Existence of symmetric objects, whose observation at different viewpoints can be identical, can deteriorate the performance of simultaneous localization and mapping (SLAM). This work proposes a system for robustly optimizing the pose of cameras and objects even in the presence of symmetric objects. We classify objects into three categories depending on their symmetry characteristics, which is efficient and effective in that it allows to deal with general objects and the objects in the same category can be associated with the same type of ambiguity. Then we extract only the unambiguous parameters corresponding to each category and use them in data association and joint optimization of the camera and object pose. The proposed approach provides significant robustness to the SLAM performance by removing the ambiguous parameters and utilizing as much useful geometric information as possible. Comparison with baseline algorithms confirms the superior performance of the proposed system in terms of object tracking and pose estimation, even in challenging scenarios where the baseline fails.