This paper presents a comprehensive error analysis of coarse alignment formulations for stationary strapdown inertial navigation systems (SINS). Analytical expressions for the residual normality, orthogonality, alignment, and Euler angle errors are systematically derived, allowing us to establish comparisons in terms of rapidity, accuracy, and autonomy requirements. For the purpose of the error analysis, geographic latitude and local gravity acceleration uncertainties are considered, in addition to the inertial sensor uncertainties. As the main contribution of this paper, an improved coarse alignment method is proposed, which is based on orthonormality constraints existing between the Euler angles and the attitude matrix. In contrast to the traditional methods, the proposed formulation does not imply normality and orthogonality errors, besides producing time-independent alignment and Euler angle errors. The latter is seen to be particularly interesting for situations wherein, due to time constraints, posterior fine alignment and orthonormalization procedures cannot be implemented. The superiority of the proposed formulation is validated through simulated and experimental tests, regardless of the SINS initial orientation. The accuracy degradation produced by each alignment formulation in the navigation stage is used as the performance index.

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 an innovative in-field coarse bias estimation (CBE) method for stationary intermediate-grade inertial measurement units (IMUs), which is based on the existence of normality and orthogonality errors in the attitude matrix supplied by the traditional three-axis attitude determination stationary coarse alignment (CA) stage. Differently from the currently existing in-field bias estimation formulations, the proposed CBE method is conceived to be conducted in stationary conditions, jointly with the CA, and it allows the down accelerometer bias and the north and down angular rate sensor biases to be adequately estimated. As a main contribution of this paper, we demonstrate that the proposed CBE method is able to greatly accelerate the estimation process of the aforementioned biases, contributing, hence, to shorten the IMU setup time. A comprehensive error analysis is presented, and the conclusions are twofold: 1) the proposed CBE method is valid regardless of the IMU orientation and 2) its estimation accuracy is mainly constrained by the north accelerometer bias and the position location uncertainty, which are, in general, very reduced. Results from simulated and experimental test confirm the adequacy of the outlined verifications, also attesting the superiority of the proposed CBE method in situations where, due to time constraints, stationary fine alignment procedures are not allowed to be carried out.