METHOD FOR ACOUSTIC DETECTION OF SHOOTER LOCATION

Abstract

A method for acoustic detection of shooter location includes the following steps: receiving acoustic signals by a microphone array; detecting muzzle blast (MB) and shock wave (SW) signals through matched filter and cross correlation processes; transforming the detected MB and SW signals from time domain into frequency domain; beamforming the signals by means of the Delay and Sum method in frequency domain; estimating the direction of arrival (DOA) for the MB and SW signals by finding the azimuth and elevation which give the maximum power of the beamforming response; performing range estimation using the difference between the arrival time of the MB and SW signals together with the DOA estimations.

Claims

1. A method for an acoustic determination of a shooter location, comprising the following procedural steps: receiving acoustic signals by a microphone array; detecting a muzzle blast (MB) signal and a shock wave (SW) signal through a matched filter and cross correlation processes; transforming the MB signal and the SW signal from a time domain into a frequency domain; beamforming the MB signal and the SW signal by means of a Delay and Sum method in the frequency domain to obtain a MB beam and a SW beam; estimating a direction of arrival (DOA) for the MB signal and a direction of arrival (DOA) for the SW signal by finding an azimuth and elevation, wherein the azimuth and elevation indicates the DOA of the MB signal having a maximum power of the MB beam and the DOA of the SW signal having a maximum power of the SW beam; performing a range estimation using a difference between arrival time of the MB signal and arrival time of the SW signal, the DOA for the MB signal, and the DOA for the SW signal.

2. The method according to claim 1, further comprising the following steps: comparing each acoustic signal of the acoustic signals with an MB signal model and an SW signal model; in case a matching between the each acoustic signal and the MB signal model or the SW signal model occurs, detecting the each acoustic signal as an MB signal or an SW signal accordingly.

3. The method according to claim 1, further comprising the following steps: performing the cross correlation processes on each acoustic signal of the acoustic signals with an MB signal model and an SW signal model by using the matched filter; in case a matching between the each acoustic signal and the MB signal model or the SW signal model occurs, detecting the each acoustic signal as an MB signal or an SW signal accordingly.

4. The method according to claim 2 wherein the MB signal model is a modified Friedlander wave model.

5. The method according to claim 2 wherein the SW signal mode is a Whitham wave model.

6. The method according to claim 1, wherein the MB signal and the SW signal are transformed from the time domain into the frequency domain through a Fast Fourier Transform.

7. The method according to claim 1, further comprising the following steps: calculating a delay of the DOA for MB the signal incident on the microphones in the frequency domain; applying the delay to the MB signal incident on the microphones to obtain a delayed MB signal; summing the delayed MB signal to form the MB beam through the Delay and Sum method in three dimensional space.

8. The method according to claim 1, further comprising the following steps: calculating a delay of the DOA for the SW signal incident on the microphones in the frequency domain; applying the delay to the SW signal incident on the microphones to obtain a delayed SW signal; summing the delayed SW signal to form the SW beam through the Delay and Sum method in three dimensional space.

9. The method according to claim 1, wherein the DOA for the MB signal is a direction with the maximum power of the MB beam.

10. The method according to claim 1, wherein the DOA for the SW signal is a direction with the maximum power of the SW beam.

11. The method according to claim 1, wherein in the step of performing the range estimation, a range is calculated by using an MB unit vector in the DOA of the MB signal an SW unit vector in the DOA of the SW signal; the difference between the arrival time of the MB signal and the SW signal is multiplied by the speed of sound to obtain a calculated product; and the calculated product is divided by (1the cosine of an angle between the MB unit vector and the SW unit vector).

12. The method according to claim 3, wherein when calculating the difference between the arrival time of the MB signal and the arrival time of the SW signal, starting time of the MB signal is given by an index of a maximum of a cross correlation between the MB signal and a corresponding theoretical MB signal model, and starting time of the SW signal is given by an index of a maximum of a cross correlation between the SW signal and a corresponding theoretical SW signal model.

13. The method according to claim 2, further comprising the following steps: performing the cross correlation processes on each acoustic signal of the acoustic signals with an MB signal model and an SW signal model by using the matched filter; in case a matching between the each acoustic signal and the MB signal model or the SW signal model occurs, detecting the each acoustic signal as an MB signal or an SW signal accordingly.

