Transcript Acoustic Triangulation Device

Group 13 Senior Design
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger
The Acoustic Triangulation Device (ATD) is an electronic system
designed to detect the location of a sonic event, specifically
gunshots or explosions, and relay that location in real time to the
user.
 Its main subsystems include but are not limited to a microphone
array, GPS locator, and real time triangulation software. These
systems will work together to determine the origin of any sonic
event within a predetermined frequency range.
 As will be shown, the philosophy of use is broad and the device will
prove useful in a variety of applications.

Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger




VIP Protection (Speeches etc.)
Inner city law enforcement
Military use
Civilian Property / National Park Regulation
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger
Requirement
Specifications
High Accuracy
Within 5 Meters of true target position
Long Range
Locates a target within 400 meters
Low Cost
Costs less than $500
Portability
Under 10lbs and less than 1 cubic meter
Ease of Use
Less than 5 minute setup time for inexperienced
users
Highly Discriminate
Able to distinguish categorized sounds with 90%
accuracy
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger
There are many algorithms for locating the origin of wave
based events.
 The majority of these techniques require the event to occur
within the area of a microphone array.
 E.g.

Mic B
Mic A
Source
Mic C
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


Many military applications use a technique called Hyperbolic
Multilateration.
In this technique the time difference of arrival (TDOA) of an
acoustic event between two microphones limits the
possibility of a source location to one half of a hyperbola.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger




A second and third TDOA are obtained from a second and third
microphone.
These TDOAs produce respective second and third hyperbolae.
The intersection of the hyperbolae is the location of the source.
In order to have an accurate measurement for the speed of sound which
we will subsequently refer to as C, we will need the temperature T.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


Due to the fact that there is a constant distance differential
along the hyberbolae this method can easily be derived from
the distance formula.
Here A, B, and C reference microphones A, B and C
respectively.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


Unfortunately since we do not know the exact time the sonic event
initially occurs we cannot know the time it takes the sound wave to travel
to the closest microphone (in this case mic A).
We do however have the TDOA between A and all subsequent
microphones, therefore we can translate the source location to A.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger



Also if we choose an origin for the system at microphone A then we can
simplify further.
This means that the locations for microphone B and C are relative
locations with respect to microphone A.
There are then two equations and two unknowns which are the xcoordinate and y-coordinate for the sound source.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


This can be easily expanded to the 3 dimensional case using
a 3rd dimensional hyperboloid.
All this takes is one additional mic and a third equation.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger




Accuracy improvement in Multilateration involves a technique known as
Nonlinear Least-Squares Stochastic Gradient Regression.
This technique involves more microphones and is an advanced way of averaging
the perceived source location from each mic.
Needless to say, this is difficult, time consuming, and increases the price of the
unit due to additional equipment.
Our initial design required eight microphones for accurate results.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


Suppose we have an acoustic event located 400 meters away from the
unit oriented directly in front of mic A with microphones spaced 1 meter
apart (as per specifications).
Mic B
This yields the equations:
400 m
Mic A
Source
Mic C
where A and B are the TDOA’s.
 Solving this yields B=0.00206025 seconds, A=0.00206025 seconds
(intuitively both TDOA’s are the same for this configuration)
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


Now suppose we have an acoustic event located 405 meters away from
the unit oriented directly in front of mic A. with microphones spaced 1
meter apart.
Mic B
This yields the equations:
405 m
Mic A
Source
Mic C
where A and B are the TDOA’s.
 Solving this yields B=0.00206026 seconds, A=0.00206026 seconds
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

Problem: A 5 meter difference in position yielded only a .00000001
second TDOA differential. That is 10 nanosecond difference.

In order to be accurate to within 5 meters we must sample nearly 100
million times a second for each of 8 microphones.
This would require a 800 MHz sample rate.
This along with the clock time for each instruction (assignment
statements, conditional operators etc.) needed to process each sample,
would require a very expensive processor.
A microcontoller with this processor would push the project out of
budget, as would a PC sound card with 8 inputs.



Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger




For 2-dimensional triangulation we need
2 arrays of 3 microphones each, oriented
in an equilateral triangle.
Each array will give us an angle which
tells us the direction of the source.
Using these two directions and the
known distance between the two arrays
we can determine the sound source’s
location.
If the microphones are close enough
together and the sound source is
sufficiently far away we can assume the
sound wave approaches as a straight
line perpendicular to the line originating
from the source.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

We can find the distance Δx1 using the
distance formula.

C is the speed of sound and tB – tA is the
difference between the time of first
detection and the time of second
detection.

Knowing the distance Δx and the side of
the array S we can find the angle θ1 using
trigonometry.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

We can find the angle α1 based on its
relationship with θ1

These equations will work regardless of
the orientation of the array, therefore
the times tA and tB will always be the
time that the first and second
microphones detect a sonic event,
respectively.
Based on these equations the sound
source could be from either side of the
line which connects the first and second
microphones. The third microphone
tells us that the source came from the
opposite side that it is located.

Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger



The relationship between the
β angles and the α angles are
determined by knowing the
orientation of each array with
respect to the line L.
This information will be
determined using a compass.
In this case:
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

Then using the Law of Sines
we can determine the
distance from the first array
to the sound source.

The coordinates for the
sound source are found by
adding each portion of the
distance (vertical and
horizontal) to the coordinates
of the GPS for the first array.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

Combining these equations
we get α for each array.

We can also combine the
previous equations to find D.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

Notice that there are two
equations which can tell us
the value of Δy1.

If these two equations are
not equal then there is some
amount of error in the
system.
Setting the two equations
equal allows us to solve for an
expected angle and compare
that angle with the one found
in the previous equations.

Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

The same equations apply to
the 3D case except that the
speed of sound is broken
into two parts.

