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1.
针对遥感反演土壤湿度空间相关的误差协方差难以估计的问题，提出了一种遥感反演数据误差空间协方差估算方法——3类数据集成分析误差协方差（triple collocation covariance，TC_Cov），将土壤湿度场的每个单元（像元）看作一个空间随机变量，用两个随机变量表示的土壤湿度值的时间序列作为样本进行空间协方差估计，由任何两个随机变量的协方差形成多个随机变量（随机场）的协方差矩阵。利用先进散射计（ad-vanced scatterometer，ASCAT）和热带降雨测量卫星（tropical rainfall measuring mission，TRMM）的遥感土壤湿度数据以及ERA-Interim土壤湿度再分析数据作为TC_Cov方法的输入数据，分别估算了ERA-Interim、AS-CAT和TRMM在澳大利亚Murrumbidgee流域的土壤湿度误差协方差矩阵，验证了估算方法的合理性和可行性。  相似文献   

2.
When combining satellite and terrestrial networks, covariance matrices are used which have been estimated from previous data. It can be shown that the least-squares estimator of the unknown parameters using such an estimated covariance matrix is not necessarily the best. There are a number of cases where a more efficient estimator can be obtained in a different way. The problem occurs frequently in geodesy, since in least-squares adjustment of correlated observations estimated covariance matrices are often used. If the general structure of the covariance matrix is known, results can often be improved by a method called covariance adjustment. The statistical model used in least-squares collocation leads to a type of covariance matrix which fits into this framework. It is shown in which way improvements can be made using a modified approach of principal component analysis. As a numerical example the combination of a satellite and a terrestrial network has been computed with varying assumptions on the covariance matrix. It is shown which types of matrices are critical and where the usual least-squares approach can be applied without hesitation. Finally, a simplified representation of covariances for spatial networks by means of a suitable covariance function is suggested. Paper presented at the International Symposium on Computational Methods in Geometrical Geodesy-Oxford, 2–8 September, 1973.  相似文献   

3.
以30个GPS基准站坐标序列为对象,提出分别采用赤池信息量准则（AIC）与贝叶斯信息准则（BIC）噪声模型估计准则判定GPS时间序列噪声特性,对比分析GPS时间序列噪声模型特性,探讨不同噪声模型对GPS站速度及其不确定度的影响. 结果表明GPS站坐标序列噪声模型主要表现为FN+WN、PL及FN+RW+WN噪声模型特性;FN+WN噪声模型对GPS站速度估计值的影响相对较小,但在U分量影响最为明显;此外,RW对站速度不确定度的影响不可忽略, 正确获取模型参数估计的实际不确定度及改正噪声分量对于合理应用GPS坐标时间序列数据具有重要的意义.   相似文献   

4.
《测量评论》2013,45(9):137-150
Abstract

The paper describes an algebraic method of forming linear equations, giving the coordinates of points in space in terms of the coordinates of their images on the photographic plates. The coefficients which enter into these linear equations form a matrix of the third order. When stereoscopic or similar methods are used for plotting detail, the elements of this matrix give in a convenient form and with the utmost obtainable accuracy the quantities required for setting the photographs in their correct relation to the map and to one another.

An easy and rapid graphical method of obtaining good approximations to all the solutions of the problem of resection in space is described. A method of refining the solutions is given. When the coordinates of the air station are known with fair accuracy an alternative procedure is described. In the absence of ground control suitable for finding the air station by resection a method of eliminating most of the uncertain quantities is obtained. The indeterminate quantities relate to strip photographs as a whole and not to individual photographs. A method of dealing with the coefficients for the complete strip is described.

