Minimize VNREDSat-1

VNREDSat-1A (Vietnam Natural Resources, Environment and Disaster-monitoring Satellite-1A)

Overview    Spacecraft    Launch    Mission Status    Sensor Complement   Ground Segment   References

VNREDSat-1A is an Earth observation satellite mission of STI-VAST (Space Technology Institute-Vietnam Academy of Science and Technology), funded in part by MOST (Ministry of Science and Technology). In August 2010, a contract for the development of VNREDSat-1 (space and ground segments) was awarded to EADS Astrium SAS of France. This follows from an intergovernmental agreement on space cooperation between France and Vietnam in November 2009, in which the French government affirmed its commitment to building a closer partnership with Vietnam in the domain of science and technology. 1) 2) 3) 4)

This program is the result of an initiative by the Vietnamese government to create a space infrastructure enabling the country to better monitor and study the effects of climate change, predict and take measures to prevent natural disasters, and optimize the management of its natural resources. More generally, it will allow the country to advance its knowledge in the field of space engineering and benefit from the ensuing economic and technological growth to create new employment opportunities.

STI-VAST is the national institution responsible for setting up Vietnam's Earth observation space program. The VNREDSat-1 program is the result of an initiative by the Vietnamese government to create a space infrastructure enabling the country to better monitor and study the effects of climate change, predict and take measures to prevent natural disasters, and optimize the management of its natural resources.

The space system comprises an optical satellite capable of capturing images with a resolution of 2.5 m, the associated ground control, image receiving and processing stations, and a cooperation and training program for the Vietnamese engineers. The satellite will be built in Toulouse by an Astrium team including 15 Vietnamese engineers. The goal of the trainee program is to develop an indigenous capability to build future small satellites in Vietnam. On August 15, 2011, the CTT team of 15 VN engineers arrived in Toulouse for training. 5) 6) 7) 8)

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Figure 1: Photo of the VAST delegation and STI trainees of the VNREDSat-1 project at Astrium, Toulouse, 2011(image credit: STI-VAST, Ref. 33)

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Figure 2: Illustration of the VNREDSAT-1 spacecraft (image credit: EADS Astrium)


Spacecraft:

The microsatellite uses the AstroSat-100 bus of EADS Astrium (a customized Myriade platform version of AlSat-2 heritage). The spacecraft structure is a box of size: 60 cm x 60 cm x 100 cm. Figure 3 shows the general platform mechanical accommodation; all 4 panels of the structure fold out during integration, allowing easy access to all equipment during platform integration. This accommodation allows a good level of flexibility with respect to the payload size.

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Figure 3: General view of the AstroSat-100 platform with mechanical accommodation of elements (image credit: Astrium SAS) 9)

VNREDSAT-1 is 3-axis stabilized. Attitude sensing is provided by 3 sun sensors, a star sensor, a magnetometer, and an IRU (Inertial Measurement Unit); actuation is provided by 4 reaction wheels (each of 0.12 Nms) and magnetorquers. A GPS receiver is used for onboard location and time services. The spacecraft has a body-pointing capability of ±30º in cross-track.

The EPS (Electric Power Subsystem) features an AsGa solar array providing a power of 180 W (EOL). In addition, there is a Li-ion battery of 15 Ah capacity. - A T805 serves as OBC (Onboard Computer). A hydrazine propulsion subsystem (N2H4, ΔV = 70 m/s) is being used for on-orbit maintenance. The spacecraft has a mass of ~130 kg. The design life is 5 years.

RF communications: VNREDSat-1 features an onboard SSR (Solid-State Recorder) of 64 Gbit capacity. Communications are provided in X-band with a downlink rate of 60 Mbit/s. For TT&C support, 2 S-band transceivers are utilized (CCSDS, 20 kbit/s TC, 25-384 kbit/s TM).

