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Sensors 2017, 17(3), 439;

On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis

Department of Engineering, Federal University of Lavras, Lavras 37200-000, Brazil
Aeronautics Institute of Technology, Division of Electronic Engineering, São José dos Campos 12228-900, Brazil
National Institute for Space Research, Division of Space Mechanics and Control, São José dos Campos 12227-010, Brazil
Author to whom correspondence should be addressed.
Academic Editor: Jörg F. Wagner
Received: 22 November 2016 / Revised: 12 January 2017 / Accepted: 18 February 2017 / Published: 23 February 2017
(This article belongs to the Special Issue Inertial Sensors and Systems 2016)
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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. View Full-Text
Keywords: SINS; alignment; calibration; error state selection; observability; estimability SINS; alignment; calibration; error state selection; observability; estimability

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Silva, F.O.; Hemerly, E.M.; Leite Filho, W.C. On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters—Part II: Observability/Estimability Analysis. Sensors 2017, 17, 439.

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