Application of acoustic detection technology in anti-sniper system

O Introduction
There has been no good technical means to deal with snipers. Generally, the method of "fighting poison with poison" is adopted, that is, using one's own snipers to deal with enemy snipers. However, this method has too many uncertainties and cannot ensure the detection of enemy snipers. Therefore, it is not suitable for security operations that cannot afford to lose. With the development of technology, many countries have developed sniper detection systems, mainly acoustic detection systems, infrared detection systems and laser detection systems. These systems either passively determine the trajectory
of the shooting and determine the position of the sniper, or actively detect lurking snipers, which to a certain extent alleviates the threat of snipers. The infrared anti-sniper detection system determines the position of the enemy sniper by detecting the infrared signal of the muzzle flash and the flying projectile. The infrared detector can detect the flash when the bullet is fired and find the target whose line of sight is not blocked within 1 km. The laser anti-sniper detection system uses the "cat's eye" effect. The cat's eye glows in the dark because the cat's retina has a stronger reflective ability than other parts of the body. Similarly, the sniper's aiming telescope has a stronger reflective ability than the surrounding background. When the laser beam in the invisible light band is irradiated on its surface, it will produce a strong reflection that is not easy for the sniper to detect but can be detected by the laser detection system, thereby discovering the sniper. The sniper acoustic detection and positioning system (as shown in Figure 1) arranges a series of acoustic sensors and accurately measures the time difference between the muzzle shock wave and the projectile flight shock wave reaching each sensor, so as to accurately calculate the shooting position, the projectile flight trajectory, the flight speed and the caliber of the gun.
Abroad, acoustic signal detection is the cheapest, most accurate and most widely used sniper detection system, while there is relatively little research in this area in China. With the purpose of applying acoustic detection technology in anti-sniper systems, the composition and positioning method of the system are studied.

1 System composition
Figure 2 shows the hardware part of the passive acoustic positioning system. The system sends the collected acoustic signals to the digital signal processor and locates the target through time delay estimation and positioning algorithm.

(1) The microphone is the ear of the intelligent mine system. It converts the acoustic signal into an electrical signal through its sensitive element, and then outputs it in the form of voltage after passing through the pre-precision amplifier circuit. Its quality and performance directly affect the accuracy of the system and whether it can correctly reflect all the information of the measured signal. This system uses an electret condenser microphone.
(2) Because the position of the sound source is different, the amplitude of the signal reaching the receiver is different, so a digital control amplifier circuit is selected.
(3) The resolution and sampling rate of the signal acquisition circuit are important factors affecting the accuracy of the delay estimation. Therefore, the design of the acquisition circuit must adopt a high-resolution, high-sampling-rate data acquisition system.
(4) DSP is the core of signal processing. The processing speed affects the reaction speed of the entire anti-sniper system. Therefore, if the cost allows, a DSP with stronger processing power and faster computing speed should be selected. This system uses TI's TMS320C6711 floating-point DSP chip, whose instruction cycle is 6.7 ns.
(5) Since the DSP direct interface requires the DSP to insert a large number of waiting cycles, it will lead to an irreconcilable contradiction between real-time display and high-speed display, affecting the general convenience. In view of this, a single-chip microcomputer is used to realize the display function. The DSP only needs to write data into the external memory, and the single-chip microcomputer checks whether to display it according to the information read out. This makes it convenient to compile a program to display the operating status of the DSP, overcoming the above contradiction.
(6) Due to the measurement accuracy (assuming that the target distance is 100 m, if the measured angle has an error of 0.1°, the target hit by the bullet will have an error of 0.17 m from the actual sound source) and fear of accidentally injuring others, this system does not include the automatic counterattack part of the sniper rifle, but only detects and displays the target position, and manually counterattacks.

2 System Positioning Principle and Algorithm
2.1 Generalized Correlation Delay Estimation Based on Wavelet Transform
The generalized correlation method is to pre-filter the received signal before estimating its correlation function, which is equivalent to weighted processing in the frequency domain, so as to whiten the signal and noise, enhance the frequency part with high signal-to-noise ratio in the signal, and suppress the noise power, so as to obtain better delay estimation accuracy. There are generally four kinds of generalized correlation weight functions, all of which require prior knowledge of the signal and noise, but in practical applications, not all of them have prior knowledge of the signal and noise, especially the prior knowledge of the noise. At the same time, it still fails to cancel the assumption that the signal must be stable. This limits the application of delay estimation and reduces the accuracy of delay estimation. For this reason, this paper introduces wavelet analysis into the correlation delay estimation method to overcome the above shortcomings.
Wavelet analysis represents the frequency domain of time domain analysis as a scale domain, that is, using a joint time and scale plane to describe the signal. Due to the multi-resolution analysis of wavelets and the multi-layer decomposition of wavelet packets, it takes into account the characteristics of short-time Fourier transform and time-frequency analysis at the same time, so it has certain advantages in processing non-stationary signals. From the relevant theory, we know that the correlation between x(t) and ψa(t) is:

