A dynamic state realization for tightly coupling Global Positioning System (GPS) measurements with an Inertial Navigation System (INS) is described. The realization, based on the direct fusion of GPS and INS systems through Kalman filter state dynamics, explicitly accounts for temporal and spatial decorrelation of GPS measurement errors (such as tropospheric, ionospheric, and multipath errors) through state augmentation, thereby ensuring Kalman filter integrity under fault-free error conditions. Predicted system performance for a Local Area Augmentation System (LAAS) aircraft precision approach application is evaluated using covariance analysis and validated with flight data.
Built-in fault detection mechanisms based on the Kalman filter innovations are also evaluated to help provide integrity under certain fault conditions. It is shown that an algorithm based on the integral of Kalman filter innovations outperforms other existing GPS fault detection methods in the detection of slowly developing ranging errors, such as those caused by ionospheric and tropospheric anomalies.