probml
replay (iterated) LOFI
Another way to avoid overcounting would be to use the buffer for updating the linearization point without updating mu or sigma. For example, at the beginning of step t we have belief state (mu_{t|t-1}, Upsilon_{t|t-1}, W_{t|t-1}) and linearized model \hat{h}{t} based at mu{t-1}. We run lofi as normal through all items in \data_{t-b:t} (a total of b+1 predict-then-update steps), yielding new belief state (mu*, Upsilon*, W*). Then we throw out Upsilon* and W* and define a new linearized model \hat{h}* based at mu*. Finally we do a single update step from (mu_{t|t-1}, Upsilon_{t|t-1}, W_{t|t-1}) using \hat{h}* and \data_t.
cf Á. F. García-Fernández, L. Svensson, and S. Särkkä, “Iterated Posterior Linearization Smoother,” IEEE Trans. Automat. Contr., vol. 62, no. 4, pp. 2056–2063, Apr. 2017, doi: 10.1109/TAC.2016.2592681. [Online]. Available: https://web.archive.org/web/20200506190022id_/https://research.chalmers.se/publication/249335/file/249335_Fulltext.pdf
