robotics//sensor//IMU//gyroscope

A gyroscope, in its modern sensor form, is an instrument that measures its own rate of rotation about one or more axes, and integrating that rate is how a drone, a car's stability system or an aircraft keeps track of its attitude over short times. A MEMS gyroscope contains a tiny mass driven to vibrate; when the chip rotates, the Coriolis force pushes the vibrating mass sideways, perpendicular to its motion and in proportion to the rotation rate, and electrodes measure that sideways motion. Optical gyroscopes for navigation (fibre-optic, ring-laser) measure instead the time difference between two beams of light sent opposite ways around a loop. A 16-bit MEMS gyroscope on a ±2000 °/s range resolves about 0.061 °/s per count.

A gyroscope, in its modern sensor form, is an instrument that measures its own rate of rotation about one or more axes, and integrating that rate is how a drone, a car's stability system or an aircraft keeps track of its attitude over short times. A MEMS gyroscope contains a tiny mass driven to vibrate; when the chip rotates, the Coriolis force pushes the vibrating mass sideways, perpendicular to its motion and in proportion to the rotation rate, and electrodes measure that sideways motion. Optical gyroscopes for navigation (fibre-optic, ring-laser) measure instead the time difference between two beams of light sent opposite ways around a loop. A 16-bit MEMS gyroscope on a ±2000 °/s range resolves about 0.061 °/s per count.

Integrated, it gives a smooth, fast and very precise angle over seconds, and an angle that wanders over minutes. The standard model of a gyroscope says why:

ωm=ω+b+n,b˙=wb.\omega_m = \omega + b + n,\qquad \dot b = w_b .ωm​=ω+b+n,b˙=wb​.

The measured rate ωm\omega_mωm​ is the true rate ω\omegaω plus white noise nnn and a bias bbb that is not constant: it walks slowly, pushed by a noise of its own, wbw_bwb​. The white noise integrates into an angle error growing as t\sqrt tt​, the bias into one growing linearly, and the walk of the bias means that a value measured at start-up is already stale a few minutes later (dead reckoning).

The two noise coefficients are read from a static recording with the Allan variance: the angle random walk from the slope at short averaging times, the bias instability at the flat minimum. Those two numbers separate a toy from a navigation instrument by four orders of magnitude (IMU).

Because the bias walks, estimators carry it as a state and let other sensors pin it down: the accelerometer's gravity for roll and pitch, the magnetometer or a moving GNSS for heading (state augmentation, sensor bias).

Its partner is the accelerometer, which is drift-free and noisy where the gyroscope is smooth and drifting; their defects live at different frequencies, which is the whole idea of the complementary filter.