Distance sensing wrist band

Hey!

I am trying to make a project for robotics competition. Problem: blind people could find the door by sensing the increase of vibration frequency. I would like to have arduino on the hand of a person and one on the door. I'm thinking that ultrasound wouldn't be precise enough. Bluetooth might also not work. What would be the best way to sense the distance?

I'm thinking that ultrasound wouldn't be precise enough.

How precise do you need it to be ?

Are you planning that the user can find the door from anywhere in the room by turning round and have the device indicate that they are facing the door and the distance to it, or something else ?