附有相对权比的PEIV模型总体最小二乘平差

发布时间：2018-05-10 20:41

本文选题：PEIV模型 + 总体最小二乘　；参考：《武汉大学学报(信息科学版)》2017年06期

【摘要】：针对观测向量和系数矩阵权分配不合理、验前随机模型不准确的情况,以部分误差变量(partial errors-in-variables,PEIV)模型为基础,推导了附有相对权比的总体最小二乘平差算法;通过在平差准则中加入相对权比,自适应调整观测向量和系数矩阵随机元素对模型参数估计的贡献,给出了确定相对权比的验前单位权方差法和判别函数最小化迭代算法,该算法普遍适用于一般性的系数矩阵和权矩阵。通过直线拟合和坐标转换模拟算例的比较分析,发现当观测值和系数矩阵的验前单位权方差已知,且较准确时,验前单位权方差法确定相对权比和参数估计的效果较好;而以s讦礯1(ε,ε_a)=ε~Tε+ε_a~Tε_a作为判别函数是判别函数最小化迭代算法中效果最好的。
[Abstract]:In view of the unreasonable weight allocation of the observation vector and coefficient matrix and the inaccuracy of the prior random model, based on the partial error variable partial errors-in-variablesl PEIVs model, the total least square adjustment algorithm with relative weight ratio is derived. By adding the relative weight ratio to the adjustment criterion and adjusting the contribution of the observation vector and the random elements of the coefficient matrix to the parameter estimation of the model, a priori unit weight variance method for determining the relative weight ratio and an iterative algorithm for minimizing the discriminant function are presented. The algorithm is generally applicable to general coefficient matrix and weight matrix. Through the comparison and analysis of straight line fitting and coordinate transformation simulation examples, it is found that when the prior unit weight variance of observation value and coefficient matrix is known and more accurate, the result of relative weight ratio and parameter estimation by prior unit weight variance method is better. However, it is the best iterative algorithm to minimize the discriminant function by using the discriminant function as a discriminant function.
【作者单位】：东华理工大学测绘工程学院;流域生态与地理环境监测国家测绘地理信息局重点实验室;武汉大学测绘学院;
【基金】：国家自然科学基金(41664001,41204003) 江西省杰出青年人才资助计划项目(20162BCB23050) 国家重点研发计划(2016YFB0501405) 测绘地理信息公益性行业科研专项(201512026) 江西省教育厅科技项目(GJJ150595) 流域生态与地理环境监测国家测绘地理信息局重点实验室项目(WE2015005) 对地观测技术国家测绘地理信息局重点实验室项目(K201502) 东华理工大学博士科研启动金(DHBK201113)~~
【分类号】：P207.2

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