Prediction of UT1–UTC,LOD and AAM χ<Subscript>3</Subscript> by combination of least-squares and multivariate stochastic methods

This article presents the application of a multivariate prediction technique for predicting universal time (UT1–UTC), length of day (LOD) and the axial component of atmospheric angular momentum (AAM χ ₃). The multivariate predictions of LOD and UT1–UTC are generated by means of the combination of (1) least-squares (LS) extrapolation of models for annual, semiannual, 18.6-year, 9.3-year oscillations and for the linear trend, and (2) multivariate autoregressive (MAR) stochastic prediction of LS residuals (LS + MAR). The MAR technique enables the use of the AAM χ ₃ time-series as the explanatory variable for the computation of LOD or UT1–UTC predictions. In order to evaluate the performance of this approach, two other prediction schemes are also applied: (1) LS extrapolation, (2) combination of LS extrapolation and univariate autoregressive (AR) prediction of LS residuals (LS + AR). The multivariate predictions of AAM χ ₃ data, however, are computed as a combination of the extrapolation of the LS model for annual and semiannual oscillations and the LS + MAR. The AAM χ ₃ predictions are also compared with LS extrapolation and LS + AR prediction. It is shown that the predictions of LOD and UT1–UTC based on LS + MAR taking into account the axial component of AAM are more accurate than the predictions of LOD and UT1–UTC based on LS extrapolation or on LS + AR. In particular, the UT1–UTC predictions based on LS + MAR during El Niño/La Niña events exhibit considerably smaller prediction errors than those calculated by means of LS or LS + AR. The AAM χ ₃ time-series is predicted using LS + MAR with higher accuracy than applying LS extrapolation itself in the case of medium-term predictions (up to 100 days in the future). However, the predictions of AAM χ ₃ reveal the best accuracy for LS + AR.     

Improving the modeling of the atmospheric delay in the data analysis of the Intensive VLBI sessions and the impact on the UT1 estimates

The very long baseline interferometry (VLBI) Intensive sessions are typically 1-h and single-baseline VLBI sessions, specifically designed to yield low-latency estimates of UT1-UTC. In this work, we investigate what accuracy is obtained from these sessions and how it can be improved. In particular, we study the modeling of the troposphere in the data analysis. The impact of including external information on the zenith wet delays (ZWD) and tropospheric gradients from GPS or numerical weather prediction models is studied. Additionally, we test estimating tropospheric gradients in the data analysis, which is normally not done. To evaluate the results, we compared the UT1-UTC values from the Intensives to those from simultaneous 24-h VLBI session. Furthermore, we calculated length of day (LOD) estimates using the UT1-UTC values from consecutive Intensives and compared these to the LOD estimated by GPS. We find that there is not much benefit in using external ZWD; however, including external information on the gradients improves the agreement with the reference data. If gradients are estimated in the data analysis, and appropriate constraints are applied, the WRMS difference w.r.t. UT1-UTC from 24-h sessions is reduced by 5% and the WRMS difference w.r.t. the LOD from GPS by up to 12%. The best agreement between Intensives and the reference time series is obtained when using both external gradients from GPS and additionally estimating gradients in the data analysis.     

Prediction of Earth orientation parameters by artificial neural networks

 Earth orientation parameters (EOPs) [polar motion and length of day (LOD), or UT1–UTC] were predicted by artificial neural networks. EOP series from various sources, e.g. the C04 series from the International Earth Rotation Service and the re-analysis optical astrometry series based on the HIPPARCOS frame, served for training the neural network for both short-term and long-term predictions. At first, all effects which can be described by functional models, e.g. effects of the solid Earth tides and the ocean tides or seasonal atmospheric variations of the EOPs, were removed. Only the differences between the modeled and the observed EOPs, i.e. the quasi-periodic and irregular variations, were used for training and prediction. The Stuttgart neural network simulator, which is a very powerful software tool developed at the University of Stuttgart, was applied to construct and to validate different types of neural networks in order to find the optimal topology of the net, the most economical learning algorithm and the best procedure to feed the net with data patterns. The results of the prediction were analyzed and compared with those obtained by other methods. The accuracy of the prediction is equal to or even better than that by other prediction methods. Received: 6 February 2001 / Accepted: 23 October 2001     

