一种卫星重力梯度数据的ARMA最优滤波模型构建方法
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摘要
由于卫星重力梯度观测的有色噪声特性和海量观测特征,在利用直接法进行重力场模型的最小二乘求解时,观测值的协方差阵为超大型的非对角阵,这给数值求解带来了极大困难.本文提出了一种基于先验误差功率谱密度的最优ARMA滤波模型构建方法,结合法方程的分块求解策略,可实现对卫星重力梯度观测值的高效滤波处理.数值仿真结果表明,利用最优ARMA滤波器进行时域滤波后,法方程的态性得到了明显改善,重力梯度观测值中的有色噪声得到了有效的"白化"处理,大地水准面精度得到了显著提升.
Due to the colored noise in the massive satellite gravity gradiometry observations,when determining the least square solution of the gravity field model using the direct method,the covariance matrix of the observations is a huge non-diagonal matrix,which brings great difficulties to numerical computation.To solve this problem,this work proposes a method of constructing the optimal ARMA filtering model based on the prior error power spectrum density,which realizes the efficient filtering of satellite gravity gradiometry observations combined with the block solving strategy.The numerical simulation analyses show that after the processing in the time domain with the optimal ARMA filter,the state of the normal equation matrix is improved obviously,and the colored noises mixed into the gravity gradiometry measurements are whitened efficiently,while the accuracy of the geoid increases significantly.
Due to the colored noise in the massive satellite gravity gradiometry observations,when determining the least square solution of the gravity field model using the direct method,the covariance matrix of the observations is a huge non-diagonal matrix,which brings great difficulties to numerical computation.To solve this problem,this work proposes a method of constructing the optimal ARMA filtering model based on the prior error power spectrum density,which realizes the efficient filtering of satellite gravity gradiometry observations combined with the block solving strategy.The numerical simulation analyses show that after the processing in the time domain with the optimal ARMA filter,the state of the normal equation matrix is improved obviously,and the colored noises mixed into the gravity gradiometry measurements are whitened efficiently,while the accuracy of the geoid increases significantly.
引文
Brockmann J M,Schuh W D,Kargoll B.2015.A case study on the potential of robust decorrelation filter design for a reprocessing of a gravity field model from GOCE data.EGU General Assembly Conference.∥EGU General Assembly Conference Abstracts.Vienna,Austria.
Broersen P M T.2000.Finite sample criteria for autoregressive order selection.IEEE Transactions on Signal Processing,48(12):3550-3558.
Broersen P M T,de Waele S.2005.Automatic identification of time-series models from long autoregressive models.IEEETransactions on Instrumentation and Measurement,54(5):1862-1868.
Bruinsma S L,F9rste C,Abrikosov O,et al.2014.ESA's satelliteonly gravity field model via the direct approach based on all GOCE data.Geophysical Research Letters,41(21):7508-7514.
deWaele S,Broersen P M T.2003.Order selection for vector autoregressive models.IEEE Transactions on Signal Processing,51(2):427-433.
Ditmar P,Klees R,Liu X.2007.Frequency-dependent data weighting in global gravity field modeling from satellite data contaminated by non-stationary noise.Journal of Geodesy,81(1):81-96.
ESA.1999.Gravity field and steady-state ocean circulation mission.Report for mission selection of the four candidate earth explorer missions,ESA Publications Division.ESA SP-1233(1).
ESA.2006.GOCE L1bproducts user handbook.Technical Note,OCE-GSEG-EOPGTN-06-0137.
Gao X H,Yu P,Zhao Y.2015.Noise attenuation of vertical components of full tensor gravity gradient data.Global Geology(in Chinese),34(1):203-209.
Jones R.1974.Identification and autoregressive spectrum estimation.IEEE Transactions on Automatic Control,19(6):894-898.
Kaderli A,Kayhan A S.2000.Spectral estimation of ARMA processes using ARMA-Cepstrum recursion.IEEESignal Processing Letters,7(9):259-261.
Kay S M,Marple S L.1981.Spectrum analysis-a modern perspective.Proceedings of the IEEE,69(11):1380-1419.
