Just add to your robots.txt - no need to submit sitemap to Google
Add that to your robots.txt. That's all you need to tell search engines where your sitemap is located.
Google Blogoscoped says, the big search players Google, Yahoo, Ask and MSN together announced they'll be adding a new way for you to tell them where you store your Sitemap XML file. As Sitemaps.org explains, Sitemaps are a way to tell search engines of your URLs to help their crawlers index them.