On the error state selection for stationary SINS alignment and calibration Kalman filters – part I: Estimation algorithms

Silva, Felipe O.; Hemerly, Elder Moreira; Filho, Waldemar C. Leite

doi:10.1016/j.ast.2016.11.019

Cited by 20 publications

(31 citation statements)

References 32 publications

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“…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. As a minor contribution of this paper, we demonstrate that the estimation accuracy of the SSAC error states is also dependent on the choice of the initial error state covariance matrix, which figures as an important subject for future investigation.…”

Section: Introductionsupporting

confidence: 89%

“…As analyzed in [36], the system dynamic matrix of the SSAC problem derives from the full propagation error dynamic model of stationary autonomous SINS, which, in state space form, can traditionally described as [36],

\overset{x}{true} = A bold-italicx + G_{P} n_{P}

with,

bold-italicx = {[\begin{matrix} φ^{l} & δ {bold-italicv}^{l} & δ {bold-italicp}^{l} & δ ω_{b i a s}^{l} & δ a_{b i a s}^{l} \end{matrix}]}^{T}

A = ([], \begin{matrix} A_{φ φ} & A_{φ v} & A_{φ p} & - I_{3 \times 3} & 0_{3 \times 3} \\ A_{v φ} & A_{v v} & A_{v p} & 0_{3 \times 3} & I_{3 \times 3} \\ 0_{3 \times 3} & A_{p v} & 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} \\ 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} \\ 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} & 0_{3 \times 3} \end{matrix})

G_{P} = ([], \begin{matrix} - I_{3 \times 3} & 0_{3 \times 3} \\ 0_{3 \times 3} & I_{3 \times 3} \\ ... \end{matrix})

…”

Section: Observability Analysismentioning

confidence: 99%

“…Proceeding as suggested, the following estimation algorithms for the SSAC error states have been derived in [36] (repeated here for clarity),

φ_{N} = - 0true \frac{1}{g_{P}} (() δ {\overset{v}{true}}_{E} - 2 Ω \sin L δ v_{N} - 2 Ω \cos L δ v_{D} - δ a_{b i a s E})

φ_{E} = 0true \frac{1}{g_{P}} (() δ {\overset{v}{true}}_{N} + 2 Ω \sin L δ v_{E} - δ a_{b i a s N})

φ_{D} = 0true \frac{1}{Ω \cos L} ([] \frac{1}{g_{P}} δ {\overset{v}{true}}_{N} + \frac{3 Ω \sin L}{g_{P}} δ {\overset{v}{true}}_{E} + (0true \frac{1}{r_{L s} + h} - 0true \frac{2 Ω^{2} \sin^{2} L}{g_{P}}) δ v_{N} - \frac{Ω^{2} \sin 2 L}{g_{P}} δ v_{D} + δ ω_{b i a s E} - \frac{Ω \sin L}{g_{P}} δ a_{b i a s E})

δ ω_{b i a s N} = 0true \frac{1}{g_{P}} δ {\ddot{v}}_{E} - 0true \frac{3 Ω \sin L}{g_{P}} δ {\dot{v}}_{N} - 0true \frac{2 Ω \cos L}{g_{P}} δ {\dot{v}}_{D} + ((), \frac{1}{r_{λ s} + h}, ...)

…”

Section: Observability Analysismentioning

confidence: 99%

“…Additionally, an “observability/estimability analysis” of the system may provide additional insight into the problem. In the first part of this study [36], we concentrated our efforts on systematically addressing the former issue. This paper, conversely, aims to investigate the SSAC observability/estimability problem.…”

Section: Introductionmentioning

confidence: 99%

“…In order to characterize the unobservable modes of the problem, initially, we analytically manipulate the estimation algorithms derived in [36]. As a result of this innovative analysis, we show that the unobservable modes are, in fact, linear combinations of the alignment errors, inertial sensor biases and position errors, which consequently, are to be considered individually unobservable in the problem.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Silva

Hemerly

Filho

2017

Sensors

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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.

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Section: Introductionsupporting

confidence: 89%