In this paper, a measuring system based on binocular vision is developed for the research on large-caliber gun muzzle vibration. The system is consisted of two high-speed cameras and other equipment. The two-step calibration method based on radial constraint is adopted in order to complete the calibration, the inter-frame differential multiplication method is used to detect the centroid of moving target accurately, the improved Kalman filter tracking algorithm is used to obtain the motion trajectory of the muzzle identification point. The system is applied to practice for a type of muzzle vibration measurement and meaningful original data is acquired

Gang Zhao

Qiang Chen

YingJun Wang

English

Journal of Vibroengineering

  © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. AUG 2015, VOLUME 17, ISSUE 5. ISSN 1392-8716 2229 
1671. Research on measuring method of large-caliber 
gun muzzle vibration 
Gang Zhao1, Qiang Chen2, YingJun Wang3 
1PLA 73906, 210041, Nanjing, P. R. China 
2, 3Department of Control and System Engineering, Nanjing University, 210093, Nanjing, P. R. China 
2Corresponding author 
E-mail: 173906zg@sina.cn, 2chenqia0772@vip.sina.com, 3wangyingjun13@126.com 
(Received 27 May 2015; received in revised form 3 August 2015; accepted 10 August 2015) 
Abstract. In this paper, a measuring system based on binocular vision is developed for the 
research on large-caliber gun muzzle vibration. The system is consisted of two high-speed cameras 
and other equipment. The two-step calibration method based on radial constraint is adopted in 
order to complete the calibration, the inter-frame differential multiplication method is used to 
detect the centroid of moving target accurately, the improved Kalman filter tracking algorithm is 
used to obtain the motion trajectory of the muzzle identification point. The system is applied to 
practice for a type of muzzle vibration measurement and meaningful original data is acquired. 
Keywords: gun muzzle vibration measurement, binocular vision, target detection, Kalman filter. 
1. Introduction 
In the projectile firing process, the great expansion force produced by propellant transient 
combustion, the friction of the relative movement between the projectile and gun and the inertia 
force of gun will lead to the muzzle vibration. The vibration response will directly affect the target 
lethality and the precision of the gun. Since many factors will influence the measuring instrument 
range and precision, such as the gun firing instantaneity, the muzzle space displacements and the 
interference of the muzzle flame and smoke, non-contact measuring method is usually adopted in 
the muzzle vibration responses detection. The conventional non-contact measurements such as 
displacement sensor or laser vibration can only be applied for the small caliber gun and 
one-dimensional motion testing, when facing with large caliber artillery and complex three 
dimensional motion form, accurate data is hard to obtain. 
2. Theoretical background 
Single camera will lost object depth information in the imaging process. In order to reconstruct 
three-dimensional information of space object, two cameras are needed to shoot the same image. 
In actual measurement, if the relative position information of the two cameras in the world 
coordinate system is known, the three-dimensional information can be measured in the field of 
space objects according to the triangle principle. 
 
