Noise vs. Bias: A Target and a Handful of Arrows
Picture an archer shooting at a bullseye. The center of the target is the true value you wish you could measure; every arrow is one sensor reading. A perfect sensor would stack every arrow dead-center. Real sensors never do — and the way the arrows scatter tells you exactly what kind of lie you are dealing with.
Sensor noise is the random jitter: arrows splattered loosely all around the bullseye, sometimes high, sometimes low, with no pattern. Average enough of them and they roughly cancel, landing near center. Noise is the unpredictable wobble in every reading — thermal flicker in the electronics, tiny vibrations, the last digit that never sits still.
Bias is something else entirely: a fixed offset. Imagine the archer's sight is bent, so every arrow clusters tightly — but always two rings to the left of center. The shots are consistent, even precise, yet systematically wrong. A pressure sensor that always reads 3 kPa high, or a gyroscope that reports a tiny turning rate while sitting perfectly still, has a bias.
Drift: How a Tiny Bias Grows Without Bound
Bias becomes truly dangerous the moment you start adding readings together over time. This is the heart of drift, and it is the reason an inertial measurement unit (IMU) cannot tell you where it is for very long. The villain is integration: turning a rate into a total.
A gyroscope measures turning rate, not angle. To know which way you face, you add up all those rates: angle = sum of (rate × time-step). Now suppose the gyro has a bias of just 0.01 degrees per second — far too small to notice in a single reading. Integrate it for ten minutes and that invisible offset has quietly become a six-degree error in heading, growing steadily and never coming back.
An accelerometer is worse still, because position needs two integrations of acceleration. A constant bias there grows not linearly but with the square of time — the error curve bends upward. This is precisely why dead reckoning (estimating your pose purely from your own motion sensors, without any outside reference) drifts away from the truth and, used on its own, eventually becomes useless.
gyro bias = 0.01 deg/s (looks harmless) after 10 s -> 0.1 deg error after 100 s -> 1.0 deg error after 600 s -> 6.0 deg error (heading is now wrong) accel bias integrated TWICE -> position error grows like t^2 small bias, short time -> fine small bias, long time -> meters off, and accelerating
Calibration: Measure the Error, Then Subtract It
Sensor calibration is the disciplined act of measuring a sensor's known errors under controlled conditions and then correcting for them in software. The simplest and most common form is zeroing out a bias: put the sensor in a situation where you already know the true answer, see what it actually reports, and store the difference as a correction.
- Zero a gyro at rest: hold the IMU perfectly still, where the true turning rate is exactly zero. Average several hundred readings; whatever nonzero value you get is the bias. Subtract it from every future reading.
- Fix the scale factor: a sensor may also report values that are systematically too big or too small by a constant percentage. Apply a known input (a precise weight on a force sensor, a measured rotation on a turntable) and compute the multiplier that makes the reading match.
- Account for conditions: because bias drifts with temperature, good calibration often records the correction at several temperatures, or re-zeros the gyro every time the robot powers up and is known to be still.
The same idea extends well beyond IMUs. A rotary encoder is given a home position so its counts map to real joint angles; a depth camera is calibrated so its distances are true; even a force/torque sensor is zeroed while holding no load so it does not mistake the gripper's own weight for a push.
Honest Expectations: Calibration Is Only Half the Story
Here is the catch beginners often miss. Calibration removes the systematic part of the error — the bias and the scale factor, the parts that are predictable and repeatable. It does nothing about the random part. You cannot subtract noise, because by definition you cannot predict it. After a flawless calibration the arrows are centered on the bullseye again, but they are still scattered.
That leftover scatter is why two more tools exist. Low-pass filtering smooths a noisy signal by averaging over time, trading a little responsiveness for steadier numbers. And sensor fusion combines several imperfect sensors so their independent errors partly cancel — a drifting gyro paired with an absolute reference like a GNSS/GPS receiver gives you the gyro's smoothness without its unbounded drift.
Knowing which error dominates a given sensor tells you which fix to reach for. The checklist below pairs the common robot sensors with the failure they suffer most — a map for deciding when to calibrate, when to filter, and when to fuse.
- Gyroscope: bias-and-drift dominates. The reading itself is fairly quiet, but integration makes a tiny bias snowball. Re-zero often; fuse with an absolute reference.
- Accelerometer: noisy in the short term, biased in the long term. Filter to tame the jitter; never integrate it twice for position on its own.
- Wheel encoder / odometry: little noise, but systematic bias from wheel slip and imperfect wheel radius accumulates as you travel.
- GNSS/GPS: no long-term drift (it is an absolute fix), but noisy and jumpy moment to moment, and it vanishes indoors. The perfect partner to fuse with a gyro.
- LiDAR and depth camera: mostly noise plus calibration offsets; no time-accumulating drift, because each scan is a fresh absolute measurement of the surroundings.