This paper proposes an iterative parameter identification algorithm based on adaptive ridge regression to establish a geometric error model for improving the absolute positioning accuracy of the end-effector of collaborative robots. The perturbation method is employed to establish the aforementioned model. This algorithm addresses the overfitting and lack of regularization issues associated with the least squares method under multicollinearity and high-dimensional data, thereby enhancing the model generalization capability. A parameter redundancy analysis was conducted on the positional error model for multi-degree-of-freedom collaborative robots. The experimental results demonstrate that the elimination of redundant parameters through analytical methods improves the reliability and accuracy of parameter identification and enhances the model robustness. In comparison to the least squares method, the proposed algorithm demonstrates superior identification accuracy and generalization capability, resulting in a notable enhancement in the absolute positioning accuracy of collaborative robots through calibration.