The BBC made new versions of all of Austen's works last year (not including Pride and Prejudice or Emma, versions of which the BBC had made in the 1990s). Those are the films that PBS is airing this winter. The Emma Thompson version of Sense and Sensibility was not a BBC work.
I saw a good version of Persuasion a while back - here's the link to in imdb. Persuasion (1995) (TV)