The aim of the work is to develop and test an algorithm of adjustment of geodetic observations, resistant to gross errors (method of robust estimations), with the use of the damping function, proposed by the author. Detailed formulae of the damping function as a component of the objective function in a modified classic least squares method were derived. The selection criteria for the controlling parameters of the damping functions have also been provided. The effectiveness of the algorithm has been verified with two numerical examples. The results have been analysed with reference to the methods of resistant compensation, which apply other damping functions, e.g. Hampel's function.