<p>It is not a silly question, but gives me the possibility to discuss the process of direction finding with 2 hydrophones.</p>
<p>The direction to the source is estimated using the time delay between the sound arrivals at the two hydrophones. Say, following the picture in OP, sound arrives first (at time t1) at hydrophone h1 (at location x1) and then (at time t0) at hydrophone h0 (at location x0), then the time delay relative to <span class="math-container">$t0$</span> is <span class="math-container">$ dt = t1-t0$</span> and the angle to the sound source is estimated by solving <span class="math-container">$cos \beta = -c*dt/dx$</span>, where <span class="math-container">$dx=|x1-x0|$</span> is the distance between the two hydrophones and c is the souns speed. The &quot;-&quot; sign is due to the fact that direction to sound is opposite to direction of sound propagation.</p>
<p>Technical speaking hydrophone h0 is the reference hydrophone and <span class="math-container">$\beta=0°$</span> means that the sound arrives along the h0-h1 axis. Now, if one were to choose hydrophone h1 as reference then the delay would simply change the sign and consequently a signal arriving along the h0-h1 axis would result in an angle estimate <span class="math-container">$\beta=180°$</span>.</p>
<p>In general, both angle estimates would be parallel, which is a consequence of the fact that using only 2 hydrophones you only can estimate sources that are assumed in the far field. For estimating angles in the near field (as in the picture in the OP) you need at least three hydrophones.</p>
<p>So, in order to answer the explicit question, the angle estimated with two hydrophones does not convey ranging capability and does not change when moving the acoustic reverence between the hydrophones, and consequently <span class="math-container">$\alpha = \beta = \gamma$</span>.</p>
<p>Typically, one references the angle to the acoustic center of the array, therefore <span class="math-container">$\beta$</span> is a good way to draw the angle to the sound source.</p>
<p>Clarifications:</p>
<ul>
<li>The estimated angle is relative to the x-axis (i.e. connecting
hydrophone h0 to h1. To ontain the true bearing to the source (<em>i.e.</em>
relative to North) then one needs to correct for the direction of the
array axis.</li>
<li>As with any line arrays, the angle describes a cone around the axis
of the line array. That is, an angle of say <span class="math-container">$\beta=90°$</span> could mean
that the source is left of the array, or right, or just below, or
exactly above the array. With a line array, one cannot resolve this
ambiguity. For resolving the 3D ambiguity one needs a volumetric
array.</li>
</ul>

CC BY-SA 4.0
2023-10-24T20:23:50.093Z
Thank you very much for this clear and enriching answer, I already read about the underlying physic/math but the way equations and physical principals were presented was not as easy to understand for a biologist. Side question, let's assume now that the array can rotate around h0 (h1 being at a given time at given position on a circle of radius h0-h1). How does this affect the bearings, assuming h0 being the centre of the array? I guess the bearings needs to be corrected for the array's heading?
Patou
CC BY-SA 4.0
2023-10-24T18:38:21.540Z
2023-10-25T05:25:12.820Z
2023-10-25T05:25:12.820Z
WMXZ
<p>Maybe a silly question but I haven't found simple obvious answer in the help of PAMGuard.
I am running the click detector on recordings from a two-fixed-hydrophone array simplified on the figure below. For each detection the click detector output a bearing. I would like to know what is the reference point for the bearing calculation, or put differently which of angle alpha, beta or gamma is calculated for each detection.</p>
<p><a href="https://i.sstatic.net/HkXPv.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/HkXPv.png" alt="enter image description here" /></a></p>

<pamguard><bearing>
What is the bearing's reference point in PAMguard
# What is the bearing's reference point in PAMguard

(Asked by: username_0 on 2023-10-24)

Maybe a silly question but I haven't found simple obvious answer in the help of PAMGuard.
I am running the click detector on recordings from a two-fixed-hydrophone array simplified on the figure below. For each detection the click detector output a bearing. I would like to know what is the reference point for the bearing calculation, or put differently which of angle alpha, beta or gamma is calculated for each detection.

[![enter image description here](https://i.sstatic.net/HkXPv.png)](https://i.sstatic.net/HkXPv.png)

**Tags:** pamguard, bearing


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## 1 answers

### Answer by username_1 on 2023-10-24. Score: 2

It is not a silly question, but gives me the possibility to discuss the process of direction finding with 2 hydrophones.

The direction to the source is estimated using the time delay between the sound arrivals at the two hydrophones. Say, following the picture in OP, sound arrives first (at time t1) at hydrophone h1 (at location x1) and then (at time t0) at hydrophone h0 (at location x0), then the time delay relative to $t0$ is $ dt = t1-t0$ and the angle to the sound source is estimated by solving $cos \beta = -c\*dt/dx$, where $dx=|x1-x0|$ is the distance between the two hydrophones and c is the souns speed. The "-" sign is due to the fact that direction to sound is opposite to direction of sound propagation.

Technical speaking hydrophone h0 is the reference hydrophone and $\beta=0°$ means that the sound arrives along the h0-h1 axis. Now, if one were to choose hydrophone h1 as reference then the delay would simply change the sign and consequently a signal arriving along the h0-h1 axis would result in an angle estimate $\beta=180°$.

In general, both angle estimates would be parallel, which is a consequence of the fact that using only 2 hydrophones you only can estimate sources that are assumed in the far field. For estimating angles in the near field (as in the picture in the OP) you need at least three hydrophones.

So, in order to answer the explicit question, the angle estimated with two hydrophones does not convey ranging capability and does not change when moving the acoustic reverence between the hydrophones, and consequently $\alpha = \beta = \gamma$.

Typically, one references the angle to the acoustic center of the array, therefore $\beta$ is a good way to draw the angle to the sound source.

Clarifications:

* The estimated angle is relative to the x-axis (i.e. connecting
  hydrophone h0 to h1. To ontain the true bearing to the source (*i.e.*
  relative to North) then one needs to correct for the direction of the
  array axis.
* As with any line arrays, the angle describes a cone around the axis
  of the line array. That is, an angle of say $\beta=90°$ could mean
  that the source is left of the array, or right, or just below, or
  exactly above the array. With a line array, one cannot resolve this
  ambiguity. For resolving the 3D ambiguity one needs a volumetric
  array.

> **Comments:**
> **username_0**: Thank you very much for this clear and enriching answer, I already read about the underlying physic/math but the way equations and physical principals were presented was not as easy to understand for a biologist. Side question, let's assume now that the array can rotate around h0 (h1 being at a given time at given position on a circle of radius h0-h1). How does this affect the bearings, assuming h0 being the centre of the array? I guess the bearings needs to be corrected for the array's heading?  

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