# Angle Random Walk vs. Rate Noise Density (MPU6050)

I’ve made a datalog from a MPU6050 (IMU: gyroscope and accelerometer) at 500Hz sample rate. Now I want to calculate the characteristics from the gyro to evaluate the sensor.

For the gyro I’ve found following values in the datasheet:

Total RMS Noise = 0.05 °/s

Low-frequency RMS noise = 0.033 °/s

Rate Noise Spectral Density = 0.005 °/s/sqrt(Hz)

Now I want to ask how I can calculate these values from my dataset?

At the moment I’ve the following values from the dataset:

Standard deviation = 0.0331 °/s

Variance = 0.0011

Angular Random Walk (ARW) = 0.003 °/sqrt(s) (From Allan deviation plot)

Bias Instability = 0.0012 °/s

Is the ARW equal to the Rate Noise Spectral Density mentioned in the datasheet? And also is the RMS Noise from the datasheet equal to the standard deviation?

edit: I found following website: http://www.sensorsmag.com/sensors/acceleration-vibration/noise-measurement-8166 There is the statement: "...Because the noise is approximately Gaussian, the standard deviation of the histogram is the RMS noise" So I guess the standard deviation is the RMS noise from the datasheet. But how about the ARW?

## 1 Answer

check page no: 11, eqn(8) from An introduction to inertial navigation by Oliver J. Woodman (Technical Report Number 696 from the University of Cambridge Computer Laboratory).

• Welcome to Robotics:SE. It's generally better to include the main points in your answer in case of 'link rot' in the future. – sempaiscuba Jan 1 '19 at 14:22
• Thank you. Yeah you're right. In the technical report FFT noise density is the Rate Noise Spectral Density from the datasheet. And with eqn(8) one can convert to ARW. – Patrick Stegers Jan 2 '19 at 9:51
• Welcome to Robotics Apz. Thanks for your answer but we prefer answers to be self contained where possible. Links tend to rot so answers which rely on a link can be rendered useless if the linked content disappears. If you add more context from the link, it is more likely that people will find your answer useful. – Mark Booth Jan 2 '19 at 11:37
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