INS ground alignment through observable degree analysis based on information theory

Observability is an important aspect of the state-estimation problem in the initial alignment of the inertial navigation system(INS). In most previous research, the authors focus on determining the observable states and unobservable states of a system, while this analysis does not provide sufficient information on the performance of error estimators. In order to provide more insight into the system error estimators, it is necessary to analysis the observable degree of the observable states. For the analysis of the degree of observability, an analysis based on information theory of an inertial navigation system in ground alignment with Bar-Itzhack and Bermans error model is presented. It is shown that through the method based on mutual information, we can not only determine which state is observable and which is not, but also calculate the exact degree of observability of the system states. Simulation results indicate that the observable degree indexes are able to predict Kalman filtering errors of system states, and demonstrate the validity of the method.