Abstract
The bidirectional steering between two accelerated partners sharing initially different classes of entangled states is discussed. Due to the decoherence, the steerability and its degree decrease either as the acceleration increases or the partners share initially a small amount of quantum correlations. The possibility of increasing the steerability is investigated by applying the filtering process. Our results show that by increasing the filtering strength, one can improve the upper bounds of the steerability and the range of acceleration at which the steerability is possible. Steering large coherent states is much better than steering less coherent ones.