I am trying to localize a robot within a rectangular room (182cm x 243cm) with completely black walls (so IR sensors and LIDAR are out of the question). I am trying to figure out if I can position enough ultrasonic sensors around my robot so that I can calculate the distance to each wall and the orientation of the robot at any heading or position within the room (assuming the bot does not get too close to any of the walls).
What is the maximum angle at which an ultrasonic sensor can reflect against a wall and still get an accurate reading? I am using these sensors specifically, which have 1mm resolution:
Any other tips on localization in this kind of environment?