This paper presents the second part of a study aiming at the error state selection in Kalman filters applied to the stationary self-alignment and calibration (SSAC) problem of strapdown inertial navigation systems (SINS). The observability properties of the system are systematically investigated, and the number of unobservable modes is established. Through the analytical manipulation of the full SINS error model, the unobservable modes of the system are determined, and the SSAC error states (except the velocity errors) are proven to be individually unobservable. The estimability of the system is determined through the examination of the major diagonal terms of the covariance matrix and their eigenvalues/eigenvectors. Filter order reduction based on observability analysis is shown to be inadequate, and several misconceptions regarding SSAC observability and estimability deficiencies are removed. As the main contributions of this paper, we demonstrate that, except for the position errors, all error states can be minimally estimated in the SSAC problem and, hence, should not be removed from the filter. Corroborating the conclusions of the first part of this study, a 12-state Kalman filter is found to be the optimal error state selection for SSAC purposes. Results from simulated and experimental tests support the outlined conclusions.

This communication presents a comparative analysis of tuning techniques for satellite launch vehicle attitude controllers. The investigated tuning techniques consist in the minimization of specific performance indexes, namely the Integral Absolute Error (IAE) index, the Integral of Time Multiplied Absolute Error (ITAE) index, the Integral Squared Error (ISE) index, and the Integral of Time Multiplied Squared Error (ITSE) index, being hence, termed optimal. By defining adequate figures of merit, relevant for evaluating the overall performance of satellite launch vehicles, and also taking into account requirements related to the physical limitations of the latter, the performance of attitude controllers tuned by the investigated techniques is compared to the one tuned by the methodology currently employed in the Brazilian Satellite Launch Vehicle (VLS), namely, the Linear Quadratic (LQ) methodology. Through simulation results, it is demonstrated that, despite sparse benefits produced by the alternative tuning techniques, in particular ​ITAE and ISE, the LQ methodology remains globally superior.