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

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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.

No MeSH data available.


Eigenvector relative to the sixth eigenvalue in the simulated test.
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sensors-17-00439-f013: Eigenvector relative to the sixth eigenvalue in the simulated test.

Mentions: In order to shed more light onto the estimability of the SSAC error states, we calculated the eigenvalues and eigenvectors of the normalized error state covariance matrix, as suggested in (45) and (46). The computed eigenvalues (in descending order) and their corresponding eigenvectors (represented as multidimensional vectors) are given in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13. For clarity, the stationary numeric values (t = 60 min) of the eigenvalues and eigenvectors are summarized in Table 1 and Table 2.


On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters — Part II: Observability/Estimability Analysis
Eigenvector relative to the sixth eigenvalue in the simulated test.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5375725&req=5

sensors-17-00439-f013: Eigenvector relative to the sixth eigenvalue in the simulated test.
Mentions: In order to shed more light onto the estimability of the SSAC error states, we calculated the eigenvalues and eigenvectors of the normalized error state covariance matrix, as suggested in (45) and (46). The computed eigenvalues (in descending order) and their corresponding eigenvectors (represented as multidimensional vectors) are given in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13. For clarity, the stationary numeric values (t = 60 min) of the eigenvalues and eigenvectors are summarized in Table 1 and Table 2.

View Article: PubMed Central - PubMed

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.

No MeSH data available.