附非负约束平差模型的最小二乘估计

Least-Squares Estimation of Nonnegative Constrained Adjustment Model

研究了不等式约束下的平差问题,即先将不等式约束的最小二乘问题转换成凸二次规划问题,然后求其最优解。给出了几个判定最优解的充分必要条件,以及非负约束下的平差问题参数最小二乘估计的一般形式,并给出了简明的算法。模拟实例说明,此算法可以很好地应用于实际测量中的平差计算。

The inequality constrained least-squares estimation in adjustment model is studied from an entirely novel angle. Inequality constrained least-square problems are first changed to convex quadratic programming problems and then solved for the optimal solutions. The necessary and sufficient conditions on the solvability for optimization solution are given, which consequently gives the general form of least-squares estimation in adjustment model, as well as algorithm that are simple and easy to understand. A comparative calculation of a simulation example indicates that this algorithm can be applied to adjustment computation in the practical measurement.