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1.
Doppler derived geocentric and relative geodetic positions are now widely used for detecting and controlling systematic scale and orientation errors in large classical terrestrial triangulation networks. However, the combined adjustment of terrestrial and space data raises several theoretical problems, including the choice of appropriate reference systems, the a priori weighting of the various types of observations, the modelling of systematic errors and the conditioning of the network in terms of internal and external rank deficiencies. Tests with large national networks show conclusively that, without correct modelling, systematic errors will largely be unaffected by “higher order” observations.  相似文献   

2.
Summary The “true” geocentric position of any terrestrial triangulation can be reached to a certain degree of approximation only. Every claimed “geocentric” terrestrial system, therefore, must be capable of undergoing some minor shifts and minor rotations. In a two dimensional solution which provides the best combination of the two systems in question, three degrees of freedom are open and must be filled by corresponding statements or conditions. But the parameters so obtained are of relative value only. Thus, every two-dimensional solution must be followed by a three-dimensional solution in order to obtain the best external parameters and the best internal consistency. This sequential processing is legitimate because an alteration of the values of the external parameters no longer changes the inner shape of the combined network. All decisions made about the model have the character of hypotheses and must be tested statistically.  相似文献   

3.
The Euclidean spaces with their inner products are used to describe methods of least squares adjustment as orthogonal projections on finite-dimensional subspaces. A unified Euclidean space approach to the least squares adjustment methods “observation equations” and “condition equations” is suggested. Hence not only the two adjustment solutions are treated from the view-point of Euclidean space theory in a unified frame but also the existing duality relation between the methods of “observation equations” and “condition equations” is discussed in full detail. Another purpose of this paper is to contribute to the development of some familiarity with Euclidean and Hilbert space concepts. We are convinced that Euclidean and Hilbert space techniques in least squares adjustment are elegant and powerful geodetic methods.  相似文献   

4.
Summary A datum change between two geodetic systems with points in common may be derived in three stages; slight adjustments of coordinates to make the networks of common points geometrically similar in the two systems; a scale factor to make them geometrically congruent; finally, an orthogonal transformation to swing them into coincidence. The geometrical concept is developed of a “datum screw”, not arbitrarily chosen as is the “origin” or “datum point” of a geodetic survey, but intrinsic to the geometry. The conditions under which it degenerates to a simple “datum shift” are discussed. Differential and other formulae for changes of spheroid and of datum are given, together with a set of tables of coefficients.  相似文献   

5.
The upward-downward continuation of a harmonic function like the gravitational potential is conventionally based on the direct-inverse Abel-Poisson integral with respect to a sphere of reference. Here we aim at an error estimation of the “planar approximation” of the Abel-Poisson kernel, which is often used due to its convolution form. Such a convolution form is a prerequisite to applying fast Fourier transformation techniques. By means of an oblique azimuthal map projection / projection onto the local tangent plane at an evaluation point of the reference sphere of type “equiareal” we arrive at a rigorous transformation of the Abel-Poisson kernel/Abel-Poisson integral in a convolution form. As soon as we expand the “equiareal” Abel-Poisson kernel/Abel-Poisson integral we gain the “planar approximation”. The differences between the exact Abel-Poisson kernel of type “equiareal” and the “planar approximation” are plotted and tabulated. Six configurations are studied in detail in order to document the error budget, which varies from 0.1% for points at a spherical height H=10km above the terrestrial reference sphere up to 98% for points at a spherical height H = 6.3×106km. Received: 18 March 1997 / Accepted: 19 January 1998  相似文献   

6.
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   

7.
Summary.  GFZ Potsdam and GRGS Toulouse/Grasse jointly developed a new pair of global models of the Earth's gravity field to satisfy the requirements of the recent and future geodetic and altimeter satellite missions. A precise gravity model is a prerequisite for precise satellite orbit restitution, tracking station positioning and altimeter data reduction. According to different applications envisaged, the new model exists in two parallel versions: the first one being derived exclusively from satellite tracking data acquired on 34 satellites, the second one further incorporating satellite altimeter data over the oceans and terrestrial gravity data. The most recent “satellite-only” gravity model is labelled GRIM4-S4 and the “combined” gravity model GRIM4-C4. The models are solutions in spherical harmonics and have a resolution up to degree and order 60 plus a few resonance terms in the case of GRIM4-S4, and up to degree/order 72 in the case of GRIM4-C4, corresponding to a spatial resolution of 555 km at the Earth's surface. The gravitational coefficients were estimated in a rigorous least squares adjustment simultaneously with ocean tidal terms and tracking station position parameters, so that each gravity model is associated with a consistent ocean tide model and a terrestrial reference frame built up by over 300 optical, laser and Doppler tracking stations. Comprehensive quality tests with external data and models, and test arc computations over a wide range of satellites have demonstrated the state-of-the-art capabilities of both solutions in long-wavelength geoid representation and in precise orbit computation. Received 1 February 1996; Accepted 17 July 1996  相似文献   

