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In this paper, the error model based on the Lie group is investigated with main focus on the Special Euclidean group SE (3) based error model construction and filtering comparison for the inertial navigation system (INS). The conventional theory of the SE (3) based error model is only focused on the state error definition. Moreover, the attitude representation is usually used by Euler angle. In order to enrich the family of the SE (3) based error model of the INS, this paper is to establish a theoretical bridge that can connect the attitude estimation to the error model construction for the Lie group. For this theoretical bridge, the SE (3) based error model based on Rodrigues parameter and modified Rodrigues parameter is proposed to fill the gap of the family of the SE (3) based error model. Further, based on the integrity of the SE (3) based error model, a uniform error model is also proposed to unify the family of the SE (3) based error model using the attitude transformation and direction cosine matrix. The field tests are carried out to assess the comprehensive performance of the existing SE (3) based error model under different conditions for the INS. [ABSTRACT FROM AUTHOR]