Drawing on the weighted method of generalized correlated time delay estimation theory, the frequency spectrum ψ*(aω) of the base wavelet at different scales is used to weight the correlation spectral density function Gx1x2(ω), thereby obtaining the generalized correlated time delay estimation based on wavelet transform.

That is to say, before correlation, wavelet is used to filter the signals x1(t) and x2(t) respectively. Because wavelet weighting does not require prior knowledge of signal and noise compared to classical weighting, it can also be said that after x1(t) and x2(t) are correlated, wavelet transform is used to process their correlation function Rx1x2(τ). [page]

2.2 Positioning algorithm
Acoustic detection and positioning technology uses the noise emitted by the target to locate the target. How to design an acoustic array with excellent performance and simple and reasonable structure is one of the key technologies of passive acoustic positioning. Microphone arrays can be divided into linear arrays, planar arrays and stereo arrays. The linear array has a simple structure, but the linear array can only locate the half plane bounded by the straight line where the array is located. The planar array can locate the target in the entire plane, or it can locate the half space bounded by the plane where the array is located. The stereo array can locate the entire space, but its algorithm is much more complicated. From the perspective of practical application, a stereo square array is used for target positioning.
The arrangement of the microphones of the stereo array acoustic detection and positioning system is shown in Figure 3. Among them, S represents the target point sound source, and M1, M2, M3 and M4 represent 4 microphones respectively. Using a rectangular coordinate system, the 4 microphones are located on the x0y plane. Assume the side length of the array is L, the height of M1 and M3 is h, then the coordinates of the microphones are M1 (L/2, L/2, h), M2 (L/2, L/2, 0), M3 (L/2, -L/2, h), M4 (L/2, -L/2, 0). The coordinates of the target point sound source are (x, y, z). The distance between point S and the origin is r, the target azimuth is ψ, and the elevation is θ. Assume that the distances from the sound source S to M1, M2, M3 and M4 are r1, r2, r3 and r4 respectively. And define dij to represent the distance difference between microphones Mi and Mj from the point sound source, that is:

In the rectangular coordinate system, we can get the following system of equations:

3 Simulation
Since the base wavelet used in wavelet transform is not unique and different wavelet bases will produce different results when analyzing the same problem in wavelet transform, the generalized correlation delay estimation method based on wavelet transform has the problem of selecting the optimal wavelet base. Here, the quality of the wavelet base is mainly determined by the error between the result of processing the signal by wavelet analysis method and the theoretical contact, and the wavelet base is selected accordingly. After analyzing the characteristics of all base wavelets and conducting a large number of simulation experiments under different conditions, this simulation determines to use dbN wavelet as the base wavelet of the delay estimation method (db8 is selected, as shown in Figure 5). It should be noted that the base wavelets symN and coifN are similar to dbN, so the simulation diagram based on sym4 and coif5 wavelets is also given here, as shown in Figure 5.

For the convenience of observation, the simulation output cross-correlation function caused by the correlation operation is shifted 500 points on the time axis, but none of them are subtracted in the figure. That is to say, the actual estimated delay time should be equal to the delay time corresponding to the peak of the output cross-correlation function minus the number of related operation points.
This simulation uses a non-stationary signal s(t)=2sin(2xft+qt), and adds Gaussian white noise with zero mean and constant variance, where f=30 and q=4. The number of operation points is L=500, and the number of delay points is D=48.
By comparing the various figures, it can be seen that the generalized correlation delay estimation method based on wavelet transform not only eliminates the assumptions of the direct correlation delay estimation method, but also improves the accuracy of delay estimation, increases the methods of delay estimation, and expands the application scope of delay estimation.

4 Conclusion This paper
summarizes the application of acoustic positioning technology in anti-sniper systems, analyzes the components of the system, and proposes a generalized correlation delay estimation method based on wavelet transform, which overcomes the shortcomings of the traditional correlation delay estimation method and improves the accuracy and application scope of delay estimation. The defect of this method is that it cannot estimate the delay well at every scale, and it is necessary to theoretically prove the optimal scale of delay estimation. The method of making this system is also applicable to anti-tank and anti-helicopter systems.