Observable Degree Analysis of SINS Initial Alignment Based on Singular Value Decomposition

In this paper, observable degree of SINS based on singular value decomposition (SVD) is analyzed during initial alignment, and an improved method using the right singular vectors to calculate the observable degrees is proposed. Firstly, an error model is introduced for SINS on rocking base. Secondly, the model is demonstrated to satisfy the piece-wise constant system (PWCS) analysis law. Thus, the observability of system states can be simply analyzed by using the stripped observability matrix (SOM) as the substitute for the complex total observability matrix (TOM). Then the observable degrees of system states of SINS are analyzed based on the SVD of PWCS observability matrix, and the method to calculate the observable degrees is improved. Finally, computer simulation is carried out, and the results of simulation indicate that observable degree indexes are able to better predict Kalman filtering errors of system states. Therefore, the improved method discussed in this paper is effective.