Possible improvement of Earth orientation forecast using autocovariance prediction procedures

 Autocovariance prediction has been applied to attempt to improve polar motion and UT1-UTC predictions. The predicted polar motion is the sum of the least-squares extrapolation model based on the Chandler circle, annual and semiannual ellipses, and a bias fit to the past 3 years of observations and the autocovariance prediction of these extrapolation residuals computed after subtraction of this model from pole coordinate data. This prediction method has been applied also to the UT1-UTC data, from which all known predictable effects were removed, but the prediction error has not been reduced with respect to the error of the current prediction model. However, the results show the possibility of decreasing polar motion prediction errors by about 50 for different prediction lengths from 50 to 200 days with respect to the errors of the current prediction model. Because of irregular variations in polar motion and UT1-UTC, the accuracy of the autocovariance prediction does depend on the epoch of the prediction. To explain irregular variations in x, y pole coordinate data, time-variable spectra of the equatorial components of the effective atmospheric angular momentum, determined by the National Center for Environmental Prediction, were computed. These time-variable spectra maxima for oscillations with periods of 100–140 days, which occurred in 1985, 1988, and 1990 could be responsible for excitation of the irregular short-period variations in pole coordinate data. Additionally, time-variable coherence between geodetic and atmospheric excitation function was computed, and the coherence maxima coincide also with the greatest irregular variations in polar motion extrapolation residuals. Received: 22 October 1996 / Accepted: 16 September 1997     

Laser station coordinates and baselines from long-ARC and short-ARC analyses of starlette

Laser ranging to Starlette from April 1983 to April 1984 has been used to determine a coordinate set, UASC.ST1, of laser reference points for 18 tracking stations. The coordinates were derived by application of the least-squares data reduction procedure in a simultaneous solution along with geodynamic parameters for 49 near consecutive 5–6 day arcs. Comparisons with the University of Texas station coordinates,LSC 8112 andLSC 8402, and theRGO, Herstmonceux, coordinates,RGOSC.LG2, reveal consistency to near 30 cm in each coordinate. Furthermore, the translation vectors of the comparisons are not significantly different from zero indicating consistency in the implied origins of the systems. The period of analysis included seven occasions in which STARLETTE was tracked near simultaneously by three or four laser stations in North America. Using the short arcs as reference frameworks, station coordinates were determined by application of two contrasting methods, namely, a multi-arc simultaneous analysis and a weighted mean of the individual pass solutions. The former compared more favourably with baselines from the long-arc solution with anRMS error of near 16 cm. Comparison against theLSC 8402 coordinates confirmed that baselines accurate to within 15 cm can be achieved by satellite laser ranging to Starlette.     

Temporal correlation for network RTK positioning

Temporal correlation in network real-time kinematic (RTK) data exists due to unmodeled multipath and atmospheric errors, in combination with slowly changing satellite constellation. If this correlation is neglected, the estimated uncertainty of the coordinates might be too optimistic. In this study, we compute temporal correlation lengths for network RTK positioning, i.e., the appropriate time separation between the measurements. This leads to more realistic coordinate uncertainty estimates, and an appropriate surveying strategy to control the measurements can be designed. Two methods to estimate temporal correlation lengths are suggested. Several monitor stations that utilize correction data from two SWEPOS^TM Network RTK services, a standard service and a project-adapted service with the mean distance between the reference stations of approximately 70 and 10–20 km, are evaluated. The correlation lengths for the standard service are estimated as 17 min for the horizontal component and 36–37 min for the vertical component. The corresponding estimates for the project-adapted service are 13–17 and 13–16 min, respectively. According to the F test, the proposed composite first-order Gauss–Markov autocovariance function shows a significantly better least-squared fit to data compared to the commonly used one-component first-order Gauss–Markov model. A second suggested method is proposed that has the potential of providing robust correlation lengths without the need to fit a model to the computed autocovariance function.     

