Showing papers in "Journal of Geodesy in 1997"
TL;DR: An integrated method for the instantaneous ambiguity resolution using dual-frequency precise pseudo-range and carrier-phase observations is suggested, which shows that the mean computation time for one epoch is less than 0.1, and that the success rate reaches 98.4%.
Abstract: An integrated method for the instantaneous ambiguity resolution using dual-frequency precise pseudo-range and carrier-phase observations is suggested in this paper. The algorithm combines the search procedures in the coordinate domain, the observation domain and the estimated ambiguity domain (and therefore benefits from the integration of their most positive elements). A three-step procedure is then proposed to enhance the reliability of the ambiguity resolution by: (1) improving the stochastic model for the double-differenced functional model in real time; (2) refining the criteria which distinguish the integer ambiguity set that generates the minimum quadratic form of residuals from that corresponding to the second minimum one; and (3) developing a fault detection and adaptation procedure. Three test scenarios were considered, one static baseline (11.3 km) and two kinematic experiments (baseline lengths from 5.2 to 13.7 km). These showed that the mean computation time for one epoch is less than 0.1 s, and that the success rate reaches 98.4% (compared to just 68.4% using standard ratio tests).
184 citations
TL;DR: The least square ambiguity decorrelation adjustment (LSA) method as mentioned in this paper is a method for fast GPS double-difference (DD) integer ambiguity estimation, which is used to identify the difficulty of computing the integer DD ambiguities.
Abstract: The least-squares ambiguity decorrelation adjustment is a method for fast GPS double-difference (DD) integer ambiguity estimation. The performance of the method will be discussed, and although it is stressed that the method is generally applicable, attention is restricted to short-baseline applications in the present contribution. With reference to the size and shape of the ambiguity search space, the volume of the search space will be introduced as a measure for the number of candidate grid points, and the signature of the spectrum of conditional variances will be used to identify the difficulty one has in computing the integer DD ambiguities. It is shown that the search for the integer least-squares ambiguities performs poorly when it takes place in the space of original DD ambiguities. This poor performance is explained by means of the discontinuity in the spectrum of conditional variances. It is shown that through a decorrelation of the ambiguities, transformed ambiguities are obtained which generally have a flat and lower spectrum, thereby enabling a fast and efficient search. It is also shown how the high precision and low correlation of the transformed ambiguities can be used to scale the search space so as to avoid an abundance of unnecessary candidate grid points. Numerical results are presented on the spectra of conditional variances and on the statistics of both the original and transformed ambiguities. Apart from presenting numerical results which can typically be achieved, the contribution also emphasizes and explains the impact on the method's performance of different measurement scenarios, such as satellite redundancy, single vs dual-frequency data, the inclusion of code data and the length of the observation time span.
153 citations
TL;DR: In this article, a potential coefficient model of the Earth's gravitational potential was used to calculate height anomalies and then reduced to geoid undulations where such quantities are needed for orthometric height determination and vertical datum definition through potential coefficient realization of the geoid.
Abstract: This paper suggests that potential coefficient models of the Earth's gravitational potential be used to calculate height anomalies which are then reduced to geoid undulations where such quantities are needed for orthometric height determination and vertical datum definition through a potential coefficient realization of the geoid. The process of the conversion of the height anomaly into a geoid undulation is represented by a height anomaly gradient term and the usual N–ζ term that is dependent on elevation and the Bouguer anomaly. Using a degree 360 expansion of 30′ elevations and the OSU91A potential coefficient model, a degree 360 representation of the correction terms was computed. The magnitude of N–ζ reached –3.4 m in the Himalaya Mountains with smaller, but still significant, magnitudes in other mountainous regions.
143 citations
TL;DR: In this paper, the link between baseline precision and ambiguity reliability is analyzed analytically and it is shown that the baseline-ambiguity correlation is related to the gain in baseline precision, to the volume of the ambiguity search space, and to the impact of potential integer ambiguity biases.
