Stochastic observability-based analytic optimization of SINS multiposition alignment

The Kalman filter has always been applied to enhance the estimation of inertial measurement unit errors and to improve estimation accuracy of navigation states under practical conditions. Therefore, understanding the behaviors and limitations of optimal estimation of the navigation states is instructive and of great importance. In order to provide comprehensive information about the observability and convergence rapidity of the navigation states when implementing a Kalman filter, the basic properties of intuitive linear-algebraic characterizations of stochastic observability will be intensively investigated in this study. We have extended the utilization of the analytic stochastic observability approach for analytic optimization of strapdown inertial navigation systems multiposition stationary alignment. The advantage of analytic explicit formulation of convergence rapidity of the implemented Kalman filter by stochastic observability approach is demonstrated. Compared to numerical simulation methods, the proposed stochastic observability approach can provide analysts with much more analytic information.