Nonstationary Spatial Texture Estimation Applied to Adaptive Speckle Reduction of SAR Data

This letter proposes a new model for the second-order statistics of spatial texture in synthetic aperture radar images. The autocovariance function is locally approximated by a two-dimensional anisotropic Gaussian kernel (AGK) to characterize texture by its local orientation and anisotropy. The estimation of texture parameters at a given scale is based on the gradient structure tensor operator and does not require the explicit computation of the autocovariance. Finally, a new filter called AGK minimum mean square error (MMSE) that takes into account this spatial information is introduced and compared with the refined MMSE filter. The proposed filter has better performance in terms of texture preservation and structure enhancement     

Accuracy analysis for the NAD 83 geodetic reference system

The North American Datum of 1983 (NAD 83) provides horizontal coordinates for more than 250,000 geodetic stations. These coordinates were derived by a least squares adjustment of existing terrestrial and space-based geodetic data. For pairs of first order stations with interstation distances between 10km and 100km, therms discrepancy between distances derived fromNAD 83 coordinates and distances derived from independentGPS data may be suitably approximated by the empirical rulee=0.008 K^0.7 where e denotes therms discrepancy in meters and K denotes interstation distance in kilometers. For the same station pairs, therms discrepancy in azimuth may be approximated by the empirical rule e=0.020 K^0.5. Similar formulas characterize therms discrepancies for pairs involving second and third order stations. Distance and orientation accuracies, moreover, are well within adopted standards. While these expressions indicate that the magnitudes of relative positional accuracies depend on station order, absolute positional accuracies are similar in magnitude for first, second, and third order stations. Adjustment residuals reveal a few local problems with theNAD 83 coordinates and with the weights assigned to certain classes of observations.     

Nonlinear least-squares method via an isomorphic geometrical setup

The resolution of a nonlinear parametric adjustment model is addressed through an isomorphic geometrical setup with tensor structure and notation, represented by a u-dimensional “model surface” embedded in a flat n-dimensional “observational space”. Then observations correspond to the observational-space coordinates of the pointQ, theu initial parameters correspond to the model-surface coordinates of the “initial” pointP, and theu adjusted parameters correspond to the model-surface coordinates of the “least-squares” point . The least-squares criterion results in a minimum-distance property implying that the vector Q must be orthogonal to the model surface. The geometrical setup leads to the solution of modified normal equations, characterized by a positive-definite matrix. The latter contains second-order and, optionally, thirdorder partial derivatives of the observables with respect to the parameters. This approach significantly shortens the convergence process as compared to the standard (linearized) method.     

Simulation of regional gravity field recovery from satellite gravity gradiometer data using collocation and FFT

When planning a satellite gravity gradiometer (SGG) mission, it is important to know the quality of the quantities to be recovered at ground level as a function of e.g. satellite altitude, data type and sampling rate, and signal variance and noise. This kind of knowledge may be provided either using the formal error estimates of wanted quantities using least-squares collocation (LSC) or by comparing simulated data at ground level with results computed by methods like LSC or Fast Fourier Transform (FFT). Results of a regional gravity field recovery in a 10^o×20^o area surrounding the Alps using LSC and FFT are reported. Data used as observations in satellite altitude (202 or161 km) and for comparison at ground level were generated using theOSU86F coefficient set, complete to degree 360. These observations are referred to points across simulated orbits. The simulated quantities were computed for a 45 days mission period and 4 s sampling. A covariance function which also included terms above degree 360 was used for prediction and error estimation. This had the effect that the formal error standard deviation for gravity anomalies were considerably larger than the standard deviations of predicted minus simulated quantities. This shows the importance of using data with frequency content above degree 360 in simulation studies. Using data at202 km altitude the standard deviation of the predicted minus simulated data was equal to8.3 mgal for gravity and0.33 m for geoid heights.     

Improving the computational efficiency of the ambiguity function algorithm

Techniques are described in this paper for improving the Ambiguity Function Method (AFM) for differential GPS positioning using phase observations, (a) that take advantage of optimal dual-frequency observable combinations to improve thereliability of the AFM, and (b) that significantly shorten the computation time necessary for the AFM. The procedure can be used for kinematic positioning applications if a Kalman filter predicted position is accurate enough as an initial position for the suggested AFM searching procedure, or pseudokinematic mode using say a triple-difference solution as an initial position for static positioning if the baseline length is short (typically <5km).     

