Adaptive filtering of satellite gravity gradiometry data for global gravity field modeling
20/09/2016 | 10:30 | Session 2: Computational Methods
Author(s): Dimitrios Piretzidis and Michael Sideris
Dimitrios Piretzidis and Michael Sideris
The European Space Agency’s Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission has provided precise gravity gradient measurements, resulting in more accurate geopotential models, especially in the medium and high part of the frequency spectrum. Before estimating the spherical harmonic coefficients of a geopotential model, filtering techniques should be applied to the gravity data to attenuate the measurement noise. This study deals with the implementation and testing of two adaptive filtering algorithms, i.e., the Least Mean-Squared (LMS) and the Recursive Least-Squares (RLS) algorithms, on preprocessed GOCE gravity gradients for precise gravity field modeling. The structure of the filter used in both algorithms is similar to a Wiener filter. The six components of the gravity gradient tensor are filtered using prior gravity field information. This information is derived from the GOCE-only geopotential model TIM-R5 and serves as the desired signal for the adaptive Wiener filtering.
Before applying the filtering in the LMS method, the algorithm should be tuned by deriving suitable filtering parameters (i.e., step-size parameter and filter order). The RLS algorithm is tuned only for the filter order. Time- and frequency-domain analysis shows that both algorithms effectively filter the noise contained in the high frequencies of the GOCE measurements. The RLS algorithm might appear a more appealing choice due to the fact that does not require a step-size parameter and the Wiener filter coefficients converge faster, however it is computationally much more intensive than the LMS. The LMS algorithm provides more stable impulse responses, as long as the filtering parameters do not lead to a divergence of the filter coefficients.
The Wiener filter is extensively used for filtering gravity gradients and estimating geopotential model coefficients, especially using the space-wise approach. With the implementation of adaptive Wiener filtering techniques, the calculation and inversion of large matrices that is required in typical stochastic and spectral methods such as the least squares collocation can be avoided, resulting in more computationally efficient algorithms.