In the co-localization algorithm of augmented information filtering robot, the Cholesky method is usually used to decompose the information matrix of the joint distribution. The augmented information filtering based on Cholesky decomposition has high requirements for the positive definite symmetry of the information matrix of the joint distribution, and in the case that the information matrix of the joint distribution does not meet the positive definite symmetry, the inversion produces anomalies, affects the information recovery of the joint distribution, and the robustness of the system decreases. An augmented information filtering algorithm based on LU decomposition was proposed, which ensures the accuracy of the robot co-localization algorithm, effectively solves the problem of information matrix decomposition anomaly of joint distribution, and finally the observability of the robot system was analyzed. The MATLAB software platform was used to simulate and verify the algorithm. The results show that the algorithm ensures the cooperative positioning accuracy of the robot and improves the robustness of the robot system.