精密重力测量中相对重力仪格值系数的贝叶斯估计方法

相对重力仪的格值系数随时间会发生微小的变化，是影响精密重力测量精度的重要因素。通常需定期对相对重力仪进行专门的基线标定来评估仪器格值系数的变化。本文提出了一种利用重力观测数据进行格值系数评估的新方法，原理是利用测网中已知的多个绝对重力基准点作为先验约束，同时考虑仪器的非线性漂移变化，将格值系数作为超参数，基于贝叶斯原理和赤池贝叶斯信息准则（ABIC）估计最优值。通过对模拟数据的测试，该方法在高斯噪声和仪器非线性漂移等不确定性存在的情况下，可以获得格值系数的准确估计结果。对实测重力数据的测试表明：估计的格值系数与测量前在基线场标定的格值系数差值在5×10^-5以内；而且相较于采用标定不准确的格值系数，该方法可以获得与绝对重力测量结果差异更小的平差重力值。本文研究结果为有效提高精密重力测量的效率和精度提供了方法保障。

Bayesian estimation of the scale factor of relative gravimeter in precise gravity survey

The scale factor of the relative gravimeter changes slightly with time, which is an important factor affecting the accuracy of precise gravity survey. It is necessary to regularly perform a special baseline calibration on the relative gravimeter to evaluate the change of the instrument’s scale factor. This study presents a new method that can be used to evaluate the scale factor based on the gravity observation data only. The principle is to use multiple absolute gravity datum stations known in the survey network as constraints, and to take into account the nonlinear drift of the instrument, and then to estimate scale factor as one of the hyper-parameters by Bayesian theory and Akaike’s Bayesian information criterion (ABIC). Through simulation data testing, this method can obtain the accurate estimation of scale factor in the presence of uncertainties such as Gaussian noise and instrument nonlinear drift. The test of the measured gravity data shows that: the differences between the estimated scale factors and the calibration results of baseline field before measurement are within 5×10^-5, and compared with using the inaccurate calibrated scale factors, this method can obtain the better estimation of gravity values which are less different from the results of absolute gravimetry. The results of this study provide method guarantee for effectively improving the efficiency and accuracy of precise gravity survey.