8.
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9.
The transformation of the instantaneous terrestrial coordinate system to the mean or average earth-fixed one is parameterized by the polar motion components which are continuously changing in time. Using the non-symmetricity of the connection coefficients connecting the above frames the errors (“misclosures”) are estimated which would be present if the instantaneous frame would be used as the geodetic reference frame.  相似文献   

10.
Selectivity estimation is crucial for query optimizers choosing an optimal spatial execution plan in a spatial database management system.This paper presents an Annular Bucket spatial histogram(AB histogram)that can estimate the selectivity in finer spatial selection and spatial join operations even when the spatial query has more operators or more joins.The AB histogram is represented as a set of bucket-range,bucket-count value pairs.The bucket-range often covers an annular region like a sin-gle-cell-sized photo frame.The bucket-count is the number of objects whose Minimum Bounding Rectangles(MBRs)fall between outer rectangle and inner rectangle of the bucket-range.Assuming that all MBRs in each a bucket distribute evenly,for every buck-et,we can obtain serial probabilities that satisfy a certain spatial selection or join conditions from the operations’ semantics and the spatial relations between every bucket-range and query ranges.Thus,according to some probability theories,spatial selection or join selectivity can be estimated by the every bucket-count and its probabilities.This paper also shows a way to generate an updated AB histogram from an original AB histogram and those probabilities.Our tests show that the AB histogram not only supports the selectivity estimation of spatial selection or spatial join with "disjoint","intersect","within","contains",and "overlap" operators but also provides an approach to generate a reliable updated histogram whose spatial distribution is close to the distribution of ac-tual query result.  相似文献   

11.
GNSS data management and processing with the GPSTk   总被引：2，自引：0，他引：2  
We organize complex problems in simple ways using a GNSS data management strategy based on “GNSS Data Structures” (GDS), coupled with the open source “GPS Toolkit” (GPSTk) suite. The code resulting from using the GDS and their associated “processing paradigm” is remarkably compact and easy to follow, yielding better code maintainability. Furthermore, the data abstraction allows flexible handling of concepts beyond mere data encapsulation, including programmable general solvers. An existing GPSTk class can be modified to achieve the goal. We briefly describe the “GDS paradigm” and show how the different GNSS data processing “objects” may be combined in a flexible way to develop data processing strategies such as Precise Point Positioning (PPP) and network-based PPP that computes satellite clock offsets on-the-fly.  相似文献   

12.
In this contribution it is shown that the so-called “total least-squares estimate” (TLS) within an errors-in-variables (EIV) model can be identified as a special case of the method of least-squares within the nonlinear Gauss–Helmert model. In contrast to the EIV-model, the nonlinear GH-model does not impose any restrictions on the form of functional relationship between the quantities involved in the model. Even more complex EIV-models, which require specific approaches like “generalized total least-squares” (GTLS) or “structured total least-squares” (STLS), can be treated as nonlinear GH-models without any serious problems. The example of a similarity transformation of planar coordinates shows that the “total least-squares solution” can be obtained easily from a rigorous evaluation of the Gauss–Helmert model. In contrast to weighted TLS, weights can then be introduced without further limitations. Using two numerical examples taken from the literature, these solutions are compared with those obtained from certain specialized TLS approaches.  相似文献   

13.
1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｏｕｒｃｏｕｎｔｒｙ ,ｔｈｅｓｕｒｖｅｙｉｎｇｗｏｒｋｏｎｉｎｄｕｓｔｒｉａｌｏｂｊｅｃｔｓｈａｖｅ ｇｒａｄｕａｌｌｙｉｎｃｒｅａｓｅｄ .Ｔｈｏｓｅｉｎｄｕｓｔｒｉａｌｏｂｊｅｃｔｓｉｎｃｌｕｄｅｒａｉｌｗａｙａｎｄｈｉｇｈｗａｙｔｕｎｎｅｌｓ,ｖａｒｉ ｏｕｓｏｉｌａｎｄｇａｓｃａｎｓ ,ｖａｒｉｏｕｓａｉｒｃｒａｆｔ,ｓｈｅｌｌｏｆｃａｒｓ,ｌａｒｇｅｍｉｌｉｔａｒｙａｎｔｅｎｎａｕｓｅｄｆｏｒｓｃｏｕｔｉｎｇｓｔｅａｌｔｈｐｌａｎｅ ,ｓｈｉｐ ,ｉｎｔｅｒｎａｌｓｔ…  相似文献   

14.
The now classical collocation method in geodesy has been derived byH. Moritz (1970; 1973) within an appropriate Mixed Linear Model. According toB. Schaffrin (1985; 1986) even a generalized form of the collocation solution can be proved to represent a combined estimation/prediction procedure of typeBLUUE (Best Linear Uniformly Unbiased Estimation) for the fixed parameters, and of type inhomBLIP (Best inhomogeneously LInear Prediction) for the random effects with not necessarily zero expectation. Moreover, “robust collocation” has been introduced by means of homBLUP (Best homogeneously Linear weakly Unbiased Prediction) for the random effects together with a suitableLUUE for the fixed parameters. Here we present anequivalence theorem which states that the robust collocation solution in theoriginal Mixed Linear Model can identically be derived as traditionalLESS (LEast Squares Solution) in amodified Mixed Linear Model without using artifacts like “pseudo-observations”. This allows us a nice interpretation of “robust collocation” as an adjustment technique in the presence of “weak prior information”.  相似文献   

