Wrong implementation of Kalman estimation using DSST propagator
Current implementation of orbit determination using both DSST propagator and Extended Kalman Filter (EKF) is not correct. Orbit determination based on semi-analytical satellite theory and recursive filter must be done using a specific algorithm: the Extended Semi-analytical Kalman Filter (ESKF). The EKF algorithm needs to re-initialize the orbital state at each observation epoch. However, the time difference between two observations is usually much smaller than the DSST step size (e.g., half a day). ESKF reconciles the conflicting goal of both theories.
Current implementation (DSSTKalmanModel) must be removed and replace by a new implementation.
For more details about the equations and the theory [1] [2] [3]
[1]: Taylor S. P., Semi-analytical Satellite Theory and Sequential Estimation, Master of Science Thesis, Department of Mechanical Engineering, MIT, September, 1981
[2]: Wagner E. A., Application of the Extended Semianalytical Kalman Filter to Synchronous Orbits, Master of Science Thesis, Department of Aeronautics and Astronautics, MIT, June, 1983
[3]: Folcik Z., Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling, Master of Sci- ence Thesis, Department of Aeronautics and Astronautics, MIT, June, 2008