A hand-eye calibration method for determining the parameters of the hand-eye pose of camera-guided apparatuses, the method comprising the following steps: (a) controlling a plurality of apparatus poses with the apparatus; (b) capturing a camera image at each apparatus pose; (c) extracting image features in the captured camera images; and (d) determining approximate values for the parameters of the hand-eye pose; characterized by (e) determining the parameters of the hand-eye pose assuming erroneous apparatus poses and erroneous extracted image features to implicitly account for erroneous camera poses, which comprises the steps of statistically modeling the accuracies of the parameters describing the apparatus pose and the accuracies of the extracted image features by a weight matrix, weight coefficient matrix, or covariance matrix, wherein the number of parameters describing the apparatus pose is at least equal to the number of degrees of freedom of the apparatus; optimizing the parameters of the hand-eye pose by simultaneously minimizing a back-projection error of the image features in the captured camera images and the errors in the parameters describing the apparatus pose, taking into account the accuracies from step; computing improved accuracies of the parameters describing the apparatus pose and the extracted image features based on the results of the optimization from step using variance component estimation; and repeating steps through until the accuracies of the parameters describing the apparatus pose and the accuracies of the extracted image features converge. (a) controlling a plurality of apparatus poses with the apparatus; (b) capturing a camera image at each apparatus pose; (c) extracting image features in the captured camera images; and (d) determining approximate values for the parameters of the hand-eye pose; characterized by (e) determining the parameters of the hand-eye pose assuming erroneous apparatus poses and erroneous extracted image features to implicitly account for erroneous camera poses, which comprises the steps of statistically modeling the accuracies of the parameters describing the apparatus pose and the accuracies of the extracted image features by a weight matrix, weight coefficient matrix, or covariance matrix, wherein the number of parameters describing the apparatus pose is at least equal to the number of degrees of freedom of the apparatus; optimizing the parameters of the hand-eye pose by simultaneously minimizing a back-projection error of the image features in the captured camera images and the errors in the parameters describing the apparatus pose, taking into account the accuracies from step; computing improved accuracies of the parameters describing the apparatus pose and the extracted image features based on the results of the optimization from step using variance component estimation; and repeating steps through until the accuracies of the parameters describing the apparatus pose and the accuracies of the extracted image features converge. statistically modeling the accuracies of the parameters describing the apparatus pose and the accuracies of the extracted image features by a weight matrix, weight coefficient matrix, or covariance matrix, wherein the number of parameters describing the apparatus pose is at least equal to the number of degrees of freedom of the apparatus; optimizing the parameters of the hand-eye pose by simultaneously minimizing a back-projection error of the image features in the captured camera images and the errors in the parameters describing the apparatus pose, taking into account the accuracies from step; computing improved accuracies of the parameters describing the apparatus pose and the extracted image features based on the results of the optimization from step using variance component estimation; and repeating steps through until the accuracies of the parameters describing the apparatus pose and the accuracies of the extracted image features converge.