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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 paper presents the design of a complete multi-rate self-alignment algorithm for strapdown inertial navigation systems (SINS), readily amenable to be implemented in a digital computer. The proposed algorithm is divided in two steps, the coarse and the fine selfalignments. As main contribution of this paper, one demonstrates that, for the particular case of stationary SINS, the fine alignment is not able to improve the orientation estimates derived from the coarse alignment. Instead, the main role of the fine alignment consists in estimating some of the uncompensated inertial sensor biases, which may be used for compensation into the navigation algorithms, greatly improving the accuracy of autonomous inertial navigators.

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