| 基于最小二乘优化的高精度参数估计研究 |
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| 引用本文： | 侯伟真,李华,刘全昌.基于最小二乘优化的高精度参数估计研究[J].泰安师专学报,2013(3):56-61. |
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| 作者姓名： | 侯伟真 李华 刘全昌 |
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| 作者单位： | [1]中国科学院遥感与数字地球研究所,北京100101 [2]北京航空航天大学航空科学与工程学院,北京100191 [3]东方电子技术中心系统部,山东烟台264000 |
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| 摘 要： | 研究了捕食者一被捕食者模型在不同观测误差条件下的非线性微分方程组参数估计问题．首先利用差分方法进行离散化，得到一个超定的线性方程组，进行最小二乘拟合优化；其次，考虑观测资料有误差而时间变量无误差的情况，通过利用周期取平均的方法，从而降低了数据的误差；最后针对时间变量也会有误差情况，对每个观测时刺的数据进行归整处理来降低时间上的观测误差，最后利用最小二乘拟合得到最优的参数值．
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| 关 键 词： | 捕食者一被捕食者模型 高精度参数估计 最小二乘拟合 超定方程组 误差处理 |
Research on High Precision Parameter Estimation based on Least Square Optimization |
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| Institution: | HOU Wei - zhen1, LI Hua2, LIU Jin - chang3 (1. Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, 100101 ; 2. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing, 100191; 3. Dongfang Electronics Information Industry Group Co. Ltd, Yantai, 264000, China) |
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| Abstract: | We study the parameter estimation problems of nonlinear differential equations in different observation error conditions in predator - prey model. Firstly, the differential method for discretization, get an overdetermined linear equations, carry out least squares fitting optimization; secondly, consider the observation error and time variabIes without error, using the method of periodic averaging, data error was reduced; finally, the time variables with errors, for each observation time data consolidation processing to reduce the observation error in time, finally get the optimal values of the parameters by using the least squares fitting. |
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| Keywords: | predator- prey model high precision parameter estimation least square fitting overdeter- mined equations error processing |
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