In finding air stations by resection, point-coordinates in the photographs must be converted into directional coordinates. In other calculations this transformation is unnecessary.  相似文献   

5.
Noise in multivariate GPS position time-series   总被引：4，自引：2，他引：2  
A methodology is developed to analyze a multivariate linear model, which occurs in many geodetic and geophysical applications. Proper analysis of multivariate GPS coordinate time-series is considered to be an application. General, special, and more practical stochastic models are adopted to assess the noise characteristics of multivariate time-series. The least-squares variance component estimation (LS-VCE) is applied to estimate full covariance matrices among different series. For the special model, it is shown that the multivariate time-series can be estimated separately, and that the (cross) correlation between series propagates directly into the correlation between the corresponding parameters in the functional model. The time-series of five permanent GPS stations are used to show how the correlation between series propagates into the site velocities. The results subsequently conclude that the general model is close to the more practical model, for which an iterative algorithm is presented. The results also indicate that the correlation between series of different coordinate components per station is not significant. However, the spatial correlation between different stations for individual components is significant (a correlation of 0.9 over short baselines) both for white and for colored noise components.  相似文献   

6.
青岛大港验潮站的地壳沉降关系到该站平均海平面的绝对变化,因而也就关系到我国高程基准面的变化。本文利用青岛GNSS基准站约10年的观测数据对该站的地壳沉降变化进行分析。首先将青岛GNSS基准站纳入由50个国际IGS站和43个国内陆态网络基准站组成的全球网中,进行单日松弛解和单日约束解解算,获得该站坐标时间序列。然后对该站垂向坐标时间序列进行分析,利用粗差探测、偏差探测、趋势项分析、频谱分析等方法对粗差、偏差、趋势项和周期项进行探测、分析,并通过时间序列模型估计获得时间序列中的周期项振幅和偏差估值。分析表明青岛GNSS基准站垂直方向近一段时间未发现存在显著性的地壳沉降变化,但受到比较明显的周年和半周年周期变化影响。结合青岛大港验潮站验潮数据分析结果得出结论:青岛大港验潮站平均海平面的绝对上升速率是1.62mm/a。  相似文献   

7.
River water-level time series at fixed geographical locations, so-called virtual stations, have been computed from single altimeter crossings for many years. Their temporal resolution is limited by the repeat cycle of the individual altimetry missions. The combination of all altimetry measurements along a river enables computing a water-level time series with improved temporal and spatial resolutions. This study uses the geostatistical method of spatio-temporal ordinary kriging to link multi-mission altimetry data along the Mekong River. The required covariance models reflecting the water flow are estimated based on empirical covariance values between altimetry observations at various locations. In this study, two covariance models are developed and tested in the case of the Mekong River: a stationary and a non-stationary covariance model. The proposed approach predicts water-level time series at different locations along the Mekong River with a temporal resolution of 5 days. Validation is performed against in situ data from four gauging stations, yielding RMS differences between 0.82 and 1.29 m and squared correlation coefficients between 0.89 and 0.94. Both models produce comparable results when used for combining data from Envisat, Jason-1, and SARAL for the time period between 2002 and 2015. The quality of the predicted time series turns out to be robust against a possibly decreasing availability of altimetry mission data. This demonstrates that our method is able to close the data gap between the end of the Envisat and the launch of the SARAL mission with interpolated time series.  相似文献   

8.
Vertical velocities of 30 European permanent Global Positioning System (GPS) stations at or close to tide gauge sites are estimated from more than 3 years of continuous observations. The results of two different solution strategies are presented and compared. The first approach accumulates the daily free network normal equations, the second introduces all sets of daily ellipsoidal height estimates and their covariance matrix into a subsequent common least squares adjustment. In both solutions, mean station heights at a reference epoch, linear vertical velocities, height discontinuities and short period height offsets are estimated. The second approach solves in addition for periodic annual signals and for site-specific pressure loading coefficients. The vertical velocities range from +8 mm/year in the center of the Fennoscandian uplift area to –4 mm/year at a few subsiding locations. Apart from these extrema, most of the sites experience only very small vertical motions. The standard deviations from the second approach providing more realistic error estimates are well below 0.15 mm/year. Some specific data problems are discussed.  相似文献   