Consistent realization of Celestial and Terrestrial Reference Frames

The Celestial Reference System (CRS) is currently realized only by Very Long Baseline Interferometry (VLBI) because it is the space geodetic technique that enables observations in that frame. In contrast, the Terrestrial Reference System (TRS) is realized by means of the combination of four space geodetic techniques: Global Navigation Satellite System (GNSS), VLBI, Satellite Laser Ranging (SLR), and Doppler Orbitography and Radiopositioning Integrated by Satellite. The Earth orientation parameters (EOP) are the link between the two types of systems, CRS and TRS. The EOP series of the International Earth Rotation and Reference Systems Service were combined of specifically selected series from various analysis centers. Other EOP series were generated by a simultaneous estimation together with the TRF while the CRF was fixed. Those computation approaches entail inherent inconsistencies between TRF, EOP, and CRF, also because the input data sets are different. A combined normal equation (NEQ) system, which consists of all the parameters, i.e., TRF, EOP, and CRF, would overcome such an inconsistency. In this paper, we simultaneously estimate TRF, EOP, and CRF from an inter-technique combined NEQ using the latest GNSS, VLBI, and SLR data (2005–2015). The results show that the selection of local ties is most critical to the TRF. The combination of pole coordinates is beneficial for the CRF, whereas the combination of \(\varDelta \hbox {UT1}\) results in clear rotations of the estimated CRF. However, the standard deviations of the EOP and the CRF improve by the inter-technique combination which indicates the benefits of a common estimation of all parameters. It became evident that the common determination of TRF, EOP, and CRF systematically influences future ICRF computations at the level of several \(\upmu \)as. Moreover, the CRF is influenced by up to \(50~\upmu \)as if the station coordinates and EOP are dominated by the satellite techniques.     

大气负荷响应计算误差估计模型

用数理统计技术，建立格林函方法计算大气变化引起重力和形焦等效应的精度评定模型，并利用中国及其邻区的大气观,蛭大气误差常数和一个计算方案的精度估计，其结果与固体潮汐检测在不同气候条件下的响应情况相一致，该系统也可应用于格林函数积分形式的其它物理模型的误差估计。     

A geodetic approach for the recovery of global kinematic plate parameters

Modern techniques of precise geodetic positioning are capable of monitoring global tectonic movements. We can avoid the tremendous effort of observing those point motions at every place on the earth, if we accept the model of rigid tectonic plates, which allows us to extrapolate from discrete point observations to the appertaining plates. The target of describing plate kinematics is the determination of its kinematic parameters, which are the coordinates of the rotation pole and the rotational velocity of each tectonic plate. A mathematical model is presented, which is capable of including geodetic observations (point coordinate shifts, distance changes) as well as geophysical quantities (sea floor spreading rates, earthquake slip vectors). The parameter estimation procedure is derived and demonstrated in simulated examples. Finally a global geodetic network for space techniques is designed, which provides an optimum parameter estimation.     

Modeling the length of day and extrapolating the rotation of the Earth

The stochastic behavior of the length of day (LOD) process is analyzed and is modeled within statistical accuracy on a time-scale ranging from weeks to millennia by a three-component model comprising a global Brownian motion process, decadal fluctuations, and a 50-day Madden–Julian oscillation. While the model is intended to be phenomenological, some possible physical models underlying the three components are speculated upon. The model is applied to estimate long-range extrapolation errors. For example, it predicts a standard error of 1 h in the clock-time correction ΔT for extrapolation by 1,500 years from 500 to 2000 BC.     

