WRMS) of the order of 8 mm in position (at the epoch of minimum variance) and about 2.5 mm/year in velocity. The quality of this cumulative solution resulting from the combination of two individual DORIS solutions is better than any individual solution. A quality assessment of polar motion embedded in the contributed DORIS solutions is performed by comparison with the results of other space-geodetic techniques and in particular GPS. The inferred WRMS of polar motion varies significantly from one DORIS solution to another and is between 0.5 and 2 mas, depending on the strategy used and in particular estimating or not polar motion rate by the analysis centers. This particular aspect certainly needs more investigation by the DORIS Analysis Centers.     

Joint analysis of celestial pole offset and free core nutation series

Three combined celestial pole offset (CPO) series computed at the Paris Observatory (C04), the United States Naval Observatory (USNO), and the International VLBI Service for Geodesy and Astrometry (IVS), as well as six free core nutation (FCN) models, were compared from different perspectives, such as stochastic and systematic differences, and FCN amplitude and phase variations. The differences between the C04 and IVS CPO series were mostly stochastic, whereas a low-frequency bias at the level of several tens of \(\upmu \)as was found between the C04 and USNO CPO series. The stochastic differences between the C04 and USNO series became considerably smaller when computed at the IVS epochs, which can indicate possible problems with the interpolation of the IVS data at the midnight epochs during the computation of the C04 and USNO series. The comparison of the FCN series showed that the series computed with similar window widths of 1.1–1.2 years were close to one another at a level of 10–20 \(\upmu \)as, whereas the differences between these series and the series computed with a larger window width of 4 and 7 years reached 100 \(\upmu \)as. The dependence of the FCN model on the underlying CPO series was investigated. The RMS differences between the FCN models derived from the C04, USNO, and IVS CPO series were at a level of approximately 15 \(\upmu \)as, which was considerably smaller than the differences among the CPO series. The analysis of the differences between the IVS, C04, and USNO CPO series suggested that the IVS series would be preferable for both precession-nutation and FCN-related studies.     

基于采样方差的卫星钟信号分析

对原子钟频率稳定度分析受到频率漂移的影响进行定性分析,明确了不同类型方差在原子钟频率稳定度分析中的适用范围,首次提出将重叠Hadamard方差应用于卫星钟信号分析。分别利用Allan方差、Hadamard方差和重叠Hadamard方差对铷钟进行了稳定度计算,结果表明Allan方差的计算结果受频率漂移影响很大,而Hadamard系列方差能够有效克服频率漂移的影响,对于卫星钟的性能表征具有良好的效果。     

Sentinel-1卫星TOPS模式影像增强谱分集配准优化

Sentinel-1卫星TOPS模式影像通常在几何配准的基础上,再次利用Burst重叠区域进行增强谱分集处理以实现高精度配准。几何配准主要依赖卫星轨道参数,难以进一步提高其配准精度,因此Sentinel-1影像配准的关键则是通过增强谱分集准确估计出几何配准后的残余偏移量。然而,增强谱分集易受失相干噪声等因素的影响,低相干条件下难以满足0.001像素的配准精度要求。因此本文首先针对单基线条件下的增强谱分集配准处理进行以下改进：①完善增强谱分集多视理论,采用前置多视处理,优化增强谱分集处理流程;②基于增强谱分集相位的残余偏移量等权估计升级为加权估计,改善参数估计方法;③完善距离向增强谱分集加权估计理论,实施距离向增强谱分集配准,增加增强谱分集的观测量。然后在单基线配准的基础上,针对时序影像处理提出优化方案：①根据影像干涉对组合所形成的增强谱分集冗余观测量进行多基线配准;②采用分布式目标技术提高增强谱分集干涉图相位质量。上述改进方案互相补充,不但能独立实施,而且可以联合使用。研究结果表明,以上改进方法能够在一定程度上提高配准精度。     

