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1.
An adjustment method of angular and distance measurements for densification of horizontal control is presented, where the resulting network has the properties of a free net. The higher order control points form an integral part of the net and serve as a source for datum definition. The relative positions of the points in the net are independent of the higher order control points and are determined by the measurements and their respective covariance matrix. The solution is equivalent to the orthogonal transformation of a minimum constraints solution of a net where the transformation parameters are determined by the control points and their a—priori covariance matrix.  相似文献   

2.
This paper is intended to demonstrate the usefulness of array algebra techniques in certain multilinear least squares problems. A typical restriction of array algebra is the need for a gridded observational structure; however, the grid does not have to be uniform and in general is not limited to any particular coordinate system nor to two- or three-dimensional spaces. Another restriction comes to light when dealing with weighted multilinear least squares adjustments. The a—priori variance-covariance matrix cannot be completely arbitrary but must be expressible in terms of certain matrix products. There exist various practical ways (not discussed herein) to bridge these restrictions. The reward for using the array algebra technique when it is appropriate lies in the great computational savings. From the theoretical point of view, the backbone of most derivations are the “R-matrix multiplications” and a simple tool, demonstrated herein, called “fundamental transformation”. It follows that the least squares solution of “array observation equations” does not have to be sought by some new and complex mathematical means. The fundamental transformation allows such an adjustment problem to be rewritten in a conventional (monolinear) form; the familiar least squares solution is then written down and transformed back to the array form using the same tool. The statistical properties of the results (e.g. minimum variance) are known from the conventional approach and do not have to be rederived in the array case.  相似文献   

3.
If satellite range-rate information is given continuously on an extra terrestrial sphere (S), the spherical harmonic coefficients of the gravitational potential of the Earth can be determined by direct integration of the data. An exact solution is given in the case when circular satellite orbits crosses S in all directions. A simpler acquisition of the data is achieved when the observations are restricted to polar satellite orbits. However, in this case the solutions become more complex due to attenuation. A solution to order sin Δ, where Δ is the separation angle of the two satellites, is given for the zonal harmonics. For tesseral hamonics a zero-order solution is derived. Corrections are given for observations out of S. Finally, the along track configuration of the satellite pair is compared with a radially designed satellite system (one above the other). The former is found most favourable for the recovery of geopotential coefficients.  相似文献   

4.
Existing position information in a network can be integrated with the densification solution in two ways: One way is to obtain a solution of the densification network followed by a merger of this and all other solutions or vice versa. Alternatively, the existing solutions (not used as weighted constraints) can be taken to be pseudo-observations in a simultaneous adjustment with the “new” observations. In both cases, all existing solutions must first be transformed to the coordinate system of the densified network and be statistically compatible with it. Simultaneous densification and integration is discussed through mathematical adjustment models in which the geometrical strength of networks is underscored. The rationale behind densifying and integrating networks either in two different steps or simultaneously is analyzed. It is concluded that the simultaneous approach should be avoided unless the various solutions turn out to be statistically compatible.  相似文献   

5.
In the determination of the preliminary geoid over Zambia, we compare three methods of the modified Stokes formula: that of Vincent and Marsh, a modified Wong and Gore method, and a modified spectral weighting method, with the final solution being estimated by the modified Wong and Gore procedure. The geoid over Zambia (based on GRS80) is rising from north-east to south-west. It coincides with the reference ellipsoid in the north-western and southern regions of Zambia. The preliminary estimate indicates maximum and minimum values of about 13.7 and −16.8m, respectively. The mean geoid over the area is −2.8m. Formal analysis of global root mean square errors for the three models leads us to conclude that for an integration cap radius of about 3 or less, the modified formula using optimal spectral weighting is superior to the Vincent and Marsh method, and to the modified and unmodified Wong and Gore. Received: 8 October 1996 / Accepted: 25 June 1997  相似文献   

6.
Urban congestion patterns have become ubiquitous and complex. Traditional, “static” approaches are no longer adequate for analyzing network flows and conducting minimum cost routing. This paper reports on a GIS-based decision support tool for modeling dynamic network congestion and conducting minimum cost routing. The system predicts network flows at a detailed level of temporal resolution, capturing dynamic congestion propagation effects. A Route Planner module solves for the combined departure time and minimum cost routing required for a trip to reach its destination by a given deadline. The GIS provides effective decision support through its database management capabilities, graphical user interfaces and cartographic visualization. This supports analyses of “what-if?” scenarios for strategic planning and tactical management subject to unplanned network disturbances. Received: 1 October 1999/Accepted: 21 September 2000  相似文献   

