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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.


Tactical-grade IMU mounted on a three-axis rotary table.
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sensors-17-00439-f014: Tactical-grade IMU mounted on a three-axis rotary table.

Mentions: Merely to validate the propriety of the observability/estimability analyses conducted so far, we repeated the simulated test, now with real datasets gathered from a tactical-grade inertial measurement unit (IMU). The employed IMU, specified in Table 3, was mounted aligned to the navigation frame, on a three-axis rotary table available at the “Identification, Navigation, Control and Simulation Laboratory” (LINCS) of the “Institute of Aeronautics and Space” (IAE), in São José dos Campos, Brazil, as shown in Figure 14. The inertial sensor outputs were processed at a cadence of 100 Hz (corresponding to the IMU sampling rate) and the Kalman filter at 1 Hz. For the purpose of the test, , , and were initialized as follows,(47)x^0=015×1(48)P0=diag[(0.1∘)2(0.1∘)2(5∘)2(0.1m/s)2(0.1m/s)2(0.1m/s)2(0.0001∘)2(0.0001∘)2(10m)2(0.5∘/h)2(0.5∘/h)2(0.5∘/h)2(0.5mg)2(0.5mg)2(0.5mg)2](49)QP=diag[(0.01∘/h)2(0.01∘/h)2(0.01∘/h)2(0.03mg/Hz)2(0.03mg/Hz)2(0.03mg/Hz)2](50)RM=diag(0.1m/s)2(0.1m/s)2(0.1m/s)2where the variances of in (50) were defined based on intuitive judgment.


On the Error State Selection for Stationary SINS Alignment and Calibration Kalman Filters — Part II: Observability/Estimability Analysis
Tactical-grade IMU mounted on a three-axis rotary table.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

sensors-17-00439-f014: Tactical-grade IMU mounted on a three-axis rotary table.
Mentions: Merely to validate the propriety of the observability/estimability analyses conducted so far, we repeated the simulated test, now with real datasets gathered from a tactical-grade inertial measurement unit (IMU). The employed IMU, specified in Table 3, was mounted aligned to the navigation frame, on a three-axis rotary table available at the “Identification, Navigation, Control and Simulation Laboratory” (LINCS) of the “Institute of Aeronautics and Space” (IAE), in São José dos Campos, Brazil, as shown in Figure 14. The inertial sensor outputs were processed at a cadence of 100 Hz (corresponding to the IMU sampling rate) and the Kalman filter at 1 Hz. For the purpose of the test, , , and were initialized as follows,(47)x^0=015×1(48)P0=diag[(0.1∘)2(0.1∘)2(5∘)2(0.1m/s)2(0.1m/s)2(0.1m/s)2(0.0001∘)2(0.0001∘)2(10m)2(0.5∘/h)2(0.5∘/h)2(0.5∘/h)2(0.5mg)2(0.5mg)2(0.5mg)2](49)QP=diag[(0.01∘/h)2(0.01∘/h)2(0.01∘/h)2(0.03mg/Hz)2(0.03mg/Hz)2(0.03mg/Hz)2](50)RM=diag(0.1m/s)2(0.1m/s)2(0.1m/s)2where the variances of in (50) were defined based on intuitive judgment.

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.