徐州矿区采空塌陷区公路工程地质灾害与防治对策分析

常规时序合成孔径雷达干涉测量(interferometric synthetic aperture radar, InSAR)技术应用于矿区地表形变监测时存在监测点少且分布不均等不足,难以全面反映采空区地表变形特征,而分布式目标受时空失相干等因素的影响相位稳定性较差,因此开展分布式目标相位优化是融合分布式目标时序InSAR形变监测的关键步骤。针对当前分布式目标相位优化中存在的空间连续性约束不足问题,提出了融合区域生长的分布式目标相位优化方法,开展时间和空间联合约束下的分布式目标相位优化,实现复杂地表环境下的精细化地表形变信息获取,并以潘安湖区域为例对分布式目标相位的优化效果进行了定性和定量分析。在此基础上,以该方法和Sentinel-1数据开展了徐州市废弃矿区2018-05—2020-05的地表形变监测,并利用连续运行参考站和裸露基岩验证了该方法的精度和可靠性。结果表明,分布式目标相位时空二维优化方法能够有效减小相位噪声影响,有助于城市废弃矿区地表形变监测。

     

乘性误差模型参数估计及精度评定的Sterling插值方法

乘性误差模型加权最小二乘参数估值是观测值的非线性函数,观测值的权是加权最小二乘参数估值的非线性函数。已有的乘性误差模型参数估计方法理论上可以达到二阶无偏,但精度评定方法只能达到一阶精度,并且参数估计逐步的迭代过程使得参数及改正数的每一步估值都具有随机性,使得最终的参数估值与观测值为复杂的非线性关系。考虑到非线性迭代过程对加权最小二乘参数带来的影响,使用一种无需求导的Sterling插值方法求解参数估值的均值和标准差。模拟实验表明,当模型非线性较高时,考虑每次迭代的随机性对参数估值的影响可以得到更接近真值的参数估值,并且所提方法的精度评定可以达到二阶精度,验证了Sterling插值方法用于乘性误差模型参数估计及其精度评定的适用性和有效性。     

On the statistical distribution of levelling errors

The nature of the deviations from normality of the distribution of mixed populations of varying means and standard deviations is examined. It is shown that heterogeneity invariably causes leptokurtosis whereas the variability of the means may induce a measure of platykurtosis in certain cases. The apparent deviation from normality of the frequency distribution of the discrepancies between the direct and the reverse measurements in levelling is discussed in the light of this analysis. The present study shows that the method of weighted analysis of variance proposed by one of the authors in a communication to the Tenth General Assembly of the International Union of Geodesy and Geophysics at Rome in 1954 is appropriate to the analysis of levelling errors.     

Effect of different tropospheric mapping functions on the TRF, CRF and position time-series estimated from VLBI

This paper compares estimated terrestrial reference frames (TRF) and celestial reference frames (CRF) as well as position time-series in terms of systematic differences, scale, annual signals and station position repeatabilities using four different tropospheric mapping functions (MF): The NMF (Niell Mapping Function) and the recently developed GMF (Global Mapping Function) consist of easy-to-handle stand-alone formulae, whereas the IMF (Isobaric Mapping Function) and the VMF1 (Vienna Mapping Function 1) are determined from numerical weather models. All computations were performed at the Deutsches Geodätisches Forschungsinstitut (DGFI) using the OCCAM 6.1 and DOGS-CS software packages for Very Long Baseline Interferometry (VLBI) data from 1984 until 2005. While it turned out that CRF estimates only slightly depend on the MF used, showing small systematic effects up to 0.025 mas, some station heights of the computed TRF change by up to 13 mm. The best agreement was achieved for the VMF1 and GMF results concerning the TRFs, and for the VMF1 and IMF results concerning scale variations and position time-series. The amplitudes of the annual periodical signals in the time-series of estimated heights differ by up to 5 mm. The best precision in terms of station height repeatability is found for the VMF1, which is 5–7% better than for the other MFs.     

