基于有效约束的附不等式约束平差的一种新算法

A New Approach to Inequality Constrained Least-squares Adjustment

不等式约束是客观实际中普遍存在的一种约束,但目前大地测量数据处理领域并没有成熟、完整并被普遍接受的处理理论和方法。首先简要总结附不等式约束平差的各种方法及其存在的问题。然后对现有测量平差中附有等式约束的平差模型进行扩展,提出一种新的处理附有线性约束(包括等式和不等式约束)的平差方法。该方法在有效约束概念下,通过库恩-塔克条件来寻找有效约束条件,把不等式约束平差问题转化为我们熟知的等式约束平差问题,因此实现解向量与观测向量之间的显式表达。最后,用一个数值算例验证新方法的可行性,同时算例分析表明:用等式约束代替有效约束或集成约束进行平差计算,能得到正确的平差结果,但得不到正确的精度评定结果。

The inequality constraints exist in anywhere in practice. However there is no mature and widely accepted approach or theory which deals with the inequality constraints in geodetic data processing. Existed methods of dealing with inequality constraints are briefly summarized first. And then, based on the traditional adjustment methods with constraints,a new algorithm for the adjustment with linear equality and inequality constraints is put forward. With the help of active constraint concept, this algorithm can transform the line inequality constraint adjustment into the line equality constraint adjustment by seeking active constraint through Kuhn-Tucker condition. By the way, the advantage of this approach is that the estimated parameters have explicit expression of the observations or the observational errors. At last, a numerical example is designed. By this example, the feasibility of the new algorithm is shown. The result also shows that by substituting inequality constraints with active constraints, the exact estimate of unknown parameters can be Rot, but it is difficult to get exact accuracy.