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1.
The multiresolution character of collocation 总被引：3，自引：0，他引：3
C. Kotsakis 《Journal of Geodesy》2000,74(3-4):275-290
An interesting theoretical connection between the statistical (non-stochastic) collocation principle and the multiresolution/wavelet
framework of signal approximation is presented. The rapid developments in multiresolution analysis theory over the past few
years have provided very useful (theoretical and practical) tools for approximation and spectral studies of irregularly varying
signals, thus opening new possibilities for `non-stationary' gravity field modeling. It is demonstrated that the classic multiresolution
formalism according to Mallat's pioneering work lies at the very core of some of the general approximation principles traditionally
used in physical geodesy problems. In particular, it is shown that the use of a spatio-statistical (non-probabilistic) minimum
mean-square-error criterion for optimal linear estimation of deterministic signals, in conjunction with regularly gridded
data, always gives rise to a generalized multiresolution analysis in the Hilbert space L
2(R), under some mild constraints on the spatial covariance function and the power spectrum of the unknown field under consideration.
Using the theory and the actual approximation algorithms associated with statistical collocation, a new constructive framework
for building generalized multiresolution analyses in L
2(R) is presented, without the need for the usual dyadic restriction that exists in classic wavelet theory. The multiresolution and `non-stationary' aspects of the statistical collocation approximation
procedure are also discussed, and finally some conclusions and recommendations for future work are given.
Received: 26 January 1999 / Accepted: 16 August 1999 相似文献
2.
Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere 总被引：2，自引：1，他引：1
The Slepian problem consists of determining a sequence of functions that constitute an orthonormal basis of a subset of ℝ
(or ℝ2) concentrating the maximum information in the subspace of square integrable functions with a band-limited spectrum. The same
problem can be stated and solved on the sphere. The relation between the new basis and the ordinary spherical harmonic basis
can be explicitly written and numerically studied. The new base functions are orthogonal on both the subspace and the whole
sphere. Numerical tests show the applicability of the Slepian approach with regard to solvability and stability in the case
of polar data gaps, even in the presence of aliasing. This tool turns out to be a natural solution to the polar gap problem
in satellite geodesy. It enables capture of the maximum amount of information from non-polar gravity field missions.
Received: 10 June 1998 / Accepted: 20 May 1999 相似文献
3.
A. Saalfeld 《Journal of Geodesy》1999,73(6):291-297
When a collection of double differences is used to compute global-positioning-system satellite orbits from a permanent network
of receiving stations, linear dependence among the double-differenced observations reduces the number of double differences
that contribute new information to the computations. A maximal linearly independent subset of a large collection of double
differences contains all the information content of the full set. If r is the number of receivers and s is the number of satellites, the original collection of double differences may have size O(r
2
s
2), whereas the linearly independent subset has size no greater than O(rs). Only such a smaller independent subset needs to participate in the more expensive double-precision matrix computations
to correctly correlate all double differences, detect cycle slips, resolve ambiguities, and compute satellite orbits and station
positions and relative velocities. Dependence among double differences is characterized using vector space methods together
with geometric characterizations of Boolean matrices. These characterizations lend themselves to fast, robust algorithms for
computing maximal linearly independent sets (bases) of double differences. An algorithm is given for constructing a generating
independent set of double differences from the Boolean array of receiving-station/satellite connections. Characterizations
of generator equivalence allow alternative generating sets to be identified and selected. An updating algorithm to handle
local changes in the satellite–receiver connection matrix is also described.
Received: 27 August 1996 / Accepted: 28 January 1999 相似文献
4.
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 相似文献
5.
Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm 总被引：4，自引：0，他引：4
Erik W. Grafarend 《GPS Solutions》2000,4(2):31-44
In order to achieve to GPS solutions of first-order accuracy and integrity, carrier phase observations as well as pseudorange
observations have to be adjusted with respect to a linear/linearized model. Here the problem of mixed integer-real valued
parameter adjustment (IRA) is met. Indeed, integer cycle ambiguity unknowns have to be estimated and tested. At first we review
the three concepts to deal with IRA: (i) DDD or triple difference observations are produced by a properly chosen difference
operator and choice of basis, namely being free of integer-valued unknowns (ii) The real-valued unknown parameters are eliminated
by a Gauss elimination step while the remaining integer-valued unknown parameters (initial cycle ambiguities) are determined
by Quadratic Programming and (iii) a RA substitute model is firstly implemented (real-valued estimates of initial cycle ambiguities)
and secondly a minimum distance map is designed which operates on the real-valued approximation of integers with respect to
the integer data in a lattice. This is the place where the integer Gram-Schmidt orthogonalization by means of the LLL algorithm (modified LLL algorithm) is applied being illustrated by four examples. In particular, we prove
that in general it is impossible to transform an oblique base of a lattice to an orthogonal base by Gram-Schmidt orthogonalization where its matrix enties are integer. The volume preserving Gram-Schmidt orthogonalization operator constraint to integer entries produces “almost orthogonal” bases which, in turn, can be used to produce the integer-valued
unknown parameters (initial cycle ambiguities) from the LLL algorithm (modified LLL algorithm). Systematic errors generated
by “almost orthogonal” lattice bases are quantified by A. K. Lenstra et al. (1982) as well as M. Pohst (1987). The solution point of Integer Least Squares generated by the LLL algorithm is = (L')−1[L'◯] ∈ ℤ
m
where L is the lower triangular Gram-Schmidt matrix rounded to nearest integers, [L], and = [L'◯] are the nearest integers of L'◯, ◯ being the real valued approximation of z ∈ ℤ
m
, the m-dimensional lattice space Λ. Indeed due to “almost orthogonality” of the integer Gram-Schmidt procedure, the solution point is only suboptimal, only close to “least squares.” ? 2000 John Wiley & Sons, Inc. 相似文献
6.
7.
几种小波基在遥感图像压缩中的应用效果比较 总被引：4，自引：0，他引：4
分析了小波基的基本性质,简述了在遥感图像小波压缩中小波基选择的常用方法; 分别用4种常用的典型小波基对8幅含有
不同典型地物的遥感图像进行小波编码实验,并用5种方法全面评价了小波基的应用效果。结果表明,在遥感图像小波压缩中,D
(9,7)小波基的应用效果最好。据此,提出了一种小波基选择的改进方法。 相似文献
8.
基于小波分析的地貌多尺度表达与自动综合 总被引：28，自引：5，他引：28
基于小波多分辨率分析原理，给出了一种尺度依赖的地表形态抽象与表达方法。基于该方法研究了多尺度的地貌自动综合，提出了利用小波系数的范数比作衡量相应尺度综合程度的数量化指标，并结合实例予以说明。 相似文献
9.
A function having some properties of a wavelet and being harmonic around a given point in R
3 is defined, and three models showing the local relationships between the disturbing density, the disturbing potential and
the disturbing gravity are established by using the function as the kernel function of the integrals in the models. The local
relationship has two meanings. One is that we can evaluate with a high accuracy the integrals in the models by using mainly
high-accuracy and high-resolution data in a local area. The other is that we can obtain a stable solution with high resolution
when we invert the integrals in the models because of the rapid decrease of the kernel function of the integrals. As a result,
with these models we evaluate one quantity with high resolution, in a band limited by the maximum degree of a set of geopotential
coefficients or by the resolution (spacing) of the local data, from another quantity (or quantities) in a local area, and
the resulting solution is stable.
Received: 6 April 1998 / Accepted: 16 June 1999 相似文献
10.
In one way or the other, numerical methods for the evaluation of integral operators can often be related to the solution of
the so-called Galerkin equations. For convolution operators and exponentials with purely imaginary exponents as base functions
the Galerkin matrix becomes diagonal and this fact is the core of the FFT techniques, used in Physical Geodesy. For non-convolution
operators the FFT technique is not applicable. This paper aims at the development of a technique, which can also be applied
for non-convolution operators. This technique is based on the use of wavelets as base functions. In this case the Galerkin
matrix is not diagonal but (after thresholding) very sparse and this leads to methods, which are similarly efficient as FFT
in the convolution case. The paper starts with the theoretical background for n-dimensional wavelet analysis and the representation of integral operators with respect to those wavelet bases. The resulting
algorithm is tested for convolution and non-convolution operators. 相似文献
11.