 

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Figure 4: Alternate view of the VNREDSat-1 spacecraft and some components (image credit: STI-VAST)

Spacecraft structure

Aluminum bus structure, Size: 60 cm x 60 cm x 100 cm

AOCS (Attitude & Orbit Control Subsystem)

- Magnetic autonomous acquisition
- Gyro-stellar attitude determination
- Autonomous GPS position determination
- 3-axis attitude control
- 4 Reaction Wheels (0.12 Nms)
- 1 hydrazine tank, 4.7 kg capacity (~65 m/s); 4 thrusters 1 N configuration

EPS (Electric Power Subsystem)

- Power generated by one deployable solar array (GaAs; 180 W EOL)
- 1 Li-ion battery 15 Ah BOL; PCDU (Power & Control Distribution Unit)

On-board data handling

- On-board computer (T805, 1 Gbit DRAM/EDAC, 8 Mbit Flash EEPROM)
- 2 S-band transceivers for communication (CCSDS, 20 kbit/s TC, 25-384 kbit/s TM)

Payload data management

- X band downlink: 60 Mbit/s
- Storage memory : 64 to 79 Gbit BOL – no compression

Spacecraft performance

- Spacecraft launch mass: ~130 kg
- Spacecraft agility: ±30º roll in 90 s
- Localization performance: 300 m CE90 (Circular Error of 90%)
- Spacecraft design life = 5 years

Table 1: Overview of spacecraft parameters

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Figure 5: Photo of VNREDSat-1 during AIT (Assembly, Integration and Test) of the spacecraft (image credit: Astrium, STI-VAST)

 

Launch: The VNREDSat-1A spacecraft was launched on May 7, 2013 as a secondary payload to the PROBA-V minisatellite of ESA and CNES. The launch vehicle was Vega (with Arianespace as launch provider); the launch site was the Guiana Space Center, Kourou. This marks the first VERTA (Vega Research, Technology and Accompaniment) flight of VEGA (designated as VERTA-1). Arianespace and Astrium signed the launch contract on January 4, 2013 for the VNREDSat-1A Earth observation satellite, on behalf of VAST (Vietnamese Academy of Science and Technology). 10) 11) 12) 13) 14) 15)

PROBA-V will ride in the upper position of the Vespa adapter, and VNREDSat-1A will sit in the lower position in the structure. The upper stage of the Vega vehicle is a liquid propulsion module with multiple re-ignition capability. The VNREDSat-1A spacecraft will be deployed last after re-ignition of the Vega upper stage.

Orbit of PROBA-V: Sun-synchronous orbit, altitude = 820 km, inclination = 98.8º, LTDN (Local Time on Descending Node) = 10:30 hours (with a drift limited between 10:30 and 11:30 AM during the mission lifetime).

Orbit of VNREDSat-1: Sun-synchronous orbit, altitude =704 km, inclination = 98.7º. VNREDSat-1A was released 1 hour 57 minutes into flight. ESTCube-1 was ejected from its dispenser three minutes later. A last burn will now place the spent upper stage on a trajectory that ensures a safe reentry that complies with new debris mitigation regulations.

 


 

Mission status:

• In March 2016, the VNREDSat-1 minisatellite is in its 3rd year on orbit, operating nominally.

• As of October 31, 2015, the VNREDSat-1 satellite has captured and downlinked more than 42,000 scenes over ASEAN countries. In Vietnam, VNREDSat‐1 satellite has captured and downlinked more than 23,000 scenes. 16)

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Figure 6: Acquired imagery of VNREDSat-1 over Vietnam as of October 31, 2015 (image credit: STI, VAST)

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Figure 7: Image of VNREDSat-1 captured flood in the Quang Ninh province on August 7, 2015 (Image credit: STI,VAST)

• Dec. 2014: The VNREDSat-1 spacecraft and its payload are operating nominally. As of Oct. 31, 2014, VNREDSat-1 had acquired and downlinked a total of 28,285 scenes ((14,171 MS and 14,114 PAN). 17)

• On 29, 2014, VNREDSat-1 had to conduct another orbit maneuver to avoid the possibility of a collision with an object in the already amended orbit. VAST received a JSpOC warning on Aug. 27 for a probable collision with an object. With the recent experience in solving this situation, the Center for Small Satellite Control and Exploitation of STI immediately reviewed the analysis, and made the necessary adjustments to the orbit of the satellite from the ground control station at Hoa Lac. - This was the second such successful adjustment to the VNREDSat-1orbit in the last two weeks. 18)

• On August 15, 2014, VNREDSat-1 conducted operations to adjust its orbit to avoid the possibility of collision with an object flying across the current orbit with a velocity of approximately 14 km/s. After receiving notification from the U.S JSpOC (Joint Space Operations Center) which warned of the possibility of a collision between VNREDSat-1 and an unknown object at 8:26 pm (Vietnam time) on August 15th 2014, with a probability of collision calculated at 0.297% (with the collision probability of 0.1%, it is necessary to adjust orbit), the Center for Small Satellite Control and Exploitation of STI (Space Technology Institute) of Vietnam conducted analysis and accessed the situation, consulted experts from Astrium (France), Satellite Control Center of GISTDA (Thailand) and decided to adjust the orbit to ensure absolutely safety for the VNREDSat-1. 19)

- A command to VNREDSat-1 was sent via the Kiruna station in Sweden to adjust the orbit, thereby avoiding a possible collision.