基于噪声估计的卡尔曼滤波用于GPS卫星钟差预报研究

利用重叠哈达玛方差确定卫星钟噪声随机模型,采用顾及钟差随机噪声模型的卡尔曼滤波进行钟差预报分析,并与最小二乘预报算法相比较,得出以下结论:卡尔曼滤波进行1 d以内的短期预报时,精度达到亚纳秒级,优于最小二乘预报算法,在长期预报或拟合数据量较少时,最小二乘预报精度优于卡尔曼滤波。     

时空Kalman滤波在变形分析中的应用研究

时空Kalman滤波可对变形监测数据进行时空滤波去噪、数据插补和变形预测,本文利用时空Kalman滤波进行变形分析,从模型原理及试验两方面比较分析了Kriged Kalman filter(KKF)、space time Kalman filter(STKF)和spatio-temporal mixed effects(STME) 3种典型时空Kalman滤波模型的性能和适用性。结果表明:3种时空Kalman滤波模型均基于空间基函数及动力学模型组合形式描述时空数据的时空相关性,其主要差异在于空间变异的描述形式不同、空间基函数和状态转移矩阵构造过程不同及模型降维方法不同。在适用性方面,KKF模型更适合于稀疏测站的变形分析,STKF模型及STME模型更适合于海量测站的变形分析。在变形分析应用效果方面,3种时空Kalman滤波模型均具有较高精度的时空滤波去噪、数据插补和变形预测性能,其滤波结果相对于普通Kalman滤波结果的平均改善率为21.1%,其缺失数据插补结果相对于Hermite时间插值结果的平均改善率为42.4%,其空间预测结果相对于Kriging空间插值结果的平均改善率为65.3%,其对已知测站未来变形的时空预测结果相对于普通Kalman滤波时间预测结果的平均改善率为20.6%,其对非观测站点未来变形的时空预测结果相对于Kalman滤波+Kriging组合模型预测结果的平均改善率为20.5%。     

A new ΔLOD series in monthly intervals (1892.0–1997.0) and its comparison with other geophysical results

Using the ΔT (integrated variation of the Earth's rotation measured in terestrial time) series (1891.5–1955.5) derived from lunar occultation observations and the UT1–UTC (universal time–coordinated universal time) series (1955.5–1997.5) of the Bureau International de L'Heure/International Earth Rotation Service, a new ΔLOD (variation of the length of day) series in monthly intervals from 1892.0 to 1997.0 is calculated. Using digital filtering, the interannual and decadal components of the ΔLOD series are separated and then compared with those inferred from other geophysical quantities. It is shown that, on the interannual time scale, atmospheric processes can play an important role in exciting astronomical ΔLOD. However, the main oscillation with a mean period of about 5.8 years and peak-to-peak amplitude of about 0.3 ms in the residuals of ΔLOD(Astr) −ΔLOD(Wind) for 1968.0–1997.0 suggests that about half of the amplitude in astronomical ΔLOD must be excited by other geophysical processes, while on the decadal time scale the atmospheric excitation is too small. Geomagnetic core–mantle coupling may be a plausible source of the excitation of ΔLOD on the decadal time scale, but the geomagnetic data are still insufficient and an improved model of core–mantle coupling is required. Received: 3 April 1998 / Accepted: 31 May 1999     

Use of atmospheric angular momentum forecasts for UT1 predictions: analyses over CONT08

Real-time orbit determination and interplanetary navigation require accurate predictions of the orientation of the Earth in the celestial reference frame and in particular that for Universal Time UT1. Much of the UT1 variations over periods ranging from hours to a couple of years are due to the global atmospheric circulation. Therefore, the axial atmospheric angular momentum (AAM) forecast series may be used as a proxy index to predict UT1. Our approach taking advantage of this fact is based on an adaptive procedure. It involves incorporating integrations of AAM estimates into UT1 series. The procedure runs on a routine basis using AAM forecasts that are based on the two meteorological series, from the US National Centers for Environmental Prediction and the Japan Meteorological Agency. It is pertinent to test the prediction method for the period that includes the special CONT08 campaign over which we expect a significant improvement in UT1 accuracy. The studies we carried out were aimed both to compare atmospheric forecasts and analyses, as well as to compare the skills of the UT1 forecasts based on the method with atmospheric forecasts and that using current statistical processes, as applied to the C04 Earth orientation parameters series derived by the International Earth rotation and Reference Systems service (IERS). Here we neglect the oceanic sub-diurnal and diurnal variations, as these signals are expected to be smaller than the UT1-equivalent of 100 μs, when averaged over a few days. The prediction performances for a 2-day forecast are similar, but at a forecast horizon of a week, the AAM-based forecast is roughly twice as skillful as the statistically based one.     

