共查询到20条相似文献，搜索用时 31 毫秒
1.
Tikhonov正则化方法在GOCE重力场求解中的模拟研究 总被引：6，自引：4，他引：2
本文在阐述Tikhonov正则化方法基本原理的基础上,给出了四类可用于重力场解算的正则化矩阵(零次、一次、二次和Kaula),以及用于确定正则化参数的L曲线法和GCV方法的数学模型。基于SA方法利用模拟数据分析讨论了零次、一次以及Kaula正则化矩阵应用于GOCE全球重力场模型确定的有效性,并由Kaula正则化矩阵分析了L曲线法和GCV方法确定正则化参数的可行性。数值结果表明三类正则化矩阵获得的最优解(以大地水准面MSE最小为准则确定)的精度水平相近,关键在于相应正则化参数的确定,数值结果同时说明了GCV方法和L曲线法可用于确定正则化参数,且前者较后者具有更好的稳定性。 相似文献
2.
The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth’s monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003–Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4 solutions (RL04) from the Center for Space Research (CSR). Post-fit residual analysis shows that the regularized solutions fit the data to within the noise level of GRACE. A time series of filtered hydrological model is used to confirm that signal attenuation for basins in the Total Runoff Integrating Pathways (TRIP) database over 320 km radii is less than 1 cm equivalent water height RMS, which is within the noise level of GRACE. 相似文献
3.
An efficient algorithm is proposed for gravity field recovery from Gravity Field and Steady-State Ocean Circulation Explorer
(GOCE) satellite gravity gradient observations. The mathematical model is formulated in the time domain, which allows the
inclusion of realistic observational noise models. The algorithm combines the iterative solution of the normal equations,
using a Richardson-type iteration scheme, with the fast computation of the right-hand side of the normal equations in each
iteration step by a suitable approximation of the design matrix. The convergence of the iteration is investigated, error estimates
are provided, and the unbiasedness of the method is proved. It is also shown that the method does not converge to the solution
of the normal equations. The performance of the approach for white noise and coloured noise is demonstrated along a simulated
GOCE orbit up to spherical harmonic degree and order 180. The results also indicate that the approximation error may be neglected.
Received: 30 November 1999 / Accepted: 31 May 2000 相似文献
4.
The recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational
task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing
the Earth's gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies (preconditioned
conjugate gradient method, semi-analytic approach, and distributed non-approximative adjustment), which are based on different
concepts, are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation regarding
the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the
coloured noise characteristics of the gradiometer. The numerical simulations show that the three methods deliver nearly identical
results—even in the case of large data gaps in the observation time series. The newly proposed distributed non-approximative
adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns
out to be a feasible method for practical applications.
Received: 17 December 2001 / Accepted: 17 July 2002
Acknowledgments. We would like to thank Prof. W.-D. Schuh, Institute of Theoretical Geodesy, University of Bonn, for providing us with the
serial version of the PCGMA algorithm, which forms the basis for the parallel PCGMA package developed at our institute. This
study was partially performed in the course of the GOCE project `From E?tv?s to mGal+', funded by the European Space Agency
(ESA) under contract No. 14287/00/NL/DC.
Correspondence to: R. Pail 相似文献
5.
Downward continuation and geoid determination based on band-limited airborne gravity data 总被引：4，自引：3，他引：4
The downward continuation of the harmonic disturbing gravity potential, derived at flight level from discrete observations
of airborne gravity by the spherical Hotine integral, to the geoid is discussed. The initial-boundary-value approach, based
on both the direct and inverse solution to Dirichlet's problem of potential theory, is used. Evaluation of the discretized
Fredholm integral equation of the first kind and its inverse is numerically tested using synthetic airborne gravity data.
Characteristics of the synthetic gravity data correspond to typical airborne data used for geoid determination today and in
the foreseeable future: discrete gravity observations at a mean flight height of 2 to 6 km above mean sea level with minimum
spatial resolution of 2.5 arcmin and a noise level of 1.5 mGal. Numerical results for both approaches are presented and discussed.
