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At least 19 records

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NASA NTRS1991

Study of geopotential error models used in orbit determination error analysis

The uncertainty in the geopotential model is currently one of the major error sources in the orbit determination of low-altitude Earth-orbiting spacecraft. The results of an investigation of different geopotential error models and modeling approaches currently used for operational orbit error analysis support at the Goddard Space Flight Center (GSFC) are presented, with emphasis placed on sequential orbit error analysis using a Kalman filtering algorithm. Several geopotential models, known as the Goddard Earth Models (GEMs), were developed and used at GSFC for orbit determination. The errors in the geopotential models arise from the truncation errors that result from the omission of higher order terms (omission errors) and the errors in the spherical harmonic coefficients themselves (commission errors). At GSFC, two error modeling approaches were operationally used to analyze the effects of geopotential uncertainties on the accuracy of spacecraft orbit determination - the lumped error modeling and uncorrelated error modeling. The lumped error modeling approach computes the orbit determination errors on the basis of either the calibrated standard deviations of a geopotential model's coefficients or the weighted difference between two independently derived geopotential models. The uncorrelated error modeling approach treats the errors in the individual spherical harmonic components as uncorrelated error sources and computes the aggregate effect using a combination of individual coefficient effects. This study assesses the reasonableness of the two error modeling approaches in terms of global error distribution characteristics and orbit error analysis results. Specifically, this study presents the global distribution of geopotential acceleration errors for several gravity error models and assesses the orbit determination errors resulting from these error models for three types of spacecraft - the Gamma Ray Observatory, the Ocean Topography Experiment, and the Cosmic Background Explorer.

Yee, C.↗

NASA NTRS2019

Efficient On-Orbit Singularity-Free Geopotential Estimation

For vehicles in orbital cruise, either in orbit around a body or in a transfer orbit, gravity is the primary external force; therefore, the complexity of the geopotential model heavily influences the accuracy of the navigation state. As this type of spacecraft requires a highly accurate geopotential model and performs the computation numerous times a second, this calculation needs to be efficient. This calculation needs to include the first and second derivatives of the geopotential because navigation systems can require both the gravitational acceleration and gradient for inertial integration and state filtering. The most efficient method for calculating the geopotential, the forward column method, is discussed in detail, as well as a method to avoid the singularities that exist when using this method. This is shown to decrease the computation time of the geopotential compared to other popular methods. In addition, methods for first and second order propagation are discussed, which decrease the rate at which the full geopotential model needs to be calculated while maintaining the accuracy required of navigation systems. These estimation methods are shown to decrease the necessary computation of the gravity model by multiple orders of magnitude. This method decreases the computation time of the Exploration Upper Stage navigation system geopotential model by potentially an order of magnitude compared with the previous model without affecting the navigation error. A properly implemented geopotential model can have the accuracy of an 8 by 8 model while approaching the computational requirement as using only the J234 coefficients.

Amert, Joel↗

NASA NTRS1977

The geopotential in nonsingular orbital elements

Singularities are eliminated from the geopotential and its partial derivatives for zero eccentricity and inclination, and an expression for the geopotential expansion based entirely on nonsingular orbital elements is developed. The argument relies on the treatments of the geopotential function given by Izsak (1964), Allan (1965) and Kaula (1966); the geopotential expansion developed does not involve mixed variables, and therefore does not require the chain rule to formulate the Lagrange planetary equations. The need for recursion relations to be used in conjunction with the nonsingular version of the geopotential expansion is also mentioned.

Nacozy, P. E.↗

NASA NTRS1986

Satellite techniques for determining the geopotential of sea surface elevations

Spaceborne altimetry with measurement accuracies of a few centimeters which has the potential to determine sea surface elevations necessary to compute accurate three-dimensional geostrophic currents from traditional hydrographic observation is discussed. The limitation in this approach is the uncertainties in knowledge of the global and ocean geopotentials which produce satellite and height uncertainties about an order of magnitude larger than the goal of about 10 cm. The quantitative effects of geopotential uncertainties on processing altimetry data are described. Potential near term improvements, not requiring additional spacecraft, are discussed. Even though there is substantial improvements at the longer wavelengths, the oceanographic goal will be achieved. The geopotential research mission (GRM) is described which should produce geopotential models that are capable of defining the ocean geoid to 10 cm and near-earth satellite position. The state of the art and the potential of spaceborne gravimetry is described as an alternative approach to improve our knowledge of the geopotential.

