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As previously mentioned, one significant drawback of WLS estimator is the lack of robustness to bad data. Other non‐quadratic estimators have been thereby developed to overcome this disadvantage, such as the aforementioned LAV method.

Quadratic‐constant and quadratic‐linear algorithms (QC and QL) combine the benefits of maximum likelihood least squares estimation and the bad data rejection properties of the LAV estimator.

Figure 2.4 allows the objective function for the QC estimator in the case of one single error. The violet and green curves correspond to a high and low weighting factor ω_i, respectively. Note that the behavior of function J(x ) for the QC estimator is the same as the WLS when the weighted measurement error y_i(x) is within the given bounds.

Figure 2.4 Objective function for the QC estimator as a function of the error (one measurement).