The direct approach can successfully be used for the downward continuation of airborne potential without any numerical instabilities
associated with the inverse approach. In addition to these two-step approaches, a one-step procedure is also discussed. This
procedure is based on a direct relationship between gravity disturbances at flight level and the disturbing gravity potential
at sea level. This procedure provided the best results in terms of accuracy, stability and numerical efficiency. As a general
result, numerically stable downward continuation of airborne gravity data can be seen as another advantage of airborne gravimetry
in the field of geoid determination.
Received: 6 June 2001 / Accepted: 3 January 2002 相似文献
6.
Targeting the multicollinearity problem in dam statistical model and error perturbations resulting from the monitoring process,we built a regularized regression model using Truncated Singular Value Decomposition(TSVD).An earth-rock dam in China is presented and discussed as an example.The analysis consists of three steps:multicollinearity detection,regularization pa-rameter selection,and crack opening modeling and forecasting.Generalized Cross-Validation(GCV) function and L-curve criterion are both adopted in the regularization parameter selection.Partial Least-Squares Regression(PLSR) and stepwise regression are also included for comparison.The result indicates the TSVD can promisingly solve the multicollinearity problem of dam regression models.However,no general rules are available to make a decision when TSVD is superior to stepwise regression and PLSR due to the regularization parameter-choice problem.Both fitting accuracy and coefficients’ reasonability should be considered when evaluating the model reliability. 相似文献
7.
GPS-based precise orbit determination of the very low Earth-orbiting gravity mission GOCE 总被引：5，自引：0，他引：5
A prerequisite for the success of future gravity missions like the European Gravity field and steady-state Ocean Circulation
Explorer (GOCE) is a precise orbit determination (POD). A detailed simulation study has been carried out to assess the achievable
orbit accuracy based on satellite-to-satellite tracking (SST) by the US global positioning system (GPS) and in conjunction
the implications for gravity field determination. An orbit accuracy at the few centimeter level seems possible, sufficient
to support the GOCE gravity mission and in particular its gravity gradiometer.
Received: 21 January 2000 / Accepted: 4 July 2000 相似文献
8.
The Somigliana–Pizzetti gravity field (the International gravity formula), namely the gravity field of the level ellipsoid
(the International Reference Ellipsoid), is derived to the sub-nanoGal accuracy level in order to fulfil the demands of modern
gravimetry (absolute gravimeters, super conducting gravimeters, atomic gravimeters). Equations (53), (54) and (59) summarise
Somigliana–Pizzetti gravity Γ(φ,u) as a function of Jacobi spheroidal latitude φ and height u to the order ?(10−10 Gal), and Γ(B,H) as a function of Gauss (surface normal) ellipsoidal latitude B and height H to the order ?(10−10 Gal) as determined by GPS (`global problem solver'). Within the test area of the state of Baden-Württemberg, Somigliana–Pizzetti
gravity disturbances of an average of 25.452 mGal were produced. Computer programs for an operational application of the new
international gravity formula with (L,B,H) or (λ,φ,u) coordinate inputs to a sub-nanoGal level of accuracy are available on the Internet.
Received: 23 June 2000 / Accepted: 2 January 2001 相似文献
9.
One of the most basic and important tools in optimal spectral gravity field modelling is the method of Wiener filtering.
Originally developed for applications in analogue signal analysis and communication engineering, Wiener filtering has become
a standard linear estimation technique of modern operational geodesy, either as an independent practical tool for data de-noising
in the frequency domain or as an integral component of a more general signal estimation methodology (input–output systems
theory). Its theoretical framework is based on the Wiener–Kolmogorov linear prediction theory for stationary random fields
in the presence of additive external noise, and thus it is closely related to the (more familiar to geodesists) method of
least-squares collocation with random observation errors. The main drawback of Wiener filtering that makes its use in many
geodetic applications problematic stems from the stationarity assumption for both the signal and the noise involved in the
approximation problem. A modified Wiener-type linear estimation filter is introduced that can be used with noisy data obtained
from an arbitrary deterministic field under the masking of non-stationary random observation errors. In addition, the sampling
resolution of the input data is explicitly taken into account within the estimation algorithm, resulting in a resolution-dependent
optimal noise filter. This provides a more insightful approach to spectral filtering techniques for noise reduction, since
the data resolution parameter has not been directly incorporated in previous formulations of frequency-domain estimation problems
for gravity field signals with discrete noisy data.