基于时间序列模型的沉降监测预报分析

时间序列模型预测具有可靠性与高效性的特点。本文结合沉降监测工程,采用Matlab进行建模预报分析,分别基于预测模型(AR、MA、ARMA)进行应用。对比自回归模型、滑动平均模型及自回归滑动平均模型预测结果的精度,表明3种模型可预测期连续分布,模型组合可提高预测精度。     

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EMD-NAR神经网络的大坝变形预测

为了使大坝变形的预测精度更高,针对大坝形变量的时间序列中存在着非平稳和非线性等曲线特性,使用一种经验模态分解(EMD)和非线性自回归动态神经网络(NAR)相结合的EMD-NAR模型对大坝形变时间序列进行预测。以某大坝实测的时间序列数据为算例,分别使用BP模型、NAR模型和EMD-NAR模型进行实验对比,结果表明,BP、NAR、EMD-NAR模型预测的均方根误差(RMSE)分别为0.9449,0.6993,0.4678;模型预测的平均相对误差(MRE)分别为0.1492,0.1065和0.0688,从三种模型预测结果对比可知,组合的EMD-NAR模型预测精度最高且稳定性最好,为时间序列的大坝形变预测提供一种新的参考思路。     

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。     

多尺度ARMA残差修正模型震前电离层TEC异常探测

为提高电离层总电子含量（total electronic content,TEC）扰动探测参考背景值的预测精度,提出了多尺度自回归移动平均（autoregressive moving average,ARMA）残差修正模型。通过对比该方法、ARMA模型、四分位距法（inter quartile range,IQR）及滑动时窗法对TEC背景值的预测精度,结果显示修正模型预测的TEC背景值平均相对精度为89.78%,分别比ARMA模型、IQR及滑动时窗法高5.18%、1.41%和1.42%,且预测值的残差绝对值小于等于3.0 TECU的百分比为91.67%,明显优于其他3种方法,说明修正模型探测震前TEC异常是可行的。利用该方法探测2013-04-20芦山县Mw7.0级地震震前电离层TEC扰动情况,验证了该方法的有效性。实验结果表明,震前第9天和第13天电离层明显的正异常和震前第1~4天明显的负异常极可能是孕育地震引起的,且正异常主要出现在08:00-10:00 UT,而负异常主要集中在0:00-14:00 UT。     

矿山开采变形观测的动态数据处理

根据随机介质理论可以导出开采引起的地表动态变形表达式。本文利用该式建立了适合动态数据处理的两种滤波模型,并把变形表达式中各参数扩充为滤波模型中的状态向量同时进行估计。两种模型的动态预报精度均高于传统方法,其中自适应模型更能明显改善预报精度。     

有色噪声情况下状态预测值修正的Kalman滤波

利用线性最小方差估计方法,以正交投影理论为工具,推导了动态线性系统在状态噪声为有色噪声情形下的状态预测值及其相应的协方差阵。在形式上,此预测值比经典Kalman滤波预测值多出一项,该项包含了前一时刻的新息。对新预测值进行分析,得出了有色状态噪声条件下Kalman滤波的新算法,扩展了经典Kalman滤波的应用范围。最后通过一个模拟算例,证明了该算法的有效性。     

GPS动态定位模型的研究

讨论当前三种动态数据处理模型(最小二乘法、卡尔曼滤波法及H∞滤波法)的特性,分析比较这三种模型各自的优点,并通过实测数据和相关软件来对这三种模型各自的应用前提、范围和应用效果进行试验。实验结果表明:当载体处于匀速状态时,这三种模型的精度相当;当载体处于机动加速度时,H∞滤波精度最好,最小二乘次之,卡尔曼滤波最差。     

