Decoupled Observability Analyses of Error States in INS/GPS Integration

The observability of error states in Inertial Navigation System/Global Positioning System (INS/GPS) integration is of great importance. Rank tests or null space tests of the observability matrix have been adopted by previous works, however, for a time-varying system with a high-dimension error state vector, it is very difficult to analyse the observability matrix by these traditional methods. In this paper, the decoupled observability analysis method is proposed for an 18-dimensional INS/GPS integration system. By reducing the dimension of coupling error states, several six-dimensional decoupled observability sub-matrices are obtained, which make the observability analyses easier. The observability results of error states are obtained by the proposed method. Covariance simulation with an Extended Kalman filter (EKF) and a flying test were performed which confirmed the theoretical results.