IMU
An IMU (Inertial Measurement Unit) measures the platform’s own motion: a 3-axis accelerometer gives linear acceleration (including gravity) and a 3-axis gyroscope gives angular velocity, both at high rate — typically 100–1000 Hz. It is the canonical proprioceptive sensor: it senses the body, not the world.
What the IMU actually measures
The standard measurement models, written in the body frame with world frame :
Two things surprise newcomers. First, the accelerometer measures specific force, not acceleration: gravity is always in the measurement, which is why a stationary IMU reads about upward rather than zero. This is a curse (gravity must be tracked and subtracted before integrating) and a blessing (the gravity direction makes roll and pitch observable). Second, every axis carries a bias — a slowly-varying offset that changes with temperature and time, so a factory calibration is never enough and are estimated online as part of the SLAM state.
Three characteristics define how IMUs behave in estimation:
- Bias: the slowly-varying DC offsets above, typically modeled as random walks.
- Noise: white Gaussian noise on every measurement axis. (Noise densities and bias instability are characterized with an Allan variance analysis — covered in the IMU noise model note at Level 6.)
- Integration drift: to get pose from an IMU you integrate — once for orientation and velocity, twice for position — so errors accumulate rather than average out.
Why dead reckoning diverges
Follow the integration chain and the failure mode becomes concrete. Orientation comes from integrating the gyro; velocity and position come from rotating the measured specific force into the world frame, adding gravity back, and integrating twice:
- A gyro bias error makes the orientation error grow roughly linearly with time.
- An orientation (tilt) error misaligns the gravity subtraction, so a component of “leaks” into the estimated horizontal acceleration — a constant fake acceleration, whose double integration grows quadratically in time.
- An accelerometer bias alone contributes a position error of order — quadratic again.
This is why pure inertial dead-reckoning with a consumer MEMS IMU diverges within seconds, while navigation-grade units (with bias stability orders of magnitude better) can dead-reckon far longer — at orders-of-magnitude higher cost, size, and power.
The camera-IMU marriage
An IMU alone cannot do SLAM, but an IMU paired with a camera is one of the most successful sensor combinations in robotics. The two are perfectly complementary:
| Camera | IMU | |
|---|---|---|
| Rate | 10–60 Hz | 100–1000 Hz |
| Measures | External world (drift-correcting) | Self-motion (drifting) |
| Fails when | Fast motion, blur, darkness, low texture | Never “fails,” but drifts |
| Scale | Unobservable (monocular) | Observable (via accelerometer) |
The IMU bridges the gaps between camera frames, predicts motion for feature tracking, makes metric scale and gravity direction observable, and rides through short visual outages; the camera in turn keeps the IMU’s biases estimated and its drift in check.
How IMU data enters the estimator
In the SLAM formulation, IMU measurements enter the motion model: , with the state extended to include velocity and biases. Because hundreds of IMU samples arrive between keyframes, modern systems use preintegration: measurements between two keyframes are accumulated into a single relative-motion constraint, compensating for bias and gravity, so the optimizer touches one factor instead of a thousand raw samples — and the factor can be cheaply corrected when the bias estimate changes, without re-integrating. This topic — along with noise models, kinematics, and observability — is the heart of Level 6 (VIO/VINS).
Practical notes that matter before Level 6: camera-IMU fusion is only as good as the extrinsic calibration (the rigid transform between camera and IMU) and the time synchronization between the two sensor clocks — both are estimated with tools like Kalibr, and both are classic sources of mysterious VIO failures.
Why it matters for SLAM
Virtually every deployed visual tracking system — phone AR, drones, headsets, robot vacuum navigation — is visual-inertial, not vision-only, because the IMU is what makes tracking robust at real-world motion speeds and metric in scale. Understanding what an IMU measures, how its errors behave, and why integration drifts is the prerequisite for everything in the VIO level.