PYTHON · NUMPY

Fuse the Sensors

Fuse a noisy altitude sensor with an accelerometer through a Kalman filter that beats either sensor alone.

01Challenge

You have a jumpy barometer (noisy position) and a drifting accelerometer (integrates to a drifting position). Neither is trustworthy alone. Fuse them so the estimate tracks the true altitude better than the raw barometer.

Predict firstYou have two noisy altitude estimates — a drifting barometer and a jittery accelerometer. Can fusing two imperfect sensors beat the BETTER of the two alone?

02Model

Every sensor lies a little, in its own way: the barometer is noisy but unbiased, the accelerometer is smooth but drifts. The Kalman filter is the optimal way to combine them: predict the state forward with the accelerometer, then correct toward the barometer by an amount set by how much you trust each. The Kalman gain is exactly that trust ratio, computed from the noise levels. The fused estimate is smoother than the barometer and drift-free unlike the accelerometer — better than either input.

03Guided practice

Worked: simulate true altitude, noisy baro, biased accel. Faded: run predict (accel) then update (baro) with a Kalman gain. Independent: verify fused RMSE beats the raw baro.

04Feedback

PASS WHEN The fused estimate has lower RMSE than the raw barometer — the filter extracts more than either sensor holds alone.

If your run fails, check:

FAIL: fused no better than baro — measurement noise R set too high, the update ignores the sensor.
FAIL: fused drifts — process noise Q too low, the filter over-trusts the drifting accelerometer.

05Retrieve & space

What does the Kalman gain represent? (How much to trust the new measurement vs the prediction — the noise ratio.)
Which sensor gives the smooth short-term motion, which fixes long-term drift? (Accel short-term; baro long-term.)
Why is this 'optimal'? (It minimizes estimate variance under the assumed Gaussian noise.)

06Mastery & project

Implements a predict/update Kalman filter that fuses two sensors to lower RMSE than either alone (L3: optimal linear state estimation).

The fused altitude is the state the Module-1 controller closes its loop on in the presence of real sensor noise.

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PYTHON · NUMPY

Fuse the Sensors

Run a 1-D Kalman filter fusing barometer and accelerometer.

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