Fig. 1. Binocular vision 
The binocular vision schematic is shown in Fig. 1, where ܣ(ݔ௪, ݕ௪, ݖ௪) is any point in the 
1671. RESEARCH ON MEASURING METHOD OF LARGE-CALIBER GUN MUZZLE VIBRATION.  
GANG ZHAO, QIANG CHEN, YINGJUN WANG 
2230 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. AUG 2015, VOLUME 17, ISSUE 5. ISSN 1392-8716  
space, two cameras’ coordinate system are (ݔଵ, ݕଵ, ݖଵ) and (ݔଶ, ݕଶ, ݖଶ), and two cameras’ image 
coordinate system are ( ଵܺ, ଵܻ) and (ܺଶ, ଶܻ), the effective focal length of two cameras are ଵ݂ and 
ଶ݂, so: 
൥ ଵܺଵܻ
1
൩ = ൥
ଵ݂ 0 0
0 ଵ݂ 0
0 0 1
൩ ൥
ݔଵ
ݕଵ
ݖଵ
൩, (1)
൥
ܺଶ
ଶܻ
1
൩ = ൥
ଶ݂ 0 0
0 ଶ݂ 0
0 0 1
൩ ൥
ݔଶ
ݕଶ
ݖଶ
൩, (2)
൥
ݔଶ
ݕଶ
ݖଶ
൩ = ൥
ݎଵଵ ݎଵଶ ݎଵଷ
ݎଶଵ ݎଶଶ ݎଶଷ
ݎଷଵ ݎଷଶ ݎଷଷ
൩ ൥
ݔଵ
ݕଵ
ݖଵ
൩ + ൥
ݐଵଵ
ݐଶଵ
ݐଷଵ
൩. (3)
The 3-D coordinates of point in the left camera in space can be expressed as Eq. (4): 
ە
ۖۖ
۔
ۖۖ
ۓݔଵ = ଵܺ
( ଶ݂ݐଶଵ − ݐଷଵ ଶܻ)
ଶܻ(ݎଷଵ ଵܺ + ݎଷଶ ଵܻ + ݎଷଷ ଵ݂) − ଶ݂(ݎଶଵ ଵܺ + ݎଶଶ ଵܻ + ݎଶଷ ଵ݂) ,
ݕଵ = ଵܻ
( ଶ݂ݐଶଵ − ݐଷଵ ଶܻ)
ଶܻ(ݎଷଵ ଵܺ + ݎଷଶ ଵܻ + ݎଷଷ ଵ݂) − ଶ݂(ݎଶଵ ଵܺ + ݎଶଶ ଵܻ + ݎଶଷ ଵ݂) ,
ݖଵ = ଵ݂
( ଶ݂ݐଶଵ − ݐଷଵ ଶܻ)
ଶܻ(ݎଷଵ ଵܺ + ݎଷଶ ଵܻ + ݎଷଷ ଵ݂) − ଶ݂(ݎଶଵ ଵܺ + ݎଶଶ ଵܻ + ݎଶଷ ଵ݂) .
 (4)
The relationship between the world coordinate system and the two camera coordinate system 
can be can be expressed as following: 
൥
ݔଵ
ݕଵ
ݖଵ
൩ = ܴଵ ൥
ݔ௪
ݕ௪
ݖ௪
൩ + ଵܶ, 
൥
ݔଶ
ݕଶ
ݖଶ
൩ = ܴଶ ൥
ݔ௪
ݕ௪
ݖ௪
൩ + ଶܶ, 
(5)
൥
ݔଶ
ݕଶ
ݖଶ
൩ = ܴଶܴଵିଵ ൥
ݔଵ
ݕଵ
ݖଵ
൩ + ൫ ଶܶ − ܴଶܴଵିଵ ଵܶ൯. (6)
3. Methods 
3.1. Experimental system 
The measurement system is shown in Fig. 2. The measurement system used in this study 
includes two high-speed cameras, camera lens, cables and triggers. The VISION RESEACH’s 
Phantom v1610 and the NIKON 400 mm f/2.8D IF-ED AF-S II Nikkor are used to build the 
system. In considering of the effects of muzzle blast wave, field illumination conditions and field 
real terrain, two high-speed cameras are placed on one side of the ground artillery and the distance 
between them is 20 meters, the vertical distance from the camera to the gun is 20 meters. Cameras 
and other equipment are connected by cables. 
3.2. Experiment procedure 
3.2.1. Calibration 
The calibration model which is self-made is fixed on one side of the muzzle by fixing device, 
1671. RESEARCH ON MEASURING METHOD OF LARGE-CALIBER GUN MUZZLE VIBRATION.  
GANG ZHAO, QIANG CHEN, YINGJUN WANG 
 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. AUG 2015, VOLUME 17, ISSUE 5. ISSN 1392-8716 2231 
and two cameras take the picture of the model from different perspectives at the same time. After 
the pictures of the model are acquired, in order to determine the external and internal parameters 
of two cameras, the two-step calibration method based on radical constraint is adopted. 
The calibration model is shown in Fig. 3, in a) ܣଵ = 75°, ܣଶ = 15°; in b) the size of each plate 
is 2400×4800 mm, the number of the mark point is 20; in c) the diameter of the mark point is 
40 mm and the center distance between each point is 80 mm. Fig. 4 shows the picture taken by 
the two cameras. 
20m
20m  
Fig. 2. Measurement system 
1A
2A
a) 
48
0.0
0
240.00
80
.0
0
80
.0
0
80.00 80.00
 
b) 
80.00
240.00
Ø40.00
c) 
Fig. 3. Calibration model 
a) Picture from left camera 
 
