PYTHON · NUMPY · IN-BROWSER

Estimating a non-cooperative target

Track a noisy, tumbling target with a constant-velocity Kalman filter and show it beats using the raw measurements.

01Challenge

A dead satellite does not report its state; you infer it from noisy returns. Implement a per-axis constant-velocity Kalman filter, then show its estimate has far lower error than the raw measurements, and that it reports its own shrinking uncertainty.

02Model

You cannot control what you cannot estimate. A non-cooperative target gives you only noisy, occasional measurements of where it is, never its velocity and never the truth. A Kalman filter turns that stream into a state estimate: it predicts the motion forward with a constant-velocity model, then corrects on each measurement, weighting the correction by how much it trusts the model versus the sensor. Crucially it also carries a covariance, its own statement of uncertainty, which shrinks as measurements accumulate and converge. That shrinking number is what the controller watches before it dares to close: the standoff comes in only as the pose estimate tightens.

03Guided practice

1. Predict. Advance position by velocity times dt; grow the covariance by process noise.

2. Update. On a measurement z of variance r, the gain is P/(P+r); correct position and velocity, and shrink P.

3. Compare. Run it on a moving target with noisy range returns and compare the filter's RMS error to the raw measurements' RMS error.

04Feedback

PASS WHEN PASS once the Kalman RMS error prints lower than the raw-measurement RMS error, and the pose sigma shrinks from start to end.

If the filter is worse than the raw data, check the update: the gain is P/(P+r) and you must shrink P after correcting.
Keep position and velocity in the state; a position-only filter cannot smooth a moving target.

05Retrieve & space

What two things does the Kalman filter produce that a raw measurement does not? (a velocity estimate and a covariance / uncertainty).
Why does the covariance shrink over time? (each measurement adds information, so the estimate gets more certain).
How does the controller use the shrinking uncertainty? (it closes the standoff only as the pose estimate tightens).

06Mastery & project

You can implement a constant-velocity Kalman filter and show it beats raw measurements while reporting its own uncertainty.

Before acting on a sensor, filter it: steer on the estimate and its uncertainty, never on the raw, noisy, delayed measurement.

GO FURTHER · THE LIVE PLAYGROUND

On-orbit capture (live) ↗ — The covariance ellipse you just computed, animated.

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PYTHON · NUMPY · IN-BROWSER

Estimating a non-cooperative target

Implement the constant-velocity Kalman filter and compare its error to the raw measurements.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you