How to find out if any signal has a noise signal and if so in what range?

Hi guys,

I have an accelerometer signal and how do I know if there is no noise signal in this signal. Also, if there is noise, in what frequency range was it?

[Walter Roberson]

A rule of thumb:

If you can afford to buy the accelerometer for personal use, without charging it as a business expense... then the signal probably has noise.

https://en.wikipedia.org/wiki/Inertial_measurement_unit#Performance

A very wide variety of IMUs exists, depending on application types, with performance ranging:[12]

from 0.1°/s to 0.001°/h for gyroscope

from 100 mg to 10 µg for accelerometers.

To get a rough idea, this means that, for a single, uncorrected accelerometer, the cheapest (at 100 mg) loses its ability to give 50-meter accuracy after around 10 seconds, while the best accelerometer (at 10 µg) loses its 50-meter accuracy after around 17 minutes.

[Mehmet Rizelioglu]

Frankly, I did not fully understand.

Answer 1

[Matt Gaidica]

Mehmet, do you have a recording from the accelerometer at rest and is that the condition which you want to test for 'noise' against? I think you might find some help here: https://stackoverflow.com/questions/67992691/how-to-calculate-95-confidence-level-of-fourier-transform-in-python

If it were me, I might record 1,000 seconds from the accelerometer, split that into 1-second recordings, perform an FFT on each, and create my own confidence interval for each frequency bin (this, of course, depends on your sampling rate). Then you could easily apply your own criteria to determine if there is some extra signal and at which frequencies it exceeds some confidence/alpha/p-value of your choosing.

[Mehmet Rizelioglu]

Dear Gaidica;

Yes, even when the system is stationary, the accelerometer give values difference than zero and i think they are noise signal and may be other noise signal too.

Also, frankly, i didn't fully understand what your mentioned above. if you want i can send you my accelerometer values with about 25 second for better understanding.

thanks in advance..

[Walter Roberson]

Yes, even when the system is stationary, the accelerometer give values difference than zero

Yes .

This is normal for accelerometers .

Imagine that you have an accelerometer that can measure down to 1/100 g. Imagine that due to random vibrations in the environment, it receives a 1/100 g jolt along the x axes. Now imagine that it receives two 1/200 g jots back in the other direction as it restores. 1/100 +x, 2*1/200 -x, total force is 0. But... it can't register those 1/200 jolts, because the smallest it can register is 1/100 -- so all it can tell you is +1/100 x.

You might say, "Okay, bad luck there, but surely at some later time, if the vibrations are random and unbiased, it will end up with a similar situation but just in the opposite direction!". Perhaps -- but in the meantime it had the same kind of thing in the -y direction, so after the combination you might be measured as back to x 0 but you are not back to y 0.

If you think about this... the system becomes equivalent to a Random Walk in 3D. And an interesting thing about Random Walks is that although in 2D random walks do statistically eventually return to the origin... in 3D, random walks do not statistically eventually return to the origin. Or rather it has only about a 34% chance of returning to the origin. https://mathworld.wolfram.com/RandomWalk3-Dimensional.html

If you have a minimum measurement threshold, but your random contributions are continuous and their sub-measurement values add up, then you will have measurement drift.

[Matt Gaidica]

Mehmet, I would be happy to look at your data. Please include sampling rate, and if you have both conditions—with and without noise—that would help.

[Mehmet Rizelioglu]

Dear Gaidica;

I have sent you both FFT and PSD results of my accelerometer data. I am also posting my 12 second output data file.

[Matt Gaidica]

Is this just one axis of the accelerometer? Can you describe what condition you are testing for 'noise'?

[Mehmet Rizelioglu]

Yes, they are datas of the z-axe and i don't know how i can find noise datas.

[Matt Gaidica]

Mehmet, you need to describe your application in detail. I think we are all a bit confused about what you mean by 'noise'.

[Mehmet Rizelioglu]

The data I send to you is a normal data I received from the accelerometer (in the z direction) and I don't know if there is a noise signal in this data. I ask how can I understand this?

[Matt Gaidica]

We don't know what you mean by noise. An accelerometer will normally have some flucuation in its signal, which you can compare with the datasheet to determine if it is within specification. If your 'noise' is some type of regular frequency or vibration, you need to capture data at rest and then compare it to the potentially noisy signal to determine if it is above your expected threshold.

[Mehmet Rizelioglu]

Unwanted data may also occur, apart from the values that must be present when electronic devices are collecting data. Undesired data can corrupt real data and prevent clean data retrieval. How can I detect unwanted data that may occur in every electronic device? I don't know if I could explain

[Image Analyst]

@Mehmet Rizelioglu did you see my suggestion below? Alternatively, can you attach two or more accelerometers to your object and average their values to try to beat down the noise?

[Mehmet Rizelioglu]

I understand bit because i am new here

Answer 2

[Walter Roberson]

I have an accelerometer signal and how do I know if there is no noise signal in this signal.

There is noise in all accelerometer signals, even the very best of them.

You cannot use only an accelerometer for accurate "dead reckoning": you need an Inertial Navigation System (INS) for that, and it takes a fair bit of work to combine information from multiple sensor types in order to get accurate position information. https://en.wikipedia.org/wiki/Inertial_navigation_system#Drift_rate

If you ever see a manufacturer claim that they have "no" noise in their accelerometers, then they are... mistaken.

Answer 3

[Image Analyst]

Yes, your accelerometer has noise -- all instruments do.

You can look at the signal spectrum with the device not moving. Presumably this signal is just all noise. Use fft() or pwelch(). However the noise may be different when it's still versus when it's moving. So then do that again with the accelerometer moving in a typical motion that you will use. Compare the two spectra and see what frequency range they are different in. Attach your signals if you need more help.

[Mehmet Rizelioglu]

Hi, not moving as 2 seconds, then starts moving. i have sent you my data's FFT and PSD. I would be very grateful if you could take a look at it in your free time.