On the error state selection for stationary SINS alignment and calibration Kalman filters - part I: Estimation algorithms

This paper presents the first part of a study aiming at error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). Estimation algorithms are derived through the analytical manipulation of the full SINS error model, thereby enabling us to investigate the dynamic coupling existing between the state variables. As contributions of this work, we demonstrate that the vertical velocity error is very important for the estimation of almost all error states. Latitude and altitude errors, in turn, are shown to uniquely affect the inertial sensor bias estimates. Besides, the longitude error is found to be totally detached from the system. As straightforward consequence, Bar-Itzhack and Berman's error model turns out to be inadequate for real implementations, and a 12-state Kalman filter is shown to be the optimal error state selection for SSAC purposes. Simulated and experimental tests confirm the adequacy of the outlined conclusions.