Kizilkaya A,Kayran A H.2006.ARMA model parameter estimation based on the equivalent MA approach.Digital Signal Processing,16(6):670-681.
Klees R,Broersen P.2002.How to Handle Colored Noise in Large Least-Squares Problems.Building the Optimal Filter.Delft:Delft University Press.
Klees R,Ditmar P,Broersen P.2003.How to handle colored observation noise in large least-squares problems.Journal of Geodesy,76(11-12):629-640.
Liu X G,Wu B,Wang X M,et al.2012.Design of color noise filter in GOCE satellite gravimetry mission.Progress in Geophysics(in Chinese),27(3):856-860,doi:10.6038/j.issn.1004-2903.2012.03.004.
Migliaccio F,Reguzzoni M,SansòF.2004.Space-wise approach to satellite gravity field determination in the presence of coloured noise.Journal of Geodesy,78(4-5):304-313.
Pail R,Bruinsma S,Migliaccio F,et al.2011.First GOCE gravity field models derived by three different approaches.Journal of Geodesy,85(11):819-843.
Piretzidis D,Sideris M G.2017.Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach.Journal of Geodesy,91(9):1069-1086.
Rummel R,Yi W Y,Stummer C.2011.GOCE gravitational gradiometry.Journal of Geodesy,85(11):777-790.
Sandgren N,Stoica P.2005.On moving average parameter estimation.Systems and Control Division,Uppsala University,Sweden.
Schuh W D.1996.Tailored numerical solution strategies for the global determination of the Earth′s gravity field.Mitteilungen der geodtischen Institute der TU Graz,Folge 81.
Schuh W D.2003.The processing of band-limited measurements:filtering techniques in the least squares context and in the presence of data gaps.Space Science Reviews,108(1-2):67-78.
Sneeuw N.2003.Space-wise,time-wise,torus and rosborough representations in gravity field modelling.Space Science Reviews,108(1-2):37-46.
Tong H.1975.Autoregressive model fitting with noisy data by Akaike′s information criterion(Corresp.).IEEE Transactions on Information Theory,21(4):476-480.
Zhang L H,Zheng B Y.2003.Stochastic Signal Processing(in Chinese).Beijing:Tsinghua University Press.
Zhong B,Ning J S,Luo Z C,et al.2012.Simulation study of rigorous gravity field recovery by combining GOCE satellite orbit and gravity gradient data.Geomatics&Information Science of Wuhan University(in Chinese),37(10):1215-1220.
高秀鹤,于平,赵玥.2015.全张量重力梯度数据垂直分量噪声滤除方法研究.世界地质,34(1):203-209.
刘晓刚,吴杉,王献民等.2012.GOCE卫星重力测量中有色噪声滤波器设计.地球物理学进展,27(3):856-860,doi:10.6038/j.issn.1004-2903.2012.03.004.
张玲华,郑宝玉.2003.随机信号处理.北京:清华大学出版社.
钟波,宁津生,罗志才等.2012.联合GOCE卫星轨道和重力梯度数据严密求解重力场的模拟研究.武汉大学学报(信息科学版),37(10):1215-1220.
Broersen P M T.2000.Finite sample criteria for autoregressive order selection.IEEE Transactions on Signal Processing,48(12):3550-3558.
Broersen P M T,de Waele S.2005.Automatic identification of time-series models from long autoregressive models.IEEETransactions on Instrumentation and Measurement,54(5):1862-1868.
Bruinsma S L,F9rste C,Abrikosov O,et al.2014.ESA's satelliteonly gravity field model via the direct approach based on all GOCE data.Geophysical Research Letters,41(21):7508-7514.
deWaele S,Broersen P M T.2003.Order selection for vector autoregressive models.IEEE Transactions on Signal Processing,51(2):427-433.
Ditmar P,Klees R,Liu X.2007.Frequency-dependent data weighting in global gravity field modeling from satellite data contaminated by non-stationary noise.Journal of Geodesy,81(1):81-96.