Rapid,high-resolution detection of environmental change over continental scales from satellite data – the Earth Observation Data Cube

The effort and cost required to convert satellite Earth Observation (EO) data into meaningful geophysical variables has prevented the systematic analysis of all available observations. To overcome these problems, we utilise an integrated High Performance Computing and Data environment to rapidly process, restructure and analyse the Australian Landsat data archive. In this approach, the EO data are assigned to a common grid framework that spans the full geospatial and temporal extent of the observations – the EO Data Cube. This approach is pixel-based and incorporates geometric and spectral calibration and quality assurance of each Earth surface reflectance measurement. We demonstrate the utility of the approach with rapid time-series mapping of surface water across the entire Australian continent using 27 years of continuous, 25?m resolution observations. Our preliminary analysis of the Landsat archive shows how the EO Data Cube can effectively liberate high-resolution EO data from their complex sensor-specific data structures and revolutionise our ability to measure environmental change.     

Fast error analysis of continuous GNSS observations with missing data

One of the most widely used method for the time-series analysis of continuous Global Navigation Satellite System (GNSS) observations is Maximum Likelihood Estimation (MLE) which in most implementations requires $\mathcal{O }(n^3)$ operations for $n$ observations. Previous research by the authors has shown that this amount of operations can be reduced to $\mathcal{O }(n^2)$ for observations without missing data. In the current research we present a reformulation of the equations that preserves this low amount of operations, even in the common situation of having some missing data.Our reformulation assumes that the noise is stationary to ensure a Toeplitz covariance matrix. However, most GNSS time-series exhibit power-law noise which is weakly non-stationary. To overcome this problem, we present a Toeplitz covariance matrix that provides an approximation for power-law noise that is accurate for most GNSS time-series.Numerical results are given for a set of synthetic data and a set of International GNSS Service (IGS) stations, demonstrating a reduction in computation time of a factor of 10–100 compared to the standard MLE method, depending on the length of the time-series and the amount of missing data.     

Multipath interference mitigation in GNSS via WRELAX

In order to suppress the multipath interference in global navigation satellite system, two algorithms based on NLS (nonlinear least square) parameter estimation are proposed. Instead of the classic delay lock loop, the first proposed algorithm estimates the parameters of the line of sight signal and the multipath interference in the correlation domain. The NLS cost function is solved by WRELAX (weighted Fourier transform and RELAXation), which decouples the multidimensional optimization problem into a sequence of one-dimensional optimization problems in a conceptually and computationally simple way. In order to further reduce the complexity, the second NLS algorithm utilizing the characteristic of the C/A code is proposed, which estimate the parameters in the data domain. Finally, the two proposed algorithms are compared with the existing multipath interference methods and show excellent performance and less computational burden.     

Improvements on the particle-filter-based GLONASS phase inter-frequency bias estimation approach

The carrier phase inter-frequency bias (IFB) of GLONASS between receivers of different types is usually not zero. This bias must be estimated and removed in data processing so that the integer double difference (DD) ambiguities can be fixed successfully. Recently, the particle filter approach has been proposed to estimate the IFB rate in real time. In this approach, the IFB rate samples are first generated and used to correct the phase IFB in the GLONASS observations. Then, the weights of the rate samples are updated with a function related to RATIO which is for ambiguity acceptance testing in integer ambiguity resolution. Afterwards, the IFB rate is estimated according to the weighted particles. This approach can estimate IFB accurately with short convergence time and without prior information. However, when the system noise is set too low, the estimated results are unstable due to the serious problem of particle diversity-loss, even though the system model is accurate. Additionally, the computational burden is dependent on the number of particles, which has to be optimized for the computation at hand. Therefore, this study proposes two improvements for the IFB estimation in regard to the above two aspects. The first improvement is to solve the noise setting problem by employing a regularized particle filter (RPF). The second improvement optimizes the number of particles in the resampling step according to the standard deviation (STD) of the weighted particles via a controlling function. The two improvements result in significantly better performances. The regularization method allows for the system noise to be set as zero without disturbing the estimates, and consequently, more precise estimates can be achieved. In addition, the approach using the controlling function for adapting the number of particles has comparable performance in precision but the computation load is largely reduced.     

