Robust biased estimation and its applications in geodetic adjustments

In this paper, a number of robust biased estimators (e.g. ordinary robust ridge estimator, robust principal components estimator, robust combined principal components estimator, robust single-parametric principal components estimator, robust root-root estimator) are established by means of a unified expression of biased estimators and based on the principle of equivalent weight. The most attractive advantage of these new estimators is that they can not only overcome the ill-conditioning of the normal equation but also have the ability to resist outliers. A numerical example is used to illustrate that these new estimators are much better than the least-squares estimator and various biased estimators even when both ill-conditioning and outliers exist.