# Combination of accelation signals from two devices

I have $x_A$, $y_A$, and $z_A$ acceleration signals collected from a smartphone and I call it: set $A$ and I also have $x_B$, $y_B$, and $z_B$ same acceleration signals from smartwatch: let's call this set $B$. I need to combine them together to obtain set $C$, but since I don't have good knowledge in signal processing I am not sure if it is this logically correct to combine them and take the average of them, or any other way should I follow to have one set of signals instead of having two separate sets?

How to select the set if it is possible? The signals are raw data.

• One search term you could try is "sensor fusion". Mar 22 '16 at 7:12
• What are you trying to achieve? You have the movement of the watch and the movement of the phone. You try combine them to get the movement of what exactly? Mar 22 '16 at 12:37
• Do you try to combine them online, or does offline suffice? Mar 22 '16 at 19:43
• 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. Regarding the online or offline not sure which to use, but after collecting the raw data I want to know if it is better to do the combination after or before extracting features.
Mar 23 '16 at 8:06
Mar 25 '16 at 4:45

May be you can find variance of acceleration along x,y, and z direction in SET A and in set B separately and choose the the device which has least variance.

As this Wikipedia page suggests, you can combine the two by weighting by their respective variances.

So, to get $x_C$ simply: $$x_C = \frac{1}{\sigma_1^{-2} + \sigma_2^{-2}} \left( \frac{x_A}{\sigma_1^2} + \frac{x_B}{\sigma_2^2}\right)$$

Putting some numbers on this, suppose $\sigma^2_1 = 1$ and $\sigma^2_2 = 0.5$, then $$\sigma_3^2 = \frac{1}{\sigma_1^{-2} + \sigma_2^{-2}} = \frac{1}{1 + 2} = \frac{1}{3}$$ which is a lower variance than either of the individual measurements.

Use the same process to find $y_C$ and $z_C$.

• thank you for your comment, but I need to have both and I want to find a way to combine them and to see how can they give me same result when they are combined comparing to the individual results. What I'm doing is that I am detecting activities from both the smartphone and the smartwatch, and I am able to detect the right activity when using each device's data separate and now I want to know how to combine their signals and run my algorithm to see if it can detect the right activities or not.