Two-step calibration method for extrinsic parameters of an airborne camera

Dongming Yuan; Dongming Yuan; Dongming Yuan; Yalin Ding; Guoqin Yuan; Feng Li; Jian Zhang; Yuanchao Wang; Yuanchao Wang; Lei Zhang

doi:10.1364/AO.412305

Applied Optics
Vol. 60,
Issue 5,
pp. 1387-1398
(2021)
•https://doi.org/10.1364/AO.412305

Two-step calibration method for extrinsic parameters of an airborne camera

Dongming Yuan, Yalin Ding, Guoqin Yuan, Feng Li, Jian Zhang, Yuanchao Wang, and Lei Zhang

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Dongming Yuan, Yalin Ding, Guoqin Yuan, Feng Li, Jian Zhang, Yuanchao Wang, and Lei Zhang, "Two-step calibration method for extrinsic parameters of an airborne camera," Appl. Opt. 60, 1387-1398 (2021)

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Abstract

In order to meet the accuracy requirements of target geo-location of a wide-area reconnaissance camera, it is necessary to calibrate the extrinsic parameters of the camera. A novel calibration method is proposed for the orientation relationship between the camera coordinate system (CCS) and the frame coordinate system (FCS). First, the calibration between the roll axis of the FCS and the CCS is carried out based on the method of the extended Kalman filter. Second, the calibration between the pitch axis of the FCS and the CCS is deduced based on the least mean square combined with the particle swarm optimization method. Then, the calibration accuracy of the proposed method is quantitatively analyzed by numerical simulation. Finally, a calibration experiment is conducted on verifying the effectiveness of the method.

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Parameters		Value
Camera	Size of pixel (m)	$7.4 \times 10^{- 6}$
parameters	Focal length (m)	1.85
True value	State variable (°)	$(0.022, 0.031, 0.013, 0.015)^{T}$
Initial value	State variable (°)	$(0.056, 0.056, 0.056, 0.056)^{T}$
Noise	Noise of process (“ $\cdot$ ”)	$d i a g (100, 100, 100, 100)$
	Noise of measure ( ${p i x e l}^{2}$ )	$d i a g (1, 1)$
Dynamic variable	Roll angle (°)	$(0, 6, 12, \dots, 354)^{T}$

Parameters		Value
True value	Coordinate of focus (pixel)	(180000,0), (−180000,0)
	a (pixel)	3500
	$θ_{F C}$ (°)	0.008
Noise	Sampling noise of pixel (pixel)	(0.212,0.229,0.364,0.541)^a

Sampling noise (pixel)	0.212	0.229	0.364	0.541
RMS of error (°)	0.0012	0.0014	0.0021	0.0029

$θ_{F C}$ (°)	−0.0139	−0.0125	−0.0111	−0.0097	−0.0083	−0.0069	−0.0056
RMS of error (°)	0.0014	0.0014	0.0013	0.0013	0.0013	0.0015	0.0012
$θ_{F C}$ (°)	−0.0042	−0.0028	−0.0014	0.0014	0.0028	0.0042	0.0056
RMS of error (°)	0.0014	0.0012	0.0013	0.0013	0.0013	0.0015	0.0012
$θ_{F C}$ (°)	0.0069	0.0083	0.0097	0.0111	0.0125	0.0139
RMS of error (°)	0.0013	0.0016	0.0014	0.0011	0.0015	0.0013

Device	Manufacture	Model	Main Parameters
Collimator	CIOMP	10 m	Focal length: 10067 mm
Airborne camera	CIOMP	EO-08	Focal length: 1815 mm
Detector	GPIXEL, China	GMAX0603	Number of active pixels: $7542 \times 5144$
Electric encoder	Netzer	DS-90-64-35H-S0	Bit: 19
			Static error: $< {0.01}^{\circ}$

Parameter
No.	$α_{0}$ (°)	$β_{0}$ (°)	$α_{F C}$ (°)	$β_{F C}$ (°)	$θ_{F C}$ (°)
1	0.0946	0.0720	0.0147	0.0104	0.0047
2	0.0948	0.0725	0.0155	0.0108	0.0015
3	0.0954	0.0719	0.0165	0.0109	0.0041
4	0.0953	0.0720	0.0162	0.0111	0.0062
5	0.0946	0.0723	0.0164	0.0101	0.0040
6	0.0948	0.0732	0.0152	0.0098	0.0055
7	0.0946	0.0721	0.0147	0.0098	0.0042
8	0.0950	0.0730	0.0149	0.0109	0.0048
9	0.0957	0.0723	0.0151	0.0105	0.0039
10	0.0957	0.0733	0.0167	0.0107	0.0040
Error ( $3 σ$ )	0.0013	0.0016	0.0024	0.0014	0.0037

