IMU Specifications¶

IMU Noise Specification Conversion to Standard Deviation¶

The following calculations convert the noise specifications from the IMX-5 inertial measurement unit (IMU) datasheet into usable standard deviation values for simulating sensor noise at a sampling rate of 100 Hz. IMUs typically provide specifications for gyroscope and accelerometer noise in terms of "Angular Random Walk" (ARW) and "Velocity Random Walk" (VRW), expressed per $\sqrt{\text{hours}}$ . These values represent the rate at which random walk (drift) accumulates over time. To model this noise accurately in simulations, we need to translate the datasheet specifications into standard deviations that correspond to the chosen sampling rate (100 Hz, or 0.01 seconds per sample). This involves converting the ARW and VRW values from per $\sqrt{\text{hour}}$ to per $\sqrt{\text{second}}$ and then adjusting them based on the sampling interval, yielding noise characteristics that realistically represent the IMU's behavior in a simulated environment.

Given IMU specifications for the IMX-5:

Gyro Angular Random Walk (ARW): $0.16 \, ^{\circ} / \sqrt{\text{hr}}$
Accelerometer Velocity Random Walk (VRW): $0.02 \, \text{m/s} / \sqrt{\text{hr}}$
Sampling Rate: 100 Hz (which corresponds to a time interval, $\Delta t$ , of $0.01$ seconds)

Time Conversion Factor¶

Since the random walk values are given per , we need to convert from hours to seconds. 1 hour is 3600 seconds, so: $\text{1 hr} = 3600 \, \text{s} \Rightarrow \sqrt{\text{1 hr}} = \sqrt{3600} = 60 \, \text{s}^{1/2}$ To convert the noise specifications from per $\sqrt{\text{hr}}$ to per $\sqrt{\text{s}}$ , divide by 60.

1. Gyroscope Noise (° and °/s)¶

Convert the Gyro Angular Random Walk (ARW) to per : $\text{ARW (per } \sqrt{\text{s}}) = \frac{0.16}{60} = 0.00267 \, \frac{^{\circ}}{\sqrt{\text{s}}}$

Now, to get the angle drift at a 100 Hz sampling rate, multiply by the square root of the time interval: $\sigma_{\text{angle}} = 0.00267 \times \sqrt{0.01} = 0.00267 \times 0.1 = 0.000267 \, ^{\circ}$ So, the angle drift standard deviation at 100 Hz is approximately 0.000267 °.

To get the angular rate noise at a 100 Hz sampling rate, divide ARW by the square root of the time interval: $\sigma_{\text{gyro}} = \frac{0.00267}{\sqrt{0.01}} = 0.00267 \times 10 = 0.0267 \, ^{\circ}/\text{s}$

2. Accelerometer Noise (m/s and m/s²)¶

Velocity Drift Standard Deviation (m/s)¶

Convert VRW from per to per : $\text{VRW (per } \sqrt{\text{s}}) = \frac{0.02}{60} = 0.000333 \, \frac{\text{m/s}}{\sqrt{\text{s}}}$

Now, multiply by the square root of the time interval to get the standard deviation at 100 Hz in terms of velocity: $\sigma_{\text{velocity}} = 0.000333 \times \sqrt{0.01} = 0.000333 \times 0.1 = 0.0000333 \, \text{m/s}$ So, the velocity drift standard deviation at 100 Hz is approximately 0.0000333 m/s.

Accelerometer Standard Deviation in Terms of Acceleration (m/s²)¶

To express the accelerometer noise as standard deviation in terms of acceleration, divide the VRW (converted per ) by the square root of the time interval: $\sigma_{\text{accel}} = \frac{0.000333}{\sqrt{0.01}} = 0.000333 \times 10 = 0.00333 \, \text{m/s}^2$ Thus, the accelerometer noise standard deviation in terms of acceleration at 100 Hz is approximately 0.00333 m/s².

Summary of Results:¶

Angle Drift Standard Deviation at 100 Hz: 0.000267 ° (denoted as $\sigma_{\text{angle}}$ )
Gyro Angular Rate Noise Standard Deviation at 100 Hz: 0.0267 °/s (denoted as $\sigma_{\text{gyro}}$ )
Velocity Drift Standard Deviation at 100 Hz: 0.0000333 m/s
Acceleration Noise Standard Deviation at 100 Hz: 0.00333 m/s²

These values represent the Gaussian noise standard deviations for each sensor at 100 Hz sampling rate.