求解自回归模型参数的整体最小二乘新方法

A New Method of TLS to Solving the Autoregressive Model Parameter

  • 摘要: 在应用整体最小二乘法求解自回归模型的参数时,针对传统的SVD方法和迭代法并没有顾及到系数矩阵和观测向量构成的增’一矩阵中不同位置上相同元素的改正数却不相同这一不足,推导了一种新的迭代解法,有效地解决了传统方法的不足,使得增’一矩阵中不同位置的同一元素具有相同的改正数,更加符合实际情况且平差精度也有所提高。最后通过具体的算例,验证了木文方法的可行性和有效性。

     

    Abstract: When using total least squares to solve the regression model parameter,both the traditional SVD and iteration methods do not consider that corrections of the same elements in different positions of the augmented matrix formed by the coefficient matrix and the observation vector are different. This paper proposes a new iteration method which can effectively solve the shortage problem in traditional methods, puts the same element in different positions of an augmented matrix into the same correction. This method is more compatible to the actual situation.Adjustment precision can also be improved. Finally, a concrete example was conducted to verify the feasibility and effectiveness of this method.

     

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