# Combination of acceleration signals

have xA, yA, and zA acceleration signals collected from a smartphone and I call it: set A and I also have xB, yB, and zB same acceleration signals from smartwatch: let's call this set B. I need to combine them together because I am trying to find which combination of devices give optimal result in regard to detect the subject's activities. I have more than these two sensors but I just ask about these two and then if I got an answer then apply it on all. I will combine smartphone with smartwatch, smartphone with sensor placed on upper arm and etc. However, I am not sure if this is right to do or doing this is eliminating necessary signals. Also, is this way better than only taking the average of these two sets. (A + B)/2 ?

Thank you

• Without knowing exactly what you are trying to figure out with the data, it's difficult to determine how best to combine the two sources. However, if you integrate both, they should match over longer intervals (a person's arm and phone don't typically wander from each other), which might be helpful. Mar 26, 2016 at 0:52

## 2 Answers

Acceleration is a 3-vector, so yes, a plausible 50-50 estimate is $$\mathbf{a} = 0.5 \mathbf{a}_1 + 0.5 \mathbf{a}_2 = \sum_{i} w_i\mathbf{a}_i$$ If you have a reason to believe more in one measurement than the other, you can use different weights, as long as they sum up to 1: $$\sum w_i = 1$$ Of course, make sure that these vectors live in the same coordinate reference frame. If there is a rotational offset, then you have to convert it from one to the other.

You should assume that it will be quite an ordeal to meld the two data sets. Not only will the two platforms have different orientations, the centrifugal force produced on the smartwatch during vigorous motion will make it difficult to align the two reference axes, since you won't be able to use the g vector as an alignment tool. Even if you can recover the g vector, the two systems can still be rotated around that axis. If you have to ask about this, I'm dubious that you have the modelling skills to pull it off.

• first, I uniformly sample the collected raw acceleration, and then to overcome orientation issue, I discount the orientation and derive a net acceleration independent of orientation by using the magnitude of the acceleration by Euclidean norm.
– Adel
Mar 27, 2016 at 0:41