团队围绕GNSS、GRACE及其他大地测量观测数据,针对数据处理过程中的遇到的实际问题开展了一系列的研究工作,研究领域涉及线性观测模型的抗差估计与可靠性理论、线性观测模型的方差-协方差分量估计理论、非线性观测模型参数估计与偏差改正、大地测量病态模型的解算方法、大地测量时空序列的信号分析等。
1.线性观测模型的抗差估计与可靠性理论
提出了一种适用于三维相关矢量观测的鲁棒M估计方法,构建了一个改进的双因子缩减模型;基于特定方向的GNSS网异常值提出了一种检测方法,使得沿该方向构建的检验统计量达到最大检验功效;提出了利用无偏的中位数方差估计来校准方差估计的偏差,构建了基于无偏中位数方差估计的M估计方法;在DIA统一框架的基础上,构建了质量控制指标,并提出了一种简化代数估计方法来计算质量控制指标。为了消除离群值对相关残差的影响,构造了等效权值来降低异常值的权重,提出了一种利用修正残差构成权重因子的减权策略。
参考文献:
[1] Yang L, Shen Y (2020)Robust M estimation for 3D correlated vector observations based on modified bifactor weight reduction model. Journal of Geodesy, 94(3), 1-17.Click
[2] Yang L, Shen Y, Li B, Rizos C (2021) Simplified algebraic estimation for the quality control of DIA estimator. Journal of Geodesy, 95(1), 1-15.Click
[3] Yang, L., Nie, Y., & Shen, Y. (2019). Characteristic analysis of 3D outlier detection method for GNSS network adjustments. Journal of Surveying Engineering, 145(4), 04019014.Click
[4] Nie, Y., Yang, L., & Shen, Y. (2019). Specific direction-based outlier detection approach for GNSS vector networks. Sensors, 19(8), 1836.Click
[5]Yang, L., Shen, Y., & Li, B. (2019). M-estimation using unbiased median variance estimate. Journal of Geodesy, 93(6), 911-925.Click
[6] Yu, H., Shen, Y., Yang, L., & Nie, Y. (2019). Robust M-estimation using the equivalent weights constructed by removing the influence of an outlier on the residuals. Survey Review, 51(364), 60-69.Click
2.线性观测模型的方差-协方差分量估计理论
基于卫星大地测量学中的局部-全局参数划分方案,提出了一种高效的VCE算法,该算法直接适用于局部参数为单一观测组所特有的简化情况,以及局部参数为不同观测组所共享的广义情况;基于等效残差建立了VCE基本方程,并以此导出了Helmert、MINQUE、极大似然和最小二乘VCE方法的估计公式。揭示了不同VCE方法的实质和相互关系;利用系数阵本身构造它的正交补矩阵,从而导出的等效残差不变,基于该等效残差导出的估计公式在确保与已有算法相同的估值的前提下,有效地提高计算效率。
参考文献:
[1] Nie, Y., Shen, Y., Pail, R., & Chen, Q. (2022). Efficient variance component estimation for large-scale least-squares problems in satellite geodesy. Journal of Geodesy, 96(2), 1-15.Click
[2] Li, B., Shen, Y., & Lou, L. (2010). Efficient estimation of variance and covariance components: a case study for GPS stochastic model evaluation. IEEE Transactions on Geoscience and Remote Sensing, 49(1), 203-210.Click
[3]李博峰,沈云中.基于等效残差积探测粗差的方差-协方差分量估计[J].测绘学报,2011,40(01):10-14+32.Click
[4]李博峰,沈云中,楼立志.基于等效残差的方差-协方差分量估计[J].测绘学报,2010,39(04):349-354+363.Click
3.大地测量病态模型的解算方法
构建了病态非线性观测方程正则化算法的估计准则及其迭代算法;建立了病态观测方程正则化解的偏差改正算法和验后方差因子无偏估计方法,阐明了正则化矩阵的构建原则;以参数估值的质量最优为准则,建立了病态观测方程的低频、中频和高频分量,正则化矩阵和方差因子自适应确定理论和方法;相关成果成功用于GNSS快速定位和长距离实时定位,高空间分辨率冰川融化信号提取,以及大地测量基准的非线性无缝转换。
参考文献:
[1] Shen Y, Li B (2007) Regularized Solution to Fast GPS Ambiguity Resolution.Journal of Surveying Engineering, 133(4):168-172.Click
[2] Li B, Shen Y, Feng Y (2010) Fast GNSS ambiguity resolution as an ill-posed problem.Journal of Geodesy, 84:683-6988.Click
[3] Shen Y, Xu P, Li B (2012) Bias-corrected regularized solution to inverse ill-posed models.Journal of Geodesy, 86: 597-608.Click
[4] Shen, Y., Xu, G. (2013) Regularization and Adjustment. In: Xu, G. (eds) Sciences of Geodesy - II. Springer, Berlin, Heidelberg.Click
[5] Chen T, Kusche J, Shen Y, et al (2020)A Combined Use of TSVD and Tikhonov Regularization for Mass Flux Solution in Tibetan Plateau.Remote Sensing, 12(12): 2045.Click
