To solve the problems existing in the observable degree analysis method based on the SVD of the observable matrix of linear time-varying systems

such as the inconsistency of state dimensions and the nonuniqueness of singular value reference

an improved method was proposed. First

the relationship between linear time-varying system and piecewise linear constant system (PWCS) was expounded

and the PWCS observability analysis theory was introduced. Under the condition of satisfying the theorem

the complexity of the analytical calculation could be effectively reduced by the stripped observability matrix (SOM) instead of the total observability matrix (TOM). Then

the SVD of SOM and its singular value as well as the corresponding singular vector were extracted by the system. Next

the observation equation of the system was deduced

and the observability index of each state of the system was obtained according to the longitudinal comparison of the observation degree of the same state under different maneuver conditions of the carrier. Finally

the SINS/DVL integrated navigation system was used for simulation verification. Simulation results show that the observability index calculated by this method was consistent with the Kalman filter state estimation error characteristics

which proves that the improved method can predict and accurately describe the state estimation effect. Meanwhile

the system adaptive feedback correction was performed according to the calculated state observability

which could effectively improve the navigation precision.