Filter tuning

Process noise Q: 0.40 Measurement noise R: 16.0

Demand scenario

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Filter state (live)

Observation #0

True demand (hidden)—

Raw POS reading—

Filter estimate—

Estimated trend/step—

Absolute error—

Uncertainty σ (√P₁₁)—

Current Kalman gain K—

Q is the filter's belief in how fast true demand can change on its own; R is how noisy each point-of-sale reading is. Raise Q to react faster to real regime shifts at the cost of a noisier estimate; raise R to trust the sensor less and smooth harder. The shaded band is the genuine 1σ (and 2σ) region from the filter's own error covariance P — it shrinks as the filter accumulates confidence and widens instantly after a regime shift.