In January 2014, a contract was signed in Hanoi in the presence of Vietnamese and the Belgium governments officials, when Spacebel, a SME (Small and Medium sized manufacturing Enterprise) of Liège, signed a contract for the supply to Vietnam of an Earth observation system "Made in Belgium" named VNREDSat-1b (Vietnam Natural Resources, Environment & Disaster Monitoring satellite-1b) for VAST (Vietnam Academy of Science and Technology), Hanoi. The satellite will be launched in 2017.

The industrial consortium under the leadership of Spacebel comprises several Belgian space companies: AMOS, QinetiQ Space, Deltatec, the Space Centre of Liege, and VITO, which will gather their skills to develop and validate the flight segment as well as the ground segment. The project also includes a training program, in partnership with the University of Liège, intended for the Vietnamese engineers in charge of the satellite data reception and analysis.

Based on ESA's PROBA satellite platform, VNREDSat-1b will be placed in a sun-synchronous orbit for a 5 year observation mission. It will allow Vietnam to strengthen its autonomy in the monitoring of phenomena such as deforestation, river and maritime pollution, flooding, agricultural and fishery activities, the effects of climate change, etc. With this information, the Vietnamese authorities will be able to better adapt their environmental management policy to the specific needs of the country.

Table 2: Spacebel and VAST signed a contract for the follow-up mission VNREDSat-1b 20)

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Figure 8: Acquired imagery of VNREDSat-1 after 1 year of operations (image credit: STI, VAST)

• VNREDSat-1 is operating nominally in 2014. Launched in May 2013, VNREDSat-1 took 20,463 images of Earth's surface in the year 2013, including 9,631 panchromatic and 10,832 multispectral images. 21) 22)

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Figure 9: Image of the Chaparrastique Volcano erupting near San Miguel City, in the East of El Salvador, acquired with VNREDSat-1 on Jan. 1, 2014 (image credit: VAST)

• December 12, 2013: After three months of taking over the control of VNREDSat -1 satellite from the French partner, Vietnam can fully master this Earth observing system. According to VAST, the total number of photos that the satellite captured, processed and stored is 18,427 with dimensions of 17.5 km x 17.5 km, including 9,817 MS (Multispectral) pictures and 8,610 panchromatic pictures. Every three days, the system provides a collection of photos of Vietnam's territory and territorial waters. The photos are handed over to the user groups. 23)

• On September 4, 2013, VAST (Vietnam Academy of Science and Technology) and Astrium SAS,France, the general contractor, held a ceremony to hand over control of VNREDSat-1 to Vietnam for official operation and exploitation. The ceremony was held after three months of stable operations since Vietnam's first Earth-observation satellite, VNREDSat-1, was successfully launched into orbit on May 7, 2013. 24)

As of September 1, 2013, VNREDSat-1 satellite had captured, transmitted, received and processed 9,271 images, of which 909 featured Vietnamese territory, mainly serving the goals of adjusting and accessing the system's effectiveness. In addition, images captured by VNREDSat-1 also met timely special requirements of national security and defense. The project's success has helped Vietnam to become the fifth ASEAN (Association of Southeast Asian Nations) nation to own a remote sensing satellite.

