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| 赋双平滑参数的广义补偿最小二乘估计 | |
| 引用本文： | 张俊,独知行,张显云,杜宁.赋双平滑参数的广义补偿最小二乘估计[J].海洋测绘,2013,33(2):20-23. |
| 作者姓名： | 张俊 独知行 张显云 杜宁 |
| 作者单位： | 1. 山东科技大学测绘科学与工程学院,山东青岛266510;贵州大学矿业学院,贵州贵阳550025 2. 山东科技大学测绘科学与工程学院,山东青岛,266510 3. 贵州大学矿业学院,贵州贵阳,550025 |
| 基金项目： | 国家自然科学基金项目，教育部博士点基金项目，贵州省自然科学基金项目，贵州省科技厅工业攻关项目(黔科合GY字 |
| 摘 要： | 基于补偿最小二乘法思想,研究推导了半参数模型解算的极小化过程中,在残差和补偿项均赋予平滑参数的广义补偿最小二乘估计解的形式及其均方误差计算公式;模拟算例表明:在这种规则下,不仅可以克服病态性对半参数模型解的影响,而且也可以正确分离系统误差。新规则下,要求赋予的两个平滑参数之和等于1,各平滑参数严格限定在区间(0,1],从而使平滑参数的选择范围得到大幅缩小,为本法的应用提供了有利条件。 |
| 关 键 词： | 测量平差 半参数模型 广义补偿最小二乘估计 病态性 平滑参数 |
The Method of Universal Penalized Least Squares by Adding Smoothing Parameters Both to the Residual and Systematic Parts |
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| ZHANG Jun,DU Zhixing,ZHANG Xianyun,DU Ning.The Method of Universal Penalized Least Squares by Adding Smoothing Parameters Both to the Residual and Systematic Parts[J].Hydrographic Surveying and Charting,2013,33(2):20-23. | |
| Authors: | ZHANG Jun DU Zhixing ZHANG Xianyun DU Ning |
| Abstract: | A new mothed that adding smoothing parameters both to the residual errors and systemic errors at the same time based on the principle of universal Penalized least squares is put forward and the solution formulation and the corresponding mean square errors are given. To ensure the balance of the residual errors and systemic errors,the sum of smoothing parameters of two parts are requested to be equal to 1, and the smoothing parameters scale must be restricted to between 0 and 1,which greatly reduces the selection range of smoothing parameter. A simulated example has been demonstrated and the results show that the new method can not only eliminate the effect of ill-condition but also can achieve satisfactory solutions of parameters and the systemic errors. |
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