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1.
Ebong  M. B. 《Journal of Geodesy》1986,60(4):279-287
Computer values of the mean square error of the Nigerian Geodetic Levelling based on the model xij = ρij/R ij 1/2 showed a uniformity between the lines of levelling, of a nature which suggest that xij = ρij/R ij 1/2 is a good fit for the data. Values of the mean square error of the levelling based on wij = ρij/Rij showed such significant variation between the lines that this alternative model does not seem to be supported by the data used in this study.  相似文献   

2.
The method of Bjerhammar is studied in the continuous case for a sphere. By varying the kernel function, different types of unknowns (u*) are obtained at the internal sphere (the Bjerhammar sphere). It is shown that a necessary condition for the existence of u* is that the degree variances (σ n 2 ) of the observations are of an order less than n−2. According to Kaula’s rule this condition is not satisfied for the earth’s gravity anomaly field (σ n 2 =n−1) but well for the geopotential (σ n 2 =n−3).  相似文献   

3.
An investigation was made of the behaviour of the variable (where ρij are the discrepancies between the direct and reverse measurements of the height of consecutive bench marks and theR ij are their distance apart) in a partial net of the Italian high precision levelling of a total length of about1.400 km. The methods of analysis employed were in general non-parametric individual and cumulative tests; in particular randomness, normality and asymmetry tests were carried out. The computers employed wereIBM/7094/7040. From the results evidence was obtained of the existence of an asymmetry in respect to zero of thex ij confirming the well-known results given firstly by Lallemand. A new result was obtained from the tests of randomness which put in evidence trends of the mean values of thex ij and explained some anomalous behaviours of the cumulative discrepancy curves. The extension of this investigation to a broader net possibly covering other national nets would be very useful to get a deeper insight into the behaviour of the errors in high precision levelling. Ad hoc programs for electronic computers are available to accomplish this job quickly. Presented at the 14th International Assembly of Geodesy (Lucerne, 1967).  相似文献   

4.
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   

5.
The mathematic theory for uncertainty model of line segment are summed up to achieve a general conception, and the line error hand model of εσ is a basic uncertainty model that can depict the line accuracy and quality efficiently while the model of εm and error entropy can be regarded as the supplement of it. The error band model will reflect and describe the influence of line uncertainty on polygon uncertainty. Therefore, the statistical characteristic of the line error is studied deeply by analyzing the probability that the line error falls into a certain range. Moreover, the theory accordance is achieved in the selecting the error buffer for line feature and the error indicator. The relationship of the accuracy of area for a polygon with the error loop for a polygon boundary is deduced and computed.  相似文献   

6.
GLONASS time is the reference for all time scales aboard GLONASS satellites. It is derived from the Central Synchronizer (CS), which consists of an ensemble of hydrogen clocks (HC) having a instability of (1...3) × 10−14 (averaging interval 24 hours). The CS time is compared to UTC(SU) in a differential mode using a TV channel of the Technical TV Center. Presently the error of GLONASS time is within 20...150 ns; however, there is a potential to decrease this value to 15 to 50 ns (3σ). The paper discusses the possible benefits of mutual phase comparisons between the HCs to determine the grouped frequency standard. These comparisons are averaged daily. The approach yields an accuracy of better than 10 ns (3σ) for CS, bringing the expected GLONASS time accuracy to the level of 15 to 50 ns (3σ). ? 2001 John Wiley & Sons, Inc.  相似文献   

7.
A set of2261 5°×5° mean anomalies were used alone and with satellite determined harmonic coefficients of the Smithsonian' Institution to determine the geopotential expansion to various degrees. The basic adjustment was carried out by comparing a terrestrial anomaly to an anomaly determined from an assumed set of coefficients. The (14, 14) solution was found to agree within ±3 m of a detailed geoid in the United States computed using1°×1° anomalies for an inner area and satellite determined anomalies in an outer area. Additional comparisons were made to the input anomaly field to consider the accuracy of various harmonic coefficient solutions. A by-product of this investigation was a new γE=978.0463 gals in the Potsdam system or978.0326 gals in an absolute system if −13.7 mgals is taken as the Potsdam correction. Combining this value of γE withf=1/298.25, KM=3.9860122·10 22 cm 3 /sec 2 , the consistent equatorial radius was found to be6378143 m.  相似文献   

8.
Modern models of the Earth's gravity field are developed in the IERS (International Earth Rotation Service) terrestrial reference frame. In this frame the mean values for gravity coefficients of the second degree and first order, C 21(IERS) and S 21(IERS), by the current IERS Conventions are recommended to be calculated by using the observed polar motion parameters. Here, it is proved that the formulae presently employed by the IERS Conventions to obtain these coefficients are insufficient to ensure their values as given by the same source. The relevant error of the normalized mean values for C 21(IERS) and S 21(IERS) is 3×10−12, far above the adopted cutoff (10−13) for variations of these coefficients. Such an error in C 21 and S 21 can produce non-modeled perturbations in motion prediction of certain artificial Earth satellites of a magnitude comparable to the accuracy of current tracking measurements. Received: 14 September 1998 / Accepted: 20 May 1999  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.
GOCE gravitational gradients along the orbit   总被引：6，自引：3，他引：3  
GOCE is ESA’s gravity field mission and the first satellite ever that measures gravitational gradients in space, that is, the second spatial derivatives of the Earth’s gravitational potential. The goal is to determine the Earth’s mean gravitational field with unprecedented accuracy at spatial resolutions down to 100 km. GOCE carries a gravity gradiometer that allows deriving the gravitational gradients with very high precision to achieve this goal. There are two types of GOCE Level 2 gravitational gradients (GGs) along the orbit: the gravitational gradients in the gradiometer reference frame (GRF) and the gravitational gradients in the local north oriented frame (LNOF) derived from the GGs in the GRF by point-wise rotation. Because the V XX , V YY , V ZZ and V XZ are much more accurate than V XY and V YZ , and because the error of the accurate GGs increases for low frequencies, the rotation requires that part of the measured GG signal is replaced by model signal. However, the actual quality of the gradients in GRF and LNOF needs to be assessed. We analysed the outliers in the GGs, validated the GGs in the GRF using independent gravity field information and compared their assessed error with the requirements. In addition, we compared the GGs in the LNOF with state-of-the-art global gravity field models and determined the model contribution to the rotated GGs. We found that the percentage of detected outliers is below 0.1% for all GGs, and external gravity data confirm that the GG scale factors do not differ from one down to the 10−3 level. Furthermore, we found that the error of V XX and V YY is approximately at the level of the requirement on the gravitational gradient trace, whereas the V ZZ error is a factor of 2–3 above the requirement for higher frequencies. We show that the model contribution in the rotated GGs is 2–35% dependent on the gravitational gradient. Finally, we found that GOCE gravitational gradients and gradients derived from EIGEN-5C and EGM2008 are consistent over the oceans, but that over the continents the consistency may be less, especially in areas with poor terrestrial gravity data. All in all, our analyses show that the quality of the GOCE gravitational gradients is good and that with this type of data valuable new gravity field information is obtained.  相似文献   

11.
 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   

12.
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   

13.
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   

14.
The short wavelength geoid undulations, caused by topography, amount to several decimeters in mountainous areas. Up to now these effects are computed by means of digital terrain models in a grid of 100–500m. However, for many countries these data are not yet available or their collection is too expensive. This problem can be overcome by considering the special behaviour of the gravity potential along mountain slopes. It is shown that 90 per cent of the topographic effects are represented by a simple summation formula, based on the average height differences and distances between valleys and ridges along the geoid profiles, δN=[30.H.D.+16.(H−H′).D] in mm/km, (error<10%), whereH, H′, D are estimated in a map to the nearest 0.2km. The formula is valid for asymmetric sides of valleys (H, H′) and can easily be corrected for special shapes. It can be used for topographic refinement of low resolution geoids and for astrogeodetic projects. The “slope method” was tested in two alpine areas (heights up to 3800m, astrogeodetic deflection points every 170km 2) and resulted in a geoid accuracy of ±3cm. In first order triangulation networks (astro points every 1000km 2) or for gravimetric deflections the accuracy is about 10cm per 30km. Since a map scale of 1∶500.000 is sufficient, the method is suitable for developing countries, too.  相似文献   

15.
Based on the gravity field models EGM96 and EIGEN-GL04C, the Earth＇s time-dependent principal moments of inertia A, B, C are obtained, and the variable rotation of the Earth is determined. Numerical results show that A, B, and C have increasing tendencies; the tilt of the rotation axis increases 2.1×10^ 8 mas/yr; the third component of the rotational angular velocity, ω3 , has a decrease of 1.0×10^ 22 rad/s^2, which is around 23% of the present observed value. Studies show in detail that both 0 and ω3 experience complex fluctuations at various time scales due to the variations of A, B and C.  相似文献   

16.
吴浩  王先华  叶函函  蒋芸  段锋华  吕松 《遥感学报》2019,23(6):1223-1231
大气温室气体监测仪GMI（Greenhouse gases Monitor Instrument）是高分五号（GF-5）卫星载荷之一,主要用于全球温室气体含量监测和碳循环研究。高精度反演是卫星大气CO2遥感的基本需求。地表反射率影响卫星遥感辐射量及辐射传输过程中的地气耦合过程,严重制约着CO2的反演精度,针对GMI开发高精度的大气CO2反演算法,地表反射是一个需要重点考虑的因素。城市是CO2重要的发射源,且城市下垫面存在明显的二向反射特性,加上城市大气条件不良,复杂的地气耦合效应存在这都考验反演算法的准确性和鲁棒性。本文针对北京城市地区,利用2011年—2016年共5年的MODIS（MODerate-resolution Imaging Spectroradiometer）地表二向反射分布函数BRDF（Bidirectional Reflectance Distribution Function）数据,构建了适合利用单次观测数据反演的BRDF模型,并提出一种同时反演地表BRDF参数和大气CO2含量的算法。结果表明在550 nm波长处气溶胶光学厚度AOD（Aerosol Optical Depth）小于0.4时,大部分GMI模拟数据的反演误差控制在0.5%（~2 ppm）内。利用GOSAT （Greenhouse gases Observing SATellite）实测数据的反演结果与修正后的日本国立环境研究所NIES（National Institute for Environmental Studies）反演结果进行对比,其平均误差为1.25 ppm,相关性达到0.85。本算法满足GMI数据在北京城市区域高精度CO2反演的需求,并使得反演高值气溶胶区域数据成为可能,增加了GMI观测数据的利用率。  相似文献   

17.
Construction of anisotropic covariance functions using Riesz-representers   总被引：1，自引：1，他引：0  
A reproducing-kernel Hilbert space (RKHS) of functions harmonic in the set outside a sphere with radius R 0, having a reproducing kernel K 0(P,Q) is considered (P, Q, and later P n being points in the set of harmonicity). The degree variances of this kernel will be denoted σ0 n . The set of Riesz representers associated with the evaluation functionals (or gravity functionals) related to distinct points P n ,n = 1,…,N, on a two-dimensional surface surrounding the bounding sphere, will be linearly independent. These functions are used to define a new N-dimensional RKHS with kernel (a n >0)
If the points all are located on a concentric sphere with radius R 1>R 0, and form an ε-net covering the sphere, and a n are suitable area elements (depending on N), then this kernel will converge towards an isotropic kernel with degree variances
Consequently, if K N (P,Q) is required to represent an isotropic covariance function of the Earth's gravity potential, COV(P,Q), σ0 n can be selected so that σ n becomes equal to the empirical degree variances. If the points are chosen at varying radial distances R n >R 0, then an anisotropic kernel, or equivalent covariance function representation, can be constructed. If the points are located in a bounded region, the kernel may be used to modify the original kernel
Values of anisotropic covariance functions constructed based on these ideas are calculated, and some initial ideas are presented on how to select the points P n . Received: 24 September 1998 / Accepted: 10 March 1999  相似文献   

18.
Caspary  W. F.  König  R. 《Journal of Geodesy》1986,60(2):143-153
In order to assess the accuracy, reliability and efficiency of current inertial surveying systems a joint project has been started at the University of the Bundeswehr Munich. As a part of this project the testnet Ebersberger Forst has been established. It consists of 60 monumented points located at cross-roads in a flat area and it makes up a grid pattern of6 N-S and9 E-W traverses with a spacing of1–2 km. The points are determined by classical surveying techniques with a standard deviation of less than1 cm forE, N andH. Observation campaigns were carried through with a Ferranti, a Honeywell and a Litton system. Each campaign consisted of three independent missions performed under identical observation schemes. The preliminary evaluation of the data sets leads to standard deviations of between8 and16 cm for each coordinate if determined in a single mission with a Honeywell or Litton system. The correlations along a traverse follow approximately the series ρ, ρ2, ρ3, ... with ρ⋟0.9. Cross correlation is only present betweenE orN, respectively, andH. The positions observed with the Ferranti system are less accurate, which might be explainable by the applied software and by two gross input errors during the missions. A rigorous post-mission adjustment of the data considerably improved the results.  相似文献   

19.
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   

20.
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   

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