These two equations can be
solved simultaneously and
will give us a horizontal
angle and a vertical angle.
The same method can then
be used as before to
determine the exact location
of the sound source.

Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


Lets return to the same event located 400 meters away from the unit
oriented directly in front of mic A of the first array with mics spaced 1 m
apart and 10 m between arrays.
Mic B
This yields the equations:
400 m
Mic A
Source
Mic C
where t1 and t2 are the TDOA’s.
 Solving this yields t1=0.00248763 seconds, t2=0.00252485 seconds
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


Now lets look at the event located 405 meters away from the unit
oriented directly in front of mic A of the first array with mics spaced 1 m
apart and 10 m between arrays.
Mic B
This yields the equations:
405 m
Mic A
Source
Mic C
where t1 and t2 are the TDOA’s.
 Solving this yields t1=0.00248810 seconds, t2=0.00252485 seconds. The
second time being the same due to the angle not changing.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

This time a 5 meter difference in position yielded only a
.00000047 second TDOA differential. That is 470
nanosecond difference.

This is a significant decrease in necessary sample rate. The
sample rate required for this worst case scenario which used
only 6 microphones is 12MHz.
This allowed us to use a significantly cheaper
microcontroller.

Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

This short piece of code
shows the pre-scale factor
for an ADC.

At maximum speed an ADC
loses some ability to give
an accurate analogue
voltage reading.

After some trial and error
we determined that a prescale factor of 16 was a
good average between
accuracy and speed.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger




Wavelet Vs. Fourier
Transforms
Time Domain Signal:
The Fourier transform
shows the frequency
spectrum of the time
domain signal.
Fourier Transform:
Frequency Domain Signal
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


Problem: Notice that the Fourier transform graph tells us nothing about
the times at which a frequency occurs.
Example: Observe the following two signals. (Note: Both the signals
contain only the frequencies 5, 10, 20, and 50 Hz)
Stationary
Non-Stationary
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger



Problem: The Fourier transform
of both functions provides the
same frequency response
graph.
Both signals contain the same
frequencies at different times.
Note that the Fourier graph
cannot provide any time
information at all… whatsoever.
This means Fourier analysis is
useless for distinguishing
between non-stationary audio
signals. (Most audio signals)
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger




How can we solve this problem?
One approach is the Short Time Fourier
Transform (STFT).
In this method the wave to be analyzed is
broken up into time segments via a window
function
The window function lets us correlate
different frequencies to different times and
as the STFT is just a Fourier transform in
two variables, we can again graph the
result.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger





Notice now that for each frequency there
exists a band in time, with a certain
amplitude (amount of that frequency, in
that time band)
Notice also that the width in frequency is
small but non-zero.
This indicates that the frequency resolution
is not perfect. We should have impulse
responses at 5, 10, 20, and 50 Hz.
Instead there are bands around these
frequencies.
This is known as frequency resolution and
the wider the band, the poorer the
resolution.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger


Recall, the Heisenberg uncertainty principal.
The same principal can be applied to the time and frequency information
of a signal.
Poor Frequency Resolution
Poor Time Resolution
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

To solve the problem of resolution, we will use wavelets in our signal
analysis.

Note: This is a STFT (a FT windowed in time) but windowed in frequency
as well.

The window function (psi in the equation) is now a frequency/time
window and is known as the mother wavelet.

Note that Psi is varied in time and scaled in frequency.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

Examples of suitable mother wavelets:
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

Gun shot comparison:

By using the wavelet
transforms of prerecorded
gunshots and comparing
the frequency time wavelet
coefficients to an event
currently occurring, we can
distinguish between
gunshot types with a high
degree of accuracy.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger









Microphones
Knowles MD9745APZ-F
Omni directional
Flat frequency response
Operates at 5V
Highly Sensitive
Cheap
Very small
Came with 100x preamp
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger







Development Board
Arduino Mega
Microcontroller
ATmega1280
16 Analog Inputs
16 Mhz clock speed
128kb Flash memory
Easy to program using C++
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger








GPS
EM 408
Extremely high
sensitivity : -159dBm
5m Positional Accuracy
Cold Start : 42s
75mA at 3.3V
20 gram weight
Outputs NMEA 0183
binary protocol
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger







Compass
HMC-6352
2.7 to 5.2V supply
range
Simple I2C interface
1 to 20Hz selectable
update rate
0.5 degree heading
resolution
1 degree repeatability
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger
Temperature Sensor
DS18B20 Digital
Temperature Sensor
 ± 0.5º C accuracy from
-10º C to +85 º C
 Converts temperature
to 12-bit digital word in
a max of 750ms
 Operates at 3.3 V


Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger
Budget
Part
Price
Compass - HMC 6352
59.95
GPS - EM 408
64.95
8 Mics/Preamps - MD9745APZ-F
31.80
Arduino Mega
64.95
Temperature Sensor - DS18B20
4.25
PCB
100.00
Total (Basic)
325.90
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger
Work Distribution


For the duration of the project our group worked together to
accomplish all goals.
Each member however had a specific area of expertise.
Johnathan Sanders
Ben Noble
Jeremy Hopfinger
Multilateration,
Software – UI, Coordinate
Translation, Wavelet
Triangulation
Software – GPS, Google
Earth, Microcontroller
PCB Design, Component
Integration, Array
Fabrication
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger

Robi Polikar – Rowan University
The Wavelet Tutorial
 Special thanks to Robi Polikar for allowing us to
use pictures from his website at
 http://users.rowan.edu/~polikar/WAVELETS/WTtu
torial.html

Special thanks to Louis Scheiferedecker for
allowing us to use several of his firearms for
testing.
Group 13 - Ben Noble, Johnathan Sanders, Jeremy Hopfinger