Adaptive dynamic adjustment star identification threshold estimation for a terrestrial star tracker

Zhen Wang; Jie Jiang; Yan Ma

doi:10.1364/AO.470116

Applied Optics
Vol. 61,
Issue 28,
pp. 8248-8257
(2022)
•https://doi.org/10.1364/AO.470116

Adaptive dynamic adjustment star identification threshold estimation for a terrestrial star tracker

Zhen Wang, Jie Jiang, and Yan Ma

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Zhen Wang, Jie Jiang, and Yan Ma, "Adaptive dynamic adjustment star identification threshold estimation for a terrestrial star tracker," Appl. Opt. 61, 8248-8257 (2022)

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Table of Contents Category
- Optical Devices, Sensors, and Detectors
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About this Article
History
- Original Manuscript: July 11, 2022
- Revised Manuscript: August 29, 2022
- Manuscript Accepted: September 4, 2022
- Published: September 22, 2022

Abstract

As the criterion to determine whether stars are identified, the star image identification matching threshold is an important parameter in terrestrial star trackers. It not only determines the identification success rate, but also affects the redundant matching quantity and identification efficiency. This paper focuses on the problem that the identification efficiency of terrestrial star trackers is restricted by inappropriate matching thresholds and presents an adaptive dynamic adjustment star identification threshold model. Compared to the existing matching threshold, the presented model clarifies the transformation of observation star angular distance errors and dynamically estimates the corresponding identification threshold as the variation of observation angular distances and attitudes. Therefore, we believe it completes the star identification with an excellent redundant matching quantity and identification efficiency. Numerical simulation and night sky experimental results showed that the identification efficiency was improved by more than 46.54% and 22.61%, respectively, while the identification success rate remained at 100%.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Variable	Annotation
S-frame	Observation system of star tracker
Ref-frame	Reference system of star catalog
$W_{i}$	Observation vector of star i in S-frame
$V_{i}$	Reference vector of star i in Ref-frame
$V_{N}$	Observation vector of star i in N-frame
$V_{H}$	Observation vector of star i in horizontal system
$d_{i, j}^{S}$	Observation angular distance of stars i and j in S-frame
$d_{i, j}^{R e f}$	Reference angular distance of stars i and j in Ref-frame
ADMP	Angular distance matching pairs
$T H_{G A D}$	Global angular distance (GAD) matching threshold
${T H}_{A D A}^{i, j}$	Adaptive dynamic adjustment (ADA) matching threshold
$ε_{A E O}$	Angular distance error observed out of the Earth
$ε_{A E S}$	Angular distance error of Earth surface imaging observation
$R ()$	Atmospheric refraction angle estimation function
$θ_{Z e t h}$	Zenith distances of star i in N-frame
$θ_{A z i}$	Azimuth of star i in N-frame
$R_{1}$ , $R_{2}$ , $R_{3}$	Unit rotation matrixes around x, y, and z axes

Parameter	Value	Parameter	Value
FOV angle $θ_{F O V}$	20º	Central wavelength	650 nm
Detection sensitivity	6.0	Lens transmissivity $τ$	0.85
Reference time $t_{0}$	2019.07.01	Imaging error $\| ε_{p} \|$	$0^{''}$
Inclinometer error	[0º, 0.01º]	Install error	[0º, 0.01º]

Parameter	Value	Parameter	Value
Focal length $f$	24.97 mm	Lens diameter D	40 mm
Principle point	1030.7,1039.8	Detection sensitivity	6.0
FOV angle $θ_{F O V}$	25º	Central wavelength	650 nm
Active pixels	$2048 \times 2048$	Pixel length	5.5 µm
Reference time $t_{0}$	2019.07.01	Imaging error $\| ε_{p} \|$	${1.8933}^{''}$
Inc. dynamic accuracy	0.2º	Inc static accuracy	0.01º
Inc. desolution	0.01º	Ins roll angles	1.6822º
Ins. pitch angles	4.5436º	Ins yaw angles	1.0520º

Variable	Annotation
S-frame	Observation system of star tracker
Ref-frame	Reference system of star catalog
$W_{i}$	Observation vector of star i in S-frame
$V_{i}$	Reference vector of star i in Ref-frame
$V_{N}$	Observation vector of star i in N-frame
$V_{H}$	Observation vector of star i in horizontal system
$d_{i, j}^{S}$	Observation angular distance of stars i and j in S-frame
$d_{i, j}^{R e f}$	Reference angular distance of stars i and j in Ref-frame
ADMP	Angular distance matching pairs
$T H_{G A D}$	Global angular distance (GAD) matching threshold
${T H}_{A D A}^{i, j}$	Adaptive dynamic adjustment (ADA) matching threshold
$ε_{A E O}$	Angular distance error observed out of the Earth
$ε_{A E S}$	Angular distance error of Earth surface imaging observation
$R ()$	Atmospheric refraction angle estimation function
$θ_{Z e t h}$	Zenith distances of star i in N-frame
$θ_{A z i}$	Azimuth of star i in N-frame
$R_{1}$ , $R_{2}$ , $R_{3}$	Unit rotation matrixes around x, y, and z axes

Parameter	Value	Parameter	Value
FOV angle $θ_{F O V}$	20º	Central wavelength	650 nm
Detection sensitivity	6.0	Lens transmissivity $τ$	0.85
Reference time $t_{0}$	2019.07.01	Imaging error $\| ε_{p} \|$	$0^{''}$
Inclinometer error	[0º, 0.01º]	Install error	[0º, 0.01º]

Abstract

Data availability

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Figures (14)

Tables (3)

Equations (26)

Applied Optics