Theoretical analysis and application of Kalman filters for ultra-tight global position system/inertial navigation system integration

When a global position system (GPS) is combined with an inertial navigation system (INS) in the ultra-tight GPS/INS integrated navigation system, their performances are both optimized. However, different from loose and tight integration, in the ultra-tight integration, the non-linearity of Kalman measurements will seriously affect the filtering result. As the performance of the Kalman filter is radically affected by the modelling strategies, this paper will discuss it in depth. Firstly, the modelling of a traditional Kalman filter for ultra-tight integration is introduced by derivation and simulation experiments based on a single-frequency GPS software receiver. Then, the theoretical analysis of its performances on observability, controllability and stability is given. According to that, a novel extended Kalman filter for the ultra-tight integration is presented, using a Q (quadrature) signal from the GPS receiver correlator and a position and velocity from both the GPS and INS to form the measurements of the extended Kalman filter. New simulation experiments under the same initial conditions are carried out, and the comparison results show that the new method can provide better precision of all navigation parameters. However, it is noted that the curves of position and velocity errors have slight oscillation; the reason for this will be studied in the future.