7.
Finite covariance functions   总被引：1，自引：0，他引：1  
Because of the full covariance matrices and the computer storage limitations the number of measurements which can be handled by the collocation method simultaneously, is limited. This paper presents a method to compute covariance functions with a finite support yielding sparse covariance matrices. The theoretical background is pointed out and, for the one- and two-dimensional case, special functions are developed which can be combined with the usually used covariance functions to get a “finite covariance function”. Simulated examples to demonstrate the behaviour of different solution methods to solve these special, sparse covariance matrices supplement our investigations.  相似文献   

8.
 The proper and optimal design and subsequent assessment of geodetic networks is an integral part of most surveying engineering projects. Optimization and design are carried out before the measurements are actually made. A geodetic network is designed and optimized in terms of high reliability and the results are compared with those obtained by the robustness analysis technique. The purpose of an optimal design is to solve for both the network configuration (first-order design) and observations accuracy (second-order design) in order to meet the desired criteria. For this purpose, an analytical method is presented for performing the first-order design, second-order design, and/or the combined design. In order to evaluate the geometrical strength of a geodetic network, the results of robustness analysis are displayed in terms of robustness in rotation, robustness in shear, and robustness in scale. Results showed that the robustness parameters were affected by redundancy numbers. The largest robustness parameters were due to the observations with minimum redundancy numbers. Received: 14 August 2000 / Accepted: 2 January 2001  相似文献   

9.
 The analytical continuation of the surface gravity anomaly to sea level is a necessary correction in the application of Stokes' formula for geoid estimation. This process is frequently performed by the inversion of Poisson's integral formula for a sphere. Unfortunately, this integral equation corresponds to an improperly posed problem, and the solution is both numerically unstable, unless it is well smoothed, and tedious to compute. A solution that avoids the intermediate step of downward continuation of the gravity anomaly is presented. Instead the effect on the geoid as provided by Stokes' formula is studied directly. The practical solution is partly presented in terms of a truncated Taylor series and partly as a truncated series of spherical harmonics. Some simple numerical estimates show that the solution mostly meets the requests of a 1-cm geoid model, but the truncation error of the far zone must be studied more precisely for high altitudes of the computation point. In addition, it should be emphasized that the derived solution is more computer efficient than the detour by Poisson's integral. Received: 6 February 2002 / Accepted: 18 November 2002 Acknowledgements. Jonas ?gren carried out the numerical calculations and gave some critical and constructive remarks on a draft version of the paper. This support is cordially acknowledged. Also, the thorough work performed by one unknown reviewer is very much appreciated.  相似文献   

10.
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   

11.
The two main inherent optical properties (IOPs) namely absorption and back scattering coefficients were estimated using a quasi analytical algorithm (QAA) for open and coastal ocean waters of Arabian Sea. Absorption due to gelbstoff and back scattering due to the particulate matter were calculated using the quasi analytical algorithm for all the in-situ measured reflectance spectra collected in the Arabian Sea. A comparative study was made to study the spectral variability of reflectance spectra in open as well as coastal waters of Arabian Sea. Spectral analysis was made for the absorption and back scattering coefficients calculated using the QAA for both open and coastal waters. The absorption coefficient in the open ocean waters vary from a minimum value of 0.029 to a maximum value of 0.445 and it varies from a minimum value of 0.081 to a maximum value of 4.000 for the coastal waters of Arabian Sea. Absorption due to gelbstoff or the CDOM ag(λ), calculated for the Arabian Sea waters show a variation of 0.000202 to 0.112437 for open ocean waters and it varies from 0.002848 to 2.8936 for coastal waters of Arabian Sea. Particulate back scattering coefficient for open ocean waters vary from 0.0000307 to 0.006575 whereas bbp(λ) vary from 0.000167 to 0.026014 for coastal ocean waters. The minimum slope for the open ocean waters is 0.989 and maximum value of 2.147 (average value of 1.7) was observed; whereas a minimum value of 0.046 and a maximum value of 1.201 (average value of 0.6) were observed from the in-situ spectra for coastal waters of Veraval. The slope ‘Y’ estimated from the model is 1.957 for open ocean waters and 0.515 for coastal waters collected in the Arabian Sea.  相似文献   

12.
Alternate formulas are given for the rigorous non-iterative solution of very long (as well as medium and very short) geodesics. They are not only shorter and simpler than the author’s original version published in the Bulletin Géodésique, but the powers of the spheroid parameter can be factored out in the same manner as in the corresponding solution of the Direct Geodetic Problem. Theoretical, as well as practical, significance is noted.  相似文献   

13.
The development of the analytical theory of the motion of an artificial satellite (Berger, 1972–1975) points out the great importance of the second, third order and coupling terms between zonal harmonics. These terms have been added to the equations established byKing-Hele andCook (1968–1973) for the determination of odd zonal harmonics. This solution is compared with theirs. It satisfies all the equations much better and especially the equations relating to near-critical inclination satellites.  相似文献   

