Boundary-value problems in the complex world of geodetic measurements

A review of recent progress and current activities towards an improved formulation and solution of geodetic boundary value problems is given. Improvements stimulated and required by the dramatic changes of the real world of geodetic measurements are focused upon. Altimetry–gravimetry problems taking into account various scenarios of non-homogeneous data coverage are discussed in detail. Other problems are related to free geodetic datum parameters, most of all the vertical datum, overdetermination or additional constraints imposed by satellite geodetic observations or models. Some brief remarks are made on pseudo-boundary value problems for geoid determination and on purely gravitational boundary-value problems. Received: 17 March 1999 / Accepted: 19 April 1999     

Numerical simulation of troposphere-induced errors in GPS-derived geodetic time series over Japan

Troposphere-induced errors in GPS-derived geodetic time series, namely, height and zenith total delays (ZTDs), over Japan are quantitatively evaluated through the analyses of simulated GPS data using realistic cumulative tropospheric delays and observed GPS data. The numerical simulations show that the use of a priori zenith hydrostatic delays (ZHDs) derived from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather model data and gridded Vienna mapping function 1 (gridded VMF1) results in smaller spurious annual height errors and height repeatabilities (0.45 and 2.55 mm on average, respectively) as compared to those derived from the global pressure and temperature (GPT) model and global mapping function (GMF) (1.08 and 3.22 mm on average, respectively). On the other hand, the use of a priori ZHDs derived from the GPT and GMF would be sufficient for applications involving ZTDs, given the current discrepancies between GPS-derived ZTDs and those derived from numerical weather models. The numerical simulations reveal that the use of mapping functions constructed with fine-scale numerical weather models will potentially improve height repeatabilities as compared to the gridded VMF1 (2.09 mm against 2.55 mm on average). However, they do not presently outperform the gridded VMF1 with the observed GPS data (6.52 mm against 6.50 mm on average). Finally, the commonly observed colored components in GPS-derived height time series are not primarily the result of troposphere-induced errors, since they become white in numerical simulations with the proper choice of a priori ZHDs and mapping functions.     

Consistent estimation of geodetic parameters from SLR satellite constellation measurements

In this paper, we consistently estimate geodetic parameters such as weekly 3-D station coordinates, Earth orientation parameters (EOP) including daily x/y-pole coordinates and the excess length of day \(\Delta \hbox {LOD}\), and selected weekly Earth’s gravitational field (Stokes) coefficients up to degree and order 6 from Satellite Laser Ranging measurements to up to 11 geodetic satellites. The SLR constellation consists of LAGEOS-1/2, Etalon-1/2, Stella, Starlette, Ajisai, Larets, LARES, BLITS and WESTPAC, and its observations cover a time span of 38 years ranging from February 16, 1979, to April 30, 2017. If multiple satellites with various altitudes and orbit inclinations are combined, correlations between estimated parameters are significantly reduced. This allows us (i) to investigate the ability of satellite constellations to reduce existing correlations and (ii) to estimate reliable parameters with higher precision compared to the standard 4-satellite constellation (LAGEOS-1/2, Etalon-1/2) which is currently used by the International Laser Ranging Service for the determination of the Terrestrial Reference Frame (TRF) and EOP products. In particular, the Stokes coefficients, EOP and TRF datum parameters (three translations, three rotations, one scale factor), which are highly correlated with satellite-specific orbit parameters, are improved. From our investigations, we found for an 11-satellite solution compared to the above-mentioned 4-satellite solution a decrease in the scatter of the TRF datum parameters of up to 37%, the transformation residuals are decreased by up to 22%, the scatter of the EOP is decreased by up to 22%, and their mean values are decreased by up to 84% w.r.t. the reference solutions. The largest improvement is obtained for the Stokes coefficients which significantly benefit from a combination of multiple satellites (inclinations and orbit altitudes). In total, single coefficients are improved by up to 93% and the overall improvement is up to 74%. Moreover, it could be clearly identified that Ajisai significantly disturbs the TRF solution due to an erroneous center-of-mass correction. We further quantify the impact of specific satellites on the determination of different geodetic parameters and finally evaluate the potential of the existing SLR-tracked spherical satellite constellation to support the goals of GGOS.     

