Apparatus and method for determining orbit of geostationary satellite

• US 8,972,184 B2
• Filed: 03/14/2013
• Issued: 03/03/2015
• Est. Priority Date: 08/24/2012
• Status: Active Grant

• Current Assignee: Electronics and Telecommunications Research Institute
• Original Assignee: Electronics and Telecommunications Research Institute
• Inventors: Hwang, Yoo La, Lee, Byoung Sun
• Primary Examiner(s): Algahaim, Helal A
• Assistant Examiner(s): ISMAIL, MAHMOUD S
• Application Number:
  US13/829,662
• Publication Number:
  US 20140055299A1
• Time in Patent Office: 719 Days
• Field of Search: 701/213, 701/475, 701/531, 701/490, 455/13.1, 455/457, 342/357.77
• US Class Current: 701/531
• CPC Class Codes: G01S 19/14 specially adapted for specific applications
• CPC Class Codes: G01S 19/42 Determining position

Abstract

An apparatus and method for determining an orbit of a geostationary satellite is provided. The orbit of the geostationary satellite may be determined using at least one pseudo-range of the geostationary satellite calculated based on an orbit and a position of at least one global positioning system (GPS) satellite, position information of the geostationary satellite, and an angle between the geostationary satellite and each GPS satellite.

Claims

1. A method comprising:

calculating, by an apparatus, an orbit and a position of at least one global positioning system (GPS) satellite;

measuring, utilizing an antenna, position information of a geostationary satellite relative to a ground station;

calculating, by the apparatus, an angle between the geostationary satellite and each of the at least one GPS satellite based on the relation

θ

=cos<sup>−

1</sup>(cos Δ

α

cos Δ

θ

)

where Δ

α

denotes an azimuth difference between the geostationary satellite and each of the at least one GPS satellite, and Δ

θ

denotes an elevation difference between the geostationary satellite and each of the at least one GPS satellite;

calculating, by the apparatus, at least one pseudo-range of the geostationary satellite using the orbit and the position of the at least one GPS satellite, the position information of the geostationary satellite, and the angle between the geostationary satellite and each of the at least one GPS satellite; and

determining, by the apparatus, an orbit of the geostationary satellite using the pseudo-range and a weight value for geometric dilution of precision (GDOP) of position data.

2. The method of claim 1, wherein the position information of the geostationary satellite comprises a distance, an azimuth angle, and an elevation angle of the geostationary satellite relative to the ground station.

3. The method of claim 1, wherein the measuring further comprises measuring the position information of the geostationary satellite through antenna tracking from the ground station.

4. The method of claim 1, further comprising calculating an ephemeris of a GPS satellite matching a time interval involved in measuring the position information of the geostationary satellite, among the at least one GPS satellite.

5. The method of claim 1, further comprising calculating an elevation difference between the geostationary satellite and each of the at least one GPS satellite relative to the ground station.

6. The method of claim 1, further comprising calculating the at least one pseudo-range r_i based on the relation

r_i=√

{square root over ((R_is)²+r²−

2r(R_is)cos θ

_i)}{square root over ((R_is)²+r²−

2r(R_is)cos θ

_i)}

where θ

_i denotes an angle between the geostationary satellite and an ith GPS satellite, r_i denotes a distance between the ground station and the geostationary satellite, and R_is corresponds to a distance between the ground station and the ith GPS satellite.

7. The method of claim 1, further comprising calculating the at least one pseudo-range r_i based on the relation

r_i=squrt((X−

x_i)^2+(Y−

y_i)^2+(Z−

z_i)^2)

where X, Y, and Z denote location coordinates of the geostationary satellite, and x_i, y_i, and z_i correspond to location coordinates of an ith GPS satellite.

8. The method of claim 7, further comprising calculating a matrix A_i for a relationship between the geostationary satellite and an ith GPS satellite based on the relation

9. The method of claim 8, further comprising determining location coordinates X of the geostationary satellite based on the relation

X=(A_i^TWA_i)⁻

1A_i^Tr_i

where W denotes a weight value for geometric dilution of precision (GDOP), and r_i corresponds to the at least one pseudo-range.

10. A method comprising:

calculating, by an apparatus, an orbit and a position of at least one global positioning system (GPS) satellite;

measuring, utilizing an antenna, position information of a geostationary satellite relative to a ground station;

determining, by a measuring apparatus, at least one elevation difference between the geostationary satellite and the at least one GPS satellite relative to the ground station, respectively;

removing, by the apparatus, at least one error in the at least one elevation difference, wherein the at least one error is at least one of a satellite clock error, an ionosphere error, a convention zone error, and a multipath error, yielding at least one corrected elevation difference;

calculating, by the apparatus, an angle between the geostationary satellite and the at least one GPS satellite based on the relation

θ

=cos<sup>−

1</sup>(cos Δ

α

cos Δ

θ

)

where Δ

α

denotes an azimuth difference between the geostationary satellite and each of the at least one GPS satellite, and Δ

θ

denotes an elevation difference between the geostationary satellite and each of the at least one GPS satellite;

estimating, by the apparatus, at least one pseudo-range of the geostationary satellite using the orbit and the position of the at least one GPS satellite, the position information of the geostationary satellite, the at least one corrected elevation difference, and the angle between the geostationary satellite and each of the at least one GPS satellite; and

determining, by the apparatus, an orbit of the geostationary satellite using the pseudo-range.