b) Picture from right camera 
Fig. 4. Calibration pictures 
3.2.2. Image acquisition 
The Phantom Camera Control Application is used to control two high-speed cameras. And the 
resolution of the camera is 1280×500, the sample rate is 10000 pps, the exposure time is 15 μm. 
3.2.3. Target detection 
In this paper, the inter-frame differential multiplication method is used to segment the video 
image sequences of two cameras. The method can produce the high correlation peak, which not 
only can effectively avoid the false moving targets, but also can amplify the difference between 
target area and background value and strengthen the movement of the target area. 
The equation of Inter-frame differential multiplication used in the paper: 
1671. RESEARCH ON MEASURING METHOD OF LARGE-CALIBER GUN MUZZLE VIBRATION.  
GANG ZHAO, QIANG CHEN, YINGJUN WANG 
2232 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. AUG 2015, VOLUME 17, ISSUE 5. ISSN 1392-8716  
ܩ(ݔ, ݕ) = | ଵ݂(ݔ, ݕ) − ଷ݂(ݔ, ݕ)| × | ଶ݂(ݔ, ݕ) − ସ݂(ݔ, ݕ)|, (7)
where ଵ݂(ݔ, ݕ), ଶ݂(ݔ, ݕ), ଷ݂(ݔ, ݕ), ସ݂(ݔ, ݕ) denote the four adjacent frames respectively, ܩ(ݔ, ݕ) 
is the result as pixel value. 
3.2.4. Target tracking 
Improved kalman filter tracking algorithm is used to obtain the motion trajectory of the muzzle 
identification point, in which the centroid of moving target is regarded as the observed value input. 
The algorithm obtain the moving target through the estimation and correction of it’s centroid 
position. 
To restrain the divergence of Kalman filter, improved Kalman filter tracking algorithm based 
on fading factor is proposed. The algorithm expand the priori estimate covariance ܲି(݇), offset 
the error accumulation and improve the estimation accuracy and robustness of the Kalman filter. 
The fading factor and the scalar factor are used: 
ܲି(݇)ᇱ = ߟ௞ܲି(݇), 
ܪ(݇)ᇱ = ߙ௞ܪ(݇). (8)
where ߟ௞ is the fading factor, ߙ௞ is the scalar factor, the new Kalman gain matrix is: 
ܭ(݇)ᇱ = ߟ௞ߙ௞ ܭ(݇). (9)
The optimal value of ߙ௞  can generally be used in window estimation method which is 
estimated as: 
ߙ௞ = max ቆ1,   
ݐݎܽܿ݁(ܪ(݇)ᇱ)
ݐݎܽܿ݁൫ܪ(݇)൯ ቇ, 
ܪ(݇)ᇱ =
ە
۔
ۓߟ௞ିଵ ௜ܰ ௜ܰ
்
1 + ߟ௞ିଵ ,   ݇ > 1,
1
2 ଴ܰ ଴ܰ
்,       ݇ = 1.
 
(10)
And the optimal value of the fading factor ߟ௞ can be estimated as: 
ߟ௞ =
ݐݎܽܿ݁൫ܪ(݇)ᇱ − ܴ(݇)൯
ݐݎܽܿ݁൫ܥ(݇)(ܣ(݇)ܲ(݇ − 1)ܣ(݇)் + ܳ(݇ − 1)ܥ(݇)்)൯. (11)
3.3. Results and analysis 
3.3.1. Calibration information 
The calibration results of two cameras are as follows: 
Left camera: 
ܴଵ = ൥
−0.9985 0.0295 0.0461
−0.0480 −0.0665 −0.9966
−0.0264 −0.9973 0.0678
൩, (12)
ଵܶ = ሾ−635.7405 880.0560 16326.698ሿ. (13)
Right camera: 
1671. RESEARCH ON MEASURING METHOD OF LARGE-CALIBER GUN MUZZLE VIBRATION.  
GANG ZHAO, QIANG CHEN, YINGJUN WANG 
 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. AUG 2015, VOLUME 17, ISSUE 5. ISSN 1392-8716 2233 
ܴଶ = ൥
−0.9862 −0.1652 −0.0069
−0.0232 0.0968 −0.9950
0.1637 −0.9815 −0.0994
൩, (14)
ଶܶ = ሾ−2352.483 −1340.9633 14722.933ሿ. (15)
3.3.2. Target detection 
To achieve the target region accurately, the inter-frame differential multiplication method is 
used for the video image sequence of two cameras through different perspectives. To calculate the 
centroid coordinate, the mathematical morphology filtering, connected domain analysis and 
feature extraction are used in the image processing. The results are shown in Fig. 5. 
 
a) Picture from left camera 
 
b) Picture from right camera 
Fig. 5. Target detection 
3.3.3. Target tracking 
The centroids of the target are used as the input value in the Kalman filter target tracking  
model, and fading factor is introduced to increase the weight of new information and avoid the 
divergence of Kalman filter. The results are shown in Fig. 6. 
a) Picture from left camera 
 
b) Picture from right camera 
Fig. 6. Target tracking 
3.3.4. Three dimensional measurement  
In the paper, the world coordinate system is determined by the calibration model, the origin of 
coordinates and coordinate axis shows in Fig. 7. The ܺ axis is parallel to the direction of the 
muzzle, the ