Perception and Sensors
IMU Drift: How Fast a Robot Loses Its Heading
An inertial measurement unit is perfect for a second and useless after a minute. The arithmetic of drift, what each grade costs, and what has to correct it.
A consumer-grade gyroscope with a bias stability of 10 degrees per hour accumulates about 0.17 degrees per minute of heading error, and on a robot travelling 30 m that is roughly 90 mm of lateral deviation. Position from double-integrated acceleration is far worse: with a bias of 1 milli-g, error grows to about 1.8 m in 60 seconds. An IMU is a short-term reference that something else must continuously correct.
The arithmetic of drift
Two integrations separate an accelerometer from a position, and each one amplifies error. A constant acceleration bias b produces a position error of b times t squared divided by two. For b of 1 milli-g, which is about 0.0098 m/s², the error is 0.0049 t².
| Elapsed time | Position error |
|---|---|
| 1 s | 5 mm |
| 5 s | 0.12 m |
| 10 s | 0.49 m |
| 30 s | 4.4 m |
| 60 s | 17.6 m |
Note the shape. Doubling the time quadruples the error, which is why inertial navigation alone is never a solution and why every practical system pairs the IMU with an absolute reference.
The grades and what they cost
| Grade | Bias stability | Heading drift | Price band | Typical use |
|---|---|---|---|---|
| Consumer MEMS | 50 to 200 deg/h | 0.8 to 3.3 deg/min | 1 to 20 | Phones, toys, orientation only |
| Industrial MEMS | 3 to 20 deg/h | 0.05 to 0.33 deg/min | 100 to 2,000 | Mobile robots, AGVs |
| Tactical | 0.1 to 3 deg/h | 0.002 to 0.05 deg/min | 2,000 to 30,000 | Survey robots, long GNSS outages |
| Navigation | 0.001 to 0.01 deg/h | negligible over minutes | 50,000+ | Aerospace, submarine |
The industrial MEMS row covers the overwhelming majority of ground robots, and the reason is straightforward: the correction sources available indoors are good enough that paying a hundredfold for a tactical unit buys very little.
What corrects the drift
- Wheel odometry. Excellent on clean flat floors, poor on wet, dusty or uneven ground where slip is unmeasurable. Usually the primary correction indoors.
- Scan matching against a map. Provides absolute heading and position at 10 to 40 Hz. The main correction in warehouse robots.
- Visual odometry. Works where features exist, fails in featureless corridors and poor light.
- GNSS with a dual antenna. Gives absolute heading outdoors, which single-antenna GNSS cannot do while stationary.
- Zero-velocity updates. When the robot is known to be stopped, any measured velocity is error and can be used to re-estimate bias. Free, and frequently unused.
- Magnetometer. Absolute heading reference, and unreliable indoors near steel structures and motors.
Point five is the free improvement most systems leave on the table. A robot that stops at a station for 20 seconds has 20 seconds of perfect information about its own velocity, and using it to re-estimate gyroscope bias measurably reduces drift on the next leg.
Building an error budget
Heading error between corrections is what a navigation designer actually has to bound. The calculation is short and worth doing before hardware is chosen.
| Gyro bias stability | After 10 s | After 60 s | Lateral error over 20 m |
|---|---|---|---|
| 100 deg/h | 0.28 deg | 1.67 deg | 580 mm |
| 20 deg/h | 0.06 deg | 0.33 deg | 116 mm |
| 10 deg/h | 0.03 deg | 0.17 deg | 58 mm |
| 3 deg/h | 0.008 deg | 0.05 deg | 17 mm |
| 0.5 deg/h | 0.001 deg | 0.008 deg | 3 mm |
Lateral error is computed for a straight 20 m run with the heading error accumulated over 60 s. Read it against the docking tolerance the task requires: if a station needs 20 mm, an industrial MEMS unit at 10 degrees per hour will not hold it for a minute without correction, and either the correction rate or the sensor grade has to change.
Practical notes
- Mount rigidly and near the centre of rotation. Vibration adds noise the filter cannot distinguish from motion.
- Let it warm up. MEMS bias changes substantially in the first minutes after power-on, and calibrating cold produces a bias estimate that is wrong once warm.
- Compensate temperature. Bias varies with temperature, and units with factory temperature calibration are worth the premium in unheated spaces.
- Log the raw data. Diagnosing a navigation fault without raw inertial data is guesswork, and the storage cost is trivial.
Frequently asked questions
How fast does an IMU drift?
Heading drift follows the gyroscope bias stability: 10 degrees per hour is about 0.17 degrees per minute. Position from double-integrated acceleration grows with time squared, reaching roughly 1.8 m in 60 seconds at 1 milli-g bias.
Can a robot navigate on an IMU alone?
No, not for more than a few seconds. Position error grows with the square of time, so inertial data must be combined continuously with wheel odometry, scan matching, visual odometry or satellite positioning.
Which IMU grade does a mobile robot need?
Industrial MEMS, with 3 to 20 degrees per hour bias stability, covers almost all ground robots. Tactical grade is worth its hundredfold price only where absolute references are unavailable for long periods.
What is a zero-velocity update?
Using periods when the robot is known to be stationary to re-estimate sensor bias, since any measured velocity during that time is error. It is free, effective and frequently unimplemented.
Is a magnetometer useful indoors?
Rarely. Steel structures, motors and current-carrying cables distort the magnetic field enough to make heading readings unreliable, which is why indoor robots depend on scan matching rather than on a compass.
Sources
- Official U.S. government information about GPSPublished positioning performance and system status
- Robotics at NISTNational Institute of Standards and Technology, robot performance measurement and test methods
- ISO 3691-4, safety requirements for driverless industrial trucksInternational Organization for Standardization, positioning requirements for guided vehicles