Theory, execution and actual construction of a 'Bullet-Shot Location' like system

 How could it be done? I have revised a version using only two microphones that once one of the microphones 'hear'  the sound, a timer will start and will stop once the next microphone 'hears' it. 

This would essentially enable you to draw a line straight down the middle of the gun. It would also allow for tracking the location in real-time.

How could you physically build it for a cheap set-up.

I'll upload a couple of diagrams some time.

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Two microphones simply will not work for this application.  The fallacy lies in the fact that there simply isn't a proper way to emulate what happens with the human ear in an effort to determine direction.  To do this, as Kelsey stated, you would need to mimic the pinnae of a human, place the microphones in a dummy head with ear canals, and decode frequency information in the same way our brains do; this process is entirely too complicated to duplicate, and the outcome still will not be very accurate.

Think of it like this: someone fires a gun in the woods and you cannot see the shooter.  You will have a good impression of the general direction of the shot, but if you point to the exact place you think you heard him, the chances are you'll be off by at least 10 degrees.

If you do not care about triangulating distance, this approach can be done easily enough with three microphones and analog circuitry.  However, it won't work in the arrangement you proposed, nor with conventional microphones.  Also, it will only work in a two-dimensional plane relative to the polar pattern of the microphones (if you need height information, you would require four microphones).

You would need two microphones with a figure-8 polar pattern, meaning they pick up sound equally from the back and front.  As they only have one diaphragm, sounds from the rear will be 180 degrees out of phase with sounds from the front.  You would then arrange them in a Blumlein array, which is a common miking technique for stereo imaging in studios.  You will also need an omnidirectional microphone, which will be used as a reference.

How to Set Up: The microphones are arranged so that they intersect at 90 degree angles at the center of their diaphragms; the front of each mic will face towards 0 degrees of the plane.  The omnidirectional microphone will point at 0 degrees, therefore bisecting the two figure-8's, and it's diaphragm will be placed as close to the center of the other two mics as possible.  The microphones will run into a decoder circuit that compares both the relative phase and amplitude of the signals.  This information will give you the direction of the sound source.

How it Works: The relative phase and amplitude between all three microphones can be compared with off-the-shelf analog circuitry and yield fairly accurate information as to the direction of the shooter.

Some examples: At 0 degrees, the gunshot will be picked up at equal amplitude and phase in all three microphones.  At 180 degrees, the shot would be common in phase to the two figure-8's, but out of phase with the omni.  At 45 degrees, one figure-8 mic will have common phase and amplitude with the omni, but the other will not have a signal for the impulse as it the sound energy falls off-axis to this microphone (the net sound pressure will cancel to zero for this microphone).

Any angles in between would be easy enough for properly calibrated analog equipment to discern.  The concept has been idealized here for clarity, so it will require a bit of tweaking to get precise results.  Not knowing enough about electronics, I couldn't give you much more than general ideas (such as a block diagram perhaps), but I can give you my opinions if this approach interests you.

I mention this arrangement since you mentioned earlier you did not want to use digital means to calculate the angle.  The discussions about Doppler shift are meaningless to your application, as a gunshot is pretty close to a single impulse and, therefore, would not last long enough to be smeared by Doppler shift.

If you have any questions, be sure to let me know.
Lance Mt. (author)  MahavishnuMan6 years ago
 I'm still trying to gather much of the infomation you've posted, VERY helpful however i'm not suggesting that we use two mics in the sense that our body does, but it is a good example to say that it is possible. Maybe not in this manner but with two mics, yes.
Re-design7 years ago
Rotate the shooter about 90 deg. counter clock wise.  You get the same result.  How do you tell which one is right?

The black line in my diagram is the second possible location.
Lance Mt. (author)  Re-design7 years ago
 Assuming your standing still, but wouldn't the vehicle moving forwards regulated that issue?
Unless you're measuring more than you show and including data not shown in your diagram it would not.  The mics have no way to know that they are moving.  I guess you could make a recording and measure the doppler effect to get and answer to whether the shot came from in front or from the rear.  But that's not shown in your diagram.

Are you measuring time between arrival, difference in volume or what?
Lance Mt. (author)  Re-design6 years ago
 Time between arrival of the sound to each mic. Its a basic, flawed concept however very cost effective in a mass-produced manner.
.  If I understand what the OP is doing (I'm not betting very much on that fact), Doppler should be able to tell you which is the true reading. If the sensors are static, I don't see how one would discriminate between the two solutions.
.  But this would only give direction, not range. But it doesn't appear that range is important to the OP.
.  As others have noted, environmental conditions (eg, buildings, trees) will most likely lead to false readings (or sophisticated hardware/software to filter out echos and such - which I suspect will only slightly reduce the number of errors).
I can't see how the sample will last long enough to use the doppler effect though.