Abstract: This contribution is the last of four parts and deals with the link between baseline precision and ambiguity reliability. It is shown analytically how and to what extent the baseline-ambiguity correlation is related to the gain in baseline precision, to the volume of the ambiguity search space, and to the impact of potential integer ambiguity biases. Also, an ambiguity DOP measure is introduced together with its closed-form formulae for the three different single-baseline models.
118 citations
TL;DR: In this article, a measure for the gain in baseline precision which is experienced when the carrier phase double-differenced ambiguities are treated as integers instead of as reals is introduced.
Abstract: The present contribution is the first of four parts. It considers the precision of the floated and the fixed baseline. A measure is introduced for the gain in baseline precision which is experienced when the carrier phase double-differenced ambiguities are treated as integers instead of as reals. The properties of this measure are analyzed, and it is shown by means of principal angles how it relates to the change over time of the relative receiver-satellite geometry. We also present canonical forms of the baseline variance matrices for different measurement scenarios. These canonical forms make the relation between the various variance matrices transparent and thus present a simple way of studying their relative merits.
118 citations
TL;DR: In this article, the precision and correlation of the least-squares estimators of the carrier phase ambiguities are investigated. And the ability of the widelane transformation to decorrelate and to improve the precision is investigated.
Abstract: The present contribution is the second of four parts. It considers the precision and correlation of the least-squares estimators of the carrier phase ambiguities. It is shown how the precision and correlation of the double-differenced ambiguities as well as of the widelane ambiguities are effected by the observation weights, by the number of satellites tracked, by the number of observation epochs used, and by the change over time of the relative receiver-satellite geometry. Also the ability of the widelane transformation to decorrelate and to improve the precision is investigated.
79 citations
TL;DR: In this article, the authors 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.
Abstract: 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.
73 citations
TL;DR: In this article, the impact of a presumed presence or absence of the ionospheric delays on the quality of the least-squares ambiguities is analyzed, and the spatial correlation and the time correlation of the ions' delays are captured in an a priori ionosphere variance matrix.
Abstract: In this contribution the impact of a presumed presence or absence of the ionospheric delays on the quality of the least-squares ambiguities is analysed. The spatial correlation and the time correlation of the ionospheric delays are captured in an a priori ionospheric variance matrix. It is shown how the size and shape of the ambiguity search space is affected by the use of these a priori ionospheric weights. As a result an exact description can be given of the interpolatory character of the ambiguity variance matrix as function of the ionospheric weights. In order to give a qualitative analysis of the various effects, analytical rather than numerical results are emphasized.
65 citations
TL;DR: In this paper, a Sobolev weight space was constructed for an unbounded domain representing the exterior of the Earth and quantitative estimates were deduced for the trace theorem and equivalent norms.
Abstract: In this paper the linear gravimetric boundary-value problem is discussed in the sense of the so-called weak solution. For this purpose a Sobolev weight space was constructed for an unbounded domain representing the exterior of the Earth and quantitative estimates were deduced for the trace theorem and equivalent norms. In the generalized formulation of the problem a special decomposition of the Laplace operator was used to express the oblique derivative in the boundary condition which has to be met by the solution. The relation to the classical formulation was also shown. The main result concerns the coerciveness (ellipticity) of a bilinear form associated with the problem under consideration. The Lax-Milgram theorem was used to decide about the existence, uniqueness and stability of the weak solution of the problem. Finally, a clear geometrical interpretation was found for a constant in the coerciveness inequality, and the convergence of approximation solutions constructed by means of the Galerkin method was proved.
59 citations
TL;DR: In this article, a heuristic solution with the help of robust estimation technique and optimization criteria for the regression equation is presented to solve the problem of selecting the suitable polynomial parameters and reducing the influences of some possibly abnormal data points.
Abstract: The polynomial interpolation of least squares and interpolation moving least squares based on control stations with known GPS (global positioning system) ellipsoidal heights and levelling orthometric heights are the most often used methods for the interpolation of the geoid heights. But in their applications there occur two problems: one lies in selecting the suitable polynomial parameters; the other in reducing the influences of some possibly abnormal data points. To solve both of the problems, without emphasizing a sound theoretical basis, a heuristic solution with the help of robust estimation technique and optimization criteria for the regression equation is presented. Through two actual numerical examples it is shown that the new solution concept is efficient and can be realized easily on computers.