BLUE, BLUP and the Kalman filter: some new results

In this contribution, we extend ‘Kalman-filter’ theory by introducing a new BLUE–BLUP recursion of the partitioned measurement and dynamic models. Instead of working with known state-vector means, we relax the model and assume these means to be unknown. The recursive BLUP is derived from first principles, in which a prominent role is played by the model’s misclosures. As a consequence of the mean state-vector relaxing assumption, the recursion does away with the usual need of having to specify the initial state-vector variance matrix. Next to the recursive BLUP, we introduce, for the same model, the recursive BLUE. This extension is another consequence of assuming the state-vector means unknown. In the standard Kalman filter set-up with known state-vector means, such difference between estimation and prediction does not occur. It is shown how the two intertwined recursions can be combined into one general BLUE–BLUP recursion, the outputs of which produce for every epoch, in parallel, the BLUP for the random state-vector and the BLUE for the mean of the state-vector.     

K-GM（1，1）模型在岩体变形监测中的应用

传统GM （1,1）模型存在着长期预测效果差、模型精度不高等问题,卡尔曼滤波能够排除建模过程中随机干扰因素,滤波值能够反映更真实的数据情况。为了能更好地提高变形监测的预测精度,基于传统GM （1,1）模型和卡尔曼滤波,提出K‐GM （1,1）模型,利用该模型对岩体变形监测数据进行建模预测,并与传统GM （1,1）模型预测结果进行对比分析,结果表明,K‐GM （1,1）模型具有较高的预测精度,可作为变形监测的一种新方法。     

混合模型在沉降监测中的组合预测方法

对建筑物沉降数据进行建模预测,以便掌握其变形规律并预测变形趋势,保障建筑物的安全。单一预测模型有自己的适用情形,也存在各自的缺点,已经不能满足当前的精度要求。选取灰色GM(1,1)和自回归两种常用的预测模型,通过两种不同的方式进行组合预测,并结合南京市地铁一号线百家湖段沉降监测数据进行计算分析,结果表明两种组合方法与单一预测模型相比精度均有所提高。     

VGOS超宽带观测的首次UT1测量数据处理及分析

在国际甚长基线干涉测量（very long baseline interferometry, VLBI）大地测量与天体测量服务组织协调下,首次利用隶属于VLBI全球观测系统（VLBI global observing system, VGOS）的美国Kokee和德国Wettzell观测站及并置的传统VLBI观测站开展了世界时（universal time, UT1）联合测量试验,观测数据在上海VLBI中心进行了干涉处理。结果表明,VGOS超宽带观测系统的UT1测量精度约为7 μs,并置基线的传统S/X双频系统测量精度约为14 μs,VGOS系统的UT1解算结果优于S/X系统。通过试验建立了从相关处理、相关后处理到UT1参数解算的完整数据处理流程,验证了上海VLBI相关处理机的VGOS数据处理能力,为承担国内和国际VGOS观测数据的相关处理任务奠定了基础。     

北斗三号卫星钟差短期预报与稳定性分析

针对北斗三号(BDS-3)卫星钟短期预报问题,在分析卫星原子钟频率稳定性的基础上,选用时间序列模型(ARIMA)、灰色模型(GM)、一次多项式(LP)以及二次多项式(QP)四种钟差预报模型对30天的数据进行拟合预报分析. 实验结果表明:1) 相对于北斗二号(BDS-2),BDS-3原子钟具有更高的稳定性. 其中BDS-3氢钟的千秒稳定性、万秒稳定性和日稳定性分别达到了4.2×10?14、1.89×10?14、4.14×10?15;2) BDS-3氢钟和BDS-3新型铷钟的预报稳定性和精度相对于BDS-2铷钟有明显提高,并且BDS-3氢钟在3 h、6 h和12 h下的预报精度分别达到了0.12 ns、0.18 ns和0.30 ns;3) 在四种模型中,时间序列模型的预报精度最高,在3 h、6 h和12 h下精度分别为0.26 ns、0.47 ns和0.96 ns.