附有相对权比的PEIV模型总体最小二乘平差

Total Least Squares Adjustment of Partial Errors-in-Variables Model with Weight Scaling Factor

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;而以珚Φ_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。

As a prior stochastic model contains inaccurate information, the weight matrices of observation and coefficient matrix are unreasonable. To address this problem, we investigate the total least squares adjustment of partial errors-in-variables（PEIV）model with a weight scaling factor that adaptively adjusts the contribution of the observation and coefficient matrix to parameter estimation. A prior unite weight variance and minimum discriminate function method are deduced, so the proposed method is valid for a structured coefficient matrix. Some conclusions are drawn from simulations of straight line fitting and coordinate transformation. When the prior unit weight variances of observation and coefficient matrix are known and accurate, the prior unit weight variance method is very effective; the minimum discriminate function method with the Ф1^（ε^,εa^）=ε^T^ε＋εa^T^εa as its discriminate function to determine weight scaling factor yielded the best performace.