• June 10, 2013: The VNREDSat-1 spacecraft is operating nominally (the transmissions between the spacecraft and the ground receiving stations are stable). Everyday, experts continue making plans to take imagery from all over the world, including Vietnam, to test and access the system, especially accessing the optical system. Analyses of both the initial data and system performance have yielded positive results. The satellite will be used for natural resources management, disaster monitoring, and other activities after a three-month system assessment. 25)

• May 13, 2013: Having reached its operational orbit, the satellite has now entered its in-orbit test phase. Official delivery to the customer, the Vietnam Academy of Science and Technologies (VAST), will take place at the end of this phase. Astrium delivers first VNREDSat-1 images just 48 hours after launch. 26) 27)

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Figure 10: Image of Hanoi's Red River, Vietnam at a resolution of 2.5 m observed just 48 hours after launch on May 9, 2013 (image credit: Astrium)

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Figure 11: VNREDSat-1 image of the city of Melbourne, Australia, acquired on May 9, 2013 (image credit: Astrium)

 


 

Sensor complement: (NAOMI)

NAOMI (New AstroSat Optical Modular Instrument):

NAOMI (of AlSat-2, SSOT and SPOT-6 heritage) is a high-resolution pushbroom imager designed and developed at EADS Astrium SAS: The instrument design is mainly driven by mission parameters and detector characteristics. The TDI (Time Delay Integration) mode in the Pan band enables to reduce the pupil size for a given GSD (Ground Sample Distance). The pupil diameter is no more sized to comply with SNR requirements which can be achieved by increasing the number of TDI stages and is only driven by MTF (Modulation Transfer Function) requirement.

The telescope is based on a Korsch combination, offering a simple, compact concept. The detector, space qualified, includes on the same die one TDI matrix of 7000 pixels for the panchromatic channel, and four lines of 1750 pixels for the multispectral bands. The detector exhibits excellent characteristics that significantly contribute to the instrument very high optical performance.

The optical assembly is based on a Korsch-type telescope including three aspheric mirrors and two folding mirrors.

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Figure 12: Illustration of the optical concept of the Korsch telescope (image credit: EADS Astrium)

The detection chain is made of three main parts: the detectors, the Front End Electronics Module (F2EM) and the Video Electronics (MEV) which are part of the IEU (Imaging and Electronics Unit). The PAN + XS focal planes are the heart of the detection chain.

Focal plane is based on a customized high performance detector architecture developed by e2v for Astrium (proprietary architecture). It takes benefit of all the heritage and skills acquired in CCD architecture definition and in operating with the ultimate conditions of speed and performances. The result of this customization offers an unrivalled level of integration and performances. All the stringent constraints of dynamic range optimization and power consumption reduction have been mastered with less than 1 watt detector dissipation.

The imager provides imagery of 2.5 m in Pan and 4 multispectral (MS) bands of 10 m GSD. The optics system of the instrument employs state-of-the-art techniques such as SiC-100 (silicon carbide) material for the mirrors and the telescope structure, specific detectors, and a modular video chain design. 28) 29)

The SiC primary mirror is mounted onto the baseplate via three isostatic Invar blades (FormoSat-2 heritage) providing good thermal decoupling between the telescope and the primary mirror. The secondary, tertiary and folding mirrors are also made of SiC. They have an incorporated isostatic foot. This type of attachment device, minimizes the number of interfaces, ensures a good thermal coupling with the structure, simplifies the integration, and improves the overall stability.

The MEV (Module Electronique Video) is the backend part of the NAOMI detection electronics. The MEV provides the F2EM with the primary power supplies and clocks necessary to front-end operation. The video signal from the F2EM is received, adapted and digitally converted to 12 bit in the MEV. The resulting data, rounded down to 10 useful bit, are then transmitted to the digital functions of the NIEU to be real-time processed and stored into the mass memory for further downlink.

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Figure 13: PAN+XS focal plane architecture (image credit: EADS Astrium)

The focal plane accommodates detectors, filters and front-end electronics. All the elements are designed to cope with a multi-modules implementation capability.

The detection chain is made of three main parts: the detectors, the F2EM (Front End Electronics Module) and the MEV (Module Electronique Video - Video Electronics Module) which are part of the NIEU (NAOMI Imaging and Electronics Unit).

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Figure 14: Overview of NAOMI detection chain (image credit: EADS Astrium SAS)

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Figure 15: Photo of the area array detector (image credit: EADS Astrium)

Instrument type

Pushbroom imager

Optics

- Korsch telescope with a TMA design in SiC (folded by 2 flat mirrors)
- Aperture diameter = 200 mm
- F/16
- Focal length = 5131 mm

Spectral band (Pan)

0.45-0.75 µm

MS (Multispectral bands), 4

B1): 0.45-0.52 µm (blue
B2): 0.53-060 µm (green
B3: 0.62-0.69 µm (red)
B4: 0.76-0.89 µm (NIR)
The multispectral bands can be matched to suit customer needs

