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I've had the basics of signal in university but little real-life practice. I've got an acceleration sensor with a digital output signal (signed 16 bit value). This signal is a little noisy. The standard deviation is about 20 (referenced to the full 2¹⁶-1 scale of the sensor).

On the hardware I have, there are two of these sensors present. Is it somehow possible to merge the signals of both sensors, in order to reduce the noise?

The reason I'm asking this is because the noise of the two sensors should be uncorrelated (at least in theory) whereas the acceleration signal is correlated. Is there a way to reduce the noise?

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Assuming that the sensors share the same characteristics, have the same timing (acceleration signals are aligned), the model with $y_1= x + n_1$ and $y_2= x + n_2$, $n_1$ and $n_2$ being uncorrelated noises of the same power, averaging them is a way to reduce the noise. The theory that asymptotically, averaging $N$ sensors reduce the variance by a factor of $N$, hence the noise amplitude by $\sqrt{N}$. For small $N=2$, and with quantization, one should not expect too much (since the asymptotic formula is not valid), but this can be tried, you may have nice surprise. If noise powers are different, this method can be improved to take this into account.

Further, this problem can be addressed as a form of source separation, for which many methods have been developed (independent component analysis, Non-negative matrix factorization, low-rank decomposition to name a few). The choice will depend on how much more information you have, and your algorithmic constraints.

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  • $\begingroup$ I tried to take the liberty of correcting your indexing error, i.e., $y_n = x + n_2$ to read $y_2 = x + n_2$. But Stackexchange wants at least six characters worth of edit. $\endgroup$ – TimWescott Oct 31 '19 at 16:39
  • $\begingroup$ Well spotted, and done $\endgroup$ – Laurent Duval Nov 1 '19 at 7:39

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