Abstract

Stringent attitude determination accuracy through a high bandwidth is required for the development of the advanced space technologies, such as earth observation and laser communication. In this work, we presented a novel proposal for a digital sun sensor with high accuracy, large Field of View (FOV) and ultra-high data update rate. The Electronic Rolling Shutter (ERS) imaging mode of an APS CMOS detector was employed and an “amplifier factor” was introduced to improve the data update rate significantly. Based on the idea of the multiplexing detector, a novel mask integrated with two kinds of aperture patterns was also introduced to implement its distinctive performance of high precision and large FOV. Test results show that the ERS based sun sensor is capable of achieving the data update rate of 1 kHz and precision of 1.1″ (1σ) within a 105° × 105° FOV. The digital sun sensor can play an important role in precise attitude determination and provide a broader application for high accuracy satellites.

© 2013 Optical Society of America

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References

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2013 (1)

2012 (2)

F. J. Delgado, J. M. Quero, J. Garcia, C. L. Tarrida, P. R. Ortega, and S. Bermejo, “Accurate and Wide-Field-of-View MEMS-Based Sun Sensor for Industrial Applications,” IEEE. Trans. Ind. Electron.59(12), 4871–4880 (2012).
[CrossRef]

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel)12(12), 6712–6726 (2012).
[CrossRef] [PubMed]

2011 (2)

H. Huo, M. Ma, Y. Li, and J. Qiu, “The application of MHD angular rate sensor in aerospace,” Vac. Cryogenics17(2), 114–120 (2011).

M. S. Wei, F. Xing, B. Li, and Z. You, “Investigation of Digital Sun Sensor Technology with an N-Shaped Slit Mask,” Sensors (Basel)11(12), 9764–9777 (2011).
[CrossRef] [PubMed]

2010 (1)

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

2009 (2)

J. Enright, D. Sinclair, and C. Li, “Embedded algorithms for the SS-411 digital sun sensor,” Acta Astronaut.64(9-10), 906–924 (2009).
[CrossRef]

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

2008 (2)

C. Zhang, P. Cui, and Z. Yang, “A design method of the sun snesor used on the miniature spinning satellite,” Deep Space Explor.1, 34–37 (2008).

F. Xing, Z. You, G. Zhang, and J. Sun, “A novel active pixels sensor (APS) based sun sensor based on a feature extraction and image correlation (FEIC) technique,” Meas. Sci. Technol.19(12), 125203 (2008).

2005 (1)

T. Iwata, “Precision attitude and position determination for the Advanced Land Observing Satellite (ALOS),” Proc. SPIE5659, 34–50 (2005).
[CrossRef]

2003 (1)

M. Wany and G. P. Israel, “CMOS image sensor with NMOS-only global shutter and enhanced responsivity,” IEEE Trans. Electron. Dev.50(1), 57–62 (2003).
[CrossRef]

Angulo, M.

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Bermejo, S.

F. J. Delgado, J. M. Quero, J. Garcia, C. L. Tarrida, P. R. Ortega, and S. Bermejo, “Accurate and Wide-Field-of-View MEMS-Based Sun Sensor for Industrial Applications,” IEEE. Trans. Ind. Electron.59(12), 4871–4880 (2012).
[CrossRef]

Bettarini, R.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

Casini, R.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

Castañer, L. M.

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Cui, P.

C. Zhang, P. Cui, and Z. Yang, “A design method of the sun snesor used on the miniature spinning satellite,” Deep Space Explor.1, 34–37 (2008).

Delgado, F. J.

F. J. Delgado, J. M. Quero, J. Garcia, C. L. Tarrida, P. R. Ortega, and S. Bermejo, “Accurate and Wide-Field-of-View MEMS-Based Sun Sensor for Industrial Applications,” IEEE. Trans. Ind. Electron.59(12), 4871–4880 (2012).
[CrossRef]

Domínguez, M.

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Enright, J.

J. Enright, D. Sinclair, and C. Li, “Embedded algorithms for the SS-411 digital sun sensor,” Acta Astronaut.64(9-10), 906–924 (2009).
[CrossRef]

Garcia, J.

F. J. Delgado, J. M. Quero, J. Garcia, C. L. Tarrida, P. R. Ortega, and S. Bermejo, “Accurate and Wide-Field-of-View MEMS-Based Sun Sensor for Industrial Applications,” IEEE. Trans. Ind. Electron.59(12), 4871–4880 (2012).
[CrossRef]

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Gras, A.

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Guo, L.

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel)12(12), 6712–6726 (2012).
[CrossRef] [PubMed]

Huo, H.

