基于先验约束信息的变形监测滤波算法研究
|
摘要
在变形观测数据处理过程中,依据客观条件合理利用约束信息,显然可以简化模型,提高变形参数估计的精度,控制滤波的发散。因为状态约束的存在改变了动态定位问题概率方面的结构,给问题的分析及滤波解算带来了一定的难度。在实际变形观测数据处理时,常用的方法一般是通过状态约束方程消去某些状态参数,然后按一般滤波方法进行处理。对于某些非线性情况,这样处理往往使计算显得复杂,同时也使原来的滤波方程发生较大的改变,在实用上显得不方便。论文通过变形观测实例探讨了变形观测中先验约束信息的获取、转换和约束滤波模型的建立,侧重研究了如何通过地质、力学信息的滑坡、地形变信息来建立变形观测滤波解算模型。在分析了变形观测滤波算法的现状和存在的问题的基础上,论文针对不同形式的约束信息,给出了一些全新的算法,保证了测量信息异常或信息不充分时解算结果的有效性,其主要贡献有以下几点：
1.通过变形观测实例探讨了变形观测中,先验约束信息的获取,模型的建立,总结各种约束的形式,并建立了相应的滤波模型。侧重研究了在考虑地质、力学信息的滑坡及地形变的数据处理与分析中相应的模型与算法及效果。
2.针对参数带有不等式约束的平差模型,给出了这些最小二乘估计解的一般形式,为变形观测中约束滤波算法的实现提供了保证。
3.针对一些先验约束信息带有未知参数无法利用的问题,提供了一种算法将其转换成含有未知参数的状态方程,采用移动窗口的系统误差拟合的方法,然后进行滤波解算方法。
4.给出一种合理利用几何信息和物理信息的滤波算法,在变形观测数据处理中,首先把一些未知的物理信息看成是未知的系统误差并对其进行估计,再利用先验约束信息来控制几何观测异常对形变参数估计的影响。
5.提出了一种状态变量带有约束的抗差滤波算法,在抗差估计情形里,无约束滤波过程首先提供一个初始的状态估计解,然后再综合利用约束信息进行更新。
在变形观测的数据处理中,将变形体的物理模型预报的位移量作为先验约束信息,用连续滤波的方法对几何观测量进行处理,调节物理模型信息和几何观测信息间的相对权重,使变形体的物理模型参数加以修正,从而能够充分利用变形体的物理模型信息和几何观测信息,将误差的影响降到最小,使形变参数估计结果达到最优。论文创新性地解决了具有先验约束信息的利用和计算问题,使它能够在变形观测数据处理中广泛应用,同时把滤波理论推广到了带有先验约束信息的情形,使动态滤波数据处理理论得到一定的发展和完善。
In the data processing of the deformation monitoring, constraint information can be properly used under certain objective conditions, which can apparently simplify the mathematical model and improve the accuracy of the estimated deformation parameters as well as control the filter divergence. But as the state constraints changes the probability structure of state parameters in the kinematic positioning, the difficulty for data analysis and filtering solutions will therefore increase. In the actual data processing, the commonly used method is to remove some state parameters by the state constraint equations, and then the left state parameters are estimated in a common filter processing. However, this tends to increase the complication of the calculation for some nonlinear cases and cause the greater change of the original filter equations. As a result, it is inconvenient in the practical application. This thesis investigates the acquisition of priori constraint information, conversion and the establishment of constraint filter model through a case study with an emphasis on how to build the mathematical model of deformation observation filter by using the geological, mechanical information of landslides and ground deformation information. Besides, based on the analysis of the current status and existing problems of the filtering algorithm, some novel algorithms have been proposed in terms of different constraint information. The new algorithms can increase the validation of the solutions when with abnormal or insufficient measurement information. The main contributions of the thesis are given as follows:
1. Discuss the acquisition of the priori constraint information, establishment of model and summarize the forms of various constraints and build the corresponding filter model through a case study, focusing on data processing with the consideration of the landslide with geological and mechanical information and result analysis on the corresponding model and algorithms.
2. For parameters with adjustment model of inequality constraint information, the general form of least square solutions is given, which facilitates the implementation of constraint filtering algorithm in deformation observations.
3. For some priori constraint information with unemployed unknown parameters, an algorithm is provided to convert it into state equation containing unknown parameters. Then the fitting method of systematic errors with moving window is adopted.
4. A filtering algorithm with a proper use of geometry information and physical information is given. Firstly, some unknown physics information is thought as unknown systematic errors, which are then estimated in the data processing. Secondly, the priori constraint information is used to control the influence of the geometric observation abnormalities on deformation parameters.
5. A filtering algorithm with the capability of resistance to blunders is proposed, in which the state parameters are constrained by constraint information. The filter solution without constraint firstly provides initial state estimates and then the state estimates are updated using comprehensively constraint information.
In the data processing of deformation observation, the displacement obtained by the forecast of physical model of deformation body is used as a priori constraint. By handling the geometric measurements by continuous filter method, and adjusting the physical model information and relative weight between the physical model information and geometric measurement information, and modifying the parameters of physical model of the deformation body, the impact of the errors can be minimized and therefore optimal deformation parameter estimates can be obtained. The thesis innovatively solves the use and calculation issue of a priori constraint information and enables the application in the data processing of deformation observation. Meanwhile, the filtering theory is extended to enable the processing for the case with the prior constraint information and the data processing method of kinematic filtering is further improved and developed.
