| “数字化科学工程”构建中的广义非线性数据处理的一种新算法 |
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| 引用本文： | 陶华学,赵长胜,郭金运.“数字化科学工程”构建中的广义非线性数据处理的一种新算法[J].测绘科学,2003,28(4):6-8. |
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| 作者姓名： | 陶华学 赵长胜 郭金运 |
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| 作者单位： | 1. 山东科技大学,山东,泰安,271019
2. 徐州师范大学,江苏,徐州,221000 |
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| 基金项目： | 国家自然科学基金,40174003, |
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| 摘 要： | 在当今各国正大力倡导的“数字国家”、“数字城市”、“数字矿山”等科学工程构建中的数据处理是基础和核心 ,其数据又具有多源、多维、多类型、多时态、多精度并具有非线性特征等特点 ,其数据处理的参数估计模型大都是复杂的非线性函数模型 ,模型中的参数有非随机参数 ,也有随机参数 ,这些系广义非线性数据处理 ,应采用广义非线性动态最小二乘数据处理的理论、方法来完成。本文提出了一种新的解算模型和解算方法 ,将问题分离 ,转换成单变量的一般非线性最小二乘问题求解。先按非线性拟合模型线性逼近法求得靠近真值的最优初值 ,再按非线性最小二乘解算方法求解参数估值。本方法使原来的高维方程得以简化 ,还不用计算二阶导数 ,大大简化了计算难度 ,并大大减少了迭代次数和计算工作量。
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| 关 键 词： | 广义非线性最小二乘 非线性拟合 分离求解 |
| 文章编号： | 1009-2307(2003)04-0006-03 |
| 修稿时间： | 2003年8月21日 |
A new solution method to process generalized nonlinear data in building of digital scientific engineering |
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| TAO Hua-xue,ZHAO Chang-sheng,GUO Jin-yun.A new solution method to process generalized nonlinear data in building of digital scientific engineering[J].Science of Surveying and Mapping,2003,28(4):6-8. |
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| Authors: | TAO Hua-xue ZHAO Chang-sheng GUO Jin-yun |
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| Institution: | TAO Hua-xue~1,ZHAO Chang-sheng~2,GUO Jin-yun1 |
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| Abstract: | Data, including the spatial data and the non-spatial data, are the basement of all digital scientific engineering projects, such as the digital earth, the digital nation, the digital city, the digital mine and so on. The spatial data has the characteristics of many sources, multi-dimensions, multi-types, many time-states and different accuracies. The spatial data processing must be made before using these data. The parametric estimating model to process the data is the more complex nonlinear model including the random parameters and the non-random parameters together. This belongs to the generalized nonlinear data processing, which should be solved by the generalized nonlinear dynamic least squares theory. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and it is more difficult to solve the former. Then a new solution method is put forward in the paper to separate the generalized problem into the common nonlinear least squares problem of single variable which is very easy to be solved. It mainly depends on the initial value of parameters to calculate the common nonlinear problem. Therefore the initial values closer to the true values are necessary to decrease the iterative calculating number and make the fast convergence. So the optimal initial values closer to the true values can be obtained firstly with the linear approaching method of nonlinear fitting model. Then the estimation values of parameters can be solved with the nonlinear least squares method. The method puts forward in the paper can simplify the original high-dimensional function. In the meantime,the second derivative cannot be calculated in the method. So the method can simplify the calculating difficulty and reduce the iterative number and word load. |
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| Keywords: | generalized nonlinear dynamic least squares problem nonlinear fitting separating solution |
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