GSD (Ground Sample Distance)

2.5 m Pan at nadir
10 m MS (or MX) at nadir

Detectors (provided by ev2 of Chelmsford, UK)

Silicon area array with 7000 pixels Pan, 1750 pixels in each MS band
Pixel pitch = 12 µm x 12 µm (Pan), Pixel pitch = 48 µm x 48 µm for MS

TDI (Time Delay Integration)

The Pan band offers TDI services for SNR improvement of the signal

Swath width

17.5 km at nadir

FOR (Field of Regard)

±30º (spacecraft tilting capability about nadir for event monitoring)

Data quantization

12 bit (10 bit coding for downlink)

Instrument mass

18.5 kg (including video electronics mass memory and payload internal harness). The camera has a mass of 13 kg.

Table 3: Specification of the NAOMI instrument 30) 31)

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Figure 16: Spectral response of the optical filters (image credit: EADS Astrium SAS)

The primary structure is composed of three main parts: a baseplate, a cylindrical tube with a spider supporting the secondary mirror, and the focal plane. The structure also supports thermal MLI (Multi Layer Insulation).

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Figure 17: Mechanical architecture of NAOMI (image credit: EADS Astrium SAS)

 


 

Ground segment:

Ground segment installation (provided by Astrium): 32) 33)

• X-band receiving station of the Vietnam NRSC (National Remote Sensing Center). MONRE (Ministry of Natural Resources and Environment) of Vietnam is funding the station.

• S-band control station of VAST (Vietnam Academy of Science and Technology) .

The overall control ground segment architecture of VNREDSat-1 is based on a well-mastered and efficient design which has been used and improved on several Astrium export programs - like the ground segments for the missions: THEOS (Thailand), AlSat-2 (Algeria), and SSOT (Chile). 34) 35)

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Figure 18: Overview of the VNREDSAT-1 project elements (image credit: STI-VAST) 36)

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Figure 19: Photos of the Vietnam's NRSC ground station (left) and its antenna (right), image credit: STI-VAST

 


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7) "Pham Anh Tuan, "Recent Development of Space Technology in Vietnam," URL: http://www.smi-online.co.uk/_Media/docs/PhamAnhTuan.pdf

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9) Charles Koeck, Didier Radola, "AstroSAT 100 : Microsatellite solution for high resolution remote sensing systems," Proceedings of IAC 2011 (62nd International Astronautical Congress), Cape Town, South Africa, Oct. 3-7, 2011, paper: IAC-11-B4.4.4

10) "ESA's Vega launcher scores new success with PROBA-V," ESA press release No 12-2013, May 7, 2013, URL: http://www.esa.int/For_Media/Press_Releases/ESA_s_Vega_launcher_scores-new_success_with_Proba-V

11) "Arianespace to launch VNREDSat-1A built by Astrium for Vietnam," Arianespace Press Release, January 4, 2013, URL: http://www.arianespace.com/news-press-release/2013/1-4-2013-VNREDSat-1A-contract.asp

12) "VNREDSat-1 successfully launched into orbit," VAST, May 21, 2013, URL: http://www.vast.ac.vn/en/index.php?option=com_content&view=article&id=1230:vnredsat-1-successfully-launched-into-orbit&catid=5:activities&Itemid=18

13) Stephen Clark, "Vietnamese satellite booked for second Vega launch," Spaceflight Now, January 4, 2013, URL: http://www.spaceflightnow.com/news/n1301/04vnredsat1a/#.UOwGWpGQk9Y

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16) Doan Minh Chung, Director STI and VAST, "Space Technology Development in Vietnam 2014-2015," APRSAF-22/Vietnam Country Report, APRSAF-22 (Asia-Pacific Regional Space Agency Forum), Bali, Indonesia, December 1-4, 2015, URL: http://www.aprsaf.org/annual_meetings/aprsaf22/pdf/program/plenary/D3_1500-Vietnam.pdf

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18) Tuyet Nhung, "VNREDSat-1 orbit second adjusted to avoid collision," VAST, October 2, 2014, URL: http://www.vast.ac.vn/en/news/science-and-technology-news/1665-vnredsat-1-orbit-second-adjusted-to-avoid-collision