H. Huo, M. Ma, Y. Li, and J. Qiu, “The application of MHD angular rate sensor in aerospace,” Vac. Cryogenics17(2), 114–120 (2011).

Israel, G. P.

M. Wany and G. P. Israel, “CMOS image sensor with NMOS-only global shutter and enhanced responsivity,” IEEE Trans. Electron. Dev.50(1), 57–62 (2003).
[CrossRef]

Iwata, T.

T. Iwata, “Precision attitude and position determination for the Advanced Land Observing Satellite (ALOS),” Proc. SPIE5659, 34–50 (2005).
[CrossRef]

Kaidy, J. T.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

Landi, A.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

Li, B.

M. S. Wei, F. Xing, B. Li, and Z. You, “Investigation of Digital Sun Sensor Technology with an N-Shaped Slit Mask,” Sensors (Basel)11(12), 9764–9777 (2011).
[CrossRef] [PubMed]

Li, C.

J. Enright, D. Sinclair, and C. Li, “Embedded algorithms for the SS-411 digital sun sensor,” Acta Astronaut.64(9-10), 906–924 (2009).
[CrossRef]

Li, Y.

H. Huo, M. Ma, Y. Li, and J. Qiu, “The application of MHD angular rate sensor in aerospace,” Vac. Cryogenics17(2), 114–120 (2011).

López-Rodríguez, G.

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Lorenzini, S.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

Ma, M.

H. Huo, M. Ma, Y. Li, and J. Qiu, “The application of MHD angular rate sensor in aerospace,” Vac. Cryogenics17(2), 114–120 (2011).

Ortega, P.

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Ortega, P. R.

F. J. Delgado, J. M. Quero, J. Garcia, C. L. Tarrida, P. R. Ortega, and S. Bermejo, “Accurate and Wide-Field-of-View MEMS-Based Sun Sensor for Industrial Applications,” IEEE. Trans. Ind. Electron.59(12), 4871–4880 (2012).
[CrossRef]

Qiu, J.

H. Huo, M. Ma, Y. Li, and J. Qiu, “The application of MHD angular rate sensor in aerospace,” Vac. Cryogenics17(2), 114–120 (2011).

Quan, W.

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel)12(12), 6712–6726 (2012).
[CrossRef] [PubMed]

Quero, J. M.

F. J. Delgado, J. M. Quero, J. Garcia, C. L. Tarrida, P. R. Ortega, and S. Bermejo, “Accurate and Wide-Field-of-View MEMS-Based Sun Sensor for Industrial Applications,” IEEE. Trans. Ind. Electron.59(12), 4871–4880 (2012).
[CrossRef]

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Reina, M.

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Ricart, J.

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Rogers, G. D.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

Schwinger, M. R.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

Sinclair, D.

J. Enright, D. Sinclair, and C. Li, “Embedded algorithms for the SS-411 digital sun sensor,” Acta Astronaut.64(9-10), 906–924 (2009).
[CrossRef]

Strikwerda, T. E.

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

Sun, J.

F. Xing, Z. You, G. Zhang, and J. Sun, “A novel active pixels sensor (APS) based sun sensor based on a feature extraction and image correlation (FEIC) technique,” Meas. Sci. Technol.19(12), 125203 (2008).

Sun, T.

Tarrida, C. L.

F. J. Delgado, J. M. Quero, J. Garcia, C. L. Tarrida, P. R. Ortega, and S. Bermejo, “Accurate and Wide-Field-of-View MEMS-Based Sun Sensor for Industrial Applications,” IEEE. Trans. Ind. Electron.59(12), 4871–4880 (2012).
[CrossRef]

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

Wany, M.

M. Wany and G. P. Israel, “CMOS image sensor with NMOS-only global shutter and enhanced responsivity,” IEEE Trans. Electron. Dev.50(1), 57–62 (2003).
[CrossRef]

Wei, M.

Wei, M. S.

M. S. Wei, F. Xing, B. Li, and Z. You, “Investigation of Digital Sun Sensor Technology with an N-Shaped Slit Mask,” Sensors (Basel)11(12), 9764–9777 (2011).
[CrossRef] [PubMed]

Xing, F.

T. Sun, F. Xing, Z. You, and M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express21(17), 20096–20110 (2013).
[CrossRef] [PubMed]

M. S. Wei, F. Xing, B. Li, and Z. You, “Investigation of Digital Sun Sensor Technology with an N-Shaped Slit Mask,” Sensors (Basel)11(12), 9764–9777 (2011).
[CrossRef] [PubMed]

F. Xing, Z. You, G. Zhang, and J. Sun, “A novel active pixels sensor (APS) based sun sensor based on a feature extraction and image correlation (FEIC) technique,” Meas. Sci. Technol.19(12), 125203 (2008).

