Shooting range estimation method based on miss distance and weapon caliber prediction for firearms

Abstract

A method providing an estimation of a shooting range with high accuracy by a miss distance estimation and a weapon caliber classification following detection of shooting of firearms with supersonic bullets, and by using novel equations constructed from field shooting data for each caliber in order to ensure a security of a patrol station, a border, troops, a society, a vehicle and a convoy is provided.

Claims

1. A method for prediction of a shooting range by a detection of acoustic signals from shooting of firearms with supersonic bullets by at least one microphone without need for any parameter adjustment or preliminary information, comprising the process steps of: detection of a shock wave and a muzzle blast from the detected acoustic signals, calculation of a shock wave central frequency by using a Fast Fourier Transform method estimation of an arrival time difference between the shock wave and the muzzle blast, estimation of a miss distance based on bullet speed, sound speed and shock wave signal slope, estimation of a bullet caliber based on the miss distance frequency and the shock wave central frequency, estimation of the shooting range by use of the arrival time difference calculated between the shock wave and the muzzle blast, the miss distance prediction and the weapon caliber prediction, wherein the shock wave signal slope can be calculated by dividing a difference between maximum signal power and minimum signal power by a difference between a time in which the signal power is minimum and a time in which the signal power is maximum.

2. A method for prediction of a shooting range by a detection of acoustic signals from shooting of firearms with supersonic bullets by at least one microphone without need for any parameter adjustment or preliminary information, comprising the process steps of: detection of a shock wave and a muzzle blast from the detected acoustic signals, calculation of a shock wave central frequency by using a Fast Fourier Transform method estimation of an arrival time difference between the shock wave and the muzzle blast, estimation of a miss distance based on bullet speed, sound speed and shock wave signal slope, estimation of a bullet caliber based on the miss distance frequency and the shock wave central frequency, estimation of the shooting range by use of the arrival time difference calculated between the shock wave and the muzzle blast, the miss distance prediction and the weapon caliber prediction, wherein the miss distance can be calculated according to formula below; $d_{\mathrm{miss}}=k_1\sqrt{\left[{\left(\frac{v_0}{c}\right)}^2-1\right]}\frac{c^2}{v_0}\frac{1}{s_{\mathrm{sw}}}$ wherein; “d.sub.miss” is the miss distance, “k.sub.1” is a fixed coefficient, “v.sub.0” is a bullet speed of constant 800 m/s, “c” is a sound speed and “s.sub.sw” is the shock wave signal slope.

3. A method for prediction of a shooting range by a detection of acoustic signals from shooting of firearms with supersonic bullets by at least one microphone without need for any parameter adjustment or preliminary information, comprising the process steps of: detection of a shock wave and a muzzle blast from the detected acoustic signals, calculation of a shock wave central frequency by using a Fast Fourier Transform method estimation of an arrival time difference between the shock wave and the muzzle blast, estimation of a miss distance based on bullet speed, sound speed and shock wave signal slope, estimation of a bullet caliber based on the miss distance frequency and the shock wave central frequency, estimation of the shooting range by use of the arrival time difference calculated between the shock wave and the muzzle blast, the miss distance prediction and the weapon caliber prediction, wherein a miss frequency can be calculated according to formula below; $f_{\mathrm{miss}}=a_0+a_1{d}_{\mathrm{miss}}+a_2{d}_{\mathrm{miss}}^2+a_3{d}_{\mathrm{miss}}^3$ wherein; “f.sub.miss” is the miss frequency, “α.sub.0, α.sub.1, α.sub.2, α.sub.3” are the fixed coefficients and “d.sub.miss” is the miss distance.

4. The method according to claim 1, wherein the bullet caliber estimation can be performed according to below equation: $\mathrm{cal}=\{\begin{array}{c}12.7\mathrm{mm};f_{\mathrm{sw}}<f_{\mathrm{miss}}-300\\ 5.56\mathrm{mm};f_{\mathrm{sw}}>f_{\mathrm{miss}}+300\\ 7.62\mathrm{mm};.Math.f_{\mathrm{sw}}-f_{\mathrm{miss}}.Math.\le 300\end{array}$ wherein; “cal” is the bullet caliber, “f.sub.sw” is the frequency of the shock wave signal and “f.sub.miss” is the frequency of the miss distance.

