Adaptive Kalman Filters With Small-Magnitude and Inaccurate Process Noise Covariance Matrix Part II: Application to Inertial-Based Integrated Navigation

The online estimation of the process noise covariance matrix (PNCM) in the inertial-based integrated navigation has always been a challenge due to the small magnitude of the PNCM and limited estimation accuracy on partial navigation states. Based on the nonadjacent state transition model proposed in the companion paper (Part I), we further propose adaptive Kalman filters based on sample screening to deal with the limited estimation accuracy on partial navigation states. The estimation of the PNCM in the inertial-based integrated navigation is abstracted as the maximum likelihood estimation of the variance based on the heterogeneous Gaussian samples. A sample screening technique is then proposed to avoid the impact of imprecise parts of the heterogeneous samples on the variance to be estimated, which improve the estimation accuracy of the PNCM in the inertial-based integrated navigation. The relative means and mean square errors of the estimated PNCM coefficients are derived for the high-dimension model of the inertial-based integrated navigation, based on which the optimal length setting of the nonadjacent state transition model is analyzed and selected, and the application scenarios of the proposed filters are recommended. Plenty of simulations and experiments are conducted, and the results validate that the proposed filters achieve more accurate estimates of the PNCM and exhibit smaller navigation errors than existing State-of-the-Art methods in the inertial-based integrated navigation.