卡尔曼滤波在大型深凹露天矿边坡变形监测预测中的应用
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摘要
为了剔除GPS边坡位移监测过程中的噪声干扰,提高监测数据的有效性,特引入随机线性卡尔曼滤波离散数学模型.以水厂铁矿GPS边坡监测数据为依据,利用该数学模型可以计算出各监测点每期变形量的滤波值和位移速度,并对各监测点下一期的变形量进行估算和预测.经实例验证,卡尔曼滤波变形量与实际变形量有较好的一致性.
A discrete mathematical model based on random linear Kalman filtering is introduced to eliminate random disturbance noise in the process of GPS slope deformation monitoring and to improve the validity of monitoring data.On the base of GPS slope monitoring data in Shuichang Iron Mine,the filtering value of deformation and the velocity of displacement at each point in each stage can be calculated with the mathematical model and the slope deformation at each point in the next stage can be estimated and predicted.It is proved with an example that the deformation obtained by Kalman filtering is more approximate to the real slope deformation.
A discrete mathematical model based on random linear Kalman filtering is introduced to eliminate random disturbance noise in the process of GPS slope deformation monitoring and to improve the validity of monitoring data.On the base of GPS slope monitoring data in Shuichang Iron Mine,the filtering value of deformation and the velocity of displacement at each point in each stage can be calculated with the mathematical model and the slope deformation at each point in the next stage can be estimated and predicted.It is proved with an example that the deformation obtained by Kalman filtering is more approximate to the real slope deformation.
引文
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[14]University of Science and Technology Beijing,the Capital steelmining Company,Tsinghua University.Study on Techniques ofHigh Efficiency Transportation System and Intensified Mining forLarge and DeepOpen-Pit Mines.Beijing,2004(北京科技大学,首钢矿业公司,清华大学.大型深凹露天矿高效运输系统及强化开采技术研究.北京,2004)
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[16]Chen J,Tao B Z.Surveying Course ofEarth Deformation.Bei-jing:Earthquake Publishing House,1987(陈健,陶本藻.大地形变测量学.北京:地震出版社,1987)
[2]Li C H,Zhang L Y,Cai MF,et al.The benchmark design of GPSlandslide monitoring and data processing.Nonferrous Met MinSect,2005,57(3):33(李长洪,张丽英,蔡美峰,等.GPS滑坡监测的基准设计和数据处理.有色金属:矿山部分,2005,57(3):33)
[3]Li C H,Wen J,Cai MF,et al.Slope reinforce and stability anal-ysis in Shuichang mine of China.J Univ Sci Technol Beijing,2005,27(2):132(李长洪,文俊,蔡美峰,等.水厂铁矿边坡加固设计及其稳定性分析.北京科技大学学报,2005,27(2):132)
[4]Li J C.Study of high and steep slope in pen-pit mine.NonferrousMet,2004(3):22(李军财.深凹露天矿高陡边坡工程的研究.有色金属,2004(3):22)
[5]Li C H,Cai MF,Li J C.Analysis of the rock mass structure anddestruction mode of Shuichang open-pit mine slope.Chin MinMag,2004,13(2):48(李长洪,蔡美峰,李军财.大型露天矿山边坡岩体结构与破坏模式分析.中国矿业,2004,13(2):48)
[6]Ma P,Wen HY.Application of discrete Kalman filtering to GPSdada processing of kinematic deformation.J Guilin Inst Technol,2002,22(3):324(马攀,文鸿雁.离散卡尔曼滤波用于GPS动态变形数据处理.桂林工学院学报,2002,22(3):324)
[7]Cui X Z,Yu Z C,Tao B Z,et al.General Surveying Adjustment.Beijing:Surveying and Mapping Press,1992(崔希璋,於宗俦,陶本藻,等.广义测量平差.北京:测绘出版社,1992)
[8]Dong X R,Tao D X.An efficient Kalman filtering algorithm andits application in kinematic GPS data processing.Acta Geod Car-togr Sin,1997,26(3):221(董绪荣,陶大欣.一个快速Kalman滤波方法及其在GPS动态数据处理中的应用.测绘学报,1997,26(3):221)
[9]Kalman R E.A new approach to linear filtering and predictionproblems.Trans ASME,1960,82(4):34
[10]Brown R G.Introduction to Random Signal Analysis and KalmanFiltering.New York:John Wiley&Sons,1983
[11]Welch G,Bishop G.An Introduction to the Kalman Filter.NewYork:SIGGRAPH,2001
[12]Wang Z M,Yi D Y.Model Establishment and ParameterEstima-tion ofMeasuring Data.Changsha:National Defense Science andTechnology University Press,1997(王正明,易东云.测量数据建模与参数估计.长沙:国防科技大学出版社,1997)
[13]Luo D D,Zhu Y M.Random parameter matrices Kalman filte-ring.JSichuan Univ Nat Sci Ed,2008,45(6):1309(罗丹丹,朱允民.随机系数矩阵卡尔曼滤波.四川大学学报:自然科学版,2008,45(6):1309)
[14]University of Science and Technology Beijing,the Capital steelmining Company,Tsinghua University.Study on Techniques ofHigh Efficiency Transportation System and Intensified Mining forLarge and DeepOpen-Pit Mines.Beijing,2004(北京科技大学,首钢矿业公司,清华大学.大型深凹露天矿高效运输系统及强化开采技术研究.北京,2004)
[15]Fan L P,Li C H,Miao S J,et al.Optimization design of slopemonitoring network in Shuichang iron mine.Chin Min Mag,2008,17(5):79(范丽萍,李长洪,苗胜军,等.水厂铁矿GPS边坡监测控制网设计优化.中国矿业,2008,17(5):79)
[16]Chen J,Tao B Z.Surveying Course ofEarth Deformation.Bei-jing:Earthquake Publishing House,1987(陈健,陶本藻.大地形变测量学.北京:地震出版社,1987)
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