With the advent of multiple Global Navigation Satellite Systems (GNSS), the feasibility of navigation using GNSS observations beyond Low Earth Orbits has been explored in recent years. An estimation algorithm is one of the critical components of a well-designed navigation system, and it must be judiciously chosen for a particular application. The non-linearity of spacecraft dynamics in a highly elliptical orbit is high and if the apogee of the orbit is higher than Medium Earth Orbit, the state vector of the spacecraft motion may be only partially observable due to the limited availability and low Signal power of GNSS signals. In this scenario, variants of the Unscented Kalman Filter (UKF) can provide better estimation performance. In this paper, GNSS-based navigation of spacecraft in elliptical and High Earth Orbits using Single Propagation type UKFs are demonstrated. These estimation algorithms provide UKF like estimation performance and require around 90% less computation time than the conventional UKF.