一种求解不等式约束秩亏平差问题的新算法

A New Algorithm for Solving Inequality Constrained Rank Deficient Adjustment Problem

提出一种求解不等式约束秩亏平差问题的新算法,该算法将先验信息表示为不等式形式,并与秩亏平差模型构成不等式约束秩亏平差模型。结合Karush-Kuhn-Tucker条件可将该模型转化为线性互补问题,然后利用Lemke算法求解,克服了秩亏网中必要起算数据不足的问题,能保证解的唯一性。最后,模拟附先验信息的秩亏的GPS观测网,并结合多种经典的秩亏平差方法,验证了Lemke算法在处理不等式约束秩亏问题上的有效性。

We propose a new algorithm for solving the inequality constrained rank deficit adjustment problem.The algorithm expresses the prior information as an inequality form and forms an inequality constrained rank deficit adjustment model with the rank deficit adjustment model.Combined with the Karush-Kuhn-Tucke condition,the model can be transformed into a linear complementarity problem and then solved by the Lemke algorithm.The method overcomes the insufficiency of the necessary starting data in the rank-deficit network,and the calculation is stable and the efficiency is higher.Finally,we simulate the GPS network with rank loss of prior information,and combine several classical rank-loss adjustment methods to verify the effectiveness of Lemke algorithm in dealing with inequality constrained rank-deficient problems.