Estimation of Simplified General Perturbations model 4 orbital elements from global positioning system data by invasive weed optimization algorithm

Abstract

In this paper, a novel approach is introduced to estimate the North American Aerospace Defense Command (NORAD)-type two-line elements (TLE) data based on the invasive weed optimization (IWO) method, which is a stochastic numerical optimization algorithm inspired by colonizing weeds. Many satellite applications use the NORAD Simplified General Perturbations model 4 (SGP4) for satellite position prediction. The input of SGP4 consists of TLEs which are published via NORAD freely through the worldwide web. Since it is generated irregular, a new TLE which is independent of NORAD is required to access data about the satellite location each time. An alternative to independent computation of TLE can be made feasible by the existing emersion of GPS receivers in the space project and using IWO. Using this stochastic algorithm increases the success probability to find a more accurate TLE. The estimation is performed for six Keplerian orbital elements and SGP4 drag term (B*) by using the satellite position data achieved from the GPS receiver. Also, the feasibility study of the concept is performed by using the actual GPS data of CHAMP and corresponding NORAD TLE. The time length of the GPS data used in the estimation is studied for practical application purposes. The results show that 500 samples of position data, with 1-min time intervals, are sufficient to keep the position error within 10 km in 3 days after epoch time in orbital elements with known drag term estimation. Moreover, for orbital elements with drag term estimation, 1000 samples of position, with 1-min time intervals, are sufficient to keep the position error within 15 km in 3 days after epoch time. If there is no considerable constraint for position-data time-length or time available for performing numerical computations, the estimated TLE can be more accurate than corresponding NORAD TLE.

Keywords

CHAMP global positioning system invasive weed optimization North American Aerospace Defense Command Simplified General Perturbations model 4 two-line element

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References

Greene M and Zee R. Increasing the accuracy of orbital position information from NORAD SGP4 using intermittent GPS readings. In: 23rd annual AIAA/USU conference on small satellite, UT, USA, 2009.

Jochim

Gill

Montenbruck

. GPS based onboard and onground orbit operations for small satellites. Acta Astronaut 1996; 39(9): 917–922.

Zhou YF. A study for orbit representation and simplified orbit determination methods. Central South University of Technology, China, 2003.

Gill

Montenbruck

Kayal

. The BIRD satellite mission as a milestone toward GPS-based autonomous navigation. Navigation-los angeles Washington 2001; 48(2): 69–76.

Kozai

. The motion of a close earth satellite. Astronomical J 1959; 64: 367–367.

Lane MH and Hoots FR. General perturbations theories derived from the 1965 lane drag theory. No. Astrodynamic-sr-2. Aerospace defense command peterson afb co office of astrodynamics, 1979.

Brouwer

. Solution of the problem of artificial satellite theory without drag. Astronomical J 1959; 64: 378–378.

Montenbruck

. A state filter for use with analytical orbit models of low earth satellites. Aerospace Sci Technol 2000; 4(4): 277–287.

http://www.n2yo.com (accessed 24 May 2014).

10.

Kahr

Montenbruck

O’Keefe

KPG

. Estimation and analysis of two-line elements for small satellites. J Spacecraft Rockets 2013; 50(2): 433–439.

11.

Nasirian

Saleh

Shojaee

. Simulation of tracking process and communication link with satellite. J Space Sci Technol 2010; 2(5): 56–51.

12.

Früh

Schildknecht

. Accuracy of two-line-element data for geostationary and high-eccentricity orbits. J Guidance Control Dyn 2012; 35(5): 1483–1491.

13.

Levit

Marshall

. Improved orbit predictions using two-line elements. Adv Space Res 2011; 62(7): 1107–1115.

14.

Wang

Liu

Zhang

. Propagation errors analysis of TLE data. Adv Space Res 2009; 43.7: 1065–1069.

15.

Boyce WH. Examination of NORAD TLE accuracy using the iridium constellation. In: Proceedings of the AAS/AIAA space flight mechanics meeting, Maui, HI, 8–12 February, vol. 119, 2004.