Since there is no fixed mic to establish a baseline then there is nothing to compare a sample to so the sample taken by the mics have nothing to compare to measure the doppler effect and thus you still won't know if the shooter is in front or behind.
.  accccckkkkkkk! I do believe you are right. One would have to know the frequency of the report for Doppler to work.
.  As far as I can tell, there are too many unknowns and variables to do this easily (ie, with two mics). It's gonna take at least something like kelsey's 3-mic setup.
kelseymh7 years ago
You need at least three microphones for triangulation.  Each microphone gives you a distance, not a direction.  That means you (effectively) draw a circle around each mic, and where they intersect is the sound location.  With two mics, you get two interesection points.

Sound travels at 330 m/s, so you need a timer with of order millisecond accuracy to get positions within 1 m.

You also need to think about how your software will deal with reflections off buildings, acoustic shadows, acoustic diffraction, and so on.
Lance Mt. (author)  kelseymh7 years ago
 But I'm not after triangulation, this would be done by using circuitry. 

 It took almost an hour of explaining to my brother, whom once finally understanding thought it better than triangulation.

This would only give direction. However, a accurate line.

I'll go dig up a diagram. 
I would definitely appreciate a diagram!  I don't see how you can get a direction at all with only a single microphone, or even a pair of microphones.

You can do "triangulation" with circuitry.  You don't need complex software, just something that can do time discrimination and the equivalent of arithmetic.  It's much easier to conceptualize with software and math, but doesn't have to be implemented that way.
Lance Mt. (author)  kelseymh7 years ago
 Diagrams up... 

The idea is that I'd be like a compass to extreme sound.

Think of it this way, We have two ears. We know direction, how loud something is defines distance, so i don't think distance is even needed. Besides, in the field distance cant be exactly helpful. It helps, but alas direction is the main thing.
There was a great article in Physics Today a couple of months ago about human sound localization.  It turns out that the shape of our pinnae (outer ears) is critical for this to work at all, because of the degeneracy (ambiguity) I described previously.  What is even more interesting, there is a frequency-dependent ambiguity that develops because of the size of the head -- some waves diffract around the head and lead to two or more apparent sound positions.
Okay, so you're just using the amplitude/intensity difference to get an angle.  That only works to zeroth order.  It doesn't take into account reflections or intervening materials, both of which will cause attenuation independent of the point of origin.

You also still get the same double solution I talked about.  You cannot resolve the ambighuity of whether the sound is in front of, or behind, the plane between the two microphones.  In fact, there's an infinite degeneracy, since the sound could originate anywhere on a circle oriented vertically, at that angle to the line of the two microphones.
.  You don't get a distance from each mic (unless in the lab). They use Time-of-arrival localization (at Wikipedia). </pedantry>
Lance Mt. (author)  NachoMahma7 years ago
 Distance isn't required.
If you have multiple pickups (more than three), then you can also do a software trick of "fitting for t0".  You have all the relative times when the sound was picked up (at the nearest mic, second nearest, and so on).  Treat the absolute time when the sound originated as an unknown parameter, and solve for it. 

Graphically, you can picture it as drawing incrementally larger and larger circles around all the mics.  As soon as you get all the circles crossing at a single point, you've found the point of origin (and the radius of the smallest circle tells you when the sound originated).
lemonie7 years ago
What are your microphones hearing?
If these are super-sonic rifle rounds you'd pick-up the shock wave at the front, when it hit the microphones. If they're not, what can the pick up after the muzzle-flash?
Like kelsey says - you'd need more than 2, probably many more for accuracy.

Lance Mt. (author)  lemonie7 years ago
 Check the diagram, this is only direction, however moving cars I'm trying to do without triangulation.
If you used multiple microphones it is possible to accomplish something called "Beam Forming" with sound waves.  This method is generally used with ultrasonic emmiters and recievers but should be transferrable to audible acoustics.  With calculated delays between the inputs of the different microphones (this can be achieved mathematically after recording the input) it is possible to (within a certain boundry) determine the direction (at least rouchly) a sound originated from. 
Lance Mt. (author)  virtualgadget7 years ago
 I have a diagram up. its not that different from beam forming, but its exuction is way off.
Re-design7 years ago
If you're doing what I think you're doing it's impossible to do with just two mikes.  Using two mikes will give you two possible locations at best if you have perfect accuracy.  The third mike tells you which of the two is the correct answer.
Lance Mt. (author)  Re-design7 years ago
 Not at all. You get two rules, bisect them into a cross.

The two sides are the microphones. The upwards ruler is the direction (inverted)

as you move the microphones, the direction changes. You move it as if it is on a graph, like on my diagram. Its the green lines, press the [i] top left of the picture to view the full size.

My dilemma occurs when i realise moving would require triangulation. I'm looking for alt.s