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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.

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  • $\begingroup$ One search term you could try is "sensor fusion". $\endgroup$ – hotpaw2 Mar 22 '16 at 7:12
  • $\begingroup$ 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? $\endgroup$ – Hilmar Mar 22 '16 at 12:37
  • $\begingroup$ Do you try to combine them online, or does offline suffice? $\endgroup$ – Laurent Duval Mar 22 '16 at 19:43
  • $\begingroup$ 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. $\endgroup$ – Adel Mar 23 '16 at 8:06
  • $\begingroup$ any answer please!! $\endgroup$ – Adel Mar 25 '16 at 4:45
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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 $z_C$.

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  • $\begingroup$ 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. $\endgroup$ – Adel Mar 22 '16 at 6:52
  • $\begingroup$ In that case you can mimic kalman filter like thing. What about, $\endgroup$ – user3219492 Mar 22 '16 at 7:04
  • $\begingroup$ What about, combined = (set A value)*(1/variance of set A) + (set B value)*(1/variance of set B) ??? $\endgroup$ – user3219492 Mar 22 '16 at 7:11
  • $\begingroup$ May I know why the answer has been down voted and the reason why it may not work... $\endgroup$ – user3219492 Mar 22 '16 at 8:12
  • $\begingroup$ I am waiting to know too, not sure why somebody voted down. $\endgroup$ – Adel Mar 22 '16 at 8:23

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