1.通过变形观测实例探讨了变形观测中,先验约束信息的获取,模型的建立,总结各种约束的形式,并建立了相应的滤波模型。侧重研究了在考虑地质、力学信息的滑坡及地形变的数据处理与分析中相应的模型与算法及效果。
2.针对参数带有不等式约束的平差模型,给出了这些最小二乘估计解的一般形式,为变形观测中约束滤波算法的实现提供了保证。
3.针对一些先验约束信息带有未知参数无法利用的问题,提供了一种算法将其转换成含有未知参数的状态方程,采用移动窗口的系统误差拟合的方法,然后进行滤波解算方法。
4.给出一种合理利用几何信息和物理信息的滤波算法,在变形观测数据处理中,首先把一些未知的物理信息看成是未知的系统误差并对其进行估计,再利用先验约束信息来控制几何观测异常对形变参数估计的影响。
5.提出了一种状态变量带有约束的抗差滤波算法,在抗差估计情形里,无约束滤波过程首先提供一个初始的状态估计解,然后再综合利用约束信息进行更新。
在变形观测的数据处理中,将变形体的物理模型预报的位移量作为先验约束信息,用连续滤波的方法对几何观测量进行处理,调节物理模型信息和几何观测信息间的相对权重,使变形体的物理模型参数加以修正,从而能够充分利用变形体的物理模型信息和几何观测信息,将误差的影响降到最小,使形变参数估计结果达到最优。论文创新性地解决了具有先验约束信息的利用和计算问题,使它能够在变形观测数据处理中广泛应用,同时把滤波理论推广到了带有先验约束信息的情形,使动态滤波数据处理理论得到一定的发展和完善。
In the data processing of the deformation monitoring, constraint information can be properly used under certain objective conditions, which can apparently simplify the mathematical model and improve the accuracy of the estimated deformation parameters as well as control the filter divergence. But as the state constraints changes the probability structure of state parameters in the kinematic positioning, the difficulty for data analysis and filtering solutions will therefore increase. In the actual data processing, the commonly used method is to remove some state parameters by the state constraint equations, and then the left state parameters are estimated in a common filter processing. However, this tends to increase the complication of the calculation for some nonlinear cases and cause the greater change of the original filter equations. As a result, it is inconvenient in the practical application. This thesis investigates the acquisition of priori constraint information, conversion and the establishment of constraint filter model through a case study with an emphasis on how to build the mathematical model of deformation observation filter by using the geological, mechanical information of landslides and ground deformation information. Besides, based on the analysis of the current status and existing problems of the filtering algorithm, some novel algorithms have been proposed in terms of different constraint information. The new algorithms can increase the validation of the solutions when with abnormal or insufficient measurement information. The main contributions of the thesis are given as follows:
1. Discuss the acquisition of the priori constraint information, establishment of model and summarize the forms of various constraints and build the corresponding filter model through a case study, focusing on data processing with the consideration of the landslide with geological and mechanical information and result analysis on the corresponding model and algorithms.
2. For parameters with adjustment model of inequality constraint information, the general form of least square solutions is given, which facilitates the implementation of constraint filtering algorithm in deformation observations.
3. For some priori constraint information with unemployed unknown parameters, an algorithm is provided to convert it into state equation containing unknown parameters. Then the fitting method of systematic errors with moving window is adopted.
4. A filtering algorithm with a proper use of geometry information and physical information is given. Firstly, some unknown physics information is thought as unknown systematic errors, which are then estimated in the data processing. Secondly, the priori constraint information is used to control the influence of the geometric observation abnormalities on deformation parameters.
5. A filtering algorithm with the capability of resistance to blunders is proposed, in which the state parameters are constrained by constraint information. The filter solution without constraint firstly provides initial state estimates and then the state estimates are updated using comprehensively constraint information.
In the data processing of deformation observation, the displacement obtained by the forecast of physical model of deformation body is used as a priori constraint. By handling the geometric measurements by continuous filter method, and adjusting the physical model information and relative weight between the physical model information and geometric measurement information, and modifying the parameters of physical model of the deformation body, the impact of the errors can be minimized and therefore optimal deformation parameter estimates can be obtained. The thesis innovatively solves the use and calculation issue of a priori constraint information and enables the application in the data processing of deformation observation. Meanwhile, the filtering theory is extended to enable the processing for the case with the prior constraint information and the data processing method of kinematic filtering is further improved and developed.
引文
[1]朱建军.变形测量的理论与方法[M].中南大学出版社,长沙,2004.
[2]朱建军,丁晓利,陈永奇.集成地质、力学信息和监测数据的滑坡动态模型[J].测绘学报,2003,32(3)：261-266.
[3]杨元喜,曾安敏.顾及几何观测信息和地球物理模型的形变参数自适应滤波解[J].2009,39(4)：437-442.
[4]陶本藻.自由平差与变形分析[M].北京：测绘出版社,1992.
[5]刘经南,施闯,许才军,等.利用局域复测GPS网研究中国大陆块体现今地壳运动速度场[J].武汉大学学报·信息科学版,2001,26(3)：189-195.
[6]刘经南,姚宜斌,施闯.中国地壳运动整体速度场模型的建立方法研究[J].武汉大学学报·信息科学版,2002,27(4)：331-336.
[7]刘根友.高精度.GPS定位及地壳形变分析若干问题的研究[D].武汉：中国科学院测量与地球物理研究所,2004.
[8]江在森,马宗晋,张希,等.GPS初步结果揭示中国大陆水平应变场与构造变形[J].地球物理学报,2003,46(3)：352-358.
[9]朱文耀,符养,李彦,等.GPS高程导出的全球高程震荡运动及其季节变化[J].中国科学D辑：地球科学,2003,33(5)：470-481.
[10]陶华学,王同孝.现代变形监测考虑先验信息的动态平差[J].勘测科学技术,1996,4：49-52.
[11]朱建军.变形网考虑先验信息时的平差[J].勘测科学技术,1993,4：42-45.
[12]余宏明,胡艳欣,滕伟福.滑坡位移动态实时跟踪预测[J].地质科技情报,2001,20(2)：83-85.