9.
The EUREF [International Association of Geodesy (IAG) Reference Frame Sub-Commission for Europe] network of continuously operating GPS stations (EPN) was primarily established for reference frame maintenance, and also plays an important role for geodynamical research in Europe. The main objective of this paper is to obtain an independent homogeneous time series of the EPN station coordinates, which is also available in SINEX format. A new combined solution of the EPN station coordinates was computed. The combination was performed independently for every week, in three steps: (1) the stated constraints on the coordinates were removed from the individual solutions of the Analysis Centers; (2) the de-constrained solutions were aligned to ITRF2000; (3) the resulting solutions were combined using the Helmert blocking technique. All the data from GPS weeks 900 to 1302 (April 1997–December 2004) were used. We investigated in detail the behavior of the transformation parameters aligning the new combined solution to ITRF2000. In general, the time series of the transformation parameters show a good stability in time although small systematic effects can be seen, most likely caused by station instabilities. A comparison of the new combined solution to the official EUREF weekly combined solution is also presented.  相似文献   

10.
为了研究我国目前建立的连续运行参考网络（CORS）GNSS基准站的坐标时间序列噪声特征是否与国际领域研究的成果相符合,对江苏CORS网连续3年24个分布均匀的GNSS基准站的数据进行处理,利用GAMIT软件获取了各基准站的坐标时间序列,并利用CATS软件采用最大似然估计法对坐标时间序列的噪声特征进行了分析,结果表明：GNSS基准站坐标时间序列不仅包含白噪声,还包含有色噪声;GNSS基准站坐标时间序列在N、E、U方向的噪声类型并不完全一致,其中N、E方向的最佳噪声模型为“WH＋FN＋RWN”,U方向的最佳噪声模型为“WH＋FN”.  相似文献   

11.
长期累积的全球卫星导航系统（Global Navigation Satellite System,GNSS）基准站坐标时间序列为大地测量学及地球动力学研究提供了基础数据。通过完善GNSS数据处理模型及策略,研究造成非线性运动的机制并进行有效建模,可以获得测站准确的位置和速度,不仅有助于合理解释板块构造运动,建立和维持动态地球参考框架,而且能更好地研究冰后回弹及海平面变化,反演冰雪质量变迁等地球动力学过程。首先从基准站坐标的精确获取、时间序列模型构建、时间序列信号分析等方面描述了GNSS坐标时间序列分析的理论与处理方法;其次,探讨了坐标时间序列噪声模型构建技术,给出了严密三维噪声模型构建方法;然后,疏理了坐标时间序列中非线性变化成因机制的研究进展;最后,总结了基于GNSS坐标时间序列的应用领域,并展望了其未来的发展方向。  相似文献   

12.
A new method through Gauss–Helmert model of adjustment is presented for the solution of the similarity transformations, either 3D or 2D, in the frame of errors-in-variables (EIV) model. EIV model assumes that all the variables in the mathematical model are contaminated by random errors. Total least squares estimation technique may be used to solve the EIV model. Accounting for the heteroscedastic uncertainty both in the target and the source coordinates, that is the more common and general case in practice, leads to a more realistic estimation of the transformation parameters. The presented algorithm can handle the heteroscedastic transformation problems, i.e., positions of the both target and the source points may have full covariance matrices. Therefore, there is no limitation such as the isotropic or the homogenous accuracy for the reference point coordinates. The developed algorithm takes the advantage of the quaternion definition which uniquely represents a 3D rotation matrix. The transformation parameters: scale, translations, and the quaternion (so that the rotation matrix) along with their covariances, are iteratively estimated with rapid convergence. Moreover, prior least squares (LS) estimation of the unknown transformation parameters is not required to start the iterations. We also show that the developed method can also be used to estimate the 2D similarity transformation parameters by simply treating the problem as a 3D transformation problem with zero (0) values assigned for the z-components of both target and source points. The efficiency of the new algorithm is presented with the numerical examples and comparisons with the results of the previous studies which use the same data set. Simulation experiments for the evaluation and comparison of the proposed and the conventional weighted LS (WLS) method is also presented.  相似文献   

