Least-squares collocation is a method for determining the anomalous gravitational field by a combination of geodetic measurements of different kinds. Its reliability is based on a precise covariance function and a suitable observation distribution as well as the smoothness of the stochastic collocation field. In this paper, three kinds of robustized collocation formulae are derived under the assumptions that both of the observations and the stochastic collocation field are contaminated by outliers, or one of them is contaminated respectively. The procedure in robustifying the covariance function and the calculations of the robust collocation is discussed. The influence functions of an observation error to the estimators are given.
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