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I am trying to understand how to use the "Rate noise density" spec on a gyro IC. It is quoted at 0.25 degrees/second/root(Hertz). I plan on sampling it at about 100Hz. Is the noise going to be root(100Hz/2)*0.25 degrees/second/root(Hz) = 7.1*0.25 degrees/second = 1.8 degrees/second ?

(edit) It is my understanding that the bandwidth is half the sampling frequency. If this is wrong please let me know.

Any help is appreciated.

If you care the chip in question is Analog Devices ADXRS649.

George Gomes
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Yes, that's the right idea.

The number you came up with is the RMS value of the noise on the angular rate coming out of the sensor. When you integrate this signal to get the actual angle, this noise becomes a gradually increasing "random walk" that degrades the accuracy of the result — on top of any drift caused by bias and scale factor errors. This is why rate gyros need to be reset to an external reference periodically in order to maintain acceptable accuracy.

Dave Tweed
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  • What distribution does the RMS value have? My guess is Gaussian. If so how often should the distribution be applied to the calculated angle so that I can calculate the distribution of the angle? – George Gomes Feb 08 '17 at 00:32
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    Yes, the rate noise is generally Gaussian. After integration, the random-walk error grows proportionally to the square root of the elapsed time since the last recalibration. [Details here](https://en.wikipedia.org/wiki/Random_walk#Gaussian_random_walk). – Dave Tweed Feb 08 '17 at 01:22