14. The method according to claim 2, wherein the MB signal and the SW signal are transformed from the time domain into the frequency domain through a Fast Fourier Transform.

15. The method according to claim 2, further comprising the following steps: calculating a delay of the DOA for the MB signal incident on the microphones in the frequency domain; applying the delay to the MB signal incident on the microphones to obtain a delayed MB signal; summing the delayed MB signal to form the MB beam through the Delay and Sum method in three dimensional space.

16. The method according to claim 2, further comprising the following steps: calculating a delay of the DOA for the SW signal incident on the microphones in the frequency domain; applying the delay to the SW signal incident on the microphones to obtain a delayed SW signal; summing the delayed SW signal to form the SW beam through the Delay and Sum method in three dimensional space.

17. The method according to claim 2, wherein the DOA for the MB signal is a direction with the maximum power of the MB beam.

18. The method according to claim 2, wherein the DOA for the SW signal is a direction with the maximum power of the SW beam.

19. The method according to claim 2, wherein in the step of performing the range estimation, a range is calculated by using an MB unit vector an SW unit vector in the DOA of the MB signal and the SW signal; the difference between the arrival time of the MB signal and the SW signal is multiplied by the speed of sound to obtain a calculated product; and the calculated product is divided by (1the cosine of an angle between the MB unit vector and the SW unit vector).

20. The method according to claim 3, wherein the MB signal model is a modified Friedlander wave model.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] A representative application of the method achieving the objectives of the present invention for shooter localization is illustrated in the attached figures in order to clarify the details of the invention. The details of the description shall be considered by taking the whole description into account. In these figures;

[0018] FIG. 1 is a flowchart of a representative application of the method of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] In the method of the present invention, acoustic signals are received by an array of acoustic receivers. Microphones, especially condenser type microphones; dynamic, capacitive, stripped, crystal, electret, and carbon powdered microphones can be used as acoustic receivers without limiting the invention. First, an MB or an SW is detected from the received acoustic signals. The received acoustic signals are cross correlated with model signals (the acoustic waveforms of the MB and SW signals) by using a matched filter. The received signal is matched with the MB or the SW model according to the result of the cross correlation. If the received acoustic signal is an MB or an SW signal, the detected MB or SW signal is converted from time domain into frequency domain by using Fast Fourier Transform (FFT).

[0020] Using the MB and SW signals received by the acoustic microphone array, beams are created for every possible direction in three dimensional space by Delay and Sum beamforming in frequency domain [B. D. Van Veen, K M Buckley, Beamforming: A Versatile Approach to Spatial Filtering, IEEE Acoustics, Speech and Signal Processing (ASSP) Magazine, 4-24 (1988)]. DOA estimations for the MB and the SW signals are the maximum power directions of the MB and the SW beams, respectively. The range (distance) that generates the arrival time difference of the MB and SW signals is calculated. The location of the shooter is determined as a result of the estimated DOA and range.

[0021] The processes in the preferred embodiment of the invention are as follows:

[0022] Acoustic Receiver Array

[0023] The method of the invention comprises an array that consists of at least two acoustic receivers that are appropriate for receiving acoustic signals such as sound waves. In a preferred embodiment of the invention an acoustic receiver array that comprises condenser type microphones as acoustic receivers. The acoustic receiver aperture in the array is approximately equal to the wavelength at 1 kHz. The acoustic receiver aperture is the distance between two furthest acoustic receivers in the array.

[0024] The Detection of the Muzzle Blast (MB) and Shock Wave (SW) Signals

[0025] The acoustic signals received by the acoustic receiver array are compared with the acoustic model waveforms of the MB and SW signals. The received acoustic signal which is matched with one of the signal models is determined as an MB signal or an SW signal correspondingly. The aforementioned comparison is made by taking the cross correlation of the MB model signal and the SW signal model with the received acoustic signal by using a matched filter.

[0026] Generation of the MB Signal Model

[0027] The MB signal model can preferably be formed as follows;

[0028] The modified Friedlander wave model is used for the MB signal model [Beck, S. D., Nakasone, H., Marr, K. W. (2011). Variations in recorded acoustic gunshot waveforms generated by small firearms, J. Acoust. Soc. Am. 129(4), 1748-1759.].

