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In this paper, A laser gyroscope strap-down inertial navigation system (SDlNS) error model with 12 system state parameters is derived, and the observability of SDINS is discussed by observability analysis of piece-wise constant system (PWCS) and observable degree analysis method based on the singular value decomposition (SVD). It is demonstrated that four-position alignment can make the system completely observable, and all the system state parameters can be estimated by Kalman filter. The simulation indicates the efficiency of the analysis results.

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