An analytical method for error analysis of GRACE-like missions based on spectral analysis
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The aim of this paper is to present an analytical relationship between the power spectral density of GRACE-like mission measurements and the accuracies of the gravity field coefficients mainly from the point of view of theory of signal and system, which indicates the one-to-one correspondence between spherical harmonic error degree variances and frequencies of the measurement noise. In order to establish this relationship, the average power of the errors due to gravitational acceleration difference and the relationship between perturbing forces and range-rate perturbations are derived, based on the orthogonality property of associated Legendre functions and the linear orbit perturbation theory, respectively. This method provides a physical insight into the relation between mission parameters and scientific requirements. By taking GRACE-FO as the object of research, the effects of sensor noises and time variable gravity signals are analyzed. If LRI measurements are applied, a mission goal with a geoid accuracy of 7.4 cm at a spatial resolution of 101 km is reachable, whereas if the KBR measurement error model is applied, a mission goal with a geoid accuracy of 10.2 cm at a spatial resolution of 125 km is reachable. Based on the discussion of the spectral matching of instrument accuracies, an improvement in accuracy of accelerometers is necessary for the match between the range errors and accelerometer noises in the future mission. Temporal aliasing caused by the time variable gravity signals is also discussed by this method.Keywords:
Aliasing
The spatial resolution of the earth's gravity field for the future GRACE Follow-On is discussed by analyzing the spatial disturbance gravity spectrum and the accumulative geoid error spectrum.The radial disturbance gravity with the height 200 km and 250 km is computed,using the EGM96 gravitational field model.Analyzing the radial gravity disturbance spectrum characteristics,a new earth's gravity field model of 281 and 242 degrees can be recovered at the two orbit heights.The accumulative geoid error spectrum model is given,and the accumulative geoid error spectrum at the height of 200 km and 250 km is computed.Analyzing the accumulative geoid error,it can be concluded that the earth's gravity field can be recovered to a degree of 286 and 228.
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Free-air gravity anomaly
Gravimetry
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Geopotential
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Least-squares function approximation
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Gravity of Earth
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In this paper we formulate the boundary-value problem for the determination of the gravimetric geoid considering a satellite gravitational model as a reference. We show that the long-wavelength part of the gravitational field generated by topographical masses must be added to the satellite model in order to prescribe a reference gravitational potential for a partly internal and partly external problem for geoid determination. We choose a reference potential that does not depend on the way topographical masses are compensated or condensed, but only on the satellite reference model and on the difference of gravitational potentials induced by topographical masses in the spaces outside the Earth and below the geoid. The latter contribution to the reference potential is expressed in the form of an ellipsoidal harmonic series, and the expansion coefficients are tabulated numerically up to degree 20.
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Spin-weighted spherical harmonics
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Aliasing
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Abstract The article deals with a non‐linear method of correlation function and spectrum power density estimation for which analogies of A. Shuster's periodic diagrams have been used. The effect of frequency expansion particularly compensates well‐known aliasing frequency effect. It was shown that if different properties of a random process are taking into account, it will allow to get the estimation of spectrum power density, the order of decrease of which corresponds to these differential properties.
Aliasing
Frequency spectrum
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In the Earth gravity-field model, potential coefficients are projections of the Earth gravitational potential on the corresponding spherical harmonics by degree and order. These coefficients reflect the spectral composition of the Earth gravitational potential in the whole space, but they cannot reflect the spectral composition in a local area. In this study, the Earth gravitational potential was projected on spherical harmonics in a local area using a window function introduced to facilitate the mathematical expressions. Then a model for the spectral structure of the Earth gravitational potential in the local area was established. The model can reflect the signal strength of any gravity-field spectrum component in the local area, which adds information for the description of the gravity field of the Earth, and which has great significance for Earth-sciences research and satellite gravity measurements. Taking the third-degree coefficients, for example, the signal-strength distributions of potential coefficients were computed. The data show that the signal-strength distributions of third-degree coefficients on the sphere surface are independent of the longitude. Among the third-degree coefficients, the zero-order, first-order and second-order coefficients are stronger near the two poles of the Earth, while the third-order coefficient is stronger near the equator.
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Gravity of Earth
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The article deals with a non‐linear method of correlation function and spectrum power density estimation for which analogies of A. Shuster's periodic diagrams have been used. The effect of frequency expansion particularly compensates well‐known aliasing frequency effect. It was shown that if different properties of a random process are taking into account, it will allow to get the estimation of spectrum power density, the order of decrease of which corresponds to these differential properties.
Aliasing
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Spin-weighted spherical harmonics
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Solid harmonics
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