5. The method according to claim 1, wherein the shooting range estimation is obtained by using the following equation based on conditions specified subject to the arrival time difference between the shock wave and the muzzle blast and caliber estimation: $R=\{\begin{array}{c}{r}_0+d_{\mathrm{miss}}+r_1\Delta T+r_2\Delta T^2;\mathrm{cal}=7.62\mathrm{mm},\Delta T>0.2s\\ r_3+d_{\mathrm{miss}}+r_4\Delta T+r_5\Delta T^2;\mathrm{cal}=12.7\mathrm{mm},\Delta T>0.2s\\ d_{\mathrm{miss}}+r_6\Delta T+r_7\Delta T^2;\mathrm{cal}=5.56\mathrm{mm},\Delta T>0.2s\\ r_8{d}_{\mathrm{miss}}+r_9\Delta T;\Delta T\le 0.2s\end{array}$ wherein; “R” is the shooting range, “r.sub.0, r.sub.1, r.sub.2, r.sub.3, r.sub.4, r.sub.5, r.sub.6, r.sub.7, r.sub.8, r.sub.9” are fixed coefficients determined according to field data, “d.sub.miss” is the miss distance, “ΔT” is the arrival time difference between the shock wave and the muzzle blast and “cal” is the estimated bullet caliber.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flow diagram of shooting location range prediction method of the invention.

(2) FIG. 2 is a graphic indicating minimum and maximum times of signal power for shock wave.

DETAILED DESCRIPTION OF THE EMBODIMENTS INVENTION

(3) In this detailed description, the preferred embodiments of the shooting range estimation method being subject of the invention have been described only for purpose of better understanding of the matter.

(4) The invention is a method for estimation of shooting range by means of detection of “acoustic signals from shooting of firearms with supersonic bullets” by at least one microphone without need for any parameter adjustment or preliminary information and characterized by comprising process steps of detection of shock wave and muzzle blast, estimation of arrival time difference between detected shock wave and muzzle blast, estimation of miss distance, bullet caliber estimation, estimation of shooting range by using the calculated time difference between shock wave and muzzle blast, miss distance prediction and bullet caliber estimation.

(5) The invention also comprises process steps of detection of shock wave by checking incoming acoustic data and Whitham shock wave model cross-correlation output and detection of central frequency of shock wave by use of Fast Fourier Transform (FFT) method. Also it comprises process step of obtaining muzzle blast detection by checking cross-correlation output of Friedlander muzzle blast model.

(6) The method for prediction of miss distance for shooting range estimation of the invention comprises process steps of estimation of bullet caliber by comparison of “shock signal frequency” with “miss frequency information” estimated by process step of estimation of the shortest distance between bullet direction and detection unit comprising at least one microphone by use of shock signal slope, bullet speed and sound speed.

(7) The invention is a method to be used for estimation of miss distance, weapon bullet caliber and range for shootings of firearms with supersonic bullets. The method disclosed hereunder can be used for purposes such as patrol station security, vehicle and convoy security, border security unit security, society security and public security.

(8) Input of the method is the acoustic signals received by detector microphones. Signals received by microphones are detected by cross correlation method in shock wave and muzzle blast detection blocks. Also shock wave detection block calculates shock wave central frequency (f.sub.sw) by FFT. Time difference (ΔT) between shock wave and muzzle blast signals is estimated as follows;

(9) $\Delta T=t_{\mathrm{mb}}-t_{\mathrm{sw}}$

(10) Here t.sub.mb refers to muzzle blast detection time, and t.sub.sw refers to shock wave detection time.

(11) Miss distance prediction yields shooting direction and trajectory information. Particularly, information on what is targeted by the shooter in the unit or vehicle convoy is obtained. In miss distance prediction block, bullet speed, sound speed and shock wave signal slope are used as inputs. Here bullet speed (v.sub.0=800 m/s) is taken as constant value Sound speed (c) is estimated by use of following formula subject to measured environment temperature (T.sub.c).

