【摘要】 针对可分离非线性函数模型的特殊结构，本文使用变量投影法(VP)将线性参数与非线性参数分离开来，并分别与矩阵的满秩分解、QR分解、奇异值分解和施密特正交化相结合，对两类参数分别求解，缩短了计算机解算方程组的运算时间，使算法更加高效，同时也使得具有一定病态程度的方程组在解算过程中保持相对较好的稳定性。本文利用Mackey-Glass时间序列拟合试验和空间直角坐标转换参数解算试验对比分析了基于不同矩阵分解方法的算法优劣性。试验结果表明，基于矩阵分解的改进变量投影法具有高效的运算效率与稳定的解算过程，也适用于解算空间直角坐标转换参数问题。更多还原

【Abstract】 For the special structure of separable function models, the variable projection(VP) method is used to separate the linear and the nonlinear parameters in this paper, and respectively combined with the full-rank decomposition, QR decomposition, singular value decomposition and Gram-Schmidt orthogon-alization to calculate the parameters, which shorten the calculation time of solving equations by computer, and enable the algorithm more efficient and equations with a certain ill-conditioning maintain the stability in the process of solving. The superiority-inferiority of the algorithms based on different matrix decomposition methods is analyzed by Mackey-Glass time series fitting experiment and parameters calculation for spatial rectangular coordinate transformation. The experimental results show that the improved VP algorithms based on matrix decomposition are highly efficient and stable, and suitable to solve the parameters of spatial rectangular coordinate transformation models.更多还原