KalmanVelocityOscillator

Summary

KalmanVelocityOscillator is RTTA's streaming implementation of: Zero-centered velocity state from a constant-velocity Kalman price model.

Update API

result = rtta.KalmanVelocityOscillator().update(close)

The update(...) call consumes one observation using close. advance(...) uses the same inputs when the caller wants to update state without materializing a Python return value.

Theory Of Operation

KalmanVelocityOscillator treats the input stream as noisy observations of a latent state. Each call performs the standard predict/update cycle, then projects the updated state into the public scalar or result fields.

Recurrence

Let \(z_t = close_t\) denote the observation consumed by one update(...) call and let \(\theta\) denote constructor parameters such as window lengths, thresholds, and smoothing constants.

\[\hat{x}_{t|t-1}=F\hat{x}_{t-1|t-1}, \qquad P_{t|t-1}=FP_{t-1|t-1}F^\top+Q\]

\[K_t=P_{t|t-1}H^\top(HP_{t|t-1}H^\top+R)^{-1}\]

\[\hat{x}_{t|t}=\hat{x}_{t|t-1}+K_t(z_t-H\hat{x}_{t|t-1}), \qquad P_{t|t}=(I-K_tH)P_{t|t-1}\]

The return value is the current scalar indicator value.

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class KalmanVelocityOscillator.

Reference

Background reference