Polar motion modeling,analysis, and prediction with time dependent harmonic coefficients

A time dependent amplitude model was proposed for the analysis and prediction of polar motion time series. The formulation was implemented to analyze part of the new combined solution, EOP (IERS) C 04, daily polar motion time series of 14 years length using a statistical model with first order autoregressive disturbances. A new solution approach, where the serial correlations of the disturbances are eliminated by sequentially differencing the measurements, was used to estimate the model parameters using weighted least squares. The new model parsimoniously represents the 14-year time series with 0.5 mas rms fit, close to the reported 0.1 mas observed pole position precisions for the x and y components. The model can also predict 6 months into the future with less than 4 mas rms prediction error for both polar motion components, and down to sub mas for one-step ahead prediction as validated using a set of daily time series data that are not used in the estimation. This study is dedicated to the memory of Prof. Urho Uotila (1923–2006) whose teaching of “Adjustment Computations” over the years influenced so much, so many of us who had the privilege of being his students.     

Linear drift and periodic variations observed in long time series of polar motion

 Two long time series were analysed: the C01 series of the International Earth Rotation Service and the pole series obtained by re-analysis of the classical astronomical observations using the HIPPARCOS reference frame. The linear drift of the pole was determined to be 3.31 ± 0.05 milliarcseconds/year towards 76.1 ± 0.80° west longitude. For the least-squares fit the a priori correlations between simultaneous pole coordinates x _p , y _p were taken into account, and the weighting function was calculated by estimating empirical variance components. The decadal variations of the pole path were investigated by Fourier and wavelet analysis. Using sliding windows, the periods and amplitudes of the Chandler wobble and annual wobble were determined. Typical periods in the variable Chandler wobble and annual wobble parameters were obtained from wavelet analyses. Received: 21 January 2000 / Accepted: 28 August 2000     

Accurate absolute GPS positioning through satellite clock error estimation

 An algorithm for very accurate absolute positioning through Global Positioning System (GPS) satellite clock estimation has been developed. Using International GPS Service (IGS) precise orbits and measurements, GPS clock errors were estimated at 30-s intervals. Compared to values determined by the Jet Propulsion Laboratory, the agreement was at the level of about 0.1 ns (3 cm). The clock error estimates were then applied to an absolute positioning algorithm in both static and kinematic modes. For the static case, an IGS station was selected and the coordinates were estimated every 30 s. The estimated absolute position coordinates and the known values had a mean difference of up to 18 cm with standard deviation less than 2 cm. For the kinematic case, data obtained every second from a GPS buoy were tested and the result from the absolute positioning was compared to a differential GPS (DGPS) solution. The mean differences between the coordinates estimated by the two methods are less than 40 cm and the standard deviations are less than 25 cm. It was verified that this poorer standard deviation on 1-s position results is due to the clock error interpolation from 30-s estimates with Selective Availability (SA). After SA was turned off, higher-rate clock error estimates (such as 1 s) could be obtained by a simple interpolation with negligible corruption. Therefore, the proposed absolute positioning technique can be used to within a few centimeters' precision at any rate by estimating 30-s satellite clock errors and interpolating them. Received: 16 May 2000 / Accepted: 23 October 2000     

Fast collocation

In this paper a new method to compute in a fast and reliable way the collocation solution is presented. In order to speed up the numerical procedures, some restrictions on input data are needed.The basic assumption is that data are gridded and homogeneous; this implies that the autocovariance matrix entering in the collocation formula is of Toeplitz type. In particular, if observations are placed on a two dimensional planar grid, the autocovariance matrix is a symmetric block Toeplitz matrix and each block is itself a symmetric Toeplitz matrix (Toeplitz/Toeplitz structure). The analysis can be extended to a regular geographical grid, considered as a generalization of the planar one, taking into account the distortions on the Toeplitz/Toeplitz structure induced by the convergence of the meridians. The devised method is based on a combined application of the Preconditioned Conjugate Gradient Method and of the Fast Fourier Transform. This allows a proper exploitation of the Toeplitz/Toeplitz structure of the autocovariance matrix in computing the collocation solution.The numerical tests proved that the application of this algorithm leads to a relevant decrease in CPU time if compared with standard methods used to solve a collocation problem (Cholesky, Levinson).     

