# Angle Random Walk Noise - MEMS Gyro Error sources

I am working in a implementation of a Dead Reckoning approach in a simulator. In order to take values more realistics I am considering this MEMS gyroscope (SMI130).

In this document is given this noise in FFT units:

0.02 º/s/sqrt(Hz)

I need to know if I am considering that the gyro is working in 10Hz the total noise in each 0.1 seconds will be:

0.02º/0.1sec/sqrt(10)Hz = 0.063245553 º/s/sqrt(Hz).


I am undestanding that in each 0.1 second the expected noise will be 0.063245553º.

Applyng the equation for the angle random walk, that grows proportional to the square root of the time:

sigma_1 = 0.063245553º;
sigma(t) = sigma_1 * sqrt(t);


I am understanding that, for example, after 2 minutes the ARW will be:

t = (0.1 * 10) * 120 = 120 seconds

sigma(120) = 0.063245553º * sqrt(120)
sigma(120) = 0.692820321 º/sqrt(s)


Is this correct?

I am in doubt mainly because I understanding if I increase the frequency (Hz) the bias also increase:

1 Hz (1 sec) -> 0.02
10Hz (0.1 sec) -> 0.063245553


Thank you for any clarification.

• It's likely to be a "rate gyro", outputting rotation rate in degrees/second, , not heading.
– user16324
Commented Feb 24, 2017 at 18:19