Working principle

The principle of operation of the acoustic locator is based on sound triangulation, where the direction of the location of the sound source is achieved with the use of two microphones. More specifically, the acoustic locator is using the Time Difference Of Arrival (TDOA) to determine the direction of the location of the sound source. As shown in figure 3(a), two microphones are placed next to each other with a predefined distance between them. If the distance from the sound source to the left microphone is greater from the distance of the sound source to the right microphone, then the right microphone will receive the sound wave earlier than the left microphone. This is due to the fact that sound waves travel in a spherical way at a predefined speed. The position of the sound source affects the distance between the two microphones, and therefore the time delay between the arrival of the sound wave to the left and the right microphones. The distance between the sound source and the left microphone is identified as RL, while the distance between the source and the right microphone is identified as RR.

The waveform at the lower part of figure 3(a) shows the reception of a typical sound wave by the two microphones. In this case the waveform with red colour corresponds to the wave received by the left microphone, and the waveform with blue colour corresponds to the wave received by the right microphone. The time difference (Δt) between the two waveforms is proportional to the distance difference RL– RR.

                     Figure 3

The direction of the position of the sound source can be determined using the distances RL, RR, the distance between the two microphones (Lm), the time difference Δt and the speed of sound.For the acoustic locator it is not necessary to calculate the exact direction of the position of the sound source. The acoustic locator needs to determine whether the sound source is at the left or at the right side of the microphones for the horizontal positioning, (or higher or lower for the vertical positioning) and signal the positioning motors to rotate the positioning mechanism (a) to the left or to the right for the horizontal direction and (b) up or down, for the vertical direction. The time difference (Δt) can be used in order to set the speed of the motors. The motors will keep running until the time difference (Δt) becomes zero. This operation is shown in figure 3(b).
Where x1 is the x-coordinate of the right microphone and x2 is the x-coordinate of the difference RL-RR. The distance RL-RR is equal to time difference Δt times the speed of sound.

Figure 4 shows the case where the sound source has moved to the right. In this case it can be seen that the distance RL – RR and consequently the time difference (Δt) have been increased.

                       Figure 4

However, for the current implementation of the acoustic locator, the direction (offset) of the position of the sound source is calculated using the equation derived in the Master Thesis report Direction of arrival estimation – A two microphones approach. The approach presented by this paper uses a hyperbolic graph to calculate an angular offset. When sound arrives at two microphones at slightly different times, this time delay can be used to calculate the extra length the sound wave has to travel to the further microphone. It turns out that the length resulting from all possible time delays can be used to plot a hyperbolic curve that is unique to that length, given by:

where l is the extra length traveled by the sound, x_mic is the fixed x-coordinate of the closer microphone relative to the normal line, and x is an arbitrary value greater than x_mic/2. The linear part of the hyperbola represents all the possible sound source locations for a particular l:

By calculating the value of the hyperbola function at two different x locations, it is possible to calculate the gradient of the linear part of the hyperbola, and therefore the angle alpha' shown above.

To calculate the offset from the normal line, i.e. straight ahead, which is what we're after, simply do:

Of course, if the time delay is negative, this simply means that the sound reached the other mic first and we just need to reverse the sign of alpha.