ESA.1999.Gravity field and steady-state ocean circulation mission.Report for mission selection of the four candidate earth explorer missions,ESA Publications Division.ESA SP-1233(1).
ESA.2006.GOCE L1bproducts user handbook.Technical Note,OCE-GSEG-EOPGTN-06-0137.
Gao X H,Yu P,Zhao Y.2015.Noise attenuation of vertical components of full tensor gravity gradient data.Global Geology(in Chinese),34(1):203-209.
Jones R.1974.Identification and autoregressive spectrum estimation.IEEE Transactions on Automatic Control,19(6):894-898.
Kaderli A,Kayhan A S.2000.Spectral estimation of ARMA processes using ARMA-Cepstrum recursion.IEEESignal Processing Letters,7(9):259-261.
Kay S M,Marple S L.1981.Spectrum analysis-a modern perspective.Proceedings of the IEEE,69(11):1380-1419.
Kizilkaya A,Kayran A H.2006.ARMA model parameter estimation based on the equivalent MA approach.Digital Signal Processing,16(6):670-681.
Klees R,Broersen P.2002.How to Handle Colored Noise in Large Least-Squares Problems.Building the Optimal Filter.Delft:Delft University Press.
Klees R,Ditmar P,Broersen P.2003.How to handle colored observation noise in large least-squares problems.Journal of Geodesy,76(11-12):629-640.
Liu X G,Wu B,Wang X M,et al.2012.Design of color noise filter in GOCE satellite gravimetry mission.Progress in Geophysics(in Chinese),27(3):856-860,doi:10.6038/j.issn.1004-2903.2012.03.004.
Migliaccio F,Reguzzoni M,SansòF.2004.Space-wise approach to satellite gravity field determination in the presence of coloured noise.Journal of Geodesy,78(4-5):304-313.
Pail R,Bruinsma S,Migliaccio F,et al.2011.First GOCE gravity field models derived by three different approaches.Journal of Geodesy,85(11):819-843.
Piretzidis D,Sideris M G.2017.Adaptive filtering of GOCE-derived gravity gradients of the disturbing potential in the context of the space-wise approach.Journal of Geodesy,91(9):1069-1086.
Rummel R,Yi W Y,Stummer C.2011.GOCE gravitational gradiometry.Journal of Geodesy,85(11):777-790.
Sandgren N,Stoica P.2005.On moving average parameter estimation.Systems and Control Division,Uppsala University,Sweden.
Schuh W D.1996.Tailored numerical solution strategies for the global determination of the Earth′s gravity field.Mitteilungen der geodtischen Institute der TU Graz,Folge 81.
Schuh W D.2003.The processing of band-limited measurements:filtering techniques in the least squares context and in the presence of data gaps.Space Science Reviews,108(1-2):67-78.
Sneeuw N.2003.Space-wise,time-wise,torus and rosborough representations in gravity field modelling.Space Science Reviews,108(1-2):37-46.
Tong H.1975.Autoregressive model fitting with noisy data by Akaike′s information criterion(Corresp.).IEEE Transactions on Information Theory,21(4):476-480.
Zhang L H,Zheng B Y.2003.Stochastic Signal Processing(in Chinese).Beijing:Tsinghua University Press.
Zhong B,Ning J S,Luo Z C,et al.2012.Simulation study of rigorous gravity field recovery by combining GOCE satellite orbit and gravity gradient data.Geomatics&Information Science of Wuhan University(in Chinese),37(10):1215-1220.
高秀鹤,于平,赵玥.2015.全张量重力梯度数据垂直分量噪声滤除方法研究.世界地质,34(1):203-209.
刘晓刚,吴杉,王献民等.2012.GOCE卫星重力测量中有色噪声滤波器设计.地球物理学进展,27(3):856-860,doi:10.6038/j.issn.1004-2903.2012.03.004.
张玲华,郑宝玉.2003.随机信号处理.北京:清华大学出版社.
钟波,宁津生,罗志才等.2012.联合GOCE卫星轨道和重力梯度数据严密求解重力场的模拟研究.武汉大学学报(信息科学版),37(10):1215-1220.
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