Non-contact and continuous heart rate measurement using Doppler radar is important for various healthcare applications. In this paper, we propose a precise heart rate measurement method assisted by machine learning based sleep posture estimation. Machine learning is used for processing time-domain signal of the Doppler radar. Doppler radar has attracted much attention due to its non-contact to the subject feature. Moreover, it will not encroach into the privacy of the subject compared to image sensors. The method proposed in this paper automatically removes the data from the raw signal while the patient is moving or is not staying on the bed. This method based on machine learning uses simple features to reduce the computational cost thereby enabling real-time application. The sleeping posture was detected with an accuracy of 88.5%, and the error ratios of heart rate estimation were reduced by 15.2% in a sleep laboratory testing on 6 subjects.