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UAV Systems Engineering · Interactive simulation · M3-L2

EKF Simulator

Step through every prediction and correction of an EKF, watch the covariance ellipse grow and shrink, and diagnose mistuning with NIS and NEES.

  • Sensor Fusion and State Estimation
  • Established engineering
  • Runs entirely in your browser

What you are looking at

A ground station at the origin measures the range and bearing of a manoeuvring UAV. An EKF with a constant-velocity model tracks position and velocity. Between measurements the filter only predicts: the dashed orange ellipse (2σ) grows. When a measurement arrives, the filter corrects: the solid blue ellipse shrinks.

Use “Next update” to jump from correction to correction, or scrub the time slider. The panels report the innovation, the Kalman gain on x from range, the NIS of each update (expected mean 2, with 95% bounds), and NEES against the truth (expected mean 4).

Try this

  1. Lower process noise σa to 0.2 m/s². The filter now trusts its constant-velocity model too much and lags the manoeuvre: NIS leaves its upper bound and NEES explodes.
  2. Raise “measurement noise scale” to 10. NIS drops below 2: the filter is underconfident and ignores useful data. Set it to 0.1: overconfident, NIS too high.
  3. Set the initial position error to 30 m with initial σ of 1 m, then with 30 m. A filter that is told it is certain cannot correct a large initial error.
  4. Reduce the update rate to 0.3 Hz. Watch the sawtooth in the uncertainty plot get deeper between updates.
  5. In zoomed view press “Next update” repeatedly and compare the innovation’s size with the ellipse: updates that land inside the ellipse produce small corrections.

Model and its limits

Included: the standard EKF equations with analytic Jacobians for the range-bearing measurement, a continuous-white-noise-acceleration process model, angle wrapping in the bearing innovation, Joseph-form covariance update, NIS (χ² with 2 degrees of freedom, 95% interval 0.05 to 7.38) and NEES (4 degrees of freedom).

Not included: a 3-D vehicle, sensor biases, correlated noise or non-Gaussian errors. The truth manoeuvres by sine-wave heading changes, so a constant-velocity model is deliberately wrong; process noise is the tuning knob that absorbs that mismatch.

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