Ranging with Frequency Dependent Ultrasound Air Attenuation

Measuring the distance between two points has multiple uses. Position can be geometrically calculated from multiple measurements of the distance between reference points and moving sensors. Distance measurement can be done by measuring the time of flight of an ultrasonic signal traveling from an emitter to receiving sensors. However, this requires close synchronization between the emitter and the sensors. This synchronization is usually done using a radio or optical channel, which requires additional hardware and power to operate. On the other hand, for many applications of great interest, low-cost, small, and lightweight sensors with very small batteries are required. Here, an innovative technique to measure the distance between emitter and receiver by using ultrasonic signals in air is proposed. In fact, the amount of the signal attenuation in air depends on the frequency content of the signal itself. The attenuation level that the signal undergoes at different frequencies provides information on the distance between emitter and receiver without the need for any synchronization between them. A mathematical relationship here proposed allows for estimating the distance between emitter and receiver starting from the measurement of the frequency dependent attenuation along the traveled path. The level of attenuation in the air is measured online along the operation of the proposed technique. The simulations showed that the range accuracy increases with the decrease of the ultrasonic transducer diameter. In particular, with a diameter of 0.5 mm, an error of less than ±2.7 cm (average value 1.1 cm) is reached along two plane sections of the typical room of the office considered (4 × 4 × 3 m3).