Modeling and Analysis of Measurements of Tightly Coupled GPS/SINS Integrated Navigation System

The tightly coupled GPS/SINS integrated navigation system introduces nonlinearity to the measurement equation of the Kalman filter due to the use of raw GPS pseudorange and pseudorange rate measurements. The Extended Kalman Filter (EKF) is a typical method to address the nonlinearity by linearizing the measurements. However, the linearization of the pseudorange rate measurement is incomplete in the conventional measurement equation. To solve this problem, this paper presents a complete linearized pseudorange rate measurement equation and analyzes the role of the corresponding state variables. Besides, one advantage of the tightly coupled GPS/SINS integrated navigation system is that the system can still work when less than four satellites are tracked. Previous literatures propose that the tightly coupled GPS/SINS integrated navigation system with less than four satellites can work normally for a short time. On this basis, this system is further analyzed from the viewpoint of observability and is not considered to work stably for a long time in this paper. The experimental results prove the analysis of the pseudorange rate measurement equation and the tightly coupled GPS/SINS integrated navigation system with less than four satellites.