Future space surveillance requires dealing with uncertainties directly in the initial orbit determination phase. We propose an approach based on Taylor differential algebra to both solve the initial orbit determination (IOD) 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 pdf mapping through nonlinear transformations. In this way the mapping is obtained in an elegant and general fashion. The proposed approach is applied to both anglesonly and two position vectors IOD for objects in LEO and GEO.