To save the settings server side the general idea is to store a unique identifier in a cookie in the client's browser, then store the settings in some sort of storage layer on your server using the same unique identifier. Then, when the user visits, read the identifier from the cookie they send, then look up the stored settings in your storage layer using that identifier. In Rails this is generally done through sessions. By default these sessions expire when the user closes their browser. If you want some or all of the session data to stick around longer you will need to either modify your Rails session configuration or manually set a long-term cookie and take care of the storage/retrieval on your own.
To save the settings client side, which you might want to do if these filters are applied through javascript, there are a number of options. Javascript can access the user's cookies too, so that is an option, and so are things like localStorage. Tools like Amplify.store take care of browser inconsistencies and make client-side storage pretty simple.