Combining accelerometer signals

The goal of this step is to increase the signal strength of the breathing signal by identifying the strongest axis from each accelerometer, and adding the two axes together (Supplementary Algorithm ²). This procedure involves three steps:

Step 1: Orienting sensor axis. We first orient an axis such that inhalation is seen as an increasing signal amplitude while exhalation is seen as a decreasing amplitude. We observe that breathing peaks caused by inhalation are larger in magnitude and prominence than exhalation. Based on this observation we check if the magnitude and prominence of maximums is greater than those of its minimums during a period of baseline breathing. If the maximums are larger, the axis is correctly oriented, otherwise, we negate the signal in order to orient it correctly.

Step 2: Selecting sensor axes. Next, we select the axis with highest signal strength from each of the two accelerometers. We define signal strength for an axis as the difference between the highest inhalation peak and lowest exhalation peak. If the signal strength for an axis is below a threshold signal_thresh, no axis is selected for that accelerometer. signal_thresh was selected as the minimum signal strength under which the signal appeared too close to the noise floor. In our implementation, we set signal_thresh to 5.

Step 3: Adding axes across accelerometers. The final step is to add the axis on the two accelerometers that are identified in the previous step. This addition produces a single stream with a higher signal strength than any one of the accelerometer signals since they were oriented in the same way in Step 1. This combined breathing signal is then used to compute breathing rate below.