Yang, Z.

C. Zhang, P. Cui, and Z. Yang, “A design method of the sun snesor used on the miniature spinning satellite,” Deep Space Explor.1, 34–37 (2008).

You, Z.

T. Sun, F. Xing, Z. You, and M. Wei, “Motion-blurred star acquisition method of the star tracker under high dynamic conditions,” Opt. Express21(17), 20096–20110 (2013).
[CrossRef] [PubMed]

M. S. Wei, F. Xing, B. Li, and Z. You, “Investigation of Digital Sun Sensor Technology with an N-Shaped Slit Mask,” Sensors (Basel)11(12), 9764–9777 (2011).
[CrossRef] [PubMed]

F. Xing, Z. You, G. Zhang, and J. Sun, “A novel active pixels sensor (APS) based sun sensor based on a feature extraction and image correlation (FEIC) technique,” Meas. Sci. Technol.19(12), 125203 (2008).

Zhang, C.

C. Zhang, P. Cui, and Z. Yang, “A design method of the sun snesor used on the miniature spinning satellite,” Deep Space Explor.1, 34–37 (2008).

Zhang, G.

F. Xing, Z. You, G. Zhang, and J. Sun, “A novel active pixels sensor (APS) based sun sensor based on a feature extraction and image correlation (FEIC) technique,” Meas. Sci. Technol.19(12), 125203 (2008).

Zhang, W.

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel)12(12), 6712–6726 (2012).
[CrossRef] [PubMed]

Acta Astronaut. (2)

G. D. Rogers, M. R. Schwinger, J. T. Kaidy, T. E. Strikwerda, R. Casini, A. Landi, R. Bettarini, and S. Lorenzini, “Autonomous star tracker performance,” Acta Astronaut.65(1–2), 61–74 (2009).
[CrossRef]

J. Enright, D. Sinclair, and C. Li, “Embedded algorithms for the SS-411 digital sun sensor,” Acta Astronaut.64(9-10), 906–924 (2009).
[CrossRef]

Deep Space Explor. (1)

C. Zhang, P. Cui, and Z. Yang, “A design method of the sun snesor used on the miniature spinning satellite,” Deep Space Explor.1, 34–37 (2008).

IEEE Sens. J. (1)

P. Ortega, G. López-Rodríguez, J. Ricart, M. Domínguez, L. M. Castañer, J. M. Quero, C. L. Tarrida, J. Garcia, M. Reina, A. Gras, and M. Angulo, “A miniaturized two axis sun sensor for attitude control of nano-satellites,” IEEE Sens. J.10(10), 1623–1632 (2010).
[CrossRef]

IEEE Trans. Electron. Dev. (1)

M. Wany and G. P. Israel, “CMOS image sensor with NMOS-only global shutter and enhanced responsivity,” IEEE Trans. Electron. Dev.50(1), 57–62 (2003).
[CrossRef]

IEEE. Trans. Ind. Electron. (1)

F. J. Delgado, J. M. Quero, J. Garcia, C. L. Tarrida, P. R. Ortega, and S. Bermejo, “Accurate and Wide-Field-of-View MEMS-Based Sun Sensor for Industrial Applications,” IEEE. Trans. Ind. Electron.59(12), 4871–4880 (2012).
[CrossRef]

Meas. Sci. Technol. (1)

F. Xing, Z. You, G. Zhang, and J. Sun, “A novel active pixels sensor (APS) based sun sensor based on a feature extraction and image correlation (FEIC) technique,” Meas. Sci. Technol.19(12), 125203 (2008).

Opt. Express (1)

Proc. SPIE (1)

T. Iwata, “Precision attitude and position determination for the Advanced Land Observing Satellite (ALOS),” Proc. SPIE5659, 34–50 (2005).
[CrossRef]

Sensors (Basel) (2)

W. Zhang, W. Quan, and L. Guo, “Blurred Star Image Processing for Star Sensors under Dynamic Conditions,” Sensors (Basel)12(12), 6712–6726 (2012).
[CrossRef] [PubMed]

M. S. Wei, F. Xing, B. Li, and Z. You, “Investigation of Digital Sun Sensor Technology with an N-Shaped Slit Mask,” Sensors (Basel)11(12), 9764–9777 (2011).
[CrossRef] [PubMed]

Vac. Cryogenics (1)

H. Huo, M. Ma, Y. Li, and J. Qiu, “The application of MHD angular rate sensor in aerospace,” Vac. Cryogenics17(2), 114–120 (2011).