57 citations
TL;DR: This contribution enables the widelaning technique to be cast into the framework of the least-squares ambiguity decorrelation adjustment (LAMBDA) and to analyse its relative merits and to provide answers to the following three questions.
Abstract: In this contribution we consider the popular widelaning technique from the viewpoint of ambiguity decorrelation. It enables us to cast the technique into the framework of the least-squares ambiguity decorrelation adjustment (LAMBDA) and to analyse its relative merits. In doing so, we will provide answers to the following three questions. Does the widelane decorrelate? Does it explicitly appear in the automated transformation step of the LAMBDA method? Can one do better than the widelane? It is shown that all three questions can be answered in the affirmative. This holds true for the ionosphere-fixed case, the ionosphere-float case, as well as for the ionosphere-weighted case.
TL;DR: In this article, the gravity potential with respect to a global spheroidal model of degree/order 360/360 has been computed by means of the orthometric heights of the GPS stations in the Finnish Height Datum N60, epoch 1993.
Abstract: 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.
TL;DR: In this paper, the authors used doubly differenced (in space) phase accelerations to obtain the relative vehicle accelerations for airborne gravimetry using INS and GPS.
Abstract: For airborne gravimetry using INS and GPS, the accelerations from both systems are differenced to yield the gravity acceleration. Usually, the GPS acceleration is determined by first solving for the position of the vehicle relative to a base station and subsequently taking two time derivatives of the vertical component. An alternative method is to time-differentiate the observed phases directly, thus avoiding the cycle ambiguity problem that must be solved for positioning and that is fraught with (certainly not insurmountable) difficulties in the event of a cycle slip. Due to the largely unpredictable receiver-clock errors and the imposition of the Selective Availability degradation, doubly differenced (in space) phase accelerations are used to obtain the relative vehicle accelerations. Test results for stationary receivers show that the acceleration vector can be determined from phase accelerations to an accuracy of 1 mgal for 40-s averages. The mathematical formulation of the acceleration determination also highlights certain other advantages over traditional methods, such as the avoidance of the Eotvos correction, although a similar kind of velocity effect must be determined.
TL;DR: In this article, the applicability of degree-variance propagation for error analysis and validation of other error prediction methods is investigated for the case of satellite gradiometry, and a rule of thumb to predict which coefficients will be affected by the polar gap is derived.
Abstract: The applicability of degree-variance propagation for error analysis and for the validation of other error prediction methods is investigated for the case of satellite gradiometry. For several idealized mission scenarios exact expressions for the a posteriori variances exist; for certain other scenarios approximate relations exist. As degree variances cannot be directly applied to a non-polar orbit, a rule of thumb to predict which coefficients will be affected by the polar gap is derived.
TL;DR: In this article, a least squares prediction using an empirically deduced local covariance function was performed to investigate the temporal change in the rates of vertical crustal movements in the Tohoku district, Japan.
Abstract: Least-squares prediction using an empirically deduced local covariance function was performed to investigate the temporal change in the rates of vertical crustal movements in the Tohoku district, Japan. Levelling data covering an area of approximately 450 × 275 km2 observed between 1966 and 1995 were used and the results shown in the form of contour maps. Firstly we derived a covariance function of the rates of vertical crustal movement with a Gaussian form function. We used this function to estimate the spatial distribution of the rates of vertical crustal movements. By the present method, a steady tilt of the Tohoku district to the east, toward the Japan Trench and an areal uplift in the southwestern part were well reproduced. Moreover, a significant temporal change in vertical movement rates is clearly seen.
TL;DR: The statistical technique known as the cumulative-sum test is described for the detection of abrupt changes in the GPS carrier-phase measurements and designed algorithms to detect failures or changes of small magnitude are designed in order to monitor and control the quality of GPS measurements for critical real-time and/or deformation applications.