The impact of radio source structure on European geodetic VLBI measurements

European geodetic very long baseline interferometry (VLBI) sessions (also known as EUROPE sessions) have been carried out on a regular basis for the past 15 years to study relative crustal motions within Europe. These sessions are based on observations of extragalactic radio sources, which serve as distant fiducial marks to establish an accurate and stable celestial reference frame for long-term geodetic measurements. The radio sources, however, are not always point-like on milliarcsecond scales, as VLBI imaging has revealed. In this work, we quantify the magnitude of the expected effect of intrinsic source structure on geodetic bandwidth synthesis delay VLBI measurements for a subset of 14 sources regularly observed during the EUROPE sessions. These sources have been imaged at both X-band (8.4 GHz) and S-band (2.3 GHz) based on dedicated observations acquired with the European VLBI Network (EVN) in November 1996. The results of this calculation indicate that the reference source 0457+024 causes significant structural effects in measurements obtained on European VLBI baselines (about 10 picoseconds on average), whereas most of the other sources produce effects that are only occasionally larger than a few picoseconds. Applying the derived source structure models to the data of the EUROPE5-96 session carried out at the same epoch as the EVN experiment shows no noticeable changes in the estimated VLBI station locations.     

Stochastic estimation of tropospheric path delays in global positioning system geodetic measurements

Water vapor radiometric (WVR) and surface meteorological (SM) measurements taken during three Global Positioning System (GPS) geodetic experiments are used to calculate process noise levels for random walk and first-order Gauss-Markov temporal models of tropospheric path delays. Entire wet and combined wet and dry zenith delays at each network site then are estimated simultaneously with the geodetic parameters without prior calibration. The path delays and corresponding baseline estimates are compared to those obtained with calibrated data and stochastic residual delays. In this manner, the marginal utility of a priori tropospheric calibration is assessed given the ability to estimate the path delays directly using only theGPS data. Estimation of total zenith path delays with appropriate random walk or Gauss-Markov models yields baseline repeatabilities of a few parts in 10⁸. This level of geodetic precision, and accuracy as suggested by analyses on collocated baselines estimated independently by very long baseline interferometry, is comparable to or better than that obtained after path delay calibration usingWVR and/orSM measurements. Results suggest thatGPS data alone have sufficient strength to resolve centimeter-level zenith path delay fluctuations over periods of a few minutes.     

低精度光纤陀螺随机误差的辨识与仿真

陀螺随机漂移是影响惯性导航和组合导航精度的重要因素。为了有效辨识出光纤陀螺随机漂移噪声的参数,采用了自相关函数、功率谱密度和Allan方差对实测陀螺数据进行分析。实验结果表明:自相关函数、功率谱密度和Allan方差都能有效辨识出陀螺输出信号中的角度随机游走噪声,只有Allan方差能辨识出其中的角速率随机游走噪声。Allan方差可以为光纤陀螺随机漂移建模提供参考。     

随机误差对七参数转换模型的影响分析

针对在七参数坐标转换过程中,控制点本身含有的各种误差会对坐标转换的结果产生影响的问题,该文探讨了随机误差对七参数转换模型的影响:以七参数坐标转换模型为研究对象,模拟不同尺度范围的空间直角坐标,给定七参数数值求解另一组空间直角坐标,然后加入不同幅度的随机误差,利用最小二乘准则求解参数,从数值角度分析随机误差对七参数数值以及坐标转换结果的影响。实验结果显示,大范围的七参数模型解算的稳定性优于小范围的模型解算,以及X、Y、Z方向某一方向上的误差对另两个方向的解算结果影响较小。     

Accuracy of geodetic solutions based on Doppler measurements of the Navstar global positioning system satellites

A dual frequency Doppler receiver is being developed by the Naval Surface Weapons Center for possible use by the Defense Mapping Agency in determining the position of ground sites based on observations of NAVSTAR Global Positioning satellites. Preliminary analysis indicates that the relative position of widely separated sites can be computed to better than 40 cm accuracy at eight hour intervals. A number of possibilities are being explored to improve the accuracy to the sub-decimeter level.     