14.
The vector-based algorithms for biaxial and triaxial ellipsoidal coordinates presented by Feltens (J Geod 82:493–504, 2008; 83:129–137, 2009) have been extended to hyperboloids of one sheet. For the backward transformation from Cartesian to hyperboloidal coordinates, of two iterative process candidates one was identified to be well suited. It turned out that a careful selection of the center of curvature is essential for the establishment of a stable and reliable iteration process. In addition, for zero hyperboloidal heights a closed solution is presented. The hyperboloid algorithms are again based on simple formulae and have been successfully tested for various theoretical hyperboloids. The paper concludes with a practical application example on a cooling tower construction.  相似文献   

15.
There is a long history of recognising and interpreting discontinuous change—phase transitions—in urban systems. In this paper, we use the aggregate retail model as an archetype to explore some new ideas. For example, we argue that the dependence of paths of development on initial conditions has been understudied, and we offer a new graphical analysis that demonstrates explicitly their influence on discrete change. We introduce an order parameter, and we plot this on a ‘results grid’ to facilitate the discovery of possible phase transitions. We illustrate the use of these new developments with an application to London. We show how retail developers can change the ‘initial conditions’ at a point in time and possibly bring about phase transitions by their actions. This also shows that it should be possible to account for the history of urban development as a sequence of initial conditions, illustrating path dependence. Secondly, the model could be deployed in relation to a new shopping zone, and the tools developed here used to calculate the minimum size of a new development in order for it to compete. We explore the ‘minimum size’ idea in relation to a new shopping zone in London.  相似文献   

16.
秩亏自由网平差的一种新解法   总被引：2，自引：1，他引：1  
提出秩亏自由网平差的一种新解法,只亲知道误差方程系数阵中ｔ０个线性无关的列向量,就能很快地得到最小二乘最小范数解,实际计算表明,这种新解法是简单有效的。  相似文献   

17.
GSPP is a computer program system which has been developed for the purposes of automatically determining and representing gravity field surfaces like the geoid, the field of gravity anomalies or deviations of the vertical at prescribed altitude, etc. The system processes gravity field information given by a heterogeneous set of linear functionals of the anomalous potential superimposed by noise, and provides automatically gravity field surfaces in terms of profiles, contour maps and/or 3-dimensional representations. The solution is generally based on least-squares collocation; for a homogeneous data set, a simple weighted average interpolation is available as well. Based on the given data, surface function values at the grid points of a regular rectangular grid are predicted. The representation of the surfaces is smooth using bicubic spline functions. GSPP has a control unit which performs all necessary decision processes and such reduces the user’s decision making to a minimum. The system has been designed for geodetic purposes only; however, because of its versatility and flexibility it presents itself also for applications in other geosciences.  相似文献   

18.
The use of the fast Fourier transform algorithm in the evaluation of the Molodensky series terms is demonstrated in this paper. The solution by analytical continuation to point level has been reformulated to obtain convolution integrals in planar approximation which can be efficiently evaluated in the frequency domain. Preliminary results show that the solution by Faye anomalies is not sufficient for highly accurate deflections of the vertical and height anomalies. The Molodensky solution up to at least the second-order term must be carried out. Part of the unrecovered deflection and height anomaly signal appears to be due to density variations, verifying the essential role of density modelling. A remove-restore technique for the terrain effects can improve the convergence of the series and minimize the interpolation errors. Paper presented at theI Hotine-Marussi Symposium on Mathematical Geodesy, Rome, June 3–6, 1985.  相似文献   

19.
Rough weather ship routing is studied using model hindcast wave climate. With the launch of IRS-P4 (OCEANSAT-I), it became possible to carry out routine wave forecasting over the Indian Ocean. The MSMR channel of the satellite gives scalar wind, which is analysed at National center for Medium Range Weather Forecasting (NCMRWF), India for converting to vector winds. The same is used as input to third generation wave model for the rough weather month of July 2000. Simulations are carried out using Cycle-4 of third generation spectral wave model WAM for regional grid system. This simulated wave climate formed the basis for computing effective ship velocity in the irregular seaway. This study gives a quantitative estimation of change in ship velocity in the open Indian Ocean for a Liberty type ship. The optimal route is charted using Dijkstra’s algorithm for minimal time path between Calcutta and Sumatra. The optimum track information has broad scope for obtaining a safer route, least time route by avoiding delay in schedule with minimum fuel consumption.  相似文献   

20.
Principles of North determination using suspended gyrocompasses are reviewed. Accuracy is evaluated and a procedure with two series of measurements symmetrical with respect to the zero torsion tape position is mathematically proven to be the “best” (minimum variance). Our purpose is to prove that a 20″ accuracy (1 σ) instrument was brought to a level of accuracy four times better by using multiple transit times and least squares fit. Over a total of 15 North determinations based on more than a thousand transit times, an external standard error of 4″.4 was obtained using a WildGAK-1.  相似文献   

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