Spectrum estimation using maximum entropy and multiresolution considerations

Summary Given a sample autocovariance sequence of finite length for some observed random process, the spectrum estimation problem involves the extension of this sequence for the required Fourier transformation. The maximum entropy approach which is based on the optimal use of information contents, leads to a dual sequence of reflection coefficients with reciprocal spectrum of the process. The estimation of the maximum entropy spectrum implies results identical to those using autoregressive modeling in one dimension under appropriate white noise assumptions. In cases of a non-white noise component, the approach is generalized to an autoregressive-moving-average model. Recent developments in multiresolution analysis with spectral domain decompositions also offer possibilities of subband spectrum estimation for specific applications. Using a simulated data sequence with two close frequencies, the estimated spectrum from a two-level decomposition with autoregressive modeling shows better resolution than with conventional processing. Geodetic and geophysical applications are briefly indicated.     

Satellite Doppler solutions in terms of a single parameter

By an appropriate combination of the integrated doppler counts for a motionless ground station over two consecutive arcs, of a satellite path, it is possible to obtain a linear mathematical model relating the coordinates of the ground station to the observations. In this mathematical model, the involvement of the fourth unknown of the problem—the frequency off-set parameter, is, however, not linear. By application of the least squares technique, the solutions for the coordinates are obtained as analytical functions of the frequency off-set, parameter only. These, in turn, reduce the basic formula for the doppler count to be an implicit function of the same single variable. The value of the variable which provides the best fit of this function with the observed doppler counts, minimizing the sum of squares of the deviations for all involved pairs of satellite positions is the best value for the unknown frequency off-set parameter and an iterative technique is devised to compute this value. The desired values for the coordinates of the ground station can then be obtained by substitution of the best value of the frequency off-set parameter into the corresponding formula, and correcting for reducing the effects of the random noise in the observed dopple data.     

道路工程GPS平面控制网建网方法

以往GPS建立的平面坐标系属法线系统,而选线设计均在垂线和水准面为基准的坐标系统下进行,其数据未做两化改正而直接用于施工放样。为了消除因GPS引入线路勘测而引发的法线系统坐标系与垂线系统坐标系之间的矛盾,本文采用逆向两化改正的方法,从理论上提出了直接用GPS建立垂线和水准面系统下平面坐标系的技术路线,并推导出逆向两化改正及其精度评定公式。     

W0: an estimate in the Finnish Height Datum N60, epoch 1993.4, from twenty-five GPS points of the Baltic Sea Level Project

Based upon a data set of 25 points of the Baltic Sea Level Project, second campaign 1993.4, which are close to mareographic stations, described by (1) GPS derived Cartesian coordinates in the World Geodetic Reference System 1984 and (2) orthometric heights in the Finnish Height Datum N60, epoch 1993.4, we have computed the primary geodetic parameter W ₀(1993.4) for the epoch 1993.4 according to the following model. The Cartesian coordinates of the GPS stations have been converted into spheroidal coordinates. The gravity potential as the additive decomposition of the gravitational potential and the centrifugal potential has been computed for any GPS station in spheroidal coordinates, namely for a global spheroidal model of the gravitational potential field. For a global set of spheroidal harmonic coefficients a transformation of spherical harmonic coefficients into spheroidal harmonic coefficients has been implemented and applied to the global spherical model OSU 91A up to degree/order 360/360. The gravity potential with respect to a global spheroidal model of degree/order 360/360 has been finally transformed by means of the orthometric heights of the GPS stations with respect to the Finnish Height Datum N60, epoch 1993.4, in terms of the spheroidal “free-air” potential reduction in order to produce the spheroidal W ₀(1993.4) value. As a mean of those 25 W ₀(1993.4) data as well as a root mean square error estimation we computed W ₀(1993.4)=(6 263 685.58 ± 0.36) kgal × m. Finally a comparison of different W ₀ data with respect to a spherical harmonic global model and spheroidal harmonic global model of Somigliana-Pizetti type (level ellipsoid as a reference, degree/order 2/0) according to The Geodesist's Handbook 1992 has been made. Received: 7 November 1996 / Accepted: 27 March 1997