M-estimation with probabilistic models of geodetic observations

The paper concerns \(M\) -estimation with probabilistic models of geodetic observations that is called \(M_{\mathcal {P}}\) estimation. The special attention is paid to \(M_{\mathcal {P}}\) estimation that includes the asymmetry and the excess kurtosis, which are basic anomalies of empiric distributions of errors of geodetic or astrometric observations (in comparison to the Gaussian errors). It is assumed that the influence function of \(M_{\mathcal {P}}\) estimation is equal to the differential equation that defines the system of the Pearson distributions. The central moments \(\mu _{k},\, k=2,3,4\) , are the parameters of that system and thus, they are also the parameters of the chosen influence function. The \(M_{\mathcal {P}}\) estimation that includes the Pearson type IV and VII distributions ( \(M_{\mathrm{PD(l)}}\) method) is analyzed in great detail from a theoretical point of view as well as by applying numerical tests. The chosen distributions are leptokurtic with asymmetry which refers to the general characteristic of empirical distributions. Considering \(M\) -estimation with probabilistic models, the Gram–Charlier series are also applied to approximate the models in question ( \(M_{\mathrm{G-C}}\) method). The paper shows that \(M_{\mathcal {P}}\) estimation with the application of probabilistic models belongs to the class of robust estimations; \(M_{\mathrm{PD(l)}}\) method is especially effective in that case. It is suggested that even in the absence of significant anomalies the method in question should be regarded as robust against gross errors while its robustness is controlled by the pseudo-kurtosis.     

FY-3B微波成像仪资料的地理定位误差与订正

风云3号B星(FY-3B)上的微波成像仪(MWRI)通过10.65 GHz,18.7 GHz,23.8GHz,36.5 GHz和189.0 GHz5个频率的双极化通道对地球表面进行监测。自卫星发射至今,MWRI资料的地理定位误差还未进行深入研究。为了提高FY-3B MWRI L1级数据地理定位精度,基于海、陆响应的升、降轨亮温差理论NDM(Node Differential Method),通过卫星位置和速度矢量建立卫星姿态模型、采用非线性最优化方法估计卫星姿态偏差,进而对MWRI 89 GHz通道的地理定位误差进行分析与订正。结果表明,2015年1—9月份俯仰、滚动和偏航角度的平均偏差分别为-0.220°,0.068°和0.062°,对应沿轨误差大约3—4 km,跨轨误差小于1 km。定位误差订正后,地中海、澳大利亚区域海岸线附近的升降轨亮温差明显减小;观测亮温在红海和南美洲东南部区域的分布和海岸线更加吻合,定位精度得到明显提高。     

On the choice of a random variable which eliminates the bias caused by variable spacing in geodetic levelling

Computer values of the mean square error of the Nigerian Geodetic Levelling based on the model x_ij = ρ_ij/R _ij ^1/2 showed a uniformity between the lines of levelling, of a nature which suggest that x_ij = ρ_ij/R _ij ^1/2 is a good fit for the data. Values of the mean square error of the levelling based on w_ij = ρ_ij/R_ij showed such significant variation between the lines that this alternative model does not seem to be supported by the data used in this study.     

Computation of geodetic direct and indirect problems by computers accumulating increments from geodetic line elements

By choosing sufficiently small elements of the length of the geodetic line, or of the latitude or longitude difference, the other two can be computed at each element and the results can be accumulated to solve the problem with more than twenty significant number accuracy if desired. Ten to twelve number accuracy was computed in the examples of this paper. The geodetic line elements are kept in correct azimuth by Clairaut’s equation for the geodetic line. The computers can do millions of necessary computations very economically in a few seconds. All other published methods solving the direct or indirect problem can be reliably checked against results obtained by this method. The run of geodetic lines around the back side of the Ellipsoid is outlined.     

不确定性平差模型的平差准则与解算方法

在测量数据的获取过程中,经常存在着不确定性,它们影响着参数估计的可靠性。本文通过把不确定度作为参数融入函数模型,建立了不确定性平差模型。依据残差中不确定性传播规律,确定了残差最大不确定度达到最小的平差准则,利用迭代算法得到了不确定性平差模型的解算方法。通过实例分析了最小二乘平差、整体最小二乘平差和不确定性平差准则下最优解的不同特点,从另一个角度探讨了不确定性观测数据处理方法,推广了现有的误差理论。     

Characterization of errors in vector wind retrievals from satellite-based polarimetric microwave radiometer measurements

We present a method for evaluating characteristics of wind vector retrieval errors from polarimetric radiometer measurements. We focus on wind direction errors due to ambiguous solutions.     

Estimation of Geodetic Parameters with VLBI Data of Last 5 Years

The meaning to research the potential of VLBI for geodetic applications is summarized. And the observation models and their related parameters of geodetic interest are investigated. Then, the principle and method of using the random model in VLBI data processing are investigated. With the world wide VLBI data from 2000-2004, the conditions to compute the parameters of geodetic interest are introduced, and so are the computing methods and processes. And the computed results of the parameters of geodetic interest are analyzed.