Pisacane, V. L.↗

NASA NTRS1991

Estimation of geopotential differences over intercontinental locations using satellite and terrestrial measurements

An error analysis study was conducted in order to assess the current accuracies and the future anticipated improvements in the estimation of geopotential differences over intercontinental locations. An observation/estimation scheme was proposed and studied, whereby gravity disturbance measurements on the Earth's surface, in caps surrounding the estimation points, are combined with corresponding data in caps directly over these points at the altitude of a low orbiting satellite, for the estimation of the geopotential difference between the terrestrial stations. The mathematical modeling required to relate the primary observables to the parameters to be estimated, was studied for the terrestrial data and the data at altitude. Emphasis was placed on the examination of systematic effects and on the corresponding reductions that need to be applied to the measurements to avoid systematic errors. The error estimation for the geopotential differences was performed using both truncation theory and least squares collocation with ring averages, in case observations on the Earth's surface only are used. The error analysis indicated that with the currently available global geopotential model OSU89B and with gravity disturbance data in 2 deg caps surrounding the estimation points, the error of the geopotential difference arising from errors in the reference model and the cap data is about 23 kgal cm, for 30 deg station separation.

Pavlis, Nikolaos K.↗

NASA NTRS1972

Geopotential representation with sampling functions.

Satellite-to-ocean altitudes measured to meter accuracy eventually can yield a geoid representation with significant short-wavelength structure over ocean areas. To cope conveniently with this expected detail, one suggested analytical technique would represent the geopotential or the geoid as an expansion in sampling functions that are linear combinations of spherical harmonics. Each of the sampling functions makes its principal contribution to the geopotential in a single geographical region. For a representation truncated after degree N, there are (N + 1) squared such functions associated with a like number of points distributed nearly regularly on the globe. The features of this geopotential representation can be illustrated by considering the case N = 22, for which an expansion in sampling functions can be produced that is equivalent to the geopotential of the 1969 Smithsonian standard earth.

Lundquist, C. A.↗

NASA NTRS1984

Satellite techniques for determining the geopotential for sea-surface elevations

Spaceborne altimetry with measurement accuracies of a few centimeters which has the potential to determine sea surface elevations necessary to compute accurate three-dimensonal geostrophic currents from traditional hydrographic observation is discussed. The limitation in this approach is the uncertainties in knowledge of the global and ocean geopotentials which produce satellite and height uncertainties about an order of magnitude larger than the goal of about 10 cm. The quantative effects of geopotential uncertainties on processing altimetry data are described. Potential near term improvements, not requiring additional spacecraft, are discussed. Even though there is substantial improvements at the longer wavelengths, the oceanographic goal will be achieved. The geopotential research mission (GRM) is described which should produce goepotential models that are capable of defining the ocean geid to 10 cm and near-Earth satellite position. The state of the art and the potential of spaceborne gravimetry is described as an alternative approach to improve our knowledge of the geopotential.

Pisacane, V. L.↗

NASA NTRS1991

Fluctuations of high clouds and 500-mb geopotential heights in baroclinic waveguides

The spatial phase relationship between the atmospheric circulation and the bandpass fluctuations in cloudiness are investigated using satellite retrievals of high cloud areas reported by Stowe et al. (1988, 1989) NMC 500-mb geopotential heights in northern extratropics. Results of the analysis suggest that the high-cloud structures of baroclinic waves are less spatially coherent than the internal geopotential-height structures. It is shown that over the North Pacific, small-scale (latitudinal wavenumber 13-18) fluctuations in geopotential play a greater role in forcing high cloudiness than do medium-scale (latitudinal wavenumber 7-12) fluctuations in geopotential.

Charlock, Thomas P.↗

NASA NTRS1996

Reducing On-Board Computer Propagation Errors Due to Omitted Geopotential Terms by Judicious Selection of Uploaded State Vector

Several future, and some current missions, use an on-board computer (OBC) force model that is very limited. The OBC geopotential force model typically includes only the J(2), J(3), J(4), C(2,2) and S(2,2) terms to model non-spherical Earth gravitational effects. The Tropical Rainfall Measuring Mission (TRMM), Wide-field Infrared Explorer (WIRE), Transition Region and Coronal Explorer (TRACE), Submillimeter Wave Astronomy Satellite (SWAS), and X-ray Timing Explorer (XTE) all plan to use this geopotential force model on-board. The Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) is already flying this geopotential force model. Past analysis has shown that one of the leading sources of error in the OBC propagated ephemeris is the omission of the higher order geopotential terms. However, these same analyses have shown a wide range of accuracies for the OBC ephemerides. Analysis was performed using EUVE state vectors that showed the EUVE four day OBC propagated ephemerides varied in accuracy from 200 m. to 45 km. depending on the initial vector used to start the propagation. The vectors used in the study were from a single EUVE orbit at one minute intervals in the ephemeris. Since each vector propagated practically the same path as the others, the differences seen had to be due to differences in the inital state vector only. An algorithm was developed that will optimize the epoch of the uploaded state vector. Proper selection can reduce the previous errors of anywhere from 200 m. to 45 km. to generally less than one km. over four days of propagation. This would enable flight projects to minimize state vector uploads to the spacecraft. Additionally, this method is superior to other methods in that no additional orbit estimates need be done. The definitive ephemeris generated on the ground can be used as long as the proper epoch is chosen. This algorithm can be easily coded in software that would pick the epoch within a specified time range that would minimize the OBC propagation error. This techniques should greatly improve the accuracy of the OBC propagation on-board future spacecraft such as TRMM, WIRE, SWAS, and XTE without increasing complexity in the ground processing.