	Target Geographic	Geo-Location Error (m)			Target Geographic	Geo-Location Error (m)
No.	Position^a	Uncalibrated	Calibrated	No.	Position^a	Uncalibrated	Calibrated
1	(34°25^′42.4″N, 113°0^′54.2″E)	430.8	142.6	21	(34°21^′19.6″N, 113°6^′30.5″E)	383.0	47
2	(34°25^′42.4″N, 113°1^′53.1″E)	245.1	49.4	22	(34°22^′01.6″N, 113°6^′30.5″E)	483.7	62.1
3	(34°25^′42.4″N, 113°2^′52.0″E)	351.9	63.7	23	(34°22^′43.7″N, 113°6^′30.5″E)	229.6	101.7
4	(34°25^′42.4″N, 113°3^′51.0″E)	368.6	39.1	24	(34°23^′25.7″N, 113°6^′30.5″E)	251.6	26.4
5	(34°25^′42.4″N, 113°4^′49.9″E)	253.3	52.1	25	(34°24^′07.7″N, 113°6^′30.5″E)	334.8	100.8
6	(34°25^′42.4″N, 113°5^′48.8″E)	395.2	36.8	26	(34°24^′49.8″N, 113°6^′30.5″E)	249.8	50.6
7	(34°25^′42.4″N, 113°6^′47.7″E)	149.7	57.4	27	(34°25^′31.8″N, 113°6^′30.5″E)	213.2	80.3
8	(34°25^′42.4″N, 113°7^′46.7″E)	361.6	61.2	28	(34°26^′13.8″N, 113°6^′30.5″E)	514.2	116.1
9	(34°25^′42.4″N, 113°8^′45.6″E)	647.1	125.9	29	(34°26^′55.9″N, 113°6^′30.5″E)	523.4	136.8
10	(34°25^′42.4″N, 113°9^′44.5″E)	472.3	51.8	30	(34°27^′37.9″N, 113°6^′30.5″E)	321.5	66.7
11	(34°24^′58.0″N, 113°0^′54.2″E)	373.7	79.4	31	(34°01^′19.4″N, 113°7^′23.5″E)	435.4	86.5
12	(34°24^′58.0″N, 113°1^′53.0″E)	306.6	55.4	32	(34°02^′01.4″N, 113°7^′23.5″E)	167.9	40.3
13	(34°24^′58.0″N, 113°2^′51.8″E)	399.5	85.3	33	(34°02^′43.4″N, 113°7^′23.5″E)	179.1	53.7
14	(34°24^′58.0″N, 113°3^′50.6″E)	280.4	94.8	34	(34°03^′25.4″N, 113°7^′23.5″E)	513.6	43.2
15	(34°24^′58.0″N, 113°4^′49.4″E)	156.4	116.8	35	(34°04^′07.4″N, 113°7^′23.5″E)	259.9	61.9
16	(34°24^′58.0″N, 113°5^′48.1″E)	561.8	127.8	36	(34°04^′49.5″N, 113°7^′23.5″E)	539.3	131.6
17	(34°24^′58.0″N, 113°6^′46.9″E)	409.4	58.4	37	(34°05^′31.5″N, 113°7^′23.5″E)	370.1	98.3
18	(34°24^′58.0″N, 113°7^′45.7″E)	398.4	132.7	38	(34°06^′13.5″N, 113°7^′23.5″E)	291.1	72.7
19	(34°24^′58.0″N, 113°8^′44.5″E)	312.1	99.2	39	(34°06^′55.5″N, 113°7^′23.5″E)	301.9	27.5
20	(34°24^′58.0″N, 113°9^′43.3″E)	370.5	78.2	40	(34°07^′37.5″N, 113°7^′23.5″E)	343.2	59.9
Uncalibrated RMS of Geo-location error (m)			372.6	Calibrated RMS of Geo-location error (m)			83.3

Algorithm	Geo-Location Error (m)	Comparative Result (m)
LMS	137.1	−53.8
PSO-GA	109.2	−25.9
Improve algorithm of this paper	83.3	–

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Applied Optics