Application of the Kalman Filter to Orbit Determination
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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The paper presents such a method by applying Kalman Filter theory to determine the position and velocity of near-earth satellites using data from a fixed observer on the Earth. The vehicle equations of motion are linearized in a Taylor Series expansion. The nominal states, position and velocity, are determined by integrating the nonlinear equations of motion, and the linear filter theory is used to estimate the errors in these states. The linear estimated errors are added to the nominal states to obtain an updated trajectory which is used as the starting point on a new nominal for the next integration. Actual tracking data from four different satellites are used in the study. Convergence of the error estimates to values less than 0.1 per cent of the best estimates of position and velocity is obtained within 50-250 seconds from the time of the initial radar contact. The program is capable of integrating for over 80 seconds with no tendency to diverge. The rate of convergence is related to the initial guess of the error covariance matrix, along with the measurement accuracy of the tracking stations. Results are presented in both tabular and graphical form.
- Spacecraft Trajectories and Reentry