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1.
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 相似文献
2.
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
3.
XU Xinyu LI Jiancheng ZOU Xiancai CHU Yonghai 《地球空间信息科学学报》2007,10(3):168-172
The principle and method for solving three types of satellite gravity gradient boundary value problems by least-squares are discussed in detail. Also, kernel function expressions of the least-squares solution of three geodetic boundary value problems with the observations {Γ zz },{Γ xz , Γ yz} and {Γ xx -Γ yy ,2 Γxy}are presented. From the results of recovering gravity field using simulated gravity gradient tensor data, we can draw a conclusion that satellite gravity gradient integral formulas derived from least-squares are valid and rigorous for recovering the gravity field. 相似文献
4.
C. C. Tscherning 《Journal of Geodesy》1978,52(1):85-92
The term “entity” covers, when used in the field of electronic data processing, the meaning of words like “thing”, “being”,
“event”, or “concept”. Each entity is characterized by a set of properties.
An information element is a triple consisting of an entity, a property and the value of a property. Geodetic information is
sets of information elements with entities being related to geodesy. This information may be stored in the form ofdata and is called ageodetic data base provided (1) it contains or may contain all data necessary for the operations of a particular geodetic organization, (2)
the data is stored in a form suited for many different applications and (3) that unnecessary duplications of data have been
avoided.
The first step to be taken when establishing a geodetic data base is described, namely the definition of the basic entities
of the data base (such as trigonometric stations, astronomical stations, gravity stations, geodetic reference-system parameters,
etc...).
Presented at the “International Symposium on Optimization of Design and Computation of Control Networks”, Sopron, Hungary,
July 1977. 相似文献
5.
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
6.
Accuracy of GPS-derived relative positions as a function of interstation distance and observing-session duration 总被引:6,自引:0,他引:6
Ten days of GPS data from 1998 were processed to determine how the accuracy of a derived three-dimensional relative position
vector between GPS antennas depends on the chord distance (denoted L) between these antennas and on the duration of the GPS observing session (denoted T). It was found that the dependence of accuracy on L is negligibly small when (a) using the `final' GPS satellite orbits disseminated by the International GPS Service, (b) fixing
integer ambiguities, (c) estimating appropriate neutral-atmosphere-delay parameters, (d) 26 km ≤ L ≤ 300 km, and (e) 4 h ≤T ≤ 24 h. Under these same conditions, the standard error for the relative position in the north–south dimension (denoted S
n
and expressed in mm) is adequately approximated by the equation S
n
=k
n
/T
0.5 with k
n
=9.5 ± 2.1 mm · h0.5 and T expressed in hours. Similarly, the standard errors for the relative position in the east–west and in the up-down dimensions
are adequately approximated by the equations S
e
=k
e
/T
0.5 and S
u
=k
u
/T
0.5, respectively, with k
e
=9.9 ± 3.1 mm · h0.5 and k
u
=36.5 ± 9.1 mm · h0.5.
Received: 5 February 2001 / Accepted: 14 May 2001 相似文献
7.
Willi Freeden 《Journal of Geodesy》1980,54(1):1-20
Summary Let S be the (regular) boundary-surface of an exterior regionE
e
in Euclidean space ℜ3 (for instance: sphere, ellipsoid, geoid, earth's surface). Denote by {φn} a countable, linearly independent system of trial functions (e.g., solid spherical harmonics or certain singularity functions)
which are harmonic in some domain containingE
e
∪ S. It is the purpose of this paper to show that the restrictions {ϕn} of the functions {φn} onS form a closed system in the spaceC (S), i.e. any functionf, defined and continuous onS, can be approximated uniformly by a linear combination of the functions ϕn.
Consequences of this result are versions of Runge and Keldysh-Lavrentiev theorems adapted to the chosen system {φn} and the mathematical justification of the use of trial functions in numerical (especially: collocational) procedures. 相似文献
8.
