Overbounding GNSS/INS Integration with Uncertain GNSS Gauss-Markov Error Parameters

The integration of GNSS with Inertial Navigation Systems (INS) has the potential to achieve high levels of continuity and availability as compared to standalone GNSS and therefore to satisfy stringent navigation requirements. However, robustly accounting for time-correlated measurement errors is a challenge when designing the Kalman filter (KF) used for GNSS/INS coupling. In particular, if the error processes are not fully known, the KF estimation error covariance can be misleading, which is problematic in safety-critical applications. In this paper, we design a GNSS/INS integration scheme that guarantees upper bounds on the estimation error variance assuming that measurement errors are first-order Gauss-Markov processes with parameters only known to reside within pre-established bounds. We evaluate the filter performance and guaranteed estimation by covariance analysis for a simulated precision approach procedure.