Error analysis for satellite gravity field determination based on two-dimensional Fourier methods

TL;DR

This paper develops an analytical method using two-dimensional Fourier transforms to directly relate measurement noise to gravity field coefficients, improving error analysis and parameter estimation for satellite gravimetry.

Contribution

It introduces a novel analytical approach linking spectral density of measurements to gravity potential coefficients, addressing numerical instability issues in traditional methods.

Findings

Low-frequency noise impacts all degrees of gravity field recovery.

Analytical expression improves parameter estimation efficiency.

Method enhances understanding of measurement error effects.

Abstract

The time-wise and space-wise approaches are generally applied to data processing and error analysis for satellite gravimetry missions. But both the approaches, which are based on least-squares collocation, address the whole effect of measurement errors and estimate the resolution of gravity field models mainly from a numerical point of indirect view. Moreover, requirement for higher accuracy and resolution gravity field models could make the computation more difficult, and serious numerical instabilities arise. In order to overcome the problems, this study focuses on constructing a direct relationship between power spectral density of the satellite gravimetry measurements and coefficients of the Earth's gravity potential. Based on two-dimensional Fourier transform, the relationship is analytically concluded. By taking advantage of the analytical expression, it is efficient and distinct for parameter estimation and error analysis of missions. From the relationship and the simulations, it is analytically confirmed that the low-frequency noise affects the gravity field recovery in all degrees for the instance of satellite gradiometer recovery mission. Furthermore, some other results and suggestions are also described.