The use of breath detection in vehicles can reduce the number of vehicular accidents caused by drivers in poor physical condition. Prior studies of contactless respiration detection mainly targeted a static person. However, there are emerging applications to sense a driver, with emphasis on contactless methods. For example, being able to detect a driver's respiration while driving by using a vehicular Wi-Fi system can significantly enhance driving safety. The sensing system can be mounted on the back of the driver's seat, and it can sense the tiny chest displacement of the driver via Wi-Fi signals. The body displacement and car vibrations could introduce significant noise in the sensed signal. The noise then needs to be filtered to obtain the driver's respiration. In this work, the noise in the sensed signal is proposed to be reduced using a Huber Kalman filter to restore the original respiration curve. Through several experiments in terms of different drivers, different car models, multiple passengers, and abnormal breathing, we demonstrate the accuracy and robustness of the Huber Kalman filter in driver's respiration.