基于高频观测值的不同GNSS卫星钟稳定性分析

在GNSS高精度数据处理中,卫星钟差往往是决定结果精度的核心因素之一。采用20 Hz的双频观测数据对GNSS星载原子钟0.05~100 s平滑时间下的短期稳定性进行分析,通过星间单差的方法消除接收机钟差,采用无电离层组合及夜间观测避免电离层高阶项短期变化的影响,同时采用经验模型和映射函数来进行对流层延迟改正。通过Lag 1自相关函数分析了影响GNSS卫星钟稳定性的主要噪声类型,并使用阿伦方差计算分析GPS、GLONASS及BDS各自系统内不同卫星组合之间的钟差。结果表明,GPS、GLONASS及BDS系统钟差稳定性0.05秒稳均可达到10-10量级,秒稳可达10-11量级。可以认定,GPS、GLONASS及BDS在短期内的稳定性量级相当,从而验证了基于星间单差的BDS掩星数据处理方案的可行性。     

基于相关分析的粗差可区分性

提出了应用偏相关系数来区分多维粗差和用复相关系数对多维粗差总体显著性进行检验并定位的方法。反复计算这些相关系数并进行检验,可以相对正确地进行多维相关观测的粗差定位。     

时空三维相位解缠算法改进研究

三维相位解缠是时序干涉合成孔径雷达（interferometric synthetic aperture radar,InSAR）技术的关键环节之一,解缠结果直接影响时序InSAR地面沉降监测的精度。针对地面沉降严重、地形坡度变化较大的区域,因相位欠采样引起的整周期解缠误差问题,提出了一种基于频域置信度的加权最小二乘相位解缠算法,并以此替代时空三维相位解缠中空间维以相位梯度为权重的加权最小二乘相位解缠算法。通过提高相位坡度变化估计的准确性,进而提高时空三维相位解缠的精度和稳定性。以北京地区地面沉降监测为例进行了验证,结果表明,与经典的时空三维相位解缠算法相比,改进算法得到的沉降监测结果精度更高,特别是对于坡度变化较大、失相干现象明显的沉降漏斗区,其沉降监测精度有明显改善。     

Estimating the noise in space-geodetic positioning: the case of DORIS

The noise spectrum in DORIS ground- station motion is investigated by means of the Allan variance method applied to the decomposition of the 3D signal into its principal components in the time domain. Sets of weekly position time-series from 1994 to 2005 derived by three IDS Analysis Centres (IGN-JPL, INASAN, and LEGOS-CLS) for 119 stations at 69 sites are considered. The observing satellites are SPOT-2, SPOT-3, SPOT-4, and SPOT-5, TOPEX/Poseidon, and ENVISAT. Annual and semi-annual perturbations, as well as the 117.3-day term associated with the TOPEX/Poseidon orbit, are found at most stations. Their amplitudes reach up to 19.3, 23.7, and 13.3 mm, respectively, for the three analysis centres (ACs). When corrected for these components and a linear drift, the time-series dominantly show white noise (WN) at the 10–45mm level the noise level is the highest in the East direction, probably in connection with the high orbit inclinations. The noise level is minimum for the high latitude stations, mostly and intensively observed by the SPOT satellites, and the determination of the noise type is unclear; longer observation spans would be needed to decide between interannual variations and flicker noise. The improvement in positioning due to the DORIS constellation extension from three to five satellites in 2002, and the network rejuvenation program initiated in 2000, results in a decrease of the noise level by a factor of 1.7 in a WN context, both before and after the changes. One example of the benefit of studying the signal in the time eigenspace domain is the detection of anomalously large WN in the East direction for station HBKB (Hartebeesthoek, Africa) that masks the above-mentioned improvement. Studying the projection on the local frame of the second and third time-eigenspace components, a noise excess is detected in the North direction for some of the ACs. Station stability derived from our time-series analysis confirms, in general, the expected performance based on the careful technical review of the station components (antenna, pillar, etc.). The respective merits of our noise qualification method, based on direct time-series analysis in the time-eigenspace domain without any a priori statistical model, in comparison with other methods, such as the selection of a mixed-noise model by maximum likelihood estimation, are discussed.