Angle Random Walk Noise - MEMS Gyro Error sources

Question

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.

Answer 1

As Brian Drummond mentions in comment above, the output of a gyroscope is rotation rate, not heading, so at 10 Hz sampling frequency, the noise should be (0.02 degrees/s/sqrt(Hz)) * sqrt(10 Hz). The frequency chosen here should be your sampling frequency. The final units of your noise should be in the same units the sensor is measuring.

To get the error for your dead reckoning, this noise then has to be integrated over time, which will leave you with units of degrees.