Greatorex, Scott↗

NASA NTRS1997

Measurement of Geopotential Heights by GPS Radio Occultation

Geopotential heights of constant pressure surfaces are retrieved from global positioning system (GPS) radio occultation data. In order to assess accuracy a subset of data obtained by GPS/MET during spring 1995 and summer 1995 are compared to the output of the European Centre for Medium-Range Weather Forecasts (ECMWF) global model. The root-mean-square measurement error is 20 m throughout the upper troposphere and lower stratosphere. Furthermore, the ECMWF global model contains enhanced errors in the southeast Pacific. In probing the data for potential utility in climate studies, a Bayesian interpolation technique is used to map the geopotential height fields in the upper troposphere during the summer. Despite limitations of the GPS/MET data set the global average 300-mbar geopotential height over a 2-week period in summer 1995 is determined with an accuracy of 7 m. By obtaining greater coverage and partially resolving synoptic variability, a future constellation of 16 orbiting receivers could obtain global average geopotential height estimates in the upper troposphere with an accuracy of 1 m each day. Accuracy would be somewhat worse for regional studies, except in the tropics where synoptic variability is depressed.

Leroy, Stephen S.↗

NASA NTRS1971

Preliminary Goddard geopotential using optical tracking data and a comparison with SAO models

A preliminary Goddard Space Flight Center (GSFC) geopotential and center of mass station coordinate solution was obtained from satellite orbital data using numerical integration theory. This geodetic solution is a prelude to a more general solution which will combine the 1971 International Satellite Geodesy Experiment (ISAGEX) laser data with the present data being employed. The present GSFC geopotential solution consists of the spherical harmonic coefficients through degree and order eight with higher order satellite resonant coefficients. The solution represents a first iteration result from 17 satellites with approximately 150 weekly orbital arcs containing some 40,000 optical observations. The GSFC preliminary result is compared with final results from the Smithsonian Astrophysical Observatory (SAO) solutions including the 1969 SAO Standard Earth II solution. One aspect of interest for the comparison is that SAO uses an analytic theory for the orbital solution whereas GSFC uses a numerical integration theory. The comparison of geopotential results shows that good agreement exists in general but that there are some areas of minor differences.

Lerch, F. J.↗

NASA NTRS1972

Satellite-satellite tracking for estimating geopotential coefficients.

Results of simulation studies of tracking of low-altitude satellites by a high-altitude satellite using range measurements between satellites. The high-altitude satellite is tracked by ground-based range trackers. The low-altitude satellites are tracked only by the high-altitude satellites. Orbital elements for one tracking satellite and four tracked low-altitude satellites are estimated, along with a set of low degree and order geopotential coefficients. Estimation of geopotential coefficients of low degree and order is shown to be considerably more accurate using satellite-to-satellite tracking than using ground-based tracking. The use of data from one high-altitude satellite tracking four low-altitude satellites in a range of inclinations is shown to produce geopotential coefficient estimates with smaller errors than presently exist in individual coefficients or would be obtained using ground-based tracking of the same satellites.

Martin, C. F.↗

NASA NTRS1974

Evaluation and comparisons of recent geopotential solutions

A statistical evaluation of some of the recent satellite determined gravity models, including some with distinct data base, indicates that the geopotential coefficients of these models are individually meaningful for frequencies with wave numbers n = 2 through 7 certainly and wave numbers n = 8 through 10 probably. Geopotential coefficients in higher frequency ranges while apparently important for computing accurate satellite orbits seem to have little geophysical significance in an individual sense. Differences between various gravity models and those satellite purely between determined geopotential models and their associated combination models show no consistent relationship to surface gravimetric coverage. Additional classical tracking data are important in improving the existing description of the earth's gravity field but their contribution in extending its frequency range beyond what is now available is uncertain.