[13]蒋征,张正禄.变形模式的拓扑约束识别[J].测绘学报,1999,28(4)：330-334.
[14]赵丽华,杨元喜.综合地球物理信息与几何观测量的地壳形变分析方法[J].武汉大学学报·信息科学版,2009,34(9)：1090-1093.
[15]李征航,张小红,朱智.利用GPS进行高精度变形监测的新模型[J].测绘学报,2002,31(3)：206-210.
[16]刘国林.顾及多因素影响的双线性变形模型及其动态参数估计[J].测绘学报,1995,24(3)：183-191.
[17]兰孝奇,黄晓时,刘迪.GPS大坝变形监测网数据处理模型[J].同济大学 学报(自然科学版),2007,35(12)：1695-1698.
[18]Schwintzer P. Generalization for deformation vector with hybrid model. In:I JoO, A. Detrekoi, eds. Deformation Measurements. Budapest:Akademiai kiado,1982.453-463.
[19]Bock Y. Estimating crustal deformations from a combination of baseline measurements and geophysical models. Bull Geod,1983,57:294-311.
[20]Bock Y, Schaffrin B. Robust predication of the Earth's crustal movements from precise geodetic data and a vague geophysical mode. The first World Congress of Bernoulli Society on Mathematical Statistics. Taschkent (USSR), 1986.
[21]Segall P, Matthews M V. Displacement calculations from geodetic data and the testing of geophysical deformation model. J Geophys Res,1988,93(B12): 14954-14966.
[22]李朝奎等.基于可靠度理论的变形监测必要精度指标的确定方法[J].武汉大学学报·信息科学版,2002,27(5)：270-273.
[23]J. Porrill. Optimal combination and constraints for geometrical sensor data. International Journal of Robotics Research,1988,7(6):66-77.
[24]A. Alouani and W. Blair. Use of a kinematic constraint in tracking constant speed, maneuvering targets. IEEE Transactions on Automatic Control,1993 38(7):1107-1111.
[25]L. Wang, Y. Chiang, and F. Chang. Filtering method for nonlinear systems with constraints. IEE Proceedings-Control Theory and Applications,2002, 149(6):525-531.
[26]胡丛伟,刘大杰,姚连璧.带约束条件的自适应滤波及其在GPS中的应用.测绘学报,2002,31(5)：39-44.
[27]党宏社,张震强.一种道路条件下车辆跟踪的多目标数据关联方法.武汉理工大学学报：交通科学与工程版,2004,28(6)：903-906.
[28]T. Chia, P. Chow, and H. Chizek. Recursive parameter identification of constrained systems:An application to electrically stimulated muscle. IEEE Transactions on Biomedical Engineering,1991,38(5):429-441.
[29]T. Chia. Parameter Identification and State Estimation of Constrained Systems. [D]. Case Western Reserve University, Cleveland, Ohio,1985.
[30]Simon D and Chia TL. Kalman filtering with state equality constraints. IEEE, Transactions on Aerospace and Electronic Systems,2002,39(1):128-136.
[31]Christopher V. Rao, James B. Rawlings, Jay H. Lee. Constrained linear state estimation-a moving horizon approach. Automatica,2001,37:1619-1628.
[32]N. Gupta and R. Hauser. Kalman Filtering with Equality and Inequality State Constraints.2007. Available at http://arxiv.org/abs/0709.2791.
[33]D. Simon. Optimal State Estimation. New York:John Wiley & Sons,2006.
[34]N. Shimada, Y. Shirai, Y. Kuno, and J. Miura. Hand gesture estimation and model refinement using monocular camera-Ambiguity limitation by inequality constraints. Third IEEE International Conference on Automatic Face and Gesture Recognition, Nara, Japan,1998:268-273.
[35]Yuanxi Yang, W. Gao, X. Zhang. Robust Kalman filtering with constraints:a case study for integrated navigation. J Geod (2010) 84:373-381
[36]Rao C V and Rawlings J B. Constrained process monitoring:Moving horizon approach. AIChE Journal,2002,48(1):97-109.
[37]Rao C V, Rawlings J B and Lee J. Constrained linear state estimation—a moving horizon approach. Automatica,2001,37:1619-1628.
[38]Robertson D G, Lee J and Rawlings J B. A moving horizon-based approach for least-squares estimation. AIChE Journal,1996,42(8):2209-2224.
[39]Simon D and Simon DL. Aircraft turbofan engine health estimation using constrained Kalman Filtering. Journal of Engineering for Gas Turbines and Power,2004,126(1):1-6.
[40]熊传祥,龚晓南,王成华.高速滑坡临滑变形能突变模型的研究.浙江大学学报(工学版),2000,34(4)：443-447.
[41]张正禄,张松林,黄全义.大坝安全监测、分析与预报的发展综述[J].大坝与安全,2002(5)：13-16.
[42]潘国荣.地铁隧道轴线贯通测量偏差控制、动态变形分析及预报方法研究[D].上海：同济大学,1999.
[43]邱斌,朱建军,贺跃光.GPS在大地及工程变形观测中的应用[J].2002,22(2)：16-18.
[44]李征航,吴云孙,李振洪,等.隔河岩大坝外观变形数据的处理和分析.武汉测绘科技大学学报,2000,25(6)：482-484.
[45]罗志才,陈永奇,刘焱雄.GPS用于监测高层建筑物动态特征的模拟研究.武汉测绘科技大学学报,2000,25(2)：100-104.
[46]Schwarz K P, Cannon M E, Wong G V C. A comparison of GPS kinemayic models for determination of position and velocity along a trajectory [J]. Manuscripta Geodaetica,14(6):345-353.
[47]杨元喜,张丽萍.坐标基准维持与动态监测网数据处理[J].武汉大学学报·信息科学版,2007,32(11)：967-971.
