Heart rate (HR) monitoring using photoplethysmographic (PPG) signals recorded from wearers' wrist greatly facilitates design of wearable devices and maximizes user experience. However, placing PPG sensors in wrist causes much stronger and complicated motion artifacts (MA) due to loose interface between sensors and skin. Therefore, developing robust HR estimation algorithms for wrist-type PPG signals has significant commercial values. In this paper, we propose a robust HR estimation algorithm for wrist-type PPG signals using multiple reference adaptive noise cancellation (ANC) technique-termed here as "MURAD." The main challenge of using ANC for MA reduction is to devise a qualified reference noise signal (RNS) to the adaptive filter. We propose a novel solution by using four RNSs, namely, the three-axis accelerometer data and the difference signal between the two PPG signals. For each RNS, we get a different version of the cleaned PPG signal. Then, a set of probable HR values is estimated using all of the cleaned PPG signals, and then, the value that is closest to the estimated HR of the previous time window is chosen to be the HR estimate of the current window. Then, some peak verification techniques are employed to ensure accurate HR estimations. The proposed technique gives lower average absolute error compared to state-of-the art methods. So, MURAD method provides a promising solution to the challenge of HR monitoring using PPG in wearable devices during severe MA conditions.