The vital sign monitoring through Impulse Radio Ultra-Wide Band (IR-UWB) radar provides continuous assessment of a patient's respiration and heart rates in a non-invasive manner. In this paper, IR UWB radar is used for monitoring respiration and the human heart rate. The breathing and heart rate frequencies are extracted from the signal reflected from the human body. A Kalman filter is applied to reduce the measurement noise from the vital signal. An algorithm is presented to separate the heart rate signal from the breathing harmonics. An auto-correlation based technique is applied for detecting random body movements (RBM) during the measurement process. Experiments were performed in different scenarios in order to show the validity of the algorithm. The vital signs were estimated for the signal reflected from the chest, as well as from the back side of the body in different experiments. The results from both scenarios are compared for respiration and heartbeat estimation accuracy.