Leaf mass per area (LMA), the ratio of leaf dry mass to leaf area, is a trait of central importance to the understanding of plant light capture and carbon gain. It can be estimated from leaf reflectance spectroscopy in the infrared region, by making use of information about the absorption features of dry matter. This study reports on the application of continuous wavelet analysis (CWA) to the estimation of LMA across a wide range of plant species. We compiled a large database of leaf reflectance spectra acquired within the framework of three independent measurement campaigns (ANGERS, LOPEX and PANAMA) and generated a simulated database using the PROSPECT leaf optical properties model. CWA was applied to the measured and simulated databases to extract wavelet features that correlate with LMA. These features were assessed in terms of predictive capability and robustness while transferring predictive models from the simulated database to the measured database. The assessment was also conducted with two existing spectral indices, namely the Normalized Dry Matter Index (NDMI) and the Normalized Difference index for LMA (NDLMA).Five common wavelet features were determined from the two databases, which showed significant correlations with LMA (R2: 0.51–0.82, p < 0.0001). The best robustness (R2 = 0.74, RMSE = 18.97 g/m2 and Bias = 0.12 g/m2) was obtained using a combination of two low-scale features (1639 nm, scale 4) and (2133 nm, scale 5), the first being predominantly important. The transferability of the wavelet-based predictive model to the whole measured database was either better than or comparable to those based on spectral indices. Additionally, only the wavelet-based model showed consistent predictive capabilities among the three measured data sets. In comparison, the models based on spectral indices were sensitive to site-specific data sets. Integrating the NDLMA spectral index and the two robust wavelet features improved the LMA prediction. One of the bands used by this spectral index, 1368 nm, was located in a strong atmospheric water absorption region and replacing it with the next available band (1340 nm) led to lower predictive accuracies. However, the two wavelet features were not affected by data quality in the atmospheric absorption regions and therefore showed potential for canopy-level investigations. The wavelet approach provides a different perspective into spectral responses to LMA variation than the traditional spectral indices and holds greater promise for implementation with airborne or spaceborne imaging spectroscopy data for mapping canopy foliar dry biomass. 相似文献
12.
The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on
reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential
coefficients
n,m
. In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal
harmonic series is developed for the geopotential and then its coefficients
n,m
e
are transformed to the unknown
n,m
. The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral
formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied
numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From
two sets of
n,m
(n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation
are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution
appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics
of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential
model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068)
by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to
apply the LS technique for evaluating geopotential coefficients.
Received: 12 December 2000 / Accepted: 21 June 2001 相似文献
13.
针对步态识别方法中加速度信号的去噪问题,提出了一种利用复合评价指标及小波熵进行步态加速度信号小波去噪的参数优选方法。均方根误差和平滑度的变化率随小波分解层数的增加表现出单调性和负相关性,根据该特性使用改进熵权法构建了一种复合评价指标,通过构建的复合评价指标确定不同小波基处理步态信号时的最优分解层数,根据步态信号小波分解后低频系数的小波熵大小来确定每一分解层次的最优小波基。实验结果表明,所提方法确定的小波去噪方案可以满足步态信号研究的滤波要求。 相似文献
14.
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
15.
A methodology for precise determination of the fundamental geodetic parameter w
0, the potential value of the Gauss–Listing geoid, as well as its time derivative 0, is presented. The method is based on: (1) ellipsoidal harmonic expansion of the external gravitational field of the Earth
to degree/order 360/360 (130 321 coefficients; http://www.uni-stuttgard.de/gi/research/ index.html projects) with respect
to the International Reference Ellipsoid WGD2000, at the GPS positioned stations; and (2) ellipsoidal free-air gravity reduction
of degree/order 360/360, based on orthometric heights of the GPS-positioned stations. The method has been numerically tested
for the data of three GPS campaigns of the Baltic Sea Level project (epochs 1990.8,1993.4 and 1997.4). New w
0 and 0 values (w
0=62 636 855.75 ± 0.21 m2/s2, 0=−0.0099±0.00079 m2/s2 per year, w
0/&γmacr;=6 379 781.502 m,0/&γmacr;=1.0 mm/year, and &γmacr;= −9.81802523 m2/s2) for the test region (Baltic Sea) were obtained. As by-products of the main study, the following were also determined: (1)
the high-resolution sea surface topography map for the Baltic Sea; (2) the most accurate regional geoid amongst four different
regional Gauss–Listing geoids currently proposed for the Baltic Sea; and (3) the difference between the national height datums
of countries around the Baltic Sea.
Received: 14 August 2000 / Accepted: 19 June 2001 相似文献
16.
Iterative vector methods for computing geodetic latitude and height from rectangular coordinates 总被引：4，自引：4，他引：4
J. Pollard 《Journal of Geodesy》2002,76(1):36-40
Two iterative vector methods for computing geodetic coordinates (φ, h) from rectangular coordinates (x, y, z) are presented. The methods are conceptually simple, work without modification at any latitude and are easy to program. Geodetic
latitude and height can be calculated to acceptable precision in one iteration over the height range from −106 to +109 m.
