Inertial measurement units

Collection of a few sensors, namely:

• accelerometer
  • for movement in space, measures change in speed/directional movement
• gyroscope
  • rotational / angular velocity
• magnetometer
  • not that useful here, mostly used for orientation

Operating Principles

Accelerometer

• Measures: linear acceleration
• Units $g^{\prime }s=9.81\frac{m}{s^2}$
• Sensing Modality: capacitive
• Mechanics “proof mass” with capacitive “fingers”. Acceleration alters capacitance $\to$ voltage

$$m\ddot{x}+b\dot{x}+kx=F_{ext}$$

For low oscillation frequencies (< 1kHz):

$$V_{meas}\approx V_{in}\cdot \frac{x}{d}$$

Gyroscope

• Measure: angular velocity
• Units: deg/s or rad/s
• Sensing modality: capacitive ( same as accelerometer )
• Mechanics: “proof mass” oscillates continuously; Coriolis force induces amplitude along radial dimension.

$$m\ddot{x}+b\dot{x}+kx=F_{ext}\propto \frac{m{v}^2}{r}$$

Magnetometer

• Measures: magnetic fields ( heading )
• Units: Teslas ( $\mu T$ )
• Sensing Modality: Hall effect
• Mechanics: voltage difference induced by magnetic field perpendicular to lfow electrical current

$$V_{Hall}=R_{Hall}\frac{IB}{t}$$

Selecting IMU Operating Parameters

Range

• Determines max/min detectable signal.

Resolution

• Varies with range (units =
  counts/degree; counts/g)
• Magnetometer: Heading accuracy

Sampling rate

• Nyquist-Shannon Sampling Theorem:
  To avoid losing information, must
  sample at 2x desired max frequency