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Two different coarse alignment algorithms for Fiber Optic Gyro (FOG) Inertial Navigation System (INS) based on inertial reference frame are discussed in this paper. Both of them are based on gravity vector integration, therefore, the performance of these algorithms is determined by integration time. In previous works, integration time is selected by experience. In order to give a criterion for the selection process, and make the selection of the integration time more accurate, optimal parameter design of these algorithms for FOG INS is performed in this paper. The design process is accomplished based on the analysis of the error characteristics of these two coarse alignment algorithms. Moreover, this analysis and optimal parameter design allow us to make an adequate selection of the most accurate algorithm for FOG INS according to the actual operational conditions. The analysis and simulation results show that the parameter provided by this work is the optimal value, and indicate that in different operational conditions, the coarse alignment algorithms adopted for FOG INS are different in order to achieve better performance. Lastly, the experiment results validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]