Abstract
The iteratively reweighted least-squares (IRLS) technique has been widely employed in geodetic and geophysical literature. The reliability measures are important diagnostic tools for inferring the strength of the model validation. An exact analytical method is adopted to obtain insights on how much iterative reweighting can affect the quality indicators. Theoretical analyses and numerical results show that, when the downweighting procedure is performed, (1) the precision, all kinds of dilution of precision (DOP) metrics and the minimal detectable bias (MDB) will become larger; (2) the variations of the bias-to-noise ratio (BNR) are involved, and (3) all these results coincide with those obtained by the first-order approximation method.
Highlights
Least-squares (LS) method exhibits a poor performance in the presence of outliers
Under the assumption of only one outlier exists, Baarda (1968) developed his famous testing procedure in the framework of mean-shift outlier model (GUO 2013), which led to the reliability theory
Extension of reliability measures for correlated observations was discussed by Wang and Chen (1994), Schaffrin (1997) and Ou (1999)
Summary
Least-squares (LS) method exhibits a poor performance in the presence of outliers. A reliable alternative to LS is given by the robust regression techniques. Updating the weights yields the iteratively reweighted least squares (IRLS) algorithm, which is the most common method for computing M-estimates (HUBER 1981, HUBER and RONCHETTI 2009). By using the first-order approximation, Guo et al (2011) investigated the variation characteristics of minimal detectable bias (MDB) and the bias-to-noise ratio (BNR) measures for an iterative robust M-estimator. This contribution serves a twofold purpose: (1) to evaluate the impact of iterative reweighting on the quality indicators by using an exact analytical method, and (2) to assess the adequacy of the first order approximation method. R(k) ii is called redundancy number and it holds that (SCHAFFRIN 1997, LEICK 2004)
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