Store AJAX parameters in URL (Rails)

I was already able to replace the posts using AJAX upon submitting the form. The problem though, is that the URL is not updating to include the params I added.

When I click on Submit, the values are passed to the controller. I can call params[:tags] and it will return the IDs. However, the URL is still localhost:3000/posts/:id and it didn't include the tag_ids.

Here are the affected files:

posts_controller.rb:

def show
  @posts = get_posts

  respond_to do |format|
    format.js
    format.html
  end
end

posts/show.html.haml:

#posts
  = render "posts", { posts: posts }

= form_tag url_for(:only_path => false), method: :get, remote: true, id: "posts-form" do
 
  @tags.each do |tag|
    = check_box_tag "tags[]", tag[:id]
    = tag[:name]

  = submit_tag "Filter"

posts/show.js.erb:

$('#posts').html("<%= j (render 'posts', posts: @posts) %>")