Three-dimensional attitude determination strategy for fused polarized
light and geomagnetism

Shan Li; Donghua Zhao; Hua Yu; Tao Jin; Chenguang Wang; Jun Tang; Chong Shen; Jun Liu; Jun Liu; Yicheng Wu; Hong Yang

doi:10.1364/AO.442754

Applied Optics
Vol. 61,
Issue 3,
pp. 765-774
(2022)
•https://doi.org/10.1364/AO.442754

Three-dimensional attitude determination strategy for fused polarized light and geomagnetism

Shan Li, Donghua Zhao, Hua Yu, Tao Jin, Chenguang Wang, Jun Tang, Chong Shen, Jun Liu, Yicheng Wu, and Hong Yang

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Shan Li, Donghua Zhao, Hua Yu, Tao Jin, Chenguang Wang, Jun Tang, Chong Shen, Jun Liu, Yicheng Wu, and Hong Yang, "Three-dimensional attitude determination strategy for fused polarized light and geomagnetism," Appl. Opt. 61, 765-774 (2022)

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Related Topics
Table of Contents Category
- Instrumentation and Measurements
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: September 7, 2021
- Revised Manuscript: December 16, 2021
- Manuscript Accepted: December 16, 2021
- Published: January 14, 2022

Abstract

Using polarized light sensors to obtain only two-dimensional heading information does meet actual needs in navigation. Instead, an alternative method is proposed that uses the positional information of the Sun and geomagnetic information to calculate the three-dimensional attitude of a vehicle. First, the theoretical background of the polarization mode of skylight is described, and the scheme in using the atmospheric polarization pattern to calculate the solar position is presented. Second, the traditional three-axis attitude-determination (TRIAD) algorithm that exploits the solar position vector and the geomagnetic vector to obtain the three-dimensional attitude and the optimized TRIAD algorithm are introduced. Static and turntable experiments are described that verify the accuracy of the attitude calculation. Experimental results show that when using the optimized TRIAD algorithm, the root mean square errors for the roll angle, pitch angle, and heading angle are 0.1225°, 0.668°, and 1.0234°, respectively. This means that the optimized TRIAD algorithm performs significantly better than the traditional TRIAD algorithm and demonstrates that using the solar position and the geomagnetic information to obtain the three-dimensional attitude of the vehicle is very effective.

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Data Availability

The data used for this work may be provided upon reasonable request to the corresponding author.

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Experimental Instrument	Model	Main Parameters
Polarization camera	Sony COMS IMX250MZR	Pixel size: $3.45 \times 3.45 µ m$ Sampling rate: 10 Hz
Embedded processing unit	NVIDIA Jetson TX2
Three-axis turntable	Three-axis non-magnetic turntable	Positioning accuracy: $\leq {0.05}^{\circ}$
Fluxgate Magnetometer	FVM-400	Range: $\pm 100, 000 n T$ Resolution: 1 nT $A c c u r a c y : \pm (0.25 % o f r e a d i n g + 5 n T$ )

	Variance (°)			RMSE (°)
	TRIAD-I	TRIAD-II	Optimized TRIAD	TRIAD-I	TRIAD-II	Optimized TRIAD
Roll	0.2657	0.3759	0.2586	0.2644	0.3738	0.2571
Pitch	0.3148	0.4738	0.3125	0.313	0.4711	0.3108
Yaw	0.6142	0.7722	0.6318	0.6108	0.7679	0.6346

	Variance (°)			RMSE (°)
	TRIAD-I	TRIAD-II	Optimized TRIAD	TRIAD-I	TRIAD-II	Optimized TRIAD
Roll	1.098	2.244	0.6558	1.1184	2.2334	0.668
Pitch	0.1239	0.7595	0.12	0.1312	0.7542	0.1255
Yaw	1.692	3.114	1.003	1.7237	3.15	1.0234

	Time(s)
	Static Experiment	Turntable Experiment
TRIAD-I	0.052	0.075
TRIAD-II	0.062	0.078
Optimized TRIAD	0.094	0.116

Experimental Instrument	Model	Main Parameters
Polarization camera	Sony COMS IMX250MZR	Pixel size: $3.45 \times 3.45 µ m$ Sampling rate: 10 Hz
Embedded processing unit	NVIDIA Jetson TX2
Three-axis turntable	Three-axis non-magnetic turntable	Positioning accuracy: $\leq {0.05}^{\circ}$
Fluxgate Magnetometer	FVM-400	Range: $\pm 100, 000 n T$ Resolution: 1 nT $A c c u r a c y : \pm (0.25 % o f r e a d i n g + 5 n T$ )

Algorithm 1: Optimized TRIAD
Step 1: input the information: $\vec{S_{b}}, \vec{H_{b}}, \vec{S_{n}}, \vec{H_{n}}$
Step 2: construct the coordinate frame: $V, W$
Step 3: calculate the transfer matrix $A_{1}, A_{2}$ : $A = \sum_{i = 1}^{3} w_{i} v_{i}^{T}$
Step 4: calculate the transfer matrix by optimized TRIAD:
$A^{'} = \frac{σ_{2}^{2}}{σ_{1}^{2} + σ_{2}^{2}}$ $A_{1} + \frac{σ_{1}^{2}}{σ_{1}^{2} + σ_{2}^{2}} A_{2}$
Step 5: establish the transformation relationship: $C_{n}^{b} = C_{e}^{b} C_{i}^{e} C_{n}^{i}$
Step 6: calculate the attitude transfer matrix:
$A^{'} = C_{n}^{b} = L (ψ) L (θ) L (γ)$
Step 7: calculate the attitude: $θ, γ$ and $ψ$

Algorithm 1: Optimized TRIAD
Step 1: input the information: $\vec{S_{b}}, \vec{H_{b}}, \vec{S_{n}}, \vec{H_{n}}$
Step 2: construct the coordinate frame: $V, W$
Step 3: calculate the transfer matrix $A_{1}, A_{2}$ : $A = \sum_{i = 1}^{3} w_{i} v_{i}^{T}$
Step 4: calculate the transfer matrix by optimized TRIAD:
$A^{'} = \frac{σ_{2}^{2}}{σ_{1}^{2} + σ_{2}^{2}}$ $A_{1} + \frac{σ_{1}^{2}}{σ_{1}^{2} + σ_{2}^{2}} A_{2}$
Step 5: establish the transformation relationship: $C_{n}^{b} = C_{e}^{b} C_{i}^{e} C_{n}^{i}$
Step 6: calculate the attitude transfer matrix:
$A^{'} = C_{n}^{b} = L (ψ) L (θ) L (γ)$
Step 7: calculate the attitude: $θ, γ$ and $ψ$

Abstract

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Equations (19)

Applied Optics