混合总体最小二乘的迭代解算算法

Iterative Algorithm for Mixed LS-TLS Estimation

总体最小二乘估计能够同时顾及线性模型中系数矩阵A和观测向量L的误差,平差理论相对更为严密。如果系数矩阵A的部分元素没有误差,这种总体最小二乘模型为混合总体最小二乘模型。针对混合总体最小二乘(Least squares-total least squares,LS-TLS)解算问题,应用测量平差中的原理和方法,推导了混合总体最小二乘的迭代逼近解算公式,通过与奇异值分解法分析比较,分析了两种解算方法具有等价性,最后通过实验数据分析得出迭代算法的有效性和合理性。

The total least squares（TLS）approximation estimates a parameter matrix from a linear model considering errors in both the observation vector Land the data matrix A.The TLS theory is more rigorous than the standard least squares.If some columns of Acan be known exactly,the problem is defined as the mixed least squares—TLS problem.An iterative algorithm is derived to solve the LS-TLS problem by using the principle of indirect adjustment.Compared with the method based on singular-value decomposition（SVD）QR decompositon,the iterative algorithm coincides with the SVD algorithm.The calculated example proves that the iterative algorithm is valid and rational.