There are several difficulties worth overcoming in how to implement precise orbit determination (POD) for low Earth orbiters (LEO) using only onboard BDS data rather than GPS. The toughest problems are the obvious errors in the final BDS orbit products according to the relative motionless geometric condition between GEO and ground static tracking stations, uneven distribution of stations, and inaccurate BDS satellite models and so on. In order to make the positive contribution of BDS GEO to LEO POD be available, the systematic errors in daily GEO orbit products are modelled as daily constant biases in along-track and cross-track in POD process. The test results show that the posteriori residuals for GEO observations can be reduced to several millimeters and the LEO POD products are improved to centimeter-level with respect to the orbits obtained by excluding GEO. Furthermore, we analyze and assess the impacts of the day boundary discontinuities (DBD) existed in BDS GEO, IGSO and MEO orbit products on LEO POD. Two optimized strategies are designed to weaken the adverse influences of DBDs on poor POD accuracy around the connection point between two consecutive days. The first method is extending the POD arc length and use more BDS observations in order to enhance the strength of solution. The second is rebuilding the original orbit products by applying the high precise dynamic orbit fitting and prediction procedure, hence the orbit interpolation at signal sending moment will not be associated with the BDS orbit products for the previous and next day. The LEO POD experiment results indicate that both of the above methods can improve the POD precision effectively and the later method plays the most important role.