Abstract: The detection of cycle slips in carrier-phase data, outliers in phase rate or in code ranges, or any other type of disorder in the measurements of the GPS system, is one of the major quality-control problems that needs to be addressed, especially where GPS is used for real-time applications or for those applications that require continuous and reliable positioning results. This study is concerned with designing algorithms to detect failures or changes of small magnitude, in order to monitor and control the quality of GPS measurements for critical real-time and/or deformation applications. In this regard, the statistical technique known as the cumulative-sum test is described for the detection of abrupt changes in the GPS carrier-phase measurements. Real GPS data have been used to test and evaluate the algorithm.
TL;DR: In this paper, the dependence of the location, the size and the shape of the ambiguity search space on different factors of the stochastic model is analyzed in a qualitative sense for the geometry-free model.
Abstract: In this contribution we analyse in a qualitative sense for the geometry-free model the dependency of the location, the size and the shape of the ambiguity search space on different factors of the stochastic model. For this purpose a rather general stochastic model is used. It includes time-correlation, cross-correlation, satellite elevation dependency and the use of an a priori weighted ionospheric model, having the ionosphere-fixed model and the ionosphere-float model as special cases. It is shown that the location is invariant for changes in the cofactor matrix of the phase observables. This also holds true for the cofactor matrix of the code observables in the ionosphere-float case. As for time-correlation and satellite elevation dependency, it is shown that they only affect the size of the search space, but not its shape and orientation. It is also shown that the least-squares ambiguities, their variance matrix and its determinant, for, respectively, the ionosphere-fixed model, the ionosphere-float model and the ionosphere-weighted model, are all related through the same scalar weighted mean, the weight of which is governed by the variance ratio of the ionospheric delays and the code observables. A closed-form expression is given for the area of the search space in which all contributing factors are easily recognized. From it one can infer by how much the area gets blown up when the ionospheric spatial decorrelation increases. This multiplication factor is largest when one switches from the ionosphere-fixed model to the ionosphere-float model, in which case it is approximately equal to the ratio of the standard deviation of phase with that of code. The area gives an indication of the number of grid points inside the search space.
TL;DR: In this article, the authors present canonical forms of the ambiguity search spaces of the geometry-based model, the time-averaged model, and the geometry free model, revealing the intrinsic geometry of the search spaces and allowing one to study their size, shape, and orientation as function of data precision, sampling rate, satellite redundancy, and change in receiver-satellite geometry.
Abstract: This contribution is the third of four parts. Based on the gain-number concept, canonical forms will be presented of the ambiguity search spaces of the geometry-based model, the time-averaged model, and the geometry-free model. These forms reveal the intrinsic geometry of the search spaces and allow one to study their size, shape, and orientation as function of data precision, sampling rate, satellite redundancy, and change in receiver-satellite geometry. The canonical forms are also used to address the problem of search halting. The phenomenon of search halting is explained and it is shown how decorrelating ambiguity transformations can largely eliminate this computational burden.
TL;DR: In this article, a least-squares approach for local gravity field representation is presented. But the use of spherical cap harmonic analysis is not suitable for modeling Laplacian potential and the corresponding field components over a spherical cap.
Abstract: Spherical cap harmonic analysis is the appropriate analytical technique for modelling Laplacian potential and the corresponding field components over a spherical cap. This paper describes the use of this method by means of a least-squares approach for local gravity field representation. Formulations for the geoid undulation and the components ξ, η of the deflection of the vertical are derived, together with some warnings in the application of the technique. Although most of the formulations have been given by another paper, these were confusing or even incorrect, mainly because of an improper application of the spherical cap harmonic analysis.
TL;DR: In this paper, the least-squares adjustment in the frequency domain and input-output system theory are employed to determine the gravity field (both geoid and anomalies) and its errors.