15.
The Doppler effect is the apparent shift in frequency of an electromagnetic signal that is received by an observer moving relative to the source of the signal. The Doppler frequency shift relates directly to the relative speed between the receiver and the transmitter, and has thus been widely used in velocity determination. A GPS receiver-satellite pair is in the Earth’s gravity field and GPS signals travel at the speed of light, hence both Einstein’s special and general relativity theories apply. This paper establishes the relationship between a Doppler shift and a user’s ground velocity by taking both the special and general relativistic effects into consideration. A unified Doppler shift model is developed, which accommodates both the classical Doppler effect and the relativistic Doppler effect under special and general relativities. By identifying the relativistic correction terms in the model, a highly accurate GPS Doppler shift observation equation is presented. It is demonstrated that in the GPS “frequency” or “velocity” domain, the relativistic effect from satellite motion changes the receiver-satellite line-of-sight direction, and the measured Doppler shift has correction terms due to the relativistic effects of the receiver potential difference from the geoid, the orbit eccentricity, and the rotation of the Earth.  相似文献   

16.
The round-trip travel time measurements made by spacecraft laser altimeters are primarily used to construct topographic maps of the target body. The accuracy of the calculated bounce point locations of the laser pulses depends on the quality of the spacecraft trajectory reconstruction. The trajectory constraints from Doppler and range radio tracking data can be supplemented by altimetric “crossovers”, to greatly improve the reconstruction of the spacecraft trajectory. Crossovers have been used successfully in the past (e.g., Mars Orbiter Laser Altimeter on Mars Global Surveyor), but only with single-beam altimeters. The same algorithms can be used with a multi-beam laser altimeter, but we present a method using the unique cross-track topographic information present in the multi-beam data. Those crossovers are especially adapted to shallow (small angle) intersections, as the overlapping area is large, reducing the inherent ambiguities of single-beam data in that situation. We call those “swath crossovers”. They prove particularly useful in the case of polar-orbiting spacecraft over slowly rotating bodies, because all the non-polar crossovers have small intersection angles. To demonstrate this method, we perform a simplified simulation based on the Lunar Reconnaissance Orbiter (LRO) and its five-beam Lunar Orbiter Laser Altimeter. We show that swath crossovers over one lunar month can independently, from geometry alone, recover the imposed orbital perturbations with great accuracy (5 m horizontal, < 1 m vertical, about one order of magnitude smaller than the imposed perturbations). We also present new types of constraints that can be derived from the swath crossovers, and designed to be used in a precision orbit determination setup. In future work, we will use such multi-beam altimetric constraints with data from LRO.  相似文献   

17.
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   

18.
This paper is to construct a “digital local, regional, region“ information framework based on the technology of “SIG“ and its significance and application to the regional sustainable development evaluation system. First, the concept of the “grid computing“ and “SIG“ is interpreted and discussed, then the relationship between the “grid computing“ and “digital region“ is analyzed, and the framework of the “digital region“ is put forward. Finally, the significance and application of “grid computing“ to the “region sustainable development evaluation system“ are discussed.  相似文献   

19.
We compare two methods for monitoring the dynamic response of tall buildings to wind loading, using data from a 280-m-high building in Singapore. The first method is based on accelerometer measurements. The second method is based on the Global Positioning System (GPS) technology. The GPS can in principle detect absolute displacements with lower frequencies than the accelerometers, but the GPS positioning signal is usually very noisy. We propose a systematic procedure for modeling the stochastic and systematic components of the GPS displacement time series and for extracting the weak structural response from the dominant noise. The spectrum of the building response obtained from the filtered GPS data exhibits a dominant peak at 0.19 Hz. The frequency of the peak coincides with that obtained from the analysis of the accelerometer data. The proposed analysis of the GPS signal provides a method for cross-validating the GPS and accelerometer measurements, and shows that “educated” filtering of the GPS signal can reveal essential features of the building’s response to wind loading.  相似文献   

20.
Astronomic azimuths are used in classical geodesy, through the Laplace equation, to control the orientation of geodetic networks. The method most commonly used by the United States National Geodetic Survey for the determination of astronomic azimuth is often referred to as the “direction method”, and is based on observations of Polaris at any hour angle. We have analyzed repeat determinations, by analysis of variance (ANOVA) techniques, to derive realistic estimates of the expected accuracy of typical astronomic azimuths to be used in the readjustment of the North American Datum. We found that the dominant errors are systematic in nature, with a very important source being observer bias, or “personal equation”. We were unable to decompose the remaining systematic error, which presumably consists primarily of instrument biases, anomalous refraction, and setup errors. We found, from an analysis of determinations that were first corrected for observer bias, an increase in the variance of repeat azimuth determinations as a function of latitude that agrees reasonably well with theoretical expectations.  相似文献   

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