Add partial and complete missing emission support in LGSSM filtering #406
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This pull requests adds support for the inclusion of missing measurements/emissions/observations$y_t$ in the Kalman filter
dynamax.linear_gaussian_ssm.lgssm_filter
. This PR covers:This PR partially addresses issues #301, #330, #399
Implementation details$P_{t+}$ by the operator that projects onto the observed values of $y_t$ . Then the update step of the Kalman filter is modified by replacing:
Let
Mathematical details are provided in the comment of issue #399.
In addition, the log-likelihood term is adjusted accordingly, e.g.,$ \int \mathrm{d} y_{t1} p(y_{t1}, y_{t2}|y_{1:t-1})= p(y_{t2}|y_{1:t-1})$ while keeping the shape of the covariance matrices static (to prevent recompilation).
Scope
Not yet included are the corresponding implementations in:
parallel_lgssm_filter
lgssm_info_filter
Which I consider out of scope of this PR.