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摘要: 观测数据受到粗差污染时，平差结果往往失真，不可采用。选择合适的统计检验量是对测量数据进行粗差处理的关键一环，而构造统计检验量必须对尺度因子做出估计。首先对样本尺度因子的绝对中位差（median absolute deviation，MAD）估计进行了讨论，并详细探讨了其中涉及到的Fisher一致性调节因子的确定；然后在此基础上，分别提出了平差模型中基于标准化残差和一致最大功效（uniformly most powerful，UMP）统计检验量序列的尺度因子的两种抗差估计方法，尺度因子的两种抗差估计都可用于构造相应的统计检验量以识别和定位可疑观测量；最后对全球导航卫星系统（global navigation satellite systems，GNSS）网平差进行具体数值计算，结果表明，尺度因子的MAD估计具有良好的抗差性，不但可用于粗差处理，还可用于平差成果的精度评定。Abstract:Objectives The least-squares method is very sensitive to outliers, and the adjustment outputs will usually be unacceptable when some of the observations are contaminated. Selection of appropriate statistical tests plays a pivotal role both in robust estimation and conventional outlier detection procedures.Methods The MAD (median absolute deviation) estimate of scale factor in the univariate case is discussed firstly. Determination of the Fisher-consistency factor is described for Gaussian normal distribution. Robust estimates of scale factor in linear adjustment model are addressed based on standardized least-squares residuals and the uniformly most powerful test statistics, respectively. Both of them can be used for constructing statistical tests, to identify the potential outlying observations, and therefore their deterioration effect will be mitigated. For illustrative purpose, Monte Carlo simulations in GPS network adjustment scenario are performed.Results Numerical results show that the MAD-based estimate of scale factor is robust and works well in accuracy assessment for adjustment outputs.Conclusions Explicit formula for estimating the scale factor, the MAD is a very robust scale estimator and has low computation complexity. It is therefore appropriate to use the MAD for adjustment computations and accuracy assessment when outliers are present.
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Keywords:
- scale factor /
- outlier detection /
- robust estimation /
- MAD estimate
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图 1 4种方案10 000次GNSS网平差模拟数据得到的尺度因子估值序列
Figure 1. Estimated Scale Factors of Four Schemes over 10 000 Repetitions in GNSS Network Adjustment
表 1 4种方案得到的尺度因子估值序列的统计结果/mm
Table 1 Statistics of Estimated Scale Factor of Four Schemes/mm
方案 最大值 平均值 中位数 方案1 1.28 1.00 1.00 方案2 1.52 1.00 1.00 方案3 2.09 0.84 0.85 方案4 1.56 0.89 0.90 
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