Other (11)

E. H. Anderson, J. P. Fumo, and R. S. Erwin, “Satellite ultraquiet isolation technology experiment (SUITE),” in Proceedings of IEEE Conference on Aerospace (Institute of Electrical and Electronics Engineers, Big Sky, MT, 2000), pp. 299–313.

F. H. Bauer and W. Dellinger, “Gyroless fine pointing on small explorer spacecraft,” in Proceedings of the AIAA Guidance, Navigation and Control Conference, (American Institute of Aeronautics and Astronautics, Monterey, CA, 1993), pp. 492–506.
[CrossRef]

C. W. Hindman, S. L. Lacy, and N. Hatten, “Image Based Acquisition and Tracking for Multi-Access Laser Communications,” in Proceedings of IEEE Conference on Aerospace (Institute of Electrical and Electronics Engineers, Big Sky, MT, 2006), pp. 1–10.
[CrossRef]

S. Mobasser and C. C. Liebe, “MEMS based sun sensor on a chip,” in Proceedings of IEEE Conference on Control Applications (Institute of Electrical and Electronics Engineers, Istanbul, 2003), pp. 1483–1487.
[CrossRef]

C. W. de Boom, J. A. P. Leijtens, L. M. H. v.Duivenbode, and N. van der Heiden, “Micro digital sun sensor: System in a package,” in Proceedings of IEEE Conference on MEMS, NANO and Smart Systems (Institute of Electrical and Electronics Engineers, Banff, Alberta, 2004), pp. 322–328.
[CrossRef]

N. Xie, A. J. Theuwissen, B. Büttgen, H. Hakkesteegt, H. Jasen, and J. Leijtens, “Micro-digital sun sensor: An imaging sensor for space applications,” in Proceedings of IEEE Conference on Industrial Electronics (Institute of Electrical and Electronics Engineers, Bari, 2010), pp. 3362–3365.

C. De Boom and N. Van Der Heiden, “A novel digital sun sensor: Development and qualification for flight,” in Proceedings of 54th International Astronautical Congress, (International Astronautical Federation, Bermen, 2003), pp. 708–715.
[CrossRef]

C. Hersom, R. Berman, J. Shah, and R. Hornsey, “Digital sun sensor using multiple pinholes,” in Proceedings of CASI Conference on Astronautics, (Canadian Aeronautics and Space Institute, Ottawa, 2002), pp. 12–14.

R. Strietzel, “Two-dimensional calibration of a sun attitude sensor,” in Proceedings of 15th International Federation of Automatic Control Triennial World Congress on Automatic Control, (IFAC, Barcelona, 2002), pp. 259–264.

J. Gu, Y. Hitomi, T. Mitsunaga, and S. Nayar, “Coded rolling shutter photography: Flexible space-time sampling,” in Proceedings of IEEE Conference on Computational Photography (Institute of Electrical and Electronics Engineers, Bari, 2010), pp. 1–8.
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Figures (9)

Fig. 1
Fig. 1

Operation mode of GS and ERS.

Fig. 2
Fig. 2

Timing and operation flow of the ERS based digital sun sensor.

Fig. 3
Fig. 3

Schematic of FOV of the digital sun sensor without multiplexing detector (a) and with multiplexing detector (b).

Fig. 4
Fig. 4

The schematic of the mask design with detail view (a), the division of sub-FOVs (b) and sub-FOV discrimination (c).

Fig. 5
Fig. 5

Cross sectional view of the sun sensor

Fig. 6
Fig. 6

Prototype of the sun sensor.

Fig. 7
Fig. 7

Test system for the sun sensor prototype.

Fig. 8
Fig. 8

The sun spots image taken by CMOS detector at static state (a) and at dynamic state (b).

Fig. 9
Fig. 9

Error statistics of sun sensor performance test for 100 times.

Tables (2)

Tables Icon

Table 1 Location information of sun spots abstracted in ERS principle test

Tables Icon

Table 2 Performance of sun sensor

Equations (11)

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t FGS = t INT +n× t RD + t WT ,
t ERS = t INT + t RD + t WT .
t INT1 = t INT2 == t INTi == t INTn ,
t RI1 = t RI2 == t RIi == t RI(n1) ,
t RI = t RD ,
f ERS = m t FERS =m f FERS ,
t INT =(n1) t RD .
f ERS = m(n1) n 1 t INT m t INT .
d α = cos 2 α d Δl h ,
FOV=2arctan( l sensor 2h ),
FOV=2arctan( l pattern + l sensor 2h ),

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