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  • Kalman Filter Approach for Re-Eentry Predictions of Risk Objects with K-S Element Equations

    Paper number

    IAC-05-B6.3.05

    Author

    Dr. Ram Krishan Sharma, Indian Space Research Organisation (ISRO), India

    Coauthor

    Dr. Anil Kumar A. K., Indian Space Research Organisation (ISRO), India

    Year

    2005

    Abstract
    KALMAN FILTER APPROACH FOR RE-ENTRY PREDICTIONS OF RISK OBJECTS WITH K-S ELEMENT EQUATIONS
    
    Ram Krishan Sharma and A. K. Anilkumar
    Applied Mathematics Division,
    Vikram Sarabhai Space Centre,
    Thiruvananthapuram – 695 022, 
    Kerala, INDIA
    Tel. No. +91-471-2565629, Fax. No. +91-471-2704134
    
    ABSTRACT
    An accurate orbital re-entry prediction of the Earth’s satellites is an important activity in the area of space debris. The problem is quite difficult due to the fact that the non-spherical effects of the Earth’s gravitational field as well as the dissipative effects of the Earth’s atmosphere influence the satellite. The effects of the atmosphere are very difficult to determine since the atmospheric density, and hence the drag, undergoes large modelled fluctuations. This paper presents a newly proposed technique for the re-entry prediction using Kalman filter approach with constant gains that are based on a minimization of a suitable cost function derived out of estimated lifetime at different epochs of Two Line Elements (TLE) sets and the measurements such as apogee height and perigee height at the epochs. Prediction of the orbital lifetime and the propagation of the osculating orbital elements are carried out by utilizing the software ‘KSNUM’. The constant gains are estimated by minimizing the suitable objective function by Genetic algorithm. In KSNUM, the K-S element equations of motion are numerically integrated with a suitable integration step size with the 4th - order Runge-Kutta-Gill method till the end of the orbital life (90 km altitude), by including the Earth’s oblateness with J2 to J6 terms, and modeling the air drag forces through an analytical oblate diurnal atmosphere with the density scale height varying with altitude. Jacchia (1977) atmospheric model, which takes into consideration the epoch, daily solar flux (F10.7) and geomagnetic index (Ap), for computation of density and density scale height, is utilized. The method of the K-S total-energy element equations (Stiefel and Scheifele, 1971) is a powerful method for numerical solution with respect to any type of perturbing forces, as the equations are less sensitive to round-off and truncation errors in the numerical algorithm. These equations are everywhere regular in contrast with the classical Newtonian equations, which are singular at the collision of the two bodies. The equations are smoothed for eccentric orbits because eccentric anomaly is the independent variable. The states considered are the semi-major axis, eccentricity and ballistic coefficient (B = CD A/m). The measurements are the apogee height and perigee heights equivalent to semi-major axis and eccentricity.  The constant Kalman gains chosen as above are able to account for the modeling and measurement errors. The main contribution in this paper is the development of an objective function, which is a weighted function of the measurements, namely apogee height and perigee height, and the variation in the predicted re-entry at different TLE epochs. Comparisons of the present approach with some of the known re-entry predictions are provided.  The predicted re-entries were found to be all along quite close to the actual re-entry time, with quite less uncertainties bands on the predictions. 
    
    Refrences   
    
    Stiefel, E.L. and G.Scheifele, Linear and Regular Celestial Mechanics, Springer, Berlin, 1971.
     Jacchia, L. G., Thermospheric temperature, density and composition: new model, SAO SR 375, 1977.
    
    Abstract document

    IAC-05-B6.3.05.pdf

    Manuscript document

    IAC-05-B6.3.05.pdf (🔒 authorized access only).

    To get the manuscript, please contact IAF Secretariat.