Training to Improve the Ability to Read People's Feelings

I don't know if it is even possible to improve your ability to read people's feelings, but if there is I would like to try it.

I am in my mid-60's and have Asperger's; although it didn't have a name when I was born. I have recently attended a mediation course but found it very difficult. I found that I cannot work out how somebody sitting in front of me is feeling speedily enough to be an effective mediator. Given a few seconds to analyse the words they used and to think about their physical expressions; I can work out how they are probably feeling and plan a suitable response. However, this makes for a very disjointed conversation.

Has anybody come across a technique that I could be taught or learn from a book (a book that is showing my age) to speed up my internal processing? Before the course, I had suspected I might have a problem, but I hadn't realised how much it would limit my ability. It hasn't been a significant issue before.

All suggestions gratefully recieved