Estimation of the Azimuth Angle of the Arrival Direction for an Ultrasonic Signal by Using Indirect Determination of the Phase Shift

The paper presents and discusses a method of azimuth determination of ultrasonic echo arrival in air. The basis of the presented approach is the assumption that the received signal is a narrowband one. In this way, the direction of the signal arrival can be determined based on its phase shift using two receivers. When the distance between the receivers exceeds half of the wavelength of the received signal, a problem of ambiguity in determining the angle of arrival arises. To solve this, a method using multiple pairs of receivers was used. Its robustness and temperature dependence is analysed. The most important advantages of the presented approach are simplified computations and low hardware requirements. Experimental data made it possible to show that for strong echoes, the accuracy is higher than 0.5 degrees. In the case of weak echos, it is reduced to about 2 degrees. Because the method is based on phase shift measurement, the ultrasonic sonar that uses this method can be compact in size. Moreover, owing to the theoretical analysis, certain properties of the mutual location of the receivers were found and formally proved. They are crucial for determining proper receivers' inter-distances.