Kalman Trend Estimator [KTE] -FibonacciFlux

OVERVIEW

Optimal linear trend filter using scalar Kalman filtering. Treats price as a noisy
measurement of a hidden trend state and recursively computes the optimal estimate. The Kalman
gain adapts automatically — no manual threshold tuning required.

HOW IT WORKS

The filter balances two noise sources:
- Process Noise (Q): how fast the true trend can change
- Measurement Noise (R): how noisy price observations are

The Kalman gain adjusts every bar:
- During clean trends: gain tightens, tracks price closely
- During choppy markets: gain loosens, smooths out noise

Innovation magnitude (prediction error) serves as a built-in regime classifier: small
innovations = trending, large innovations = noisy/ranging.

FEATURES

- Adaptive Kalman gain — zero manual tuning
- Innovation-based regime coloring (green = trend, red = noise)
- Confidence bands derived from estimation uncertainty (P matrix)
- Signal dots at trend direction changes
- Works on all timeframes and instruments

SETTINGS

Process Noise Q: Controls trend tracking speed. Higher = faster adaptation. Default 0.01.
Measurement Noise R: Controls price smoothing. Higher = smoother output. Default 1.0.
Show Bands: Toggle confidence bands on/off.

Based on: R.E. Kalman (1960), "A New Approach to Linear Filtering and Prediction Problems",
Journal of Basic Engineering.