[6]Ji K, Shen Y, Chen Q, Li B, Wang W (2022) An Adaptive Regularized Solution to Inverse Ill-Posed Models.IEEE Transactions on Geoscience and Remote Sensing, 60, 1-15.Click
[7]沈云中,刘大杰.正则化解的单位权方差无偏估计公式[J].武汉大学学报(信息科学版),2002(06):604-606+610.Click
[8]沈云中,许厚泽.基于积分方程正则化的重力异常超定问题解法[J].同济大学学报(自然科学版),2002(11):1337-1341.Click
[9]沈云中,许厚泽.不适定方程正则化算法的谱分解式[J].大地测量与地球动力学,2002(03):10-14.Click
[10]沈云中,许厚泽.应用CHAMP星历精化地球重力场的正则化算法与模拟结果[J].测绘学报,2003(01):11-14.Click
[11]沈云中.基于滤波因子的病态方程解法[J].同济大学学报(自然科学版),2006(06):844-847.Click
[12]沈云中,胡雷鸣,李博峰.Bursa模型用于局部区域坐标变换的病态问题及其解法[J].测绘学报,2006(02):95-98.Click
[13]嵇昆浦,沈云中.TSVD正则化解法的单位权方差无偏估计[J].武汉大学学报(信息科学版),2020,45(04):626-632.DOI:10.13203/j.whugis20180270.Click
4.大地测量时空序列数据的信号分析
大地测量时间序列数据通常给出精度因子且经常发生数据缺失,课题组根据时域与频域数据的再生关系并利用精度因子加权处理,建立了顾及精度因子且不需对缺失数据进行插值的时间序列数据的频谱分析理论;完善了传统小波分析、主成分分析和奇异谱分析方法,并成功从全球和区域时间序列数据提取更可靠的信号;将被乘积型误差污染的时间序列数据转换为被不同精度因子的加型误差污染的时间序列数据后,再引入权因子进行谱分析,这是目前最有效的乘积型误差时间序列的谱分析方法。相关成果在 Nonlinear Process in Geophysics,Journal of Hydrology等国际重要地学刊物上发表了12篇国际SCI论文。这些算法的相关引用量已近170次。利用这些理论方法,成功内插了GRACE与GRACE Follow On卫星之间11月的数据缺失,分析了青藏高原地区2003年至2015年的质量变化,发现大部分青藏冰川融水仍驻留在高原湖泊。
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参考文献:
[1] Shen, Y., Li, W., Xu, G., & Li, B. (2014). Spatiotemporal filtering of regional GNSS network’s position time series with missing data using principle component analysis. Journal of Geodesy, 88(1), 1-12.Click
[2] Shen Y, Peng F, Li B (2015) Improved singular spectrum analysis for time series with missing data. Nonlinear Process Geophys 22(4): 371-376.Click
[3] Li, W.; Shen, Y.; Li, B. Weighted spatiotemporal filtering using principal component analysis for analyzing regional GNSS position time series. Acta Geod. Geophys. 2015, 50, 419–436.Click
[4] Li, W., & Shen, Y. (2018). The consideration of formal errors in spatiotemporal filtering using principal component analysis for regional GNSS position time series. Remote Sensing, 10(4), 534.Click
[5] Wang F, Shen Y, Chen T, Chen Q, Li W (2020) Improved multichannel singular spectrum analysis for post-processing GRACE monthly gravity field models. Geophys J Int 223(2): 825-839.Click
[6] Shen, Y., Wang, F., & Chen, Q. (2021). Weighted multichannel singular spectrum analysis for post-processing GRACE monthly gravity field models by considering the formal errors. Geophysical Journal International, 226(3), 1997-2010.Click
[7] Wang, F., Shen, Y., Chen, Q., & Wang, W. (2021). Bridging the gap between GRACE and GRACE follow-on monthly gravity field solutions using improved multichannel singular spectrum analysis. Journal of Hydrology, 594, 125972.Click
[8] Ji, K., Shen, Y., & Wang, F. (2020). Signal extraction from GNSS position time series using weighted wavelet analysis. Remote Sensing, 12(6), 992.Click
[9] Wang, F., Shen, Y., Chen, Q., & Li, W. (2019). A heuristic singular spectrum analysis method for suspended sediment concentration time series contaminated with multiplicative noise. Acta Geodaetica et Geophysica, 54(4), 483-497.Click
[10] Wang, F., Shen, Y., Li, W., & Chen, Q. (2018). Singular spectrum analysis for heterogeneous time series by taking its formal errors into account. Acta Geodyn Geomater, 4(192), 395-403.Click
[11]嵇昆浦,沈云中.含缺值GNSS基准站坐标序列的非插值小波分析与信号提取[J].测绘学报,2020,49(05):537-546.Click