<p>Considering the contact between robot feet and the ground is unpredictable in unstructured terrains, robots require fast and accurate contact detection capability. This paper presents a contact detection method through estimating external force that benefits from compensating friction torque and driving torque effectively. For estimating external force, a new estimation method for joint angular velocity/acceleration is proposed. Furthermore, filter parameters are selected theoretically based on the leg control model, which achieves the optimal solution of the parameters. A control compensation strategy of the low-velocity zone of the motor is also implemented for optimizing the estimation of contact force. In contrast to the classic generalized momentum method, the proposed method allows high bandwidth estimation. The proposed contact detection method and the angular velocity/acceleration estimation method using only discrete position feedback information are verified on the developed quadruped robot platform SCIT Dog.</p>