[48]吕慧,黄希德.对几种变形分析方法适用性的实践与探讨[J].测绘通报,2001,3：29-28.
[49]王成余,马建良.沉降观测监测网的稳定性分析[J].2010,12：51-53.
[50]黄兵杰,周剑,白洁,王祥.变形监测网基准一致性的变换与灵敏度分析[J].大地测量与地球动力学,2010,30(6)：120-125.
[51]易庆林,曾怀恩,黄海峰.基于GPS监测数据的某滑坡变形分析[J].地质科技情报,2010,29(6)：106-109.
[52]薄万举.形变异常与干扰关系的再认识[J].大地测量与地球动力学,2010,30(1)：5-8.
[53]李杰,唐廷梅,等.跨断层形变测量异常特征分析[J].地震,2010,30(2)：100-111.
[54]杨博,董运洪,韩月萍.形变强度与地壳变形分析[J].地震,2010,30(2)：112-120.
[55]ZHU J, Santerre R, CHANG X W. A bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning[J]. J Geod 78(9):528-534.
[56]Junhuan Peng et al. An aggregate constraint method for inequality-constrained least squares problems [J]. J Geod 79(12):705-713.
[57]宋迎春,朱建军等.部分参数有非负约束平差模型的一种新算法.武汉大学学报信息版,2007,32(10)：881-887.
[58]宋迎春,左廷英,朱建军.带有线性不等式约束平差模型算法研究.测绘学报,2008,37(04)：433-436.
[59]Song Yingchun, et al. The Least-Squares Estimation in Adjustment Model With Some Nonnegative Constrained Parameters. Survey Reviewer,2010,42, 315:62-71.
[60]朱建军,欧阳文森,文小岳.基于遗传算法解决附有不等式约束的最小二乘平差问题的研究.工程勘察,2006,3：61-64.
[61]Bucy R S, Renne K D. Digital Synthesis of Nonlinear Filters[J]. Automation, 1971,7(3):287～289.
[62]Caballero-Gil P, Fuster-Sabater A. A wide family of nonlinear filter functions with a large linear span[J]. Information Sciences,2003,164(1-4):197-207.
[63]Julier S. J. and Uhlmann. J.K. A New Extension of the Kalman Filter to Nolinear Systems[A]. In the Proc of Aerosense:The 11th Int Symposium Aerospace/Defense Sensing, Simulation and Controls[C], Orlando,1997: 54-65.
[64]茅旭初.一种用于GPS定位估计滤波算法的非线性模型[J].上海交通大学学报,2004,(4)：610-615.
[65]王新洲.非线性模型参数估计理论与应用[M].武汉：武汉大学出版社,2002.
[66]彭竞,李献球,王飞雪.基于UKF的GPS非线性动态滤波算法.全球定位系统,2005,6：30-33.
[67]Christopher V. Rao, James B. Rawlings, Jay H. Lee. Constrained linear state estimation-a moving horizon approach. Automatica,2001,37:1619-1628.
[68]C. Zangerl, E. Eberhardt, S. Perzlmaier. Kinematic behaviour and velocity characteristics of a complex deep-seated crystalline rockslide system in relation to its interaction with a dam reservoir [J]. Engineering Geology 2010, 112:53-67.
[69]Bonzanigo, L., Eberhardt, E., Loew, S. Long-term investigation of a deep-seated creeping landslide in crystalline rock-geological and hydromechanical factors controlling the Campo Vallemaggia landslide. Canadian Geotechnical Journal,2007,44 (10):1157-1180.
[70]朱建军,丁晓利,陈永奇.集成地质、力学信息和监测数据的滑坡动态模型[J].测绘学报,2003,32(3)：261-266.
[71]Yang Yuanxi, Zeng Anmin. Adaptive filtering for deformation parameter estimation in consideration of geometrical models. Science in China Series D: Earth Science,2009,52(8):1216-1222.
[72]Shi G. H. Block System Modeling by Discontinuous Deformation analysis[M] Computational Mechanics Publications, Southampton UK and Boston USA, 1993
[73]P. Bonaldi. Displacement forecasting for concrete dams via deterministic mathematical models[J]. Water Power & Dam Construction,1977, 29(9):74-78.
[74]E. Purer. Application of statistical methods in monitoring dam behavior [J]. Water Power & Dam Construction,1986,38(12):16-19.
[75]A. DeSortis, P. Paoliani. Statistical analysis and structural identification in concrete dam monitoring [J]. Engineering Structures,2007,29:110-120.
[76]Schwintzer P. Generalization for deformation vector with hybrid model. In:I JoO, A. Detrekoi, eds. Deformation Measurements. Budapest:Akademiai kiado,1982:453-463.
[77]Bock Y. Estimating crustal deformations from a combination of baseline measurements and geophysical models [J]. Bull Geod,1983,57:294-311
[78]Bock Y, Schaffrin B. Robust predication of the Earth's crustal movements from precise geodetic data and a vague geophysical mode[C]. The first World Congress of Bernoulli Society on Mathematical Statistics. Taschkent (USSR), 1986
[79]Segall P, Matthews M V. Displacement calculations from geodetic data and the testing of geophysical deformation model [J]. J Geophys Res,1988,93(B12): 14954-14966
[80]杨元喜,张双成.导航解算中的系统误差及其协方差矩阵拟合[J],测绘学报,2004,33(3)：189-194.
[81]Lu W C, Xu S Q. Kalman filtering algorithm research for the deformation information series of the similar single difference model [J]. Journal of China University of Mining and Technology.2004,14(2):189-194.
[82]Hoek, E. and Bray, J.W. Rock slope engineering[R]. the institution of mining and Metallurgy, London,1981.
[83]刘国林,潘行庄.时变的变形监测系统模型及参数的动态估计[J].工程勘察, 1995,1：64-69.
