Error Analysis and Filtering Methods for Absolute Ocean Gravity Data

Abstract

The atomic gravimeter has advantages of high accuracy and long-term stability, which is suitable for high-resolution absolute sea-surface and deep-sea gravity measurements. The absolute gravity data measured by the atomic gravimeter are affected by rough sea conditions, with significant nonsmooth and nonlinear noise signals, which reduce the accuracy of gravity measurements. To eliminate the noises in measured gravity data, this article analyzed the noise sources and innovatively introduced the variational modal decomposition algorithm according to the noise characteristics. Since the filtering result of variational modal decomposition algorithm is limited by the selection of parameters like modal number <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> and penalty factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> , a particle swarm optimization (PSO) algorithm and envelope entropy were introduced to adaptively determine the parameters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> , obtaining the optimal decomposition solution. To verify the reliability of the method, we processed the ocean gravity data, which were dynamically measured by atomic gravimeter (ZAG-M), using the empirical mode decomposition (EMD) algorithm, the complete ensemble EMD (EEMD) with adaptive noise algorithm, and the PSO of variational mode decomposition (PSO-VMD) algorithm, respectively. The evaluated external coincidence accuracy acquired by comparing the ZAG-M with the ocean relative gravimeter (KSS-32) deployed on the same ship are 0. 71, 0.54, and 0.48 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}\cdot $ </tex-math></inline-formula> Gal, respectively, confirming that the PSO-VMD filtering algorithm has a better filtering performance. Finally, the PSO-VMD was applied to all the lines of this ocean measurement experiment with an internal coincidence accuracy of 0.62 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}\cdot $ </tex-math></inline-formula> Gal, verifying the stability of the ZAG-M atomic absolute gravimeter in ocean dynamic measurements and the effectiveness of the proposed algorithm.