Ukf

polars_ts.bayesian.ukf

Unscented Kalman Filter (UKF).

Propagates sigma points through user-defined nonlinear transition and observation functions, then recovers the posterior mean and covariance via a weighted combination.

Reference

Julier & Uhlmann (1997). A New Extension of the Kalman Filter to Nonlinear Systems.

UnscentedKalmanFilter

Unscented Kalman Filter for nonlinear state-space models.

Parameters

f State transition function f(x) -> x_next. Takes a 1D state array and returns the predicted state. h Observation function h(x) -> y. Takes a 1D state array and returns the predicted observation. Q Process noise covariance (n, n). R Observation noise covariance (m, m). x0 Initial state mean (n,). P0 Initial state covariance (n, n). alpha Spread of sigma points around the mean. Default 1e-3. beta Prior knowledge of distribution (2.0 is optimal for Gaussian). kappa Secondary scaling parameter. Default 0.0.

filter(y)

Run the UKF forward pass.

Parameters

y Observations (T,) or (T, m). Use np.nan for missing.

Returns

KalmanResult

_sigma_points(x, P, alpha, beta, kappa)

Generate sigma points and weights for the unscented transform.