11. The method of claim 10, wherein the position information of the geostationary satellite comprises a distance, an azimuth angle, and an elevation angle of the geostationary satellite relative to the ground station.

12. The method of claim 10, further comprising calculating an ephemeris of a first GPS satellite matching a time interval involved in measuring the position information of the geostationary satellite, among the at least one GPS satellite.

13. The method of claim 10, wherein the calculating of the at least one pseudo-range comprises calculating the at least one pseudo-range r_i based on the relation

r_i=√

{square root over ((R_is)²+r²−

2r(R_is)cos θ

_i)}{square root over ((R_is)²+r²−

2r(R_is)cos θ

_i)}

where θ

_i denotes an angle between the geostationary satellite and an ith GPS satellite, r_i denotes a distance between the ground station and the geostationary satellite, and R_is corresponds to a distance between the ground station and the ith GPS satellite.

14. The method of claim 10, wherein the calculating of the at least one pseudo-range comprises calculating the at least one pseudo-range r_i based on the relation

r_i=squrt((X−

x_i)^2+(Y−

y_i)^2+(Z−

z_i)^2)

where X, Y, and Z denote location coordinates of the geostationary satellite, and x_i, y_i, and z_i correspond to location coordinates of an ith GPS satellite.

15. The method of claim 14, wherein the calculating of the at least one pseudo-range further comprises calculating a matrix A_i for a relationship between the geostationary satellite and an ith GPS satellite based on the relation

16. The method of claim 15, wherein the determining of the orbit of the geostationary satellite comprises determining location coordinates X of the geostationary satellite based on the relation

X=(A_i^TWA_i)⁻

1A_i^Tr_i

where W denotes a weight value for geometric dilution of precision (GDOP), and r_i corresponds to the at least one pseudo-range.

17. A method comprising:

calculating, by an apparatus, an orbit and a position of at least one global positioning system (GPS) satellite;

measuring, utilizing an antenna, position information of a geostationary satellite relative to a ground station;

calculating, by the apparatus, an angle between the geostationary satellite and each of the at least one GPS satellite;

calculating, by the apparatus, at least one pseudo-range of the geostationary satellite using the orbit and the position of the at least one GPS satellite, the position information of the geostationary satellite, and the angle between the geostationary satellite and each of the at least one GPS satellite, based on the relation

r_i=√

{square root over ((R_is)²+r²−

2r(R_is)cos θ

_i)}{square root over ((R_is)²+r²−

2r(R_is)cos θ

_i)}

where θ

_i denotes an angle between the geostationary satellite and an ith GPS satellite, r_i denotes a distance between the ground station and the geostationary satellite, and R_is corresponds to a distance between the ground station and the ith GPS satellite; and

determining, by the apparatus, an orbit of the geostationary satellite using the pseudo-range and a weight value for geometric dilution of precision (GDOP) of position data.

18. The method of claim 17, wherein the position information of the geostationary satellite comprises a distance, an azimuth angle, and an elevation angle of the geostationary satellite relative to the ground station.

19. The method of claim 17, wherein the measuring further comprises measuring the position information of the geostationary satellite through antenna tracking from the ground station.

20. The method of claim 17, further comprising calculating an ephemeris of a GPS satellite matching a time interval involved in measuring the position information of the geostationary satellite, among the at least one GPS satellite.

21. The method of claim 17, further comprising calculating an elevation difference between the geostationary satellite and each of the at least one GPS satellite relative to the ground station.

22. The method of claim 17, further comprising calculating the angle θ

between the geostationary satellite and each of the at least one GPS satellite based on the relation

θ

=cos<sup>−

1</sup>(cos Δ

α

cos Δ

θ

)

where Δ

α

denotes an azimuth difference between the geostationary satellite and the at least one GPS satellite, and Δ

θ

denotes an elevation difference between the geostationary satellite and each of the at least one GPS satellite.

23. The method of claim 17, further comprising calculating the at least one pseudo-range r_i based on the relation

r_i=squrt((X−

x_i)^2+(Y−

y_i)^2+(Z−

z_i)^2)

where X, Y, and Z denote location coordinates of the geostationary satellite, and x_i, y_i, and z_i correspond to location coordinates of an ith GPS satellite.

24. The method of claim 23, further comprising calculating a matrix A_i for a relationship between the geostationary satellite and an ith GPS satellite based on the relation

25. The method of claim 24, further comprising determining location coordinates X of the geostationary satellite based on the relation

X=(A_i^TWA_i)⁻

1A_i^Tr_i

where W denotes a weight value for geometric dilution of precision (GDOP), and r_i corresponds to the at least one pseudo-range.