[84]张正禄,张松林,黄全义.大坝安全监测、分析与预报的发展综述[J].大坝与安全,2002(5)：13-16.
[85]刘宝琛,张家生.近地表开挖引起的地表沉降的随机介质方法[J].岩石力学与工程学报,1995,14(4)：289-296.
[86]黄宏伟,张冬梅.盾构隧道施工引起的地表沉降及现场监控[J].岩石力学与工程学报,2001,20(增)：1814-1820.
[87]田胜利,周拥军,葛修润,卢允德.基于小波分解的建筑物变形监测数据处理[J].岩石力学与工程学报,2004,23(15)：2639-2642.
[88]吕慧,黄希德.对几种变形分析方法适用性的实践与探讨[J].测绘通报,2001,3：29-31.
[89]江在森,张希,陈文胜,等.地形变资料求解应变值的尺度相对性问题研究[J].地震学报,2000,22(4)：352-359.
[90]江在森,牛安福,王敏,等.活动断裂带构造变形定量分析[J].地震学报,2004, 27(6)：610-619.
[91]陈亮,黄腾.基于灰色关联分析的卡尔曼滤波在桥梁变形监测中的应用[J].测绘工程.2010,19(4)：47-49.
[92]陈光保,陈永奇,何秀凤.基于改进最小二乘配置的地壳垂直形变分析[J].大地测量与地球动力学,2010,30(4)：128-132.
[93]许才军,李志才.华北地区活动地块边界带运动及块体内部变形分析[J].武汉大学学报(信息科学版).2002,27(4)：348-351.
[94]莫颖军,袁昌茂,文鸿雁.形变监测数据的多尺度滤波[J].城市勘测,2010,4：154-156.
[95]张小红,李征航,徐绍铨.高精度GPS形变监测的新方法及模型研究[J].武汉大学学报·信息科学版,2001,26(5)：451-454.
[96]马如坤.工程变形监测网多点位移的可发现性[J].地矿浏绘,1998,1：13-15.
[97]梁桂兰,徐卫亚,谈小龙,王林伟.高边坡安全监测资料反馈分析研究[J].水利与建筑工程学报,2010,8(4)：37-39.
[98]陆付民,王尚庆,李劲,严学清.顾及地下水位因子的卡尔曼滤波模型在滑坡变形预测中的应用[J].武汉大学学报·信息科学版,2010,35(10)：1184-1187.
[99]李杰,马玉香.MD数字化断层形变测量仪资料的应用分析[J].地壳形变与地震,2001,(4)：95-102.
[100]李朝奎,黄建柏,黄力民.基于正演理论的先验性位移量化[J].工程勘察,1999,6：48-50.
[101]淘华学,王同孝.现代变形监测考虑先验信息的动态平差[J].勘察科学技术,1996,4：49-52.
[102]朱建军.变形网考虑先验信息时的平差[J].勘察科学技术,1993,4：42-45.
[103]王小亚,朱文耀,符养. GPS监测的中国及其周边现时地壳形变[J].地球物理学报,2002,45(2)：198-208.
[104]张华海,李景芝,余学祥,吕伟才.GPS形变监测网的数据处理模型[J].中国矿业大学学报,2000,29(4)：423-427.
[105]Yang Y X, HeH. Xu G. A New Adaptively Robust Filtering for Kinematic Geodetic Positioning[J]. Journal of Geodesy,2001,75(2):109-116.
[106]杨元喜,徐天河.基于移动开窗法协方差估计和方差分量估计的自适应滤波[J].武汉大学学报·信息科学版,2003,28(6)：714-718.
[107]Yang Y, He H and Xu G. Adaptively robust filtering for kinematic geodetic positioning[J]. Journal of Geodesy,2001,75(2/3):109-116.
[108]Yang Y, Gao W, Zhang X. Robust Kalman filtering with constraints:a case study for integrated navigation [J]. Journal of Geodesy,2010,84:373-381.
[109]Yang Y, Gao W. An optimal adaptive Kalman filter[J]. Journal of Geodesy, 2006,80:177-183.
[110]张双成,杨元喜,张勤.一种基于抗差自校正Kalman滤波的GPS导航算法[J].武汉大学学报·信息科学版,2005,30(10)：881-884.
[111]Tsai C, Kurz L. An adaptive robustifying approach to Kalman filtering[J]. Automatica 1983,19:279-288.
[112]Wang J, Stewart MP, Tsakiri M. Adaptive Kalman filtering for integration of GPS with GLONASS and INS. In:Schwarz K-P (ed) Geodesy Beyond 2000. Springer, Berlin Heidelberg New York, pp 325-330.
[113]Xu T, Yang YImproved sage adaptive filtering. Sci Surv Mapp[J].2000, 25(3):22-25.
[114]Cui X, Yang Y. Adaptively robust filtering with classified adaptive factors [J]. Prog Nat Sci,2006,16(8):846—851
[115]Yang Y, Gao W. An optimal adaptive Kalman filter[J]. J Geodesy,2006,80: 177—183.
[2]朱建军,丁晓利,陈永奇.集成地质、力学信息和监测数据的滑坡动态模型[J].测绘学报,2003,32(3)：261-266.
[3]杨元喜,曾安敏.顾及几何观测信息和地球物理模型的形变参数自适应滤波解[J].2009,39(4)：437-442.
[4]陶本藻.自由平差与变形分析[M].北京：测绘出版社,1992.
[5]刘经南,施闯,许才军,等.利用局域复测GPS网研究中国大陆块体现今地壳运动速度场[J].武汉大学学报·信息科学版,2001,26(3)：189-195.
[6]刘经南,姚宜斌,施闯.中国地壳运动整体速度场模型的建立方法研究[J].武汉大学学报·信息科学版,2002,27(4)：331-336.
[7]刘根友.高精度.GPS定位及地壳形变分析若干问题的研究[D].武汉：中国科学院测量与地球物理研究所,2004.