Abstract: . Satellite altimetry derived geoid heights and marine gravity anomalies can be combined to determine a detailed gravity field over the oceans using the least-squares collocation method and spectral combination techniques. Least-squares collocation, least-squares adjustment in the frequency domain and input-output system theory are employed to determine the gravity field (both geoid and anomalies) and its errors. This paper intercompares these three techniques using simulated data. Simulation studies show that best results are obtained by the input-output system theory among the three prediction methods. The least-squares collocation method gives results which are very close to but a little bit worse than those obtained using input-output system theory. This slightly poorer performance of the least-squares collocation method can be explained by the fact that it uses isotropic structured covariance (thus approximate signal PSD information) while the system theory method uses detailed signal PSD information. The method of least-squares adjustment in the frequency domain gives the poorest results among these three methods because it uses less information than the other two methods (it ignores the signal PSDs). The computations also show that the least-squares collocation and input-output system theory methods are not as sensitive to noise levels as the least-squares adjustment in the frequency domain method is.
TL;DR: In this paper, the perspective 4 point (P4P) problem is solved by means of a new algorithm: at first the unknown Cartesian coordinates of the perspective center are computed by meansof Mobius barycentric coordinates.
Abstract: The perspective 4 point (P4P) problem - also called the three-dimensional resection problem - is solved by means of a new algorithm: At first the unknown Cartesian coordinates of the perspective center are computed by means of Mobius barycentric coordinates. Secondly these coordinates are represented in terms of observables, namely space angles in the five-dimensional simplex generated by the unknown point and the four known points. Substitution of Mobius barycentric coordinates leads to the unknown Cartesian coordinates (2.8)–(2.10) of Box 2.2. The unknown distances within the five-dimensional simplex are determined by solving the Grunert equations, namely by forward reduction to one algebraic equation (3.8) of order four and backward linear substitution. Tables 1.–4. contain a numerical example. Finally we give a reference to the solution of the 3 point (P3P) problem, the two-dimensional resection problem, namely to the Ansermet barycentric coordinates initiated by C.F. Gaus (1842), A. Schreiber (1908) and A.␣Ansermet (1910).
TL;DR: In this paper, the effects of the sea surface topography on gravity and geoid computations from altimetry are significant over areas with major oceanographic phenomena, and the authors concluded that sea surface gradient is a better data type than sea surface height.
Abstract: This paper analyzes several systematic errors affecting sea surface gradients derived from Seasat, Geosat/ERM, Geosat/GM, ERS-1/35d, ERS-1/GM and TOPEX/POSEIDON altimetry. Considering the data noises, the conclusion is: (1) only Seasat needs to correct for the non-geocentricity induced error, (2) only Seasat and Geosat/GM need to correct for the one cycle per revolution error, (3) only Seasat, ERS-1/GM and Geosat/GM need to correct for the tide model error; over shallow waters it is suggested to use a local tide model not solely from altimetry. The effects of the sea surface topography on gravity and geoid computations from altimetry are significant over areas with major oceanographic phenomena. In conclusion, sea surface gradient is a better data type than sea surface height. Sea surface gradients from altimetry, land gravity anomalies, ship gravity anomalies and elevation data were then used to calculate the geoid over Taiwan by least-squares collocation. The inclusion of sea surface gradients improves the geoid prediction by 27% when comparing the GPS-derived and the predicted geoidal heights, and by 30% when comparing the observed and the geoid-derived deflections of the vertical. The predicted geoid along coastal areas is accurate to 2 cm and can help GPS to do the third-order leveling.
TL;DR: In this article, a linear least squares parametric model analysis is carried out of the structure of the projection operator transforming the vector of standardised observations into the standardised residuals, and the properties of the model responses to observational disturbances are derived.
Abstract: For a linear least-squares parametric model analysis is carried out of the structure of the projection operator transforming the vector of standardised observations into the vector of standardised residuals. On this basis the properties of the model responses to observational disturbances (i.e. gross errors or blunders) are derived. A final outcome of the research can be summarised as: (1) proposing the robustness characteristics of a model and linking them with the local measures of internal reliability, being the diagonal elements in the projection operator; (2) determining the internal reliability levels satisfying specified robustness requirements, i.e. the possibility of detecting at least one of the k observational disturbances (k=1,2,…) having most disadvantageous locations in the system. The theory and a numerical example show that for the systems which have been designed to a proper level of internal reliability, the least-squares estimation can demonstrate an accordingly high level of robustness.