Received: 13 December 2000 / Accepted: 13 July 2001 相似文献
17.
Soil erodibility, which is difficult to estimate and upscaling, was determined in this study using multiple spectral models of soil properties (soil organic matter (SOM), water-stable aggregates (WSA) > 0.25 mm, the geometric mean radius (Dg)). Herein, the soil erodibility indicators were calculated, and soil properties were quantitatively analyzed based on laboratory simulation experiments involving two selected contrasting soils. In addition, continuous wavelet transformation was applied to the reflectance spectra (350–2500 nm) of 65 soil samples from the study area. To build the relationship, the soil properties that control erodibility were identified prior to the spectral analysis. In this study, the SOM, Dg and WSA >0.25 mm were selected to represent the most significant soil properties controlling erodibility and describe the erodibility indicator based on a logarithmic regression model as a function of SOM or WSA > 0.25 mm. Five, six and three wavelet features were observed to calibrate the estimated soil properties model, and the best performance was obtained with a combination feature regression model for SOM (R2 = 0.86, p < 0.01), Dg (R2 = 0.79, p < 0.01) and WSA >0.25 mm (R2 = 0.61, p < 0.01), respectively. One part of the wavelet features captured amplitude variations in the broad shape of the reflectance spectra, and another part captured variations in the shape and depth of the soil dry substances. The wavelet features for the validated dataset used to predict the SOM, WSA >0.25 mm and Dg were not significantly different compared with the calibrated dataset. The synthesized spectral models of soil properties, and the formation of a new equation for soil erodibility transformed from the spectral models of soil properties are presented in this study. These results show that a spectral analytical approach can be applied to complex datasets and provide new insights into emerging dynamic variation with erodibility estimation. 相似文献
18.
A 2×2 arc-minute resolution geoid model, CARIB97, has been computed covering the Caribbean Sea. The geoid undulations refer
to the GRS-80 ellipsoid, centered at the ITRF94 (1996.0) origin. The geoid level is defined by adopting the gravity potential
on the geoid as W
0=62 636 856.88 m2/s2 and a gravity-mass constant of GM=3.986 004 418×1014 m3/s2. The geoid model was computed by applying high-frequency corrections to the Earth Gravity Model 1996 global geopotential
model in a remove-compute-restore procedure. The permanent tide system of CARIB97 is non-tidal. Comparison of CARIB97 geoid
heights to 31 GPS/tidal (ITRF94/local) benchmarks shows an average offset (h–H–N) of 51 cm, with an Root Mean Square (RMS) of 62 cm about the average. This represents an improvement over the use of a global
geoid model for the region. However, because the measured orthometric heights (H) refer to many differing tidal datums, these comparisons are biased by localized permanent ocean dynamic topography (PODT).
Therefore, we interpret the 51 cm as partially an estimate of the average PODT in the vicinity of the 31 island benchmarks.
On an island-by-island basis, CARIB97 now offers the ability to analyze local datum problems which were previously unrecognized
due to a lack of high-resolution geoid information in the area.
Received: 2 January 1998 / Accepted: 18 August 1998 相似文献
19.
20.
Z. Martinec 《Journal of Geodesy》1998,72(7-8):460-472
Green's function for the boundary-value problem of Stokes's type with ellipsoidal corrections in the boundary condition for
anomalous gravity is constructed in a closed form. The `spherical-ellipsoidal' Stokes function describing the effect of two
ellipsoidal correcting terms occurring in the boundary condition for anomalous gravity is expressed in O(e
2
0)-approximation as a finite sum of elementary functions analytically representing the behaviour of the integration kernel
at the singular point ψ=0. We show that the `spherical-ellipsoidal' Stokes function has only a logarithmic singularity in
the vicinity of its singular point. The constructed Green function enables us to avoid applying an iterative approach to solve
Stokes's boundary-value problem with ellipsoidal correction terms involved in the boundary condition for anomalous gravity.
A new Green-function approach is more convenient from the numerical point of view since the solution of the boundary-value
problem is determined in one step by computing a Stokes-type integral. The question of the convergence of an iterative scheme
recommended so far to solve this boundary-value problem is thus irrelevant.
Received: 5 June 1997 / Accepted: 20 February 1998 相似文献