# How are units of noise measurement related to units of a sensor's data measurement?

I'm trying to understand how noise is represented for accelerometers, gyroscopes, and magnetometers so that I can match the requirements of my project with the standard specs of these sensors.

I want the output of a 3 axis inertial sensor to be values in meters/sec/sec, gauss, and radians/sec for each axis, and noise to be represented by a range around the true value (so X as in +/- X m/s/s, gauss, and radians/sec) for accelerometers, magnetometers, and gyroscopes respectively. Switching out gauss for teslas, meters for feet, radians for degrees, etc. would all be fine.

After looking at a few datasheets, I'm surprised to find that...

What do these units mean, and how do they (or can they) translate into what I want?

• @Ian Shouldn’t ‘mu’ or u be 10^-6 That is in ms^-2 it will be 0.0000098 ms^-2 for 1 ug – Mithun varma diddi Oct 16 '17 at 22:22
• I'm not sure I understand your comment, and I think @Robz is the one you should be addressing it to. (I don't see what part of the question you're referring to.) – Ian Oct 17 '17 at 14:14

"LSB RMS" means the root-mean-squared value of the total noise in least significant bits of the digital channel. Roughly, that's the standard deviation of the noise times the weight of one step of the digital value.

"$$\mu g/\sqrt{Hz}$$" means the power spectral density in micro-g's ($$1\mu g \simeq 0.0000098 m/s^2$$). If the power spectral density is flat, then you can square this number, multiply it by the bandwidth, take the square root, and get to the noise as LSB RMS. The power spectral density is useful when you try to figure out the effect of sensor noise on velocity and/or position when integrating.

"$$^\circ / s$$-rms" has a similar meaning to the "LSB RMS", except the noise is referred to the rate measurement rather than the ADC bits.

"$$^\circ /s / \sqrt{Hz}$$" is, again, the power spectral density.

It should be obvious at this point what the magnetometer specifications mean.

If you haven't got a background in random processes and signal analysis then you're going to have a rough time relating this back to real-world numbers, particularly if you're doing any kind of sensor fusion. Even the "big boys" in the sensor fusion game can't easily map sensor noise to system behavior without lots of simulation and head-scratching.

Simpler problems will yield to analysis, however.

• Not enough rep to comment (sorry for breaking rule about answering question), so referencing TimWescott & ROB answer above: Is LSB-RMS the same as noise density? How would one derive random walk from PSD? Here from robotics.stackexchange.com/questions/8860/… – errolflynn Mar 3 '18 at 20:27
• Welcome to Robotics @errolflynn but on Stack exchange answers need to answer the question. If you have a related question, it should be asked as a new question (ideally referencing this one). Note that we prefer practical, answerable questions based on actual problems that you face. Please take a look at How to Ask and tour for more information on how stack exchange works. For advice on how to write a good question, see the Robotics question checklist. – Mark Booth Mar 5 '18 at 1:14
• 0.000098 incorrect? correct 0.0000098 = 1 * 1.0e-6 * 9.8 – minorlogic Apr 20 at 11:25
• @minorlogic: thank you; I've corrected the number. It was only a zero, so it's zero difference, right? I was hoping that there was a known planet with a surface gravity 10x the earth, so I could claim to be posting from there -- but no luck. – TimWescott Apr 20 at 14:57