Received: 1 November 2000 / Accepted: 19 June 2001 相似文献
10.
基于最小二乘配置法向下延拓航空重力的过程中,由于协方差矩阵严重病态,影响延拓结果的稳定性和精度。针对这一问题,提出了航空重力向下延拓的最小二乘配置Tikhonov正则化法。基于全球协方差函数模型建立航空重力数据与地面重力数据的协方差关系,引入基于广义交叉验证法,选择正则化参数的Tikhonov正则化法改善协方差矩阵的病态性,抑制观测噪声对延拓结果的放大影响。基于EGM2008重力场模型,设计了山区、丘陵和海域3种不同地形区域的航空重力数据向下延拓的仿真实验,实验结果验证了该方法的有效性。 相似文献
11.
Multi-level arc combination with stochastic parameters 总被引：1，自引：1，他引：0
P. H. Andersen 《Journal of Geodesy》2000,74(7-8):531-551
The method of square root information filtering and smoothing (SRIF/S) is reviewed and has been implemented in the combined
square root information filter and smoother (CSRIFS) program. CSRIFS is a part of the GEOSAT space geodesy software developed
at Forsvarets forskningsinstitutt (FFI, The Norwegian Defence Research Establishment). The state vectors and complete variance–covariance
matrices from the analyses of a number of independent arcs of space geodesy data can be combined using CSRIFS. Four parameter
levels are available and any parameter can, at each level, be represented as either a constant or a stochastic parameter (white
noise, colored noise, or random walk). The batch length (i.e. the time interval between the addition of noise to the SRIF
array) can be made time and parameter dependent. CSRIFS was applied in the combination of 623 very long baseline interferometry
(VLBI) observing sessions. The purpose of this test was to validate the computer implementation of the SRIF/S method and to
give an example of how this method can be used in the analysis of a large number of space geodetic observations. The results
show that the implementation is very satisfactory.
Received: 28 May 1999 / Accepted: 15 June 2000 相似文献
12.
P. Moore 《Journal of Geodesy》2001,75(5-6):241-254
Dual satellite crossovers (DXO) between the two European Remote Sensing satellites ERS-1 and ERS-2 and TOPEX/Poseidon are
used to (1) refine the Earth's gravity field and (2) extend the study of the ERS-2 altimetric range stability to cover the
first four years of its operation. The enhanced gravity field model, AGM-98, is validated by several methodologies and will
be shown to provide, in particular, low geographically correlated orbital error for ERS-2. For the ERS-2 altimetric range
study, TOPEX/Poseidon is first calibrated through comparison against in situ tide gauge data. A time series of the ERS-2 altimeter
bias has been recovered along with other geophysical correction terms using tables for bias jumps in the range measurements
at the single point target response (SPTR) events. On utilising the original version of the SPTR tables the overall bias drift
is seen to be 2.6±1.0 mm/yr with an RMS of fit of 12.2 mm but with discontinuities at the centimetre level at the SPTR events.
On utilising the recently released revised tables, SPTR2000, the drift is better defined at 2.4±0.6 mm/yr with the RMS of
fit reduced to 3.7 mm. Investigations identify the sea-state bias as a source of error with corrections affecting the overall
drift by close to 1.2 mm/yr.
Received: 25 May 2000 / Accepted: 24 January 2001 相似文献
13.
A special class of regularization methods for satellite gravity gradiometry based on Tikhonov spherical regularization wavelets
is considered, with particular emphasis on the case of data blurred by random noise. A convergence rate is proved for the
regularized solution, and a method is discussed for choosing the regularization level a posteriori from the gradiometer data.
Received: 23 March 2000 / Accepted: 20 September 2000 相似文献
14.
