Photoplethysmography (PPG) is a noninvasive optical signal that measures the change in blood volume. This particular signal can be interpreted to yield heart rate (HR) information which is commonly used in medical settings and diagnostics through wearable devices. The noninvasive nature of the measurement of the signal however causes it to be susceptible to noise sources such as motion artifacts (MA). This research starts by describing an end-to-end embedded HR estimation system that leverages noisy PPG and accelerometer data through machine learning (ML) to estimate HR. Through embedded ML for HR estimation, the limitations and challenges are highlighted, and a different HR estimation method is proposed. Next, a point-based value iteration (PBVI) framework is proposed to optimally select HR estimation filters based on the observed user activity. Lastly, the underlying dynamics of the PPG are explored in order to create a sparse dynamic expression of the PPG signal, which can be used to simulate PPG data to improve ML or remove MA from PPG.