We develop a drift-free roll and pitch attitude estimation scheme for monopedal jumping robots. The estimator uses only onboard rate gyroscopes and encoders and does not rely on external sensing or processing. It is capable of recovering from attitude estimate disturbances and, together with onboard velocity estimation, enables fully autonomous stable hopping control. The estimator performs well on a small untethered robot capable of large jumps and extreme stance accelerations. We demonstrate that the robot can follow a rectangular path using onboard dead-reckoning with less than 2 meters of drift over 200 seconds and 300 jumps covering 60 m. We also demonstrate that the robot can operate untethered outdoors under human wireless joystick direction.