# Normalization of Accelerometer Data

I have two different boards, one from TI and one from ST Microelectronics. Both these boards have one accelerometer of different brand. These two accelerometer sensors have different sensitivity.

I take the boards and give each a sudden upward and downward motion, one by one.

I get two graphs for such motions, which shows me the point on time axis where the sudden motion was imparted.

Ultimately I have to find cross correlation of these two data. In theory the cross correlation should have a high peak, because I gave same kind of motion to the two boards.

My friend says I should first normalize by energy. Can someone help me understand what do we mean by normalization with respect to energy? I guess it is something about making the two data equivalent so that an apple::apple comparison can be made.

Can someone help me understand this normalization?

• Basic principle - how do ensure that both accelerometers are subjected to an identical stimulus. Moving something in roughly the same way doesn't cut it for accurate measurement. – JIm Dearden Jan 2 '15 at 11:31
• Build a test jig that subjects the DUT board to a specific acceleration stimulus? Use a desk drawer as linear slide, and use a spring to close with repeatable force? – MarkU Jan 2 '15 at 11:37
• Better yet build a test jig that has both of the accelerometer boards side by side and subject both boards to the same stimulus and capture data from both at the same time. – Michael Karas Jan 2 '15 at 11:58
• Start with converting each board's output to g's. Then they are apples to apples. This is covered on most datasheets for accelerometers. – caveman Jan 2 '15 at 13:10

the point is: what do you want to compare? of course the two graphs you obtain should have a similar shape, but it could be that you will need some arrangement if you need to compare the values.

I don't know what your friend meant with "energy", but he is absolutely right when he speaks about normalisation. Let's imagine you want to compare the sensisivity of the two accelerometer: you need to have the data belonging to the same interval. the output interval depends on several things like accelerometer itself, ADC resolution, maybe scale settings and so on. in that case, you should normalise on "output dynamic" or "output range".

If your problem is more general, let say is "what is the normalisation?", imagine the situation I described above, and suppose you have the data from the first accelerometer coming from a 10bit ADC, and from the second one coming from a 12 bit ADC.

The first bunch of data will belong to the [0,1023] inverval, the second one to the [0, 4095] interval. In this case, if we suppose that both accelerometers have the same sensitivity and max acceleration range, when the body is moved at 75% of his maximum acceleration the first one will give you 75% of 1023, the second one 75% of 4095...these two data represent the same acceleration but are clearly different.

To compare mathematically the two bunches of data, in this case, you should just make the ranges equal with some operation that is called "normalisation". In this case, you could simply use the range of the first accelerometer as "normalised range" and divide all the data coming from the second one by 4, or use float numbers and divide the first by 1023, the second by 4095 normalising to the normalised range [0, 1].

hope this helps Cristiano

The easiest way to compare the sensitivities is to orient them so they see the earth's gravity (close enough to 1g for most purposes)- get the maximum possible reading- and then invert the accelerometers and repeat. If you subtract the two quantities for each accelerometer, the bias cancels out and you'll get the 'gain' for a 2g acceleration. This can be done statically, which eliminates any response time complexities.

I suspect your friend is talking about compensating for the response time differences by looking a the area under the curve, so that if the response is smeared out over time due to low pass filtering or digital artifacts you'll be able to compare apples to apples.