Kalman Trend Filter (price + velocity)
A two-state Kalman filter that tracks price and its velocity (trend speed). Each bar it predicts where price should be, compares with the real close and corrects itself by an amount that depends on how noisy the market has been. The result is a smooth line with much less lag than a moving average of similar smoothness, plus a velocity estimate.
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How to use it
Line colour follows the filtered velocity: green = rising, red = falling. Arrows mark velocity sign changes (trend turns). The band shows the filter's own uncertainty: closes outside it are surprises. "Responsiveness" is the process-to-measurement noise ratio; 0.01 suits 1h-4h crypto, 0.05 is faster, 0.002 is very smooth. Noise is measured on a rolling window, so the settings work on any symbol or price scale. Concept: R. E. Kalman, "A New Approach to Linear Filtering and Prediction Problems" (1960); constant-velocity (alpha-beta) tracking model.
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Back-tests and forward tests are simulations; past results do not predict future ones. Nothing here is financial advice. Trading carries a high risk of loss.