rts

rts#

Functions#

IntegratedRTSSmoother(kernel, t_states, obsid, instid, ...)

Wrapper for jitted integrated_rts_smoother function

integrated_rts_smoother(A_aug, RESET, t_states, obsid, ...)

Jax implementation of the integrated RTS smoothing algorithm

integrated_rts_gains(A_aug, RESET, t_states, obsid, ...)

The y-independent smoothing gains for the integrated smoother,

integrated_rts_smoother_batched_mean(G_all, ...)

Batched-mean-path replay of integrated_rts_smoother, given precomputed

Module Contents#

smolgp.solvers.integrated.rts.IntegratedRTSSmoother(kernel, t_states, obsid, instid, stateid, kalman_results)[source]#

Wrapper for jitted integrated_rts_smoother function

Parameters:

  • kernel – IntegratedStateSpaceModel kernel

  • t_states – Array of size K, sorted time coordinate of all states (exposure starts and ends)

  • obsid – Array of size N, which observation (0,…,N-1) is being made at each state k

  • instid – Array of size N, which instrument (0,…,Ninst-1) recorded observation n

  • stateid – Array of size K, 0 for exposure-start, 1 for exposure-end

  • kalman_results – output from Kalman filter (m_filtered, P_filtered, m_predicted, P_predicted)

Returns:

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

Return type:

m_filtered

smolgp.solvers.integrated.rts.integrated_rts_smoother(A_aug, RESET, t_states, obsid, instid, stateid, m_filtered, P_filtered, m_predicted, P_predicted)[source]#

Jax implementation of the integrated RTS smoothing algorithm

See Section 3.2.2 in Rubenzahl & Hattori et al. (in prep) for detailed description of the algorithm and notation.

smolgp.solvers.integrated.rts.integrated_rts_gains(A_aug, RESET, t_states, obsid, instid, stateid, P_filtered, P_predicted)[source]#

The y-independent smoothing gains for the integrated smoother, mirroring smooth_start/smooth_end’s gain formulas exactly (both use get_smoothing_gain, matching integrated_rts_smoother). Pointwise in k (jax.vmap, no scan needed).

Returns:

shape (K-1, dim, dim)

Return type:

G_all

smolgp.solvers.integrated.rts.integrated_rts_smoother_batched_mean(G_all, m_filtered_batch, m_predicted_batch, stateid)[source]#

Batched-mean-path replay of integrated_rts_smoother, given precomputed G_all (integrated_rts_gains) and the BATCHED filtered/predicted means (integrated_kalman_filter_batched_mean).

stateid selects, per state, whether the mean carried forward is the pre-reset prediction (m_predicted_T[k], matching smooth_start’s m_k_pre) or the filtered mean (m_filtered_T[k], matching smooth_end’s m_k) – Reset itself only enters via G_k (already baked into integrated_rts_gains), not applied again here.

Parameters:

  • G_all – (K-1, dim, dim)

  • m_filtered_batch – (M, K, dim)

  • m_predicted_batch – (M, K, dim)

  • stateid – (K,)

Returns:

(M, K, dim)

Return type:

m_smoothed_batch