Gravity and gravity gradient data are widely used in geodesy, geodynamics, oil and mineral exploration, and aided navigation. The measured gravity and gravity gradient data include high-frequency noise caused by instrument system error, environmental conditions, and human factors. Separating noise from the measured gravity and gravity gradient data is one of the most challenging tasks in processing the measured data. Traditional low-pass digital filters can remove the noise of an individual component in real-time, which cannot realize the joint filtering of gravity and gravity gradient data. As a postprocessing method, the inversion-based methods can combine gravity and all the gradient components to remove the noise constrained by the Laplace equation. However, a real-time filter method that combines gravity and all gradient components is needed for some special applications, such as submarine gravity and gravity gradient-aided navigation. In this study, gravity and gravity gradient data are combined in establishing system equation and measurement equation of the standard Kalman filter, and denoised in real-time by the improved Kalman filter (IKF). Based on the model test, this method can simultaneously remove the noise in gravity and gravity gradient data in real-time, and ensure denoising performance. Finally, we apply this method to real gravity and gravity gradient data in St. George’s Bay, Canada, acquired by Bell Geospace, and compared the denoised results by full tensor noise reduction (FTNR) and Gaussian low-pass filter, which verified that the performance of IKF is well in real-time joint filtering of gravity and gravity gradient data.

中文翻译：

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基于改进卡尔曼滤波器的重力和重力梯度数据实时联合滤波


重力和重力梯度数据广泛应用于大地测量学、地球动力学、石油和矿产勘探以及辅助导航等领域。测量的重力和重力梯度数据包括仪器系统误差、环境条件和人为因素引起的高频噪声。从测量的重力和重力梯度数据中分离噪声是处理测量数据中最具挑战性的任务之一。传统的低通数字滤波器只能实时去除单个分量的噪声，无法实现重力和重力梯度数据的联合滤波。作为一种后处理方法，基于反演的方法可以结合重力和所有梯度分量来消除受拉普拉斯方程约束的噪声。然而，对于一些特殊应用，例如潜艇重力和重力梯度辅助导航，需要结合重力和所有梯度分量的实时滤波方法。本研究将重力和重力梯度数据结合建立标准卡尔曼滤波器的系统方程和测量方程，并通过改进的卡尔曼滤波器（IKF）进行实时去噪。经过模型测试，该方法能够同时实时去除重力和重力梯度数据中的噪声，保证去噪性能。最后，我们将该方法应用到贝尔地理空间公司获取的加拿大圣乔治湾的真实重力和重力梯度数据上，并通过全张量降噪（FTNR）和高斯低通滤波器的去噪结果进行比较，验证了IKF在重力和重力梯度数据的实时联合滤波方面表现良好。