TL;DR: In this article, a method to calculate mean sea surface heights and gravity anomalies from altimeter-derived sea surface height and along-track sea surface slopes using the least-squares collocation procedure is derived.
Abstract: Procedures to calculate mean sea surface heights and gravity anomalies from altimeter-derived sea surface heights and along-track sea surface slopes using the least-squares collocation procedure are derived. The slope data is used when repeat track averaging is not possible to reduce ocean variability effects. Tests were carried out using Topex, Geosat, ERS-1 [35-day and 168-day (2 cycle)] data. Calculations of gravity anomalies in the Gulf Stream region were made using the sea surface height and slope data. Tests were also made correcting the sea surface heights for dynamic ocean topography calculated from a degree 360 expansion of data from the POCM-4B global ocean circulation model. Comparisons of the anomaly predictions were carried out with ship data using anomalies calculated for this paper as well as others.
TL;DR: The most important results of the analysis are that daily SLR station coordinate solutions could be generated with a few cm accuracy and the contribution of laser data on the `SLR-GPS' combined orbit is significant.
Abstract: . Laser tracking to GPS satellites (PRN5 and 6) provides an opportunity to compare GPS and laser systems directly and to combine data of both in a single solution. A few examples of this are given in this study. The most important results of the analysis are that (1) daily SLR station coordinate solutions could be generated with a few cm accuracy; (2) coordinates of nine stations were determined in a 2.3-year-long arc solution; (3) the contribution of laser data on the `SLR-GPS' combined orbit, resulting from the simultaneous processing of SLR and GPS data, is significant and (4) laser-only orbits have an accuracy of 10–20 cm, 1-day predictions of SLR orbits differ from IGS orbits by about 20–40 cm, 2-day predictions by 50–60 cm.
TL;DR: In this article, a closed form of Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid of revolution has been constructed.
Abstract: Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same degree as that of the original spherical Poisson kernel.
TL;DR: In this article, it is shown that if a smoothing procedure is applied, the analytical downward continuation can be used to determine the earth's gravitational potential on and above the surface to any required accuracy.
Abstract: The error of the analytical downward continuation was studied under planar approximation in a previous paper by the author (1994). This error is studied further by taking the earth's curvature into account in this paper. It is shown that if a smoothing procedure is applied, the analytical downward continuation can be used to determine the earth's gravitational potential on and above the earth's surface to any required accuracy. For the potential inside the earth's topographic mass the error can also be controlled and corrected.
TL;DR: The effect of the combined estimation/elimination of station coordinates, tropospheric zenith delay, dispersive ionosphere and station clock error on the precision achievable with geodetic GPS is analyzed.
Abstract: We analyse the effect of the combined estimation/elimination of station coordinates, tropospheric zenith delay, dispersive ionosphere and station clock error on the precision achievable with geodetic GPS. We also sketch a method to eliminate the major part of the precision deteriorating effect of this combined estimation of the unknowns, by a dual antenna arrangement.
TL;DR: In this paper, the authors adapted the GRIM series of gravity field models to dynamic GPS data processing, which is simultaneous processing of all available observables and all available satellite orbits (i.e. GPS, TOPEX/POSEIDON) can now be performed.
Abstract: In the framework of the GRIM series of gravity field models, the CNES/GRGS GINS precise orbit determination software has been adapted to dynamic GPS data processing. That is simultaneous processing of all available observables (i.e. GPS, DORIS, Laser) and all available satellite orbits (i.e. GPS, TOPEX/POSEIDON) can now be performed.
TL;DR: In this article, the impact of using satellite geometry or dispensing with it, on the least square estimators, on teststatistics and their associated reliability, and on the integer ambiguity estimation, is presented and analyzed.
Abstract: In this contribution GPS statistics are presented for the case that the relative receiver-satellite geometry is included in the single baseline model and for the case that the relative receiver-satellite geometry is excluded. It is shown that the statistics are linked through a particular form of a phased adjustment. Based on the stepwise approach of a phased adjustment, the impact of using satellite geometry or dispensing with it, on the least-squares estimators, on the teststatistics and their associated reliability, and on the integer ambiguity estimation, is presented and analyzed.