[8]江在森,马宗晋,张希,等.GPS初步结果揭示中国大陆水平应变场与构造变形[J].地球物理学报,2003,46(3)：352-358.
[9]朱文耀,符养,李彦,等.GPS高程导出的全球高程震荡运动及其季节变化[J].中国科学D辑：地球科学,2003,33(5)：470-481.
[10]陶华学,王同孝.现代变形监测考虑先验信息的动态平差[J].勘测科学技术,1996,4：49-52.
[11]朱建军.变形网考虑先验信息时的平差[J].勘测科学技术,1993,4：42-45.
[12]余宏明,胡艳欣,滕伟福.滑坡位移动态实时跟踪预测[J].地质科技情报,2001,20(2)：83-85.
[13]蒋征,张正禄.变形模式的拓扑约束识别[J].测绘学报,1999,28(4)：330-334.
[14]赵丽华,杨元喜.综合地球物理信息与几何观测量的地壳形变分析方法[J].武汉大学学报·信息科学版,2009,34(9)：1090-1093.
[15]李征航,张小红,朱智.利用GPS进行高精度变形监测的新模型[J].测绘学报,2002,31(3)：206-210.
[16]刘国林.顾及多因素影响的双线性变形模型及其动态参数估计[J].测绘学报,1995,24(3)：183-191.
[17]兰孝奇,黄晓时,刘迪.GPS大坝变形监测网数据处理模型[J].同济大学 学报(自然科学版),2007,35(12)：1695-1698.
[18]Schwintzer P. Generalization for deformation vector with hybrid model. In:I JoO, A. Detrekoi, eds. Deformation Measurements. Budapest:Akademiai kiado,1982.453-463.
[19]Bock Y. Estimating crustal deformations from a combination of baseline measurements and geophysical models. Bull Geod,1983,57:294-311.
[20]Bock Y, Schaffrin B. Robust predication of the Earth's crustal movements from precise geodetic data and a vague geophysical mode. The first World Congress of Bernoulli Society on Mathematical Statistics. Taschkent (USSR), 1986.
[21]Segall P, Matthews M V. Displacement calculations from geodetic data and the testing of geophysical deformation model. J Geophys Res,1988,93(B12): 14954-14966.
[22]李朝奎等.基于可靠度理论的变形监测必要精度指标的确定方法[J].武汉大学学报·信息科学版,2002,27(5)：270-273.
[23]J. Porrill. Optimal combination and constraints for geometrical sensor data. International Journal of Robotics Research,1988,7(6):66-77.
[24]A. Alouani and W. Blair. Use of a kinematic constraint in tracking constant speed, maneuvering targets. IEEE Transactions on Automatic Control,1993 38(7):1107-1111.
[25]L. Wang, Y. Chiang, and F. Chang. Filtering method for nonlinear systems with constraints. IEE Proceedings-Control Theory and Applications,2002, 149(6):525-531.
[26]胡丛伟,刘大杰,姚连璧.带约束条件的自适应滤波及其在GPS中的应用.测绘学报,2002,31(5)：39-44.
[27]党宏社,张震强.一种道路条件下车辆跟踪的多目标数据关联方法.武汉理工大学学报：交通科学与工程版,2004,28(6)：903-906.
[28]T. Chia, P. Chow, and H. Chizek. Recursive parameter identification of constrained systems:An application to electrically stimulated muscle. IEEE Transactions on Biomedical Engineering,1991,38(5):429-441.
[29]T. Chia. Parameter Identification and State Estimation of Constrained Systems. [D]. Case Western Reserve University, Cleveland, Ohio,1985.
[30]Simon D and Chia TL. Kalman filtering with state equality constraints. IEEE, Transactions on Aerospace and Electronic Systems,2002,39(1):128-136.
[31]Christopher V. Rao, James B. Rawlings, Jay H. Lee. Constrained linear state estimation-a moving horizon approach. Automatica,2001,37:1619-1628.
[32]N. Gupta and R. Hauser. Kalman Filtering with Equality and Inequality State Constraints.2007. Available at http://arxiv.org/abs/0709.2791.
[33]D. Simon. Optimal State Estimation. New York:John Wiley & Sons,2006.
[34]N. Shimada, Y. Shirai, Y. Kuno, and J. Miura. Hand gesture estimation and model refinement using monocular camera-Ambiguity limitation by inequality constraints. Third IEEE International Conference on Automatic Face and Gesture Recognition, Nara, Japan,1998:268-273.
[35]Yuanxi Yang, W. Gao, X. Zhang. Robust Kalman filtering with constraints:a case study for integrated navigation. J Geod (2010) 84:373-381
[36]Rao C V and Rawlings J B. Constrained process monitoring:Moving horizon approach. AIChE Journal,2002,48(1):97-109.
[37]Rao C V, Rawlings J B and Lee J. Constrained linear state estimation—a moving horizon approach. Automatica,2001,37:1619-1628.
[38]Robertson D G, Lee J and Rawlings J B. A moving horizon-based approach for least-squares estimation. AIChE Journal,1996,42(8):2209-2224.
[39]Simon D and Simon DL. Aircraft turbofan engine health estimation using constrained Kalman Filtering. Journal of Engineering for Gas Turbines and Power,2004,126(1):1-6.
[40]熊传祥,龚晓南,王成华.高速滑坡临滑变形能突变模型的研究.浙江大学学报(工学版),2000,34(4)：443-447.
[41]张正禄,张松林,黄全义.大坝安全监测、分析与预报的发展综述[J].大坝与安全,2002(5)：13-16.
[42]潘国荣.地铁隧道轴线贯通测量偏差控制、动态变形分析及预报方法研究[D].上海：同济大学,1999.
