In geodesy, in addition to observation information, there are also parameters additional useful information. Making full use of them can make up for the lack of observation information and form effective constraints on unknown parameters. In order to make the adjustment results unique and stable, we build a function model to solve inequality constraints, and based on the linear complementarity theory, propose to use the potential function descent interior point algorithm to solve the rank deficient problem. After that, we also extend this idea to the study of the ill-posed problem in this paper. Finally, examples are given to demonstrate the efficiency of the proposed algorithm. It is shown that this algorithm satisfies the uniqueness and stability of the solution, and provides a new reference for the research of rank-deficient and ill-posed problems in the future.

在大地测量学中，除了观测信息外，还有参数附加有用的信息。充分利用它们可以弥补观测信息的不足，对未知参数形成有效的约束。为了使调整结果具有唯一性和稳定性，我们建立了求解不等式约束的函数模型，并基于线性互补理论，提出使用势函数下降内点算法解决秩亏问题。之后，我们还将这一思想扩展到本文中不适定问题的研究中。最后，给出了例子来证明所提出算法的效率。表明该算法满足解的唯一性和稳定性，