This paper develops a robust M estimation approach applied for three-dimensional (3D) correlated vector observations. A modified bifactor reduction model is constructed, where the weight shrinking factor of the 3D vector observation is determined by a new test statistic that coincides with the estimated direction of the outlier vector and thus is more sensitive to vector-type outliers than the standardized residual used for most conventional robust M methods. With the proposed bifactor reduction model, the outlying vector observation is down-weighted directly along a specific direction, rather than separately at the three components. The new equivalent weight matrix derived from the proposed bifactor model still keeps symmetry, based on which the parameter estimation procedure is developed. A real 3D control network of GNSS vector observations is processed by simulating outliers with different types, sizes and locations. The results show the effectiveness of the proposed approach by comparing with other four conventional robust M method (IGGIII, Danish, Huber and Hampel).

中文翻译：

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基于改进的双因子减重模型的 3D 相关矢量观测的鲁棒 M 估计

本文开发了一种适用于三维 (3D) 相关矢量观测的稳健 M 估计方法。构建了一个改进的双因子减少模型，其中 3D 矢量观察的权重收缩因子由一个新的检验统计量确定，该统计量与异常值向量的估计方向一致，因此对向量类型异常值比使用的标准化残差更敏感对于大多数传统的鲁棒 M 方法。使用所提出的双因子减少模型，外围向量观测值直接沿特定方向降低权重，而不是分别在三个分量处进行加权。由所提出的双因子模型导出的新等效权重矩阵仍然保持对称，在此基础上开发了参数估计程序。GNSS 矢量观测的真实 3D 控制网络是通过模拟具有不同类型、大小和位置的异常值来处理的。通过与其他四种常规稳健 M 方法（IGGIII、丹麦、Huber 和 Hampel）的比较，结果表明了所提出方法的有效性。