GPS/IMU Sensor Fusion 2D: Vehicle Localization Drift

GPS & IMU Setup

GPS update interval 2.0 s

GPS measurement noise 3.0 m

IMU accelerometer noise 0.30 m/s²

Vehicle speed 1.0×

Live State

GPS: LOCK · next fix in 2.0 s

IMU-only error

0.0 m

GPS-only error

0.0 m

Kalman fused error

0.0 m

Filter uncertainty (1σ)

0.0 m

Elapsed

0.0 s

Mean fused / IMU error

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How it works

A vehicle's IMU integrates noisy acceleration into position, drifting further off course the longer it goes uncorrected. GPS gives an absolute fix but arrives slowly and noisily. A Kalman filter fuses both: it predicts forward from the IMU every frame, then corrects toward each GPS fix by exactly the amount the numbers justify.

Predict (every physics step, from IMU):
  p += v·dt + ½a·dt²
  v += a·dt
  P  = F·P·Fᵀ + Q         (uncertainty grows)

Update (only when a GPS fix arrives):
  y = z_gps − H·x           (innovation)
  S = H·P·Hᵀ + R
  K = P·Hᵀ·S⁻¹              (Kalman gain)
  x = x + K·y                (uncertainty shrinks)
  P = (I − K·H)·P

Green (true path) — the vehicle's real position, unknown to any real sensor; shown for reference only.
Red (IMU only) — dead-reckoning from accelerometer integration alone. Small noise and bias compound every step, so error grows roughly with time².
Amber (GPS only) — the last GPS fix held fixed until the next one arrives. Accurate but stale and jumpy — error saws up between fixes then drops.
Blue (Kalman fused) — the same IMU prediction, corrected by GPS whenever a fix arrives. Error stays lower and steadier than either raw sensor.
The chart below plots all three errors live. The tunnel button cuts GPS for 5 s — watch the fused error fall back toward the IMU curve and its uncertainty ring inflate, then snap down the moment GPS returns.

True path IMU dead-reckoning GPS only (held) Kalman fused

Position error vs time (m)