利用最优正则化方法确定Tikhonov正则化参数 总被引：4，自引：0，他引：4
基于均方误差最小意义下运用最优正则化方法确定正则参数,推导了计算最优正则参数的公式,并结合算例分析比较了求解病态方程的L-曲线法、GCV法等常用的方法,算例表明,基于最小均方误差的Tikhonov正则化参数优化选取方法是一种可行有效的方法。 相似文献
15.
In many geoscientific applications, one needs to recover the quantities of interest from indirect observations blurred by
colored noise. Such quantities often correspond to the values of bounded linear functionals acting on the solution of some
observation equation. For example, various quantities are derived from harmonic coefficients of the Earth’s gravity potential.
Each such coefficient is the value of the corresponding linear functional. The goal of this paper is to discuss new means
to use information about the noise covariance structure, which allows order-optimal estimation of the functionals of interest
and does not involve a covariance operator directly in the estimation process. It is done on the basis of a balancing principle
for the choice of the regularization parameter, which is new in geoscientific applications. A number of tests demonstrate
its applicability. In particular, we could find appropriate regularization parameters by knowing a small part of the gravitational
field on the Earth’s surface with high precision and reconstructing the rest globally by downward continuation from satellite
data. 相似文献
16.
Local geoid determination combining gravity disturbances and GPS/levelling: a case study in the Lake Nasser area, Aswan, Egypt 总被引：1，自引：0，他引：1
C. C. Tscherning Awar Radwan A. A. Tealeb S. M. Mahmoud M. Abd El-Monum Ramdan Hassan I. El-Syaed K. Saker 《Journal of Geodesy》2001,75(7-8):343-348
The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and
the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity
data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not
using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with
gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general
gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan
Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using
only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was
in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used,
as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave
difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the
agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances
and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account
for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads.
Received: 14 August 2000 / Accepted: 28 February 2001 相似文献
17.
一种解算病态问题的方法--两步解法 总被引：10，自引：0，他引：10
提出了一种解算病态问题的方法———两步解法。在两步计算中,均采用L曲线法来确定正则化参数α。通过算例,比较了该方法和LS估计、岭估计及截断奇异值方法的效果。结果表明,该方法要明显优于LS估计、岭估计及截断奇异值法。 相似文献
18.
G. Ramillien 《Journal of Geodesy》2002,76(3):139-149
A fast spherical harmonic approach enables the computation of gravitational or magnetic potential created by a non-uniform
shell of material bounded by uneven topographies. The resulting field can be evaluated outside or inside the sphere, assuming
that density of the shell varies with latitude, longitude, and radial distance. To simplify, the density (or magnetization)
source inside the sphere is assumed to be the product of a surface function and a power series expansion of the radial distance.
This formalism is applied to compute the gravity signal of a steady, dry atmosphere. It provides geoid/gravity maps at sea
level as well as satellite altitude. Results of this application agree closely with those of earlier studies, where the atmosphere
contribution to the Earth's gravity field was determined using more time-consuming methods.
Received: 14 August 2000 / Accepted: 19 March 2001 相似文献
19.
A formula for computing the gravity disturbance from the second radial derivative of the disturbing potential 总被引：6，自引：0，他引：6
J. Li 《Journal of Geodesy》2002,76(4):226-231
A formula for computing the gravity disturbance and gravity anomaly from the second radial derivative of the disturbing potential
is derived in detail using the basic differential equation with spherical approximation in physical geodesy and the modified
Poisson integral formula. The derived integral in the space domain, expressed by a spherical geometric quantity, is then converted
to a convolution form in the local planar rectangular coordinate system tangent to the geoid at the computing point, and the
corresponding spectral formulae of 1-D FFT and 2-D FFT are presented for numerical computation.
Received: 27 December 2000 / Accepted: 3 September 2001 相似文献
20.
连续密集的全球导航卫星系统(global navigation satellite system,GNSS)地表形变监测为反演精细的区域地表质量变化提供了有效技术手段.针对格林函数方法反演区域地表质量变化的病态问题,给出了一种改进的正则化拉普拉斯约束矩阵,讨论了广义交叉检验(generalized cross-vali... 相似文献