Feedback from F4

I think I could understand the first part, (I think it was almost particle filtering). I spent more time on the second part and made sure to read all parts,

I did not completely understand the second part,(not because of the writing)
but I think the notation ${\textbf {x}}_{n}$ does not include the history of a sample in the second part unlike how it was defined earlier, and if so it is slightly confusing