In November 1968, a marine geodetic control point was established in the Pacific Ocean at a water depth of6,200 feet. The control point (reference point) consists of three underwater acoustic transponders, two of which are powered with
lead-acid batteries and the third with an underwater radioisotope power source “URIPS” with a10- to20- year life expectancy. Four independent measuring techniques (LORAC airborne line-crossing, satellite, ship inertial, and
acoustic techniques) were used to measure and determine the coordinates of the control point. Preliminary analysis of the
acoustic and airborne data indicates that high accuracies can be achieved in the establishment of geodetic reference points
at sea. Geodetic adjustment by the method of variation of coordinates yielded a standard point error of±50 to±66 feet in determining the unknown ship station. The original location of the ship station as determined by shipboard navigation
equipment was off by about1,600 feet.
Paper previously published in the Proceedings of the Second Marine Geodesy Symposium of the Marine Technology Society. 相似文献
9.
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
10.
Z. Martinec 《Journal of Geodesy》2003,77(1-2):41-49
Three independent gradiometric boundary-value problems (BVPs) with three types of gradiometric data, {Γ
rr
}, {Γ
r
θ,Γ
r
λ} and {Γθθ−Γλλ,Γθλ}, prescribed on a sphere are solved to determine the gravitational potential on and outside the sphere. The existence and
uniqueness conditions on the solutions are formulated showing that the zero- and the first-degree spherical harmonics are
to be removed from {Γ
r
θ,Γ
r
λ} and {Γθθ−Γλλ,Γθλ}, respectively. The solutions to the gradiometric BVPs are presented in terms of Green's functions, which are expressed in
both spectral and closed spatial forms. The logarithmic singularity of the Green's function at the point ψ=0 is investigated
for the component Γ
rr
. The other two Green's functions are finite at this point. Comparisons to the paper by van Gelderen and Rummel [Journal of
Geodesy (2001) 75: 1–11] show that the presented solution refines the former solution.
Received: 3 October 2001 / Accepted: 4 October 2002 相似文献
11.
Mohammad Asadullah Khan 《Journal of Geodesy》1973,47(3):227-235
An intrresting variation on the familiar method of determining the earth's equatorial radius ae, from a knowledge of the earth's equatorial gravity is suggested. The value of equatorial radius thus found is 6378,142±5
meters. The associated parameters are GM=3.986005±.000004 × 1020 cm3 sec-−2 which excludes the relative mass of atmosphere ≅10−6 ξ GM, the equatorial gravity γe 978,030.9 milligals (constrained in this solution by the Potsdam Correction of 13.67 milligals as the Potsdam Correction
is more directly, orless indirectly, measurable than the equatorial gravity) and an ellipsoidal flattening of f=1/298.255. 相似文献
12.
Urho A. Rauhala 《Journal of Geodesy》1979,53(4):317-342
Array algebra forms the general base of fast transforms and multilinear algebra making rigorous solutions of a large number
(millions) of parameters computationally feasible. Loop inverses are operators solving the problem of general matrix inverses.
Their derivation starts from the inconsistent linear equations
by a parameter exchangeX→L
0, where
X is a set of unknown observables,A
0 forming a basis of the so called “problem space”. The resulting full rank design matrix of parameters L0 and its ℓ-inverse reveal properties speeding the computational least squares solution
expressed in observed values
. The loop inverses are found by the back substitution expressing ∧X in terms ofL through
. Ifp=rank (A) ≤n, this chain operator creates the pseudoinverseA
+. The idea of loop inverses and array algebra started in the late60's from the further specialized case,p=n=rank (A), where the loop inverse A
0
−1
(AA
0
−1
)ℓ reduces into the ℓ-inverse Aℓ=(ATA)−1AT. The physical interpretation of the design matrixA A
0
−1
as an interpolator, associated with the parametersL
0, and the consideration of its multidimensional version has resulted in extended rules of matrix and tensor calculus and mathematical
statistics called array algebra. 相似文献
13.
Least-squares by observation equations is applied to the solution of geodetic boundary value problems (g.b.v.p.). The procedure is explained solving the vectorial Stokes problem in spherical and constant radius approximation. The results
are Stokes and Vening-Meinesz integrals and, in addition, the respective a posteriori variance-covariances.
Employing the same procedure the overdeterminedg.b.v.p. has been solved for observable functions potential, scalar gravity, astronomical latitude and longitude, gravity gradients
Гxz, Гyz, and Гzz and three-dimensional geocentric positions. The solutions of a large variety of uniquely and overdeterminedg.b.v.p.'s can be obtained from it by specializing weights. Interesting is that the anomalous potential can be determined—up to a
constant—from astronomical latitude and longitude in combination with either {Гxz,Гyz} or horizontal coordinate corrections Δx and Δy, or both. Dual to the formulation in terms of observation equations the overdeterminedg.b.v.p.'s can as well be solved by condition equations.
Constant radius approximation can be overcome in an iterative approach. For the Stokes problem this results in the solution
of the “simple” Molodenskii problem. Finally defining an error covariance model with a Krarup-type kernel first results were
obtained for a posteriori variance-covariance and reliability analysis. 相似文献
14.
A new local existence and uniqueness theorem is obtained for the scalar geodetic boundary-value problem in spherical coordinates.
The regularities H
α and H
1+α are assumed for the boundary data g (gravity) and v (gravitational potential) respectively.
Received: 27 July 1998 / Accepted: 19 April 1999 相似文献
15.
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
16.
Sheshakumar K. Goroshi R. P. Singh S. Panigrahy J. S. Parihar 《Journal of the Indian Society of Remote Sensing》2011,39(3):315-321
This paper highlights the spatial and temporal variability of atmospheric columnar methane (CH4) concentration over India and its correlation with the terrestrial vegetation dynamics. SCanning IMaging Absorption spectrometer
for Atmospheric CHartographY (SCIAMACHY) on board ENVIronmental SATellite (ENVISAT) data product (0.5° × 0.5°) was used to
analyze the atmospheric CH4 concentration. Satellite Pour l'Observation de la Terre (SPOT)-VEGETATION sensor’s Normalized Difference Vegetation Index
(NDVI) product, aggregated at 0.5° × 0.5° grid level for the same period (2004 and 2005), was used to correlate the with CH4 concentration. Analysis showed mean monthly CH4 concentration during the Kharif season varied from 1,704 parts per billion volume (ppbv) to 1,780 ppbv with the lowest value in May and the highest value
in September. Correspondingly, mean NDVI varied from 0.28 (May) to 0.53 (September). Analysis of correlation between CH4 concentration and NDVI values over India showed positive correlation (r = 0.76; n = 6) in Kharif season. Further analysis using land cover information showed characteristic low correlation in natural vegetation region
and high correlation in agricultural area. Grids, particularly falling in the Indo-Gangetic Plains showed positive correlation.
This could be attributed to the rice crop which is grown as a predominant crop during this period. The CH4 concentration pattern matched well with growth pattern of rice with the highest concentration coinciding with the peak growth
period of crop in the September. Characteristically low correlation was observed (r = 0.1; n = 6) in deserts of Rajasthan and forested Himalayan ecosystem. Thus, the paper emphasizes the synergistic use of different
satellite based data in understanding the variability of atmospheric CH4 concentration in relation to vegetation. 相似文献
17.
O. Remmer 《Journal of Geodesy》1969,43(2):99-122
A method for filtering of geodetic observationwhich leaves the final result normally distributed, is presented. Furthermore, it is shown that if you sacrifice100.a% of all the observations you may be (1−β).100% sure that a gross error of the size Δ is rejected.
Another and, may be intuitively, more appealing method is presented; the two methods are compared and it is shown why Method
1 should be preferred to Method 2 for geodetic purposes.
Finally the two methods are demonstrated in some numerical examples. 相似文献
18.
As a conformal mapping of the sphere S 2
R
or of the ellipsoid of revolution E 2
A
,
B
the Mercator projection maps the equator equidistantly while the transverse Mercator projection maps the transverse metaequator,
the meridian of reference, with equidistance. Accordingly, the Mercator projection is very well suited to geographic regions
which extend east-west along the equator; in contrast, the transverse Mercator projection is appropriate for those regions
which have a south-north extension. Like the optimal transverse Mercator projection known as the Universal Transverse Mercator Projection (UTM), which maps the meridian of reference Λ0 with an optimal dilatation factor &ρcirc;=0.999 578 with respect to the World Geodetic Reference System WGS 84 and a strip [Λ0−Λ
W
,Λ0 + Λ
E
]×[Φ
S
,Φ
N
]= [−3.5∘,+3.5∘]×[−80∘,+84∘], we construct an optimal dilatation factor ρ for the optimal Mercator projection, summarized as the Universal Mercator Projection (UM), and an optimal dilatation factor ρ0 for the optimal polycylindric projection for various strip widths which maps parallel circles Φ0 equidistantly except for a dilatation factor ρ0, summarized as the Universal Polycylindric Projection (UPC). It turns out that the optimal dilatation factors are independent of the longitudinal extension of the strip and depend
only on the latitude Φ0 of the parallel circle of reference and the southern and northern extension, namely the latitudes Φ
S
and Φ
N
, of the strip. For instance, for a strip [Φ
S
,Φ
N
]= [−1.5∘,+1.5∘] along the equator Φ0=0, the optimal Mercator projection with respect to WGS 84 is characterized by an optimal dilatation factor &ρcirc;=0.999 887 (strip width 3∘). For other strip widths and different choices of the parallel circle of reference Φ0, precise optimal dilatation factors are given. Finally the UPC for the geographic region of Indonesia is presented as an
example.
Received: 17 December 1997 / Accepted: 15 August 1997 相似文献
19.
Burkhard Schaffrin 《Journal of Geodesy》1987,61(3):276-280
The Bayesian estimates
b of the standard deviation σ in a linear model—as needed for the evaluation of reliability—is well known to be proportional
to the square root of the Bayesian estimate (s
2)
b
of the variance component σ2 by a proportionality factor
involving the ratio of Gamma functions. However, in analogy to the case of the respective unbiased estimates, the troublesome
exact computation ofa
b may be avoided by a simple approximation which turns out to be good enough for most applications even if the degree of freedom
ν is rather small.
Paper presented to the Int. Conf. on “Practical Bayesian Statistics”, Cambridge (U.K.), 8.–11. July 1986. 相似文献
20.
Beena Kumari 《Journal of the Indian Society of Remote Sensing》2005,33(4):541-546
The accuracy of satellite derived chlorophylla (chla) using empirical algorithms (OC2 and OC4) is about ± 30–35%, which is attributed mainly to the sensor and atmospheric constraints
and also the bio-optical algorithms. However errors inin situ measurement of chla may also contribute to the retrieval accuracy. The fluorometric method of chla measurement can significantly under or overestimate chla concentrations. This is mainly because of the overlap of the absorption and fluorescence bands of co-occurring chlorophyllsb andc, chlorophyll degradation products, and accessory pigment. Accurate chla measurements are important for validating satellite derived chla accuracy and algorithm development. The focus of this study was to understand the discrepancy between fluorometric and HPLC
(High Performance Liquid Chromatography) derived chla using unialgal cultures, natural field samples from Bedford Basin and samples from MinOx cruise to analyse divinyl chla. Approximately 50% underestimation of chla both in the natural samples as well as cultured samples has been observed by fiuorometer. The results of MinOx cruise data
indicated shifting of the blue absorption maxima towards longer wavelengths (~450nm), which is consistent with high concentration
of divinyl chla (chla
2) associated with prochlorophytes. 相似文献