16.

Chan Joseph

Navarro

. Comparisons of NORAD two-line elements with INTELSAT orbital elements. Space Debris 2001; 473: 771–779.

17.

Bolandi

Larki

Abedi

. GPS based onboard orbit determination system providing fault management features for a LEO satellite. J Navigation 2013; 66: 539–559.

18.

Ernandes

. Vector to two-line elements (VEC2TLE) orbit computation software. AMSAT J 1994; 17: 26–26.

19.

Lee

B-S

. NORAD TLE conversion from osculating orbital element. J Astronomy Space Sci 2002; 19: 395–402.

20.

Cho

C-H

Lee

. NORAD TLE type orbit determination of LEO satellites using GPS navigation solutions. J Astronomy Space Sci 2002; 19(3): 197–206.

21.

Gill E, Montenbruck O. Terzibaschian, an autonomous navigation system for the German small satellite mission BIRD. In: AAS/AIAA space flight mechanics meeting, Clearwater, FL, 23–26 January 2000.

22.

Mehrabian

Lucas

. A novel numerical optimization algorithm inspired from weed colonization. Ecol Inform 2006; 1(4): 355–366.

23.

Sedighy

Mallahzadeh

Soleimani

. Optimization of printed Yagi antenna using invasive weed optimization (IWO). Antennas Wireless Propagation Lett IEEE 2010; 9: 1275–1278.

24.

Khakzad H, Sedighy SH, Khalaj Amirhosseini M. Compact step impedance transmission line (SITL) low pass filter by using. ACES 2013; 28(3): 228–233.

25.

Mallahzadeh

Es' haghi

Alipour

. Design of an E-shaped MIMO antenna using IWO algorithm for wireless application at 5.8 GHz. Prog Electromagn Res 2009; 90: 187–203.

26.

Mallahzadeh

Oraizi

Davoodi-Rad

. Application of the invasive weed optimization technique for antenna configurations. Prog Electromagn Res 2008; 79: 137–150.

27.

Pahlavani

Delavar

Frank

. Using a modified invasive weed optimization algorithm for a personalized urban multi-criteria path optimization problem. Int J Appl Earth Observation Geoinform 2012; 18: 313–328.

28.

Nikoofard

. Multiobjective invasive weed optimization: application to analysis of Pareto improvement models in electricity markets. Appl Soft Comput 2012; 12.1: 100–112.

29.

Mehrabian

Yousefi-Koma

. A novel technique for optimal placement of piezoelectric actuators on smart structures. J Franklin Inst 2011; 348(1): 12–23.

30.

Pourjafari

Mojallali

. Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering. Swarm Evol Comput 2012; 4: 33–43.

31.

Kundu

Suresh

Ghosh

. Multi-objective optimization with artificial weed colonies. Inf Sci 2011; 181(12): 2441–2454.

32.

ftp://sayatnova.jpl.nasa.gov/pub/genesis/ (accessed 24 May 2014).

33.

Vallado DA. Fundamentals of astrodynamics and applications. Vol. 12. Springer, 2001, Microcosm.

34.

Battin RH. An introduction to the mathematics and methods of astrodynamics. AIAA, 1999, New York.

35.

Hoots FR and Roehrich RL. Models for propagation of NORAD element sets. Project Spacecraft Report No. 3, Aerospace Defense Command, United States Air Force, 1980.

36.

Baranov IV. SGP4 propagation program design and validation. University of Waterloo, 2009.

37.

Bandyopadhyay

Sharma

Adimurthy

. Space debris proximity analysis in powered and orbital phases during satellite launch. Adv Space Res 2004; 34(5): 1125–1129.

38.

Byoung

Jae

. Estimation of the sgp4 drag term from two osculating orbit states. J Astronomy Space Sci 2003; 20(1): 11–20.

39.

Curtis H. Orbital mechanics for engineering students. 2nd ed. Butterworth-Heinemann: Elsevier, 2009.

40.