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.