[0029] The positive phase part of the MB is calculated by the following equation;

pp=Psp*(1tp/T0p).*exp(b*tp/T0p)

[0030] Terminology: [0031] pp=the positive phase part of the MB [0032] Psp=the maximum pressure of the positive phase (in Pascals) [0033] tp=the time vector for the positive phase (in seconds) [0034] T0p=the duration of the positive phase (in seconds) [0035] b=an exponential coefficient (unitless) [0036] =multiplication [0037] .*=element-wise multiplication

[0038] In addition to the positive phase part, the second part of the MB signal, which is named as the negative phase, is calculated by the following equation;

pn=Pnp*(tn/T0n).*(1tn/T0n).*exp(4*tn/T0n)

[0039] Terminology: [0040] pn=the negative phase part of the MB [0041] Pnp=the maximum pressure of the negative phase (in Pascals) [0042] tn=the time vector of the negative phase (in seconds) [0043] T0n=the duration of the negative phase (in seconds) [0044] *=multiplication [0045] .*=element-wise multiplication

[0046] The MB signal model is obtained by concatenating the positive and negative phase parts.

[0047] Generation of the SW Signal Model

[0048] The SW signal model can be preferably created as follows;

[0049] For the SW signal model, Whitham wave model [Stoughton, R. (1997). Measurements of small-caliber ballistic shock waves in air, J. Acoust. Soc. Am. 102(2), 781-787.] is used.

p_kernel_SD=Pmax*(12*(t/tmax))

[0050] Terminology: [0051] p_kernel_S=SW signal model [0052] t=time in seconds

Pmax=(0.53*P0*(M.sup.21).sup.(1/8)*d)/(b.sup.(3/4)*l.sup.(1/4)) [0053] P0=ambient pressure (in Pascals) [0054] M=v/c Mach number (unitless) [0055] v=speed of the bullet (meters/seconds) [0056] c=speed of sound (meters/seconds) [0057] d=caliber (in meters) [0058] b=miss distance (in meters) [0059] l=bullet length (in meters)

tmax=(1.82*M*b.sup.(1/4)*d)/(c*(M.sup.21).sup.(3/8)*l.sup.(1/4) [0060] M=v/c Mach number (unitless) [0061] v=speed of the bullet (meters/seconds) [0062] c=speed of sound (meters/seconds) [0063] d=caliber (in meters) [0064] b=miss distance (in meters) [0065] l=bullet length (in meters)

[0066] Matched Filter and Cross Correlation Process

[0067] Separate cross correlations (matched filter) are carried out for the detection of MB and SW signals. The cross correlation between the received signal (vector x of size Nx1) and the theoretical signal model (vector y of size Ny1) corresponding to the m-th delay is calculated as follows:

Cxy(m)=.sub.n[x(n)*y(n+m)]

[0068] Terminology: [0069] Cxy(m)=Cross correlation [0070] x(n)=Received signal [0071] y=Theoretical signal model [0072] n=Time index [0073] m=Time delay index

[0074] The time delay index (m) stands for the time difference in matching the received signal with the MB or SW signal model. The summation is calculated over the time index n.

[0075] If a matching occurs as a result of the cross correlation, the received acoustic signal is detected either as an MB or as an SW signal.

[0076] Delay and Sum Beamforming

[0077] If an MB or an SW is detected, the received acoustic signal is transformed from time domain into frequency domain by means of the Fast Fourier transform (FFT). The aforementioned transformation process is preferably performed as follows; [0078] The acoustic signal of size (NtM), which is received by M microphones at time index N is transformed into frequency domain by FFT:

X(l,m)=.sub.nx(n,m)*exp(i*2**n*l/Nt)

[0079] Terminology: [0080] X(l, m)=FFT output of the signal of length Nt received by M microphones [0081] x(n, m)=The signal received by the microphones [0082] i=(1).sup.(1/2) complex number [0083] l=[0, Nfft1] frequency index [0084] m=[1, M] acoustic receiver channel [0085] n=[1, Nt] time index [0086] Nt=Number of samples in the received signal

[0087] The maximum amplitude in any channel (for example, at the 2nd channel/column that belongs to a reference acoustic receiver) of the Fourier coefficient matrix X with dimensions of ((Nfft/2+1)M) is found. The frequency index (l0) and the frequency value (f0) corresponding to the maximum amplitude is determined.

