kalman

Functions

ParallelKalmanFilter(kernel, X, y, R[, return_v_S])	Wrapper for the parallel Kalman filter.
make_associative_params(Phi, H, Q, R, t, y, m0, P0)	Generate the associative parameters needed for parallel Kalman
_combine_per_pair(left, right)	See Eqn. 13 & 14 of Sarkka & Garcia-Fernandez (2020) for
parallel_kalman_filter(asso_params)	Jax implementation of the parallel Kalman filter algorithm
postprocess(Phi, H, Q, R, X, t, y, b, C, m0, P0)

Module Contents

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

Wrapper for the parallel Kalman filter.

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:

b: filtered means C: filtered covariances eta: J:

Return type:

A

smolgp.solvers.parallel.kalman.make_associative_params(Phi, H, Q, R, t, y, m0, P0)

Generate the associative parameters needed for parallel Kalman

See Eqns. 10, 11, 12 from Sarkka & Garcia-Fernandez (2020)

smolgp.solvers.parallel.kalman._combine_per_pair(left, right)

See Eqn. 13 & 14 of Sarkka & Garcia-Fernandez (2020) for a the algorithm and notation.

smolgp.solvers.parallel.kalman.parallel_kalman_filter(asso_params)

Jax implementation of the parallel Kalman filter algorithm

See Section 4A of Sarkka & Garcia-Fernandez (2020) for a detailed description of the algorithm and notation.

Total runtime (span) complexity is ~O(logN) where N is the number of time steps.

smolgp.solvers.parallel.kalman.postprocess(Phi, H, Q, R, X, t, y, b, C, m0, P0)