I need my robot to be able to find its position in a room with ±10cm accuracy. For that I have decided to place two radios right at where the door is and the third radio on the robot. The room is small, about 8×4 meters, and as I understand, on small distances the delay between radio signals, which is used for calculating our position using trilateration, would be very small. Signals from one radio will be received by another so fast, that Raspberry PI wouldn't be able to measure the delay accurate enough with its system clock to calculate an accurate position.
Can someone suggest how can I measure the position more accurately with the same set up — two radios at the door and one on the robot and using trilateration. Maybe using some specific radios, or using something else instead of the Raspberry PI, or covering radios with something to slow down the signals, or something else.
Note: can't use ultrasound.