Abstract
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.
Highlights
Inertial navigation is the process of continuously determining the position, velocity and orientation of a vehicle, relying solely on the information provided by rigidly-mounted accelerometers and angular rate sensors [1]
To validate the propriety of the observability/estimability analyses conducted so far, we repeated the simulated test, with real datasets gathered from a tactical-grade inertial measurement unit (IMU)
The behavior of the covariance matrix eigenvalues in the experimental test proved to be very similar to what has been observed in the simulated test, including the steady state values reached by the eigenvector directions
Summary
Inertial navigation is the process of continuously determining the position, velocity and orientation (attitude) of a vehicle, relying solely on the information provided by rigidly-mounted (strapped down) accelerometers and angular rate sensors [1]. As properly analyzed by Baram and Kailath [43], the source of the latter misconceptions derives mostly from a misinterpretation of the concepts “observability” and “estimability”, which has led authors to, not infrequently, draw misleading conclusions about filter order-reduction in practical estimation problems [32,33,34] Another very detrimental limitation of the covariance analysis refers to the fact that it is usually limited to the mere evaluation of the terms along the major diagonal of the covariance matrix [29]. Despite being unobservable, the horizontal accelerometer biases and the east angular rate sensor bias are “estimable” quantities and, should not be eliminated from the Kalman filter state vector, under the risk of impairing the overall estimation performance The latter verifications corroborate the conclusions achieved in the first part of this study [36], where a 12-state Kalman filter was considered the optimal error state selection for SSAC purposes.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
