# accelerometer accuracy determination

I was looking in to some accelerometer and wondering how I could determine the smallest acceleration change, certain sensors are able to detect. if I wanted to calculated this for example for this accelerometer can I just do it like this: Sensitivity:5 mV/g noise floor : 35 µV typical (12 mA)
35 *10^-3 /(5/9.81)=> 0.0392 m/s2 assuming we are in the Dynamic measuring range or am I over simplifying this this not really my area of expertise so I appreciate your help

edit1: back ground info

I’m an aerospace student trying to make a first rough estimation if it would make sense to install a basic of the shell accelerometer (low cost) in order to make a rough drag estimation of the drag acting on a satellite in LEO orbit ( +- 600km) in order to do this I’m interested Measurement level in m/s2 preferably. (the final goal of the mission is to measure temporal gravity changes with a COST GNSS receiver mounted on cube sate the accelerometer will be used to correct for drag) the accelerometer I have used in my question Is just an example ( the frequency range is way too high) I’m just trying to see how I would get an idea of the acceleration I would be able to measure

First of all, despite the initial paraphraph in Andy aka's answer, your use of 9.81 m/s^2 is correct (if not well explained): You correctly converted your sensor's output noise amplitude from voltage units to the corresponding noise amplitude in acceleration units. Where you seem to be stuck is how to make sense of it.

To use the output of your accelerometer, you will pass it through some kind of (likely digital) filter or other algorithm. After all, the direct output is an instantaneous acceleration where, as you calculated, the noise alone means any individual value on its own will typically be off by 4 mm/s^2 and hence larger than the deceleration due to the drag you are interested in. So how much can you lower this noise by making more than one measurement?

The most obvious thing would be to average measurements, but that may be more difficult than it sounds, unless you can guarantee that your sensor is always perfectly aligned with the motion of your satellite. However, it is something that can be calculated relatively easily, without referring to things you'll learn later in aerospace engineering. But since it should interest you, let me at least drop the keywords: I'm thinking about sensor fusion and Kalman filtering.

So let's hypothetically say you have one full orbit to determine your acceleration value (this won't work in practice due to sensor drift, see the next paragraph). Essentially, you will be integrating (or averaging) your sensor output. The noise level you will see depends on what the actual, frequency-dependent noise is after taking into account only the frequencies that pass through your (integrating or averaging) filter. Andy aka's answer tells you the answer for one specific case assuming you have white (frequency-independent) noise and a specific frequency cut-off value. A better prediction will take the frequency-dependence of the noise into account. Just remember to calculate in what makes physical sense, noise power (the squares of noise amplitude), and only convert to what makes sense to us electrical engineers after you're done calculating/filtering/integrating. That way you'll likely get the right result immediately and conveniently avoid having to ask "what is root-Hz, and how do you calculate with it." At sub-Hz frequencies, the frequency dependence of your noise will almost certainly be 1/f noise, and your accelerometer datasheet may actually list a value for it.

Now for the caveat: Your frequency range for using an entire orbit for averaging, sub-mHz, is so low that the noise will probably have an even worse frequency dependence than 1/f. Because it's just too slow to measure conveniently, engineers often invent other names for it, talking about drift instead. Of concern is both the kind of drift that a theoretical scientist might prefer to call some worse-than-1/f-noise and that induced by environmental factors like temperature changes. Have a look at what all of this does in your application (the relevant figures are likely specified in your accelerometer's datasheet as worst-case limits for temperature-output coupling and longterm drift). If you're clever, you may find ways to custom design an algorithm (or complicated nonlinear filter) that removes part of the drift by comparing "coming" and "going" parts of the orbit, or rotating the sensor to be in and then opposed to the direction of motion. At some point, knowing something about Kalman filters may help...

• thank you quick question sometimes I have sensitivity expressed in pc/g I guest they actually mean pC/g => Pico coulomb /g ? – sander Nov 22 '13 at 15:00
• regarding the filtering that’s something for later the first step was to find out if there was something in the acceptable price rang that could meet some requirements. – sander Nov 22 '13 at 15:08
• 1. (pC/g) I'm not sure. The only sensor type for which such a unit might make sense would be a piezoelectric accelerometer, and until I just started thinking and googling about it, I had no idea they existed. 2. (filtering) I am afraid that some kind of filtering will have to enter into your estimation of meeting or not meeting requirements, as reducing your frequency sensitivity from 10 kHz to 0.1 Hz might already gain as much a 2 orders of magnitude in noise amplitude---that alone might be the difference between unsuitable for your application and indeed adequate. – pyramids Nov 22 '13 at 15:40
• fortunately my professor will be back on Monday so I can ask him so more questions this is really a blind spot in my knowledge and the lack of data and clear explanation of the different between the different sensor types make it even more difficult. I was also think that it is probably a piezoelectric accelerometer but the fact they use a small c instaed of the big C for coulomb in the datasheet made me think it might be a different unit. – sander Nov 22 '13 at 15:52
• 2 looking at comparable mission they have Sensitivity Extended bandwidth between 1 hz and 10^-5 hz. thanks for helping me geting started – sander Nov 22 '13 at 15:57

No it doesn't work like that. Firstly you are using 9.81 in your equation and this is the gravitional force exerted by the earth on mass. This has nothing to do with measuring g-forces when a body is accelerating due to it spinning (for instance).

Secondly, the noise floor, I believe is the total noise produced across the full range of frequencies (1 Hz to 20 kHz) that the accelerometer can work with and can't be simply used to compare the signal you might get from say accelerating at a constant g in one direction or the other.

Thirdly, your question has the word "accuracy" and I think your calculations were aimed at measuring resolution - these are different things. For instance a 12-bit DAC has a resolution that is one in 4096 but it's accuracy may only be 1% - accuracy and resolution are not usually interchangeable.

If you had an experiment to determine the g-force on an object spinning at say 100 revs per second, you know that the frequency of the signal will be 100 Hz and you can apply filters to extract this signal and counteract the 35 uV broadband noise.

35 uV with a 20kHz bandwidth is about 247 nV per $\sqrt{Hz}$ and so if your filter has a dc to 200Hz bandwidth, the noise will be 3.5 uV. This is a lot different to comparing it with 35 uV.

• 1 thank you for your response I get that the Noise floor is for the full frequency rang I was kind of trying to calculated for the worst case scenario just trying to understand what all the unit stood for. what does 'g'then stand for in this case? let me maybe first sketch for a better understanding of what I’m trying to do tell you wath I’m using it for. – sander Nov 22 '13 at 11:58
• 2I’m an aerospace student trying to make a first rough estimation if it would make sense to install a basic of the shell accelerometer (low cost) in order to make a rough drag estimation of the drag acting on a satellite in LEO orbit ( +- 600km) in order to do this I’m interested Measurement level in m/s2 preferably. (the final goal of the mission is to measure temporal gravity changes with a COST GNSS receiver mounted on cube sate the accelerometer will be used to correct for drag) – sander Nov 22 '13 at 11:58
• 3the accelerometer I have used in my question Is just an example ( the frequency range is way too high) I’m just trying to see how I would get an idea of the acceleration I would be able to measure. I got a bunch of possible accelerometers with only limit information (same information as in the example) any idea how I should approach this. – sander Nov 22 '13 at 11:59
• I don't understand what you mean by drag. – Andy aka Nov 22 '13 at 17:16
• “drag’’ might have not been the best word for it in this case. what I meant by it are all non-gravity related disturbances (accelerations). we are still in top layer of the F layer of the ionosphere so really small aerodynamic drag, some magnetic drag, etc. – sander Nov 23 '13 at 10:05