[0088] Subsequently, using the MB and SW signals received by the acoustic microphone array, beams are created for every possible direction in three dimensional space by Delay and Sum beamforming in frequency domain [B. D. Van Veen, K. M. Buckley, Beamforming: A Versatile Approach to Spatial Filtering, IEEE Acoustics, Speech and Signal Processing (ASSP) Magazine, 4-24 (1988)].

[0089] An MB or an SW signal is incident on each of the array microphones with a different delay. This delay is due to the spatial location differences of the microphones in the acoustic receiver array. In the Delay and Sum method, for an acoustic signal incident on the microphone array, delays are calculated in frequency domain for every possible DOA. These delays are applied to the received acoustic signals, and then the signals are summed up to form a beam for every possible DOA in three dimensional space. The abovementioned procedure is carried out for MB and SW signals.

[0090] Azimuth () vector of size (3591) and elevation () vector of size (1811) are created with a resolution of 1 degree for [0, 359] degrees and [90, 90] degrees, respectively. [0091] The beamforming response corresponding to the (azimuth , elevation ) angle pair is calculated as:

r(,)=.sub.mX(l0,m)*w(m)

[0092] Terminology: [0093] X(l0, m)=Fourier coefficient at the frequency corresponding to the maximum amplitude of channel m

w(m)=(1/M)*exp(i*(2**f0/c)*Rs(1,m)*(cos(Rs(2,m))*cos()*cos(Rs(3,m))+sin()*sin(Rs(3,m))) [0094] Rs(1, m)=Distance of m-th microphone to the center of the receiver array [0095] Rs(2, m)=Azimuth of m-th microphone with respect to the center of the receiver array [0096] Rs(3, m)=Elevation of m-th microphone with respect to the center of the receiver array

[0097] DOA Estimation for MB and SW Signals

[0098] DOA estimations for the MB and the SW signals are the directions with the maximum power for the MB and the SW beams, respectively.

[0099] The signal power in each direction of the beam is given by the following equation:

b(,)=|r(,)|.sup.2

[0100] Terminology: [0101] r(,)=The beamforming response corresponding to the (azimuth (), elevation () angle pair [0102] b(, )=Signal power in each direction [0103] After beamforming for all azimuth and elevation directions, the azimuth and the elevation of the incoming acoustic signal is given by the maximum of the beamforming response:

(.sub.0,.sub.0)=max.sub.(,)(b(,))

[0104] Terminology:

[0105] .sub.0=The azimuth DOA with the maximum response

[0106] .sub.0=The elevation DOA with the maximum response

[0107] Range Estimation

[0108] The range (distance) that generates the arrival time difference of the MB and SW signals is calculated. The location of the shooter is determined as a result of the estimated DOA and range.

[0109] The range is calculated by using the difference of velocities of MB and SW signals in air. Their arrival times at the acoustic receiver array are different. In a preferred embodiment of the invention, the difference between the arrival times of MB and SW signals is taken as the difference between the starting points of these signals, which are determined according to their cross correlations with the corresponding signal models. [0110] Using the (azimuth, elevation) DOA estimations for MB and SW signals, which are denoted by (.sub.SW, .sub.SW) and (.sub.MB, .sub.MB), unit vectors in these DOA directions are generated.

u.sub.SW=[cos(.sub.SW)*cos(.sub.SW), sin(.sub.SW)*cos(.sub.SW), sin(.sub.SW)].sup.T

u.sub.MB=[cos(.sub.MB)*cos(.sub.MB), sin(.sub.MB)*cos(.sub.MB), sin(.sub.MB)].sup.T

[0111] Terminology: [0112] .sub.SW=The azimuth DOA estimation for the SW signal [0113] .sub.SW=The elevation DOA estimation for the SW signal [0114] .sub.MB=The azimuth DOA estimation for the MB signal [0115] .sub.MB=The elevation DOA estimation for the MB signal [0116] u.sub.SD=Unit vector for the SW signal that has a DOA of (.sub.SW, .sub.SW) [0117] u.sub.MB=Unit vector for the MB signal that has a DOA of (.sub.MB, .sub.MB) [0118] The cosine of the angle between these two unit vectors is obtained by means of scalar multiplication:

cos()=(u.sub.SW(1)*u.sub.MB(1))+(u.sub.SW(2)*u.sub.MB(2))+(u.sub.SW(3)*u.sub.MB(3)) [0119] Consequently, the firing range is calculated by using t value that is the difference between the arrival times of the MB and SW signals. The range value is calculated by

range=(t*c)/(1cos()).