带球约束的平差算法及应用

Adjustment Algorithm with Spherical Constraint and Application

针对测量数据处理中由于观测信息不充分以及对参数物理信息和先验信息的利用不充分引起的病态问题,利用先验信息对参数加以约束,将测量平差问题转化为凸二次规划问题,提出一种带有球约束的平差模型。根据最优化理论,基于Kuhn-Tucker条件,研究球约束下的平差问题,并针对该模型提出解算方法。模拟数值实验和测边网实例应用结果表明,该方法在处理病态问题上具有明显的更优估计,可以广泛应用于大地测量病态数据处理。

Aiming at solving the ill-conditioned problem caused by inadequate observation,inadequate utilization of parameter physical information and prior information in measurement data processing,this paper transforms the measurement adjustment problem into a convex quadratic programming problem by constraining the parameters with prior information,and proposes an adjustment model with spherical constraints.Based on the optimization theory and Kuhn-Tucker condition,the adjustment problem under spherical constraints is studied,and a solution method is proposed for the model.The results of numerical simulation and practical application of trilateration network show that this method has obvious better estimation in dealing with ill-conditioned problems,and can be widely used in geodetic ill-conditioned data processing.