基于椭球不确定性的平差模型与算法

测量平差模型中的参数通常存在一些不确定的附加信息或先验信息,充分利用它们可以对部分参数进行约束,从而保证参数解的唯一性和稳定性。本文利用椭球集合描述不确定性,建立了一个新的带有椭球不确定性的平差模型。以两个椭球交集的外接椭球的特征矩阵的迹最小平差准则,分析了不确定度的传播规律,给出了带有椭球不确定性的平差方法。最后,通过算例验证了算法的有效性,说明了平差解与带权混合估计的关系。

Adjustment model and algorithm based on ellipsoid uncertainty

In surveying adjustment models, there usually is some uncertain additional information or prior information on parameters, which can constraint on the parameters, and guarantee uniqueness and stability of parameters solution.In this paper, ellipsoidal sets are used to describe uncertainty, so an adjustment model with ellipsoidal uncertainty is established. The minimization in matrix trace of circumscribed ellipsoid with two ellipsoid intersections is regarded as a proposed adjustment criterion, the propagation law of uncertainty is analyzed, and the adjustment method with ellipsoid uncertainty is given. Finally, a numerical example is given to test and verify the effectiveness of the proposed algorithm, and the relation between the adjustment result and the weighted mixed estimation is illustrated.