The paper focuses on the calibration of serial industrial robots using partial pose measurements. In contrast to other works, the developed advanced robot calibration technique is suitable for geometrical and elastostatic calibration. The main attention is paid to the model parameters identification accuracy. To reduce the impact of measurement errors, it is proposed to use directly position measurements of several points instead of computing orientation of the end-effector. The proposed approach allows us to avoid the problem of non-homogeneity of the least-square objective, which arises in the classical identification technique with the full-pose information. The developed technique does not require any normalization and can be efficiently applied both for geometric and elastostatic identification. The advantages of a new approach are confirmed by comparison analysis that deals with the efficiency evaluation of different identification strategies. The obtained results have been successfully applied to the elastostatic parameters identification of the industrial robot employed in a machining work-cell for aerospace industry.