19) Tuyet Nhung, "VNREDSat-1 urgent orbit adjustment to avoid collision with object," VAST, Sept. 29, 2014, URL: http://www.vast.ac.vn/en/news/science-and-technology-news/1664-vnredsat-1-urgent-orbit-adjustment-to-avoid-collision-with-object

20) "A First for Belgium: Commercial Contract for the Supply of a Satellite Signed SPACEBEL to Vietnam," SPACEBEL, Jan. 21, 2014, URL: http://www.spacebel.be/a-first-for-belgium-commercial-contract-for-the-supply-of-a-satellite-signed-spacebel-to-vietnam/

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24) "VNREDSat-1 satellite system handover ceremony," VAST, Sept. 16, 2013, URL: http://www.vast.ac.vn/en/news/activities/1537-vnredsat-1-satellite-system-handover-ceremony

25) "Several photos from VNREDSat-1 satellite," VAST, June 10, 2013, URL: http://www.vast.ac.vn/en/index.php?option=com_content&view=article&id=1234:several-photos-from-vnredsat-1-satellite&catid=28:national-science-and-technogory-news&Itemid=34

26) "First VNREDSat-1 images," Astrium, May 13, 2013, URL: http://www.astrium.eads.net/en/news2/first-vnredsat-1-images.html

27) http://www.vast.ac.vn/en/index.php?option=com_content&view=article&id=1234:several-photos-from-vnredsat-1-satellite&catid=28:national-science-and-technogory-news&Itemid=34

28) Eric Maliet, Laure Brooker, Dominique Pawlak, "Global High Resolution Imaging for new Markets," Proceedings of the 59th IAC (International Astronautical Congress), Glasgow, Scotland, UK, Sept. 29 to Oct. 3, 2008, IAC-08-B1.2.7

29) P. Luquet, A. Chikouche, A. B Benbouzid, J. J. Arnoux, E. Chinal, C Massol, P. Rouchit(1), S. de Zotti, "NAOMI instrument: a product line of compact & versatile cameras designed for high resolution missions in Earth observation," Proceedings of the 7th ICSO (International Conference on Space Optics) 2008, Toulouse, France, Oct. 14-17, 2008

30) Information provided by Hervé Lambert of EADS Astrium SAS, Toulouse, France

31) "e2v image sensors launched into space on board Vietnam's first optical Earth observation satellite," Space Daily, May 14, 2013, URL: http://www.spacedaily.com/reports/e2v_image_sensors_launched_into_space_on-board_Vietnams_first_optical_Earth_observation_satellite_999.html

32) Trong Tuyen Bui, Minh Tuan Pham, "VNREDSat-1 Vietnam's first earth observation satellite system," Sept. 19, 2012, URL: http://www.asiageospatialforum.org/2012/proceeding/bui%20trong%20Tuyen.pps

33) Doan Minh Chung, "Space Technology Development of Vietnam in 2011-2012," Proceedings of APRSAF-19 (The 19th Session of the Asia-Pacific Regional Space Agency Forum), Kuala Lumpur, Malaysia, December 11-14, 2012, URL: http://www.aprsaf.org/annual_meetings/aprsaf19/pdf/program/day3/13_Country-20report_VIETNAM.pdf

34) Jean-Michel Dussauze, Alain Gevert, Jacques Troillard, "AstroTerra Control Ground Segment: Cost reduction through automation and product line," Proceedings of the SpaceOps 2010 Conference, Huntsville, ALA, USA, April 25-30, 2010, paper: AIAA 2010-1916

35) Jean-Michel Dussauze, Gérard Feltrin, Jacques Troillard, "AstroTerra Control Ground Segment: Operations concept and implementation," Proceedings of SpaceOps 2012, The 12th International Conference on Space Operations, Stockholm, Sweden, June 11-15, 2012

36) Nguyen Khoa Son, "Space Technology in Vietnam: 2010 Country Report," APRSAF-17 (17th Session of the Asia-Pacific Regional Space Agency Forum), Melbourne, Australia, Nov. 23-26, 2010, URL: http://www.aprsaf.org/data/aprsaf17_data/D3-1330_N_Khoa_Son.pdf
 


The information compiled and edited in this article was provided by Herbert J. Kramer from his documentation of: "Observation of the Earth and Its Environment: Survey of Missions and Sensors" (Springer Verlag) as well as many other sources after the publication of the 4th edition in 2002. - Comments and corrections to this article are always welcome for further updates (herb.kramer@gmx.net).

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