(12) $c=331+0.6T_c$

(13) For the shock wave signal shown in FIG. 2 S.sub.max shows the maximum signal power, S.sub.min is the minimum signal power, t.sub.max is the time when signal power is maximum and t.sub.min is the time when signal power is minimum. Accordingly, the expression giving the slope of the shock wave signal (s.sub.sw) is as follows,

(14) $s_{\mathrm{sw}}=\frac{s_{\max }-s_{\min }}{t_{\min }-t_{\max }}$

(15) After sound speed, bullet speed and shock wave signal slope are obtained, miss distance estimation (d.sub.miss) is calculated by following equation,

(16) $d_{\mathrm{miss}}=k_1\sqrt{\left[{\left(\frac{v_0}{c}\right)}^2-1\right]}\frac{c^2}{v_0}\frac{1}{s_{\mathrm{sw}}}$

(17) Here k.sub.1 refers to a fixed coefficient, v.sub.0 is the bullet speed, c refers to the sound speed, s.sub.sw is the shock wave signal slope.

(18) The obtained miss distance prediction is used for miss frequency determination (f.sub.miss) using a third degree equation.

(19) $f_{\mathrm{miss}}=a_0+a_1{d}_{\mathrm{miss}}+a_2{d}_{\mathrm{miss}}^2+a_3{d}_{\mathrm{miss}}^3$

(20) Here d.sub.miss refers to the estimated miss distance and, α.sub.0, α.sub.1, α.sub.2, and α.sub.3 are fixed coefficients.

(21) Successful estimation of weapon caliber provides correct prediction of threat potential, enables correct counter-measures against shooting, and helps accurate tactical decisions to be determined with high accuracy. Bullet caliber estimation in multiple shooting scenario helps taking primarily measure against heavy weapons. Also weapon caliber estimation is used as input to minimize error rate in range estimation and to make required updating. The calculated miss distance frequency (f.sub.miss) and shock signal frequency (f.sub.sw), are compared in as follows in weapon caliber estimation block and weapon caliber estimation (cal) is made

(22) $\mathrm{cal}=\{\begin{array}{c}12.7\mathrm{mm};f_{\mathrm{sw}}<f_{\mathrm{miss}}-300\\ 5.56\mathrm{mm};f_{\mathrm{sw}}>f_{\mathrm{miss}}+300\\ 7.62\mathrm{mm};.Math.f_{\mathrm{sw}}-f_{\mathrm{miss}}.Math.\le 300\end{array}$

(23) Here weapon caliber estimation is made as 5.56 mm, 7.62 mm and 12.7 mm by means of comparing conditions, and thus weapon can be classified.

(24) Using weapon bullet caliber estimation (cal) miss distance prediction (d.sub.miss) and time difference between shock wave and muzzle blast signals (ΔT), shooting range estimation (R) is obtained by using the following equation based on conditions specified subject to time difference and caliber values,

(25) $B-\{\begin{array}{c}{r}_0+d_{\mathrm{miss}}+r_1\Delta T+r_2\Delta T^2;\mathrm{cal}=7.62\mathrm{mm},\Delta T>0.2s\\ r_3+d_{\mathrm{miss}}+r_4\Delta T+r_5\Delta T^2;\mathrm{cal}=12.7\mathrm{mm},\Delta T>0.2s\\ d_{\mathrm{miss}}+r_6\Delta T+r_7\Delta T^2;\mathrm{cal}=5.56\mathrm{mm},\Delta T>0.2s\\ r_R{d}_{\mathrm{miss}}+r_9\Delta T;\Delta T\le 0.2s\end{array}$

(26) Here r.sub.0, r.sub.1, r.sub.2, r.sub.3, r.sub.4, r.sub.5, r.sub.6, r.sub.7, r.sub.8 and r.sub.9 are fixed coefficients determined according to field data.