白亿同. 新投影定理及其在平差中的应用[J]. 武汉大学学报 ( 信息科学版), 1986, 11(1): 10-19.
引用本文: 白亿同. 新投影定理及其在平差中的应用[J]. 武汉大学学报 ( 信息科学版), 1986, 11(1): 10-19.
Bai Yitong. A New Theorem of Projection and Its Application to Adjustment[J]. Geomatics and Information Science of Wuhan University, 1986, 11(1): 10-19.
Citation: Bai Yitong. A New Theorem of Projection and Its Application to Adjustment[J]. Geomatics and Information Science of Wuhan University, 1986, 11(1): 10-19.

新投影定理及其在平差中的应用

A New Theorem of Projection and Its Application to Adjustment

  • 摘要: 本文将内积空间中的投影概念作了推广,定义了内积空间中任意向量在线性子流形上的投影,并证明了与其相应的新投影定理。用它作为理论基础,结合微分几何中的一些知识,以流形的观点导出了测量平差中的一些公式。对"投影方法"应用于解非线性平差问题的可能性,本文也作了探讨。

     

    Abstract: This paper extends the concept of projection in inner product space, defines the projection of an arbitrary vector in this space onto a linear submanifold and proves the new theorem of projection associated with the definition. On the basis of the formulated definition and proved theorem as well as relevant knowledge of differential geometry, some formulas for adjustment are derived from the point of view of manifold.In addition, the present paper discusses the possibility of the application of "projective method" to solving problems of nonlinear model for adjustment.

     

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