MAD Estimate of Scale Factor and Its Applications in Measurement Adjustment

  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.