论测量控制网定位的各种处理方法

Study on Various Methods of Positioning for Control Networks

从实现控制网定位这一基本出发点来论述控制网的各种平差方法,为此,对长期流行的一些平差观念有所更新。首先,从能够实现控制网定位这一角度来定义基准数据,而不再将其限定为在平差中保持不变的固定数据,这样既符合于现代大型大地网测设的客观实际,同时也表明按不同平差方法定位的控制网都必定具有基准数据,只是其形式及处理方式各不相同。仅有相对量观测的一切控制网都是秩亏网,基于伪逆的解法只是消除秩亏的若干种手段之一,它所解得的坐标改正数正是将最佳相对网形最优拟合于基准数据的余差。为说明平差定位的实质,从定位这一角度简要地推证了有关公式,使其意义更为明确,并列举了按伪逆求解法的应用示例。

Various methods are discussed in this paper from the starting point i. e. positioning of control networks. Therefore,some prevalent concepts of adjustment should be renewed. At first, the principal aspect of the definition for reference data is necessary to achieve the positioning for control networks, rather than delimiting it as unchanged data in adjustment. It is manifested that various control networks are all in the nature of reference data only in all forms and definitely rank deficient. The solution based on the pseudo inverse is only one of several means by which the rank deficient is eliminated. The coordinate correction obtained by the method based on the pseudo inverse is the residual between the reference data and the optimal relative shape of network which has been optimal approximated to the reference data. In order to illustrate the existence of positioning by adjustment,relevant formulas are proved from the positioning, applying example with the method based on the pseudo inverse adduced.