kalman

Functions

KalmanFilter(kernel, X, y, R[, return_v_S])	Wrapper for jitted kalman_filter function
kalman_filter(A, Q, H, R, t, y, m0, P0)	Jax implementation of the Kalman filter algorithm

Module Contents

smolgp.solvers.kalman.KalmanFilter(kernel, X, y, R, return_v_S=False)

Wrapper for jitted kalman_filter function

Parameters:

• kernel – StateSpaceModel kernel

• X – data coordinates, e.g. time or (time, texp, instid)

• y – observations, shape (N, D)

• R – observation noise covariance, shape (N, D, D)

Returns:

filtered means P_filtered: filtered covariances m_predicted: predicted means P_predicted: predicted covariances

Return type:

m_filtered

smolgp.solvers.kalman.kalman_filter(A, Q, H, R, t, y, m0, P0)

Jax implementation of the Kalman filter algorithm

See Theorem 4.2 (pdf page 77) in “Bayesian Filtering and Smoothing” by Simo S{“a}rkk{“a} for detailed description of the algorithm and notation.

e.g. _prev is _{k-1}

_pred is _k^{-}

Total runtime complexity is O(N*d^3) where N is the number of time steps and d is the dimension of the state vector.