Khan, M. A.↗

NASA NTRS1975

GRAVSAT/GEOPAUSE covariance analysis including geopotential aliasing

A conventional covariance analysis for the GRAVSAT/GEOPAUSE mission is described in which the uncertainties of approximately 200 parameters, including the geopotential coefficients to degree and order 12, are estimated over three different tracking intervals. The estimated orbital uncertainties for both GRAVSAT and GEOPAUSE reach levels more accurate than presently available. The adjusted measurement bias errors approach the mission goal. Survey errors in the low centimeter range are achieved after ten days of tracking. The ability of the mission to obtain accuracies of geopotential terms to (12, 12) one to two orders of magnitude superior to present accuracy levels is clearly shown. A unique feature of this report is that the aliasing structure of this (12, 12) field is examined. It is shown that uncertainties for unadjusted terms to (12, 12) still exert a degrading effect upon the adjusted error of an arbitrarily selected term of lower degree and order. Finally, the distribution of the aliasing from the unestimated uncertainty of a particular high degree and order geopotential term upon the errors of all remaining adjusted terms is listed in detail.

Koch, D. W.↗

NASA NTRS1976

Zonal and tesseral harmonic coefficients for the geopotential function, from zero to 18th order

Zonal and tesseral harmonic coefficients for the geopotential function are usually tabulated in normalized form to provide immediate information as to the relative significance of the coefficients in the gravity model. The normalized form of the geopotential coefficients cannot be used for computational purposes unless the gravity model has been modified to receive them. This modification is usually not done because the absolute or unnormalized form of the coefficients can be obtained from the simple mathematical relationship that relates the two forms. This computation can be quite tedious for hand calculation, especially for the higher order terms, and can be costly in terms of storage and execution time for machine computation. In this report, zonal and tesseral harmonic coefficients for the geopotential function are tabulated in absolute or unnormalized form. The report is designed to be used as a ready reference for both hand and machine calculation to save the user time and effort.

Kirkpatrick, J. C.↗

NASA NTRS1977

Geopotential resonances on Vanguard orbits

Since their establishment in 1959 the orbits of Vanguard 3 (1959-7A) and the Vanguard 2 rocket (1959-2B) have been slowly contracting through at least five strong resonances of eleventh order. Tracking with Baker-Nunn cameras and the U.S. Navy space surveillance (radio interferometer) system over a 14-year period has revealed resonant fluctuations on them of up to 0.035 deg in inclination (peak to peak). Six geopotential terms (lumped coefficients) of eleventh order and three of twenty-second order have been measured by using orbit inclinations derived from this tracking record. The terms of eleventh order are significantly smaller than is predicted by Kaula's rule. (The lumped coefficients are sensitive to geopotential effects as high as thirty-seventh degree.) These observed terms are compatible with a recent 27-satellite geopotential solution (GEM 7) whose formal coefficent errors are increased by a factor of 3.3.

Wagner, C. A.↗

NASA NTRS1985

The error associated with use of various forms of the divergence equation to diagnose geopotential and temperature

An experimental study was made of errors arising from diagnosing the geopotential and temperature for numerical weather prediction models by means of an inviscid divergence equation (DE). The experiment consisted of a simulation of a snow storm which occurred in 1979, with observational data being input for every point of the model grid and for the geopotential boundary condition, thereby eliminating errors in the horizontal and vertical analysis. The DE terms were recorded at each grid point, and were found to include synoptic-scale geopotential height errors up to 23 m and rms temperature errors exceeding 26 C in the PBL. The errors were minimal above 800 mb. The various unsuccessful attempts to reduce or eliminate the errors are described.

Modica, G. M.↗

NASA NTRS1997

Geopotential Error Analysis from Satellite Gradiometer and Global Positioning System Observables on Parallel Architecture

The recovery of a high resolution geopotential from satellite gradiometer observations motivates the examination of high performance computational techniques. The primary subject matter addresses specifically the use of satellite gradiometer and GPS observations to form and invert the normal matrix associated with a large degree and order geopotential solution. Memory resident and out-of-core parallel linear algebra techniques along with data parallel batch algorithms form the foundation of the least squares application structure. A secondary topic includes the adoption of object oriented programming techniques to enhance modularity and reusability of code. Applications implementing the parallel and object oriented methods successfully calculate the degree variance for a degree and order 110 geopotential solution on 32 processors of the Cray T3E. The memory resident gradiometer application exhibits an overall application performance of 5.4 Gflops, and the out-of-core linear solver exhibits an overall performance of 2.4 Gflops. The combination solution derived from a sun synchronous gradiometer orbit produce average geoid height variances of 17 millimeters.

Schutz, Bob E.↗