附有模糊先验信息的病态问题解算方法

以模糊理论为基础，用模糊数集来描述未知参数向量中的模糊先验信息，将其以约束条件的形式纳入数学模型。给出带有模糊先验信息的平差模型，并基于正态模糊数建立新的平差准则，提出一种带有模糊先验信息的平差新算法。实例验证，新方法可以较好地解决测量平差中法方程病态问题。未知参数的误差分析显示，新方法解算病态方程优于最小二乘估计、截断奇异值法以及岭估计。

A Method for Solving Ill-Posed Problems with Fuzzy Prior Information

This paper uses fuzzy sets to describe the fuzzy priori information of the unknown parameter vector based on the fuzzy theory, which is included in the mathematical model in the form of constraint conditions.The adjustment model with fuzzy prior information is given.The new adjustment criterion is established by using the normal fuzzy number, and proposes a new adjustment algorithm with fuzzy priori information. The new method can effectively solve the ill-posed problem of normal equations in surveying adjustment.The error analysis shows that the new method is better than the least squares estimation, the truncated singular value method and ridge estimation.