[43]邱斌,朱建军,贺跃光.GPS在大地及工程变形观测中的应用[J].2002,22(2)：16-18.
[44]李征航,吴云孙,李振洪,等.隔河岩大坝外观变形数据的处理和分析.武汉测绘科技大学学报,2000,25(6)：482-484.
[45]罗志才,陈永奇,刘焱雄.GPS用于监测高层建筑物动态特征的模拟研究.武汉测绘科技大学学报,2000,25(2)：100-104.
[46]Schwarz K P, Cannon M E, Wong G V C. A comparison of GPS kinemayic models for determination of position and velocity along a trajectory [J]. Manuscripta Geodaetica,14(6):345-353.
[47]杨元喜,张丽萍.坐标基准维持与动态监测网数据处理[J].武汉大学学报·信息科学版,2007,32(11)：967-971.
[48]吕慧,黄希德.对几种变形分析方法适用性的实践与探讨[J].测绘通报,2001,3：29-28.
[49]王成余,马建良.沉降观测监测网的稳定性分析[J].2010,12：51-53.
[50]黄兵杰,周剑,白洁,王祥.变形监测网基准一致性的变换与灵敏度分析[J].大地测量与地球动力学,2010,30(6)：120-125.
[51]易庆林,曾怀恩,黄海峰.基于GPS监测数据的某滑坡变形分析[J].地质科技情报,2010,29(6)：106-109.
[52]薄万举.形变异常与干扰关系的再认识[J].大地测量与地球动力学,2010,30(1)：5-8.
[53]李杰,唐廷梅,等.跨断层形变测量异常特征分析[J].地震,2010,30(2)：100-111.
[54]杨博,董运洪,韩月萍.形变强度与地壳变形分析[J].地震,2010,30(2)：112-120.
[55]ZHU J, Santerre R, CHANG X W. A bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning[J]. J Geod 78(9):528-534.
[56]Junhuan Peng et al. An aggregate constraint method for inequality-constrained least squares problems [J]. J Geod 79(12):705-713.
[57]宋迎春,朱建军等.部分参数有非负约束平差模型的一种新算法.武汉大学学报信息版,2007,32(10)：881-887.
[58]宋迎春,左廷英,朱建军.带有线性不等式约束平差模型算法研究.测绘学报,2008,37(04)：433-436.
[59]Song Yingchun, et al. The Least-Squares Estimation in Adjustment Model With Some Nonnegative Constrained Parameters. Survey Reviewer,2010,42, 315:62-71.
[60]朱建军,欧阳文森,文小岳.基于遗传算法解决附有不等式约束的最小二乘平差问题的研究.工程勘察,2006,3：61-64.
[61]Bucy R S, Renne K D. Digital Synthesis of Nonlinear Filters[J]. Automation, 1971,7(3):287～289.
[62]Caballero-Gil P, Fuster-Sabater A. A wide family of nonlinear filter functions with a large linear span[J]. Information Sciences,2003,164(1-4):197-207.
[63]Julier S. J. and Uhlmann. J.K. A New Extension of the Kalman Filter to Nolinear Systems[A]. In the Proc of Aerosense:The 11th Int Symposium Aerospace/Defense Sensing, Simulation and Controls[C], Orlando,1997: 54-65.
[64]茅旭初.一种用于GPS定位估计滤波算法的非线性模型[J].上海交通大学学报,2004,(4)：610-615.
[65]王新洲.非线性模型参数估计理论与应用[M].武汉：武汉大学出版社,2002.
[66]彭竞,李献球,王飞雪.基于UKF的GPS非线性动态滤波算法.全球定位系统,2005,6：30-33.
[67]Christopher V. Rao, James B. Rawlings, Jay H. Lee. Constrained linear state estimation-a moving horizon approach. Automatica,2001,37:1619-1628.
[68]C. Zangerl, E. Eberhardt, S. Perzlmaier. Kinematic behaviour and velocity characteristics of a complex deep-seated crystalline rockslide system in relation to its interaction with a dam reservoir [J]. Engineering Geology 2010, 112:53-67.
[69]Bonzanigo, L., Eberhardt, E., Loew, S. Long-term investigation of a deep-seated creeping landslide in crystalline rock-geological and hydromechanical factors controlling the Campo Vallemaggia landslide. Canadian Geotechnical Journal,2007,44 (10):1157-1180.
[70]朱建军,丁晓利,陈永奇.集成地质、力学信息和监测数据的滑坡动态模型[J].测绘学报,2003,32(3)：261-266.
[71]Yang Yuanxi, Zeng Anmin. Adaptive filtering for deformation parameter estimation in consideration of geometrical models. Science in China Series D: Earth Science,2009,52(8):1216-1222.
[72]Shi G. H. Block System Modeling by Discontinuous Deformation analysis[M] Computational Mechanics Publications, Southampton UK and Boston USA, 1993
[73]P. Bonaldi. Displacement forecasting for concrete dams via deterministic mathematical models[J]. Water Power & Dam Construction,1977, 29(9):74-78.
[74]E. Purer. Application of statistical methods in monitoring dam behavior [J]. Water Power & Dam Construction,1986,38(12):16-19.
[75]A. DeSortis, P. Paoliani. Statistical analysis and structural identification in concrete dam monitoring [J]. Engineering Structures,2007,29:110-120.
[76]Schwintzer P. Generalization for deformation vector with hybrid model. In:I JoO, A. Detrekoi, eds. Deformation Measurements. Budapest:Akademiai kiado,1982:453-463.