13.
Stochastic significance of peaks in the least-squares spectrum   总被引：3，自引：1，他引：2  
The least-squares spectral analysis method is reviewed, with emphasis on its remarkable property to accept time series with an associated, fully populated covariance matrix. Two distinct cases for the input covariance matrix are examined: (a) it is known absolutely (a-priori variance factor known); and (b) it is known up to a scale factor (a-priori variance factor unknown), thus the estimated covariance matrix is used. For each case, the probability density function that underlines the least-squares spectrum is derived and criteria for the statistical significance of the least-squares spectral peaks are formulated. It is shown that for short series (up to about 150 values) with an estimated covariance matrix (case b), the spectral peaks must be stronger to be statistically significant than in the case of a known covariance matrix (case a): the shorter the series and the lower the significance level, the higher the difference becomes. For long series (more than about 150 values), case (b) converges to case (a) and the least-squares spectrum follows the beta distribution. The results of this investigation are formulated in two new theorems. Received: 27 May 1997/Accepted: 30 September 1998  相似文献   

14.
A proper perturbation theory of a mathematical model and the quantities derived by means of least-squares adjustments is indispensable if the results have to be interpreted in a wider context. The sensitivity of some characteristic results of least-squares adjustments such as the estimated values of the parameters and their variance–covariance matrix due to imminent uncertainties of the stochastic model is discussed in detail. Linearizations are used with rigorous error measures and interval mathematics. Numerical examples conclude the investigations. Received: 27 December 1997 / Accepted: 19 April 1999  相似文献   

15.
Most time series of geophysical phenomena have temporally correlated errors. From these measurements, various parameters are estimated. For instance, from geodetic measurements of positions, the rates and changes in rates are often estimated and are used to model tectonic processes. Along with the estimates of the size of the parameters, the error in these parameters needs to be assessed. If temporal correlations are not taken into account, or each observation is assumed to be independent, it is likely that any estimate of the error of these parameters will be too low and the estimated value of the parameter will be biased. Inclusion of better estimates of uncertainties is limited by several factors, including selection of the correct model for the background noise and the computational requirements to estimate the parameters of the selected noise model for cases where there are numerous observations. Here, I address the second problem of computational efficiency using maximum likelihood estimates (MLE). Most geophysical time series have background noise processes that can be represented as a combination of white and power-law noise, \(1/f^{\alpha }\) with frequency, f. With missing data, standard spectral techniques involving FFTs are not appropriate. Instead, time domain techniques involving construction and inversion of large data covariance matrices are employed. Bos et al. (J Geod, 2013. doi: 10.1007/s00190-012-0605-0) demonstrate one technique that substantially increases the efficiency of the MLE methods, yet is only an approximate solution for power-law indices >1.0 since they require the data covariance matrix to be Toeplitz. That restriction can be removed by simply forming a data filter that adds noise processes rather than combining them in quadrature. Consequently, the inversion of the data covariance matrix is simplified yet provides robust results for a wider range of power-law indices.  相似文献   

16.
Least squares adjustment processes occasionally utilize constants with a known degree of uncertainty. If the covariance matrix of the adjusted parameters is estimated without considering those uncertainties the resulting estimate is invariably too optimistic. A method is proposed by which without altering the values of the adjusted parameters their a posteriori (after the adjustment) covariance matrix can be improved by the inclusion of the effect of uncertainties in the constants.  相似文献   

17.
As one of the major contributors to the realisation of the International Terrestrial Reference System (ITRS), the Global Navigation Satellite Systems (GNSS) are prone to suffer from irregularities and discontinuities in time series. While often associated with hardware/software changes and the influence of the local environment, these discrepancies constitute a major threat for ITRS realisations. Co-located GNSS at fundamental sites, with two or more available instruments, provide the opportunity to mitigate their influence while improving the accuracy of estimated positions by examining data breaks, local biases, deformations, time-dependent variations and the comparison of GNSS baselines with existing local tie measurements. With the use of co-located GNSS data from a subset sites of the International GNSS Service network, this paper discusses a global multi-year analysis with the aim of delivering homogeneous time series of coordinates to analyse system-specific error sources in the local baselines. Results based on the comparison of different GNSS-based solutions with the local survey ties show discrepancies of up to 10 mm despite GNSS coordinate repeatabilities at the sub-mm level. The discrepancies are especially large for the solutions using the ionosphere-free linear combination and estimating tropospheric zenith delays, thus corresponding to the processing strategy used for global solutions. Snow on the antennas causes further problems and seasonal variations of the station coordinates. These demonstrate the need for a permanent high-quality monitoring of the effects present in the short GNSS baselines at fundamental sites.  相似文献   

18.
With the advances in the field of GPS positioning and the global densification of permanent GPS tracking stations, it is now possible to determine at the highest level of accuracy the transformation parameters connecting various international terrestrial reference frame (ITRF) realizations. As a by-product of these refinements, not only the seven usual parameters of the similarity transformations between frames are available, but also their rates, all given at some epoch t k . This paper introduces rigorous matrix equations to estimate variance–covariance matrices for transformed coordinates at any epoch t based on a stochastic model that takes into consideration all a priori information of the parameters involved at epoch t k , and the coordinates and velocities at the reference frame initial epoch t 0. The results of this investigation suggest that in order to attain maximum accuracy, the agencies determining the 14-parameter transformations between reference frames should also publish their full variance–covariance matrix. Electronic Publication  相似文献   

19.
针对北京市CORS站的稳定性问题,该文利用GAMIT/GLOBK软件对北京市13个CORS站2016—2018年的观测数据进行了处理,获取了原始坐标时间序列和坐标残差时间序列,通过极大似然估计的方法对CORS基准站进行了噪声模型分析和区域速度场估计。结果表明,北京市CORS站坐标时间序列的最佳噪声模型为WN+FN+RWN组合模型;采用NEU方向的最佳噪声组合模型对北京市CORS站进行区域速度场估计,BJTZ、CHAO、DSQI、XNJC站的沉降较为严重,其他CORS站N方向速度估值在7.2~14.3 mm/a,E方向速度估值在27.5~32.5 mm/a,U方向速度估值在2.0~8.5 mm/a。  相似文献   

20.
By considering a deformable geodetic network, deforming in a linear-in-time mode, according to a coordinate-invariant model, it becomes possible to get an insight into the rank deficiency of the stacking procedure, which is the standard method for estimating initial station coordinates and constant velocities, from coordinate time series. Comparing any two out of the infinitely many least squares estimates of stacking unknowns (initial station coordinates, velocity components and transformation parameters for the reference system in each data epoch), it is proven that the two solutions differ only by a linear-in-time trend in the transformation parameters. These pass over to the initial coordinates (the constant term) and to the velocity estimates (the time coefficient part). While the difference in initial coordinates is equivalent to a change of the reference system at the initial epoch, the differences in velocity components do not comply with those predicted by the same change of reference system for all epochs. Consequently, the different velocity component estimates, obtained by introducing different sets of minimal constraints, correspond to physically different station velocities, which are therefore non-estimable quantities. The theoretical findings are numerically verified for a global, a regional and a local network, by obtaining solutions based on four different types of minimal constraints, three usual algebraic ones (inner or partial inner) and the lately introduced kinematic constraints. Finally, by resorting to the basic ideas of Felix Tisserand, it is explained why the station velocities are non-estimable quantities in a very natural way. The problem of the optimal choice of minimal constraints and, hence, of the corresponding spatio-temporal reference system is shortly discussed.  相似文献   

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