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This is an ongoing project started 2020-08-29, last updated 20-10-12 to create the page.

Purpose and Justification

Analysis of the Problems

The Basic Math

Purpose and Justification

    Even on-site when a recording is made, it can be problematic to accurately determine the direction a sound came from. Basic recorders lack the resolution to accurately determine the direction a sound came from. After some research on this problem, it turns out that even multiple independent recorders alone can only contribute to a rather inaccurately estimated direction.

    I found several relevent sources for how to solve these problems, but the most relevant is a master's thesis¹ from which I am deriving most of the solutions in this project.

1 - Locating Acoustic Sources with Multilateration Daniel Dalskov

Analysis of the Problems

    When I started into this project I expected that using 3 independent recorders and measuring their relative locations it would be as simple, in principle, to find the source of a sound as solving for the common center of the concentric circles accounting for the arrival times at each recorder. This can serve as an illustrative picture for the phrase: Easier said than done...

    Continuing that original thought for a few more moments: Measuring the relative positions of the recorders within about a meter, and sound arrival times around 0.01Sec, it seemed that positioning the source within about 15-20 meters would be achievable... But then I started into the math, and the story was over. First is the drift in sample time cause by different and independent clocks in each recorder causing an increasing error with each moment surround a required synchronization event to calibrate the absolute time for samples.

    In theory, using 3 microphones this way is workable. In practice there are problems with the approach of sloving for the center of the circles. There are easier solutions that will work, depending on the available equipment. So I will be exploring the same basic solution using a couple different approaches.

    The simpler solution is to use two microphones to resolve what turns out to be a pair of directions devined by the alignment of the microphones. The accuracy of this solution depends mostly on the distance between the microphones and the sample rate. The elegance of this solution is that it requires only 2 channels - and many audio recorders support true stereo recording, so there is the beginning of a possible off-the-shelf solution.

    The problem is that the simpler math yields a solution with some ambiguity: It is impossible to determine which side of the line defined by the microphones was the direction the sound came from...

    The solution is to use 2 or more stereo recorders, or to use a recorder capable of recording 3 or more channels in synchronization.

    The complications begin with the fact that accuracy is best with broadly separated microphones. The alignment of all microphones on a recorder is critical, as is the accuracy in measuring the relative location of the centerpoint between multiple recorders.

    The math makes resolution somewhat greater where the sound source is more perpendicular to the line between the pairs of microphones. The math is simpler treating 3 or more microphones as pairs within a set. The source is located by finding the intersection of the lines that become the solution for the direction from each pair of microphones.

    In a set of 3 microphones, for example, there are effectively 3 paris of microphones. Each pair will resolve a relative direction set for the source. The point where all 3 intersect is the source of the sound. In practice there will be a locus of 3 intersecting lines, and the centroid will be the best solution.

    In a set of 2 stereo recorders, for example, there will be a most likely intersection point with accuracy depending on the accuracy of the measurement of alignment of each pair of microphones and the measurement of the direction and distance between the centerpoints.

    A third stereo recorder would provide a means to resolve a solution similar to that of a single recorder with 3 microphones.

    This is mostly a geometric math project.

    The audio analysis programs I have been using permit the gathering of timestamp information with some accuracy. The absolute accuracy would need to be determined, and would become part of the uncertainty of both the model construction and the source location process.

    A procedure needs to be worked out, and then experiments to validate it.

    The desired procedure would be something like this:

• Start all recorders in a common location.
• Record a reference sound with all recorders in the same place - this proivdes a common time-stamp.
• As each recorder is placed, record a reference sound - this provides a location time-stamp.
• Back at the camp, and periodically record a reference sound - this will help account for time drift.
• Before collection, record a final reference sound.

    The reference sound must not be one that is known to result in interactions with the subjects. By this I mean not a loud shout, which may be a territorial challenge and has been reported to bring in large males. Also ruled out is a scream which may be an alarm call that is also reported to bring in large males. Evidence from the first year is that even whoops will cause interactions from the subjects¹.

    The reference sound may be a sports whistle, or a car alarm beep - it should be something that all recorders will pick up.

    The relative time-stamps of any given sound will help identify the relative direction of the source of a sound.

1 - Of 10 visits to the research area in 2020, in 5 we were just people around the camp. In 5 we behaved largely the same way, but called 3 whoops into the dusk... On 4 of these 5 evenings we had apparent reactions from the subjects including branch breaks and trees falling down.

The Basic Math

    At 68°F at sea level the speed of sound is 343 meters per second. This will absolutely affect the accuracy of the system, but it is a relatively complex relation between air pressure, humidity, and temperature.

    Initial experiments will have to measure relative poistions more accurately to verify results. I would like accuracy in the range of 10-20 meters to provide a starting point to search for the source of a sound, such as a branch break or a tree that fell.

    This absolutely requires accuracy of better than 0.06s from the audio file.

    A first experiment with 2 recorders at a fixed distance used to detect a reference sound where both recorders are on a line from the source would help to determine if this level of accuracy can be expected - or to measure the level of accuracy that may be achieved...

    That experiment could be extended with time to allow for different clocks in each recorder drifting over time. This could also verify if a periodic reference sound could be used to recalibrate for that drift. An extension of this experiment would determine if the drift is relatively constant with time.

    Along the way we want to determine if the relative locations of recorders can be triangulated accurately enough by reference sounds. This is more of a mathematical exercise for which the accuracy of the results depend on the first practical experiments.

    Finally is the need to estimate the source location based on the captured audio files by triangulating suspected sounds. This is also more of a mathematical exercise for which the accuracy depends on the accuracy of estimating the recorder placement and the first practical experiments.