[77]Bock Y. Estimating crustal deformations from a combination of baseline measurements and geophysical models [J]. Bull Geod,1983,57:294-311
[78]Bock Y, Schaffrin B. Robust predication of the Earth's crustal movements from precise geodetic data and a vague geophysical mode[C]. The first World Congress of Bernoulli Society on Mathematical Statistics. Taschkent (USSR), 1986
[79]Segall P, Matthews M V. Displacement calculations from geodetic data and the testing of geophysical deformation model [J]. J Geophys Res,1988,93(B12): 14954-14966
[80]杨元喜,张双成.导航解算中的系统误差及其协方差矩阵拟合[J],测绘学报,2004,33(3)：189-194.
[81]Lu W C, Xu S Q. Kalman filtering algorithm research for the deformation information series of the similar single difference model [J]. Journal of China University of Mining and Technology.2004,14(2):189-194.
[82]Hoek, E. and Bray, J.W. Rock slope engineering[R]. the institution of mining and Metallurgy, London,1981.
[83]刘国林,潘行庄.时变的变形监测系统模型及参数的动态估计[J].工程勘察, 1995,1：64-69.
[84]张正禄,张松林,黄全义.大坝安全监测、分析与预报的发展综述[J].大坝与安全,2002(5)：13-16.
[85]刘宝琛,张家生.近地表开挖引起的地表沉降的随机介质方法[J].岩石力学与工程学报,1995,14(4)：289-296.
[86]黄宏伟,张冬梅.盾构隧道施工引起的地表沉降及现场监控[J].岩石力学与工程学报,2001,20(增)：1814-1820.
[87]田胜利,周拥军,葛修润,卢允德.基于小波分解的建筑物变形监测数据处理[J].岩石力学与工程学报,2004,23(15)：2639-2642.
[88]吕慧,黄希德.对几种变形分析方法适用性的实践与探讨[J].测绘通报,2001,3：29-31.
[89]江在森,张希,陈文胜,等.地形变资料求解应变值的尺度相对性问题研究[J].地震学报,2000,22(4)：352-359.
[90]江在森,牛安福,王敏,等.活动断裂带构造变形定量分析[J].地震学报,2004, 27(6)：610-619.
[91]陈亮,黄腾.基于灰色关联分析的卡尔曼滤波在桥梁变形监测中的应用[J].测绘工程.2010,19(4)：47-49.
[92]陈光保,陈永奇,何秀凤.基于改进最小二乘配置的地壳垂直形变分析[J].大地测量与地球动力学,2010,30(4)：128-132.
[93]许才军,李志才.华北地区活动地块边界带运动及块体内部变形分析[J].武汉大学学报(信息科学版).2002,27(4)：348-351.
[94]莫颖军,袁昌茂,文鸿雁.形变监测数据的多尺度滤波[J].城市勘测,2010,4：154-156.
[95]张小红,李征航,徐绍铨.高精度GPS形变监测的新方法及模型研究[J].武汉大学学报·信息科学版,2001,26(5)：451-454.
[96]马如坤.工程变形监测网多点位移的可发现性[J].地矿浏绘,1998,1：13-15.
[97]梁桂兰,徐卫亚,谈小龙,王林伟.高边坡安全监测资料反馈分析研究[J].水利与建筑工程学报,2010,8(4)：37-39.
[98]陆付民,王尚庆,李劲,严学清.顾及地下水位因子的卡尔曼滤波模型在滑坡变形预测中的应用[J].武汉大学学报·信息科学版,2010,35(10)：1184-1187.
[99]李杰,马玉香.MD数字化断层形变测量仪资料的应用分析[J].地壳形变与地震,2001,(4)：95-102.
[100]李朝奎,黄建柏,黄力民.基于正演理论的先验性位移量化[J].工程勘察,1999,6：48-50.
[101]淘华学,王同孝.现代变形监测考虑先验信息的动态平差[J].勘察科学技术,1996,4：49-52.
[102]朱建军.变形网考虑先验信息时的平差[J].勘察科学技术,1993,4：42-45.
[103]王小亚,朱文耀,符养. GPS监测的中国及其周边现时地壳形变[J].地球物理学报,2002,45(2)：198-208.
[104]张华海,李景芝,余学祥,吕伟才.GPS形变监测网的数据处理模型[J].中国矿业大学学报,2000,29(4)：423-427.
[105]Yang Y X, HeH. Xu G. A New Adaptively Robust Filtering for Kinematic Geodetic Positioning[J]. Journal of Geodesy,2001,75(2):109-116.
[106]杨元喜,徐天河.基于移动开窗法协方差估计和方差分量估计的自适应滤波[J].武汉大学学报·信息科学版,2003,28(6)：714-718.
[107]Yang Y, He H and Xu G. Adaptively robust filtering for kinematic geodetic positioning[J]. Journal of Geodesy,2001,75(2/3):109-116.
[108]Yang Y, Gao W, Zhang X. Robust Kalman filtering with constraints:a case study for integrated navigation [J]. Journal of Geodesy,2010,84:373-381.
[109]Yang Y, Gao W. An optimal adaptive Kalman filter[J]. Journal of Geodesy, 2006,80:177-183.
[110]张双成,杨元喜,张勤.一种基于抗差自校正Kalman滤波的GPS导航算法[J].武汉大学学报·信息科学版,2005,30(10)：881-884.
[111]Tsai C, Kurz L. An adaptive robustifying approach to Kalman filtering[J]. Automatica 1983,19:279-288.
[112]Wang J, Stewart MP, Tsakiri M. Adaptive Kalman filtering for integration of GPS with GLONASS and INS. In:Schwarz K-P (ed) Geodesy Beyond 2000. Springer, Berlin Heidelberg New York, pp 325-330.
[113]Xu T, Yang YImproved sage adaptive filtering. Sci Surv Mapp[J].2000, 25(3):22-25.
[114]Cui X, Yang Y. Adaptively robust filtering with classified adaptive factors [J]. Prog Nat Sci,2006,16(8):846—851
[115]Yang Y, Gao W. An optimal adaptive Kalman filter[J]. J Geodesy,2006,80: 177—183.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |