In the process of using the ball bar to identify the geometric error of the translational axis, the parameter vector matrix at any position in the formulated identification model is an ill-posed matrix, which may result in inaccurate solutions or no solutions in solving the identification model. To address these issues, a method of ridge estimation based on the virtual observation method to solve the identification model solution is proposed. The translational axis of the machine tool is taken as the research object. Based on the rod length data measured by the ball bar, they are substituted into the established mapping relationship between the error element and the change of the ball bar rod length. The geometry is solved by the virtual observation method the polynomial coefficient of the error term. This method improves the ill-condition of the identification matrix from the cause of the matrix. Then, the identification of the error elements related to each axis is identified. Finally, simulation and experimental results show the correctness of the identification method. And the ill-posed of the identification matrix is improved. The results provide the theoretical basis for accurately identifying the geometric errors of the machine tool.