欧空局早期公布的时域法和空域法解算的GOCE模型均采用能量守恒法处理轨道数据, 但恢复的长波重力场信号精度较低, 而且GOCE卫星在两极存在数据空白, 利用其观测数据恢复重力场模型是一个不适定问题, 导致解算的模型带谐项精度较低, 需进行正则化处理。本文分析了基于轨道数据恢复重力场模型的方法用于处理GOCE数据的精度, 对最优正则化方法和参数的选择进行研究。利用GOCE卫星2009-11-01—2010-01-31共92 d的精密轨道数据, 采用不依赖先验信息的能量守恒法、短弧积分法和平均加速度法恢复GOCE重力场模型, 利用Tikhonov正则化技术处理病态问题。结果表明, 平均加速度法恢复模型的精度最高, 能量守恒法的精度最低, 短弧积分法的精度稍差于平均加速度法。未来联合处理轨道和梯度数据时, 建议采用平均加速度法或短弧积分法处理轨道数据, 并且轨道数据可有效恢复120阶次左右的模型。Kaula正则化和SOT处理GOCE病态问题的效果最好, 并且两者对应的最优正则化参数基本一致, 但利用正则化技术不能完全抑制极空白问题的影响, 需要联合GRACE等其他数据才能获得理想的结果。
The energy conservation approach has been adopted to exploit GOCE orbit information in earlier GOCE time-wise and space-wise gravity field models which are two kinds of official ESA products, but the accuracy of long-wavelength gravity signal is low. Gravity field recovery with GOCE satellite data is an ill-posed problem and the precision of zonal coefficients is low due to the polar gaps, which needs be processed by regularization technique. This paper analyzes the accuracy of existing approaches for gravity field recovery in processing GOCE data and the selection of optimal regularization techniques and parameters. Several gravity field models were recovered based on GOCE precise orbits of 92-days from 2009-11-01 to 2010-01-31 with the energy conservation approach, short-arc integral approach and average acceleration approach. These approaches do not require any initial values of unknown parameters and reference gravity models. Besides, the Tikhonov regularization technique was applied to tackle the ill-posed problem. The results show that the highest accuracy of the model is recovered by the average acceleration approach, the lowest accuracy is the energy conservation approach, and the accuracy of short-arc integral approach is slightly worse than average acceleration approach. Therefore, such methods as the average acceleration approach or short-arc integral approach should be recommended to be applied when processing the GOCE orbit data. Gravity field models can effectively recovered by GOCE orbit data with the order and degree 120 when orbit and gradiometer data are combined to processes in the future. Kaula regularization and second-order Tikhonov (SOT) are superior to other regularization techniques in dealing with ill-posed problem of GOCE, and the corresponding optimal regularization parameters of both techniques are consistent. However, the effects of polar gaps could not be completely inhibited by regularization technique; it should be combined with other data, such as GRACE satellite data, to get the desired results.
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