Probabilistic Optical and Radar Initial Orbit Determination

Future space surveillance requires dealing with uncertainties directly in the initial orbit determination phase. An approach based on Taylor differential algebra is proposed to both solve the initial orbit determination problem and to map uncertainties from the observables space into the orbital elements space. This is achieved by approximating in Taylor series the general formula for probability density function mapping through nonlinear transformations. In this way, the mapping is obtained in an elegant and general fashion. The proposed approach is applied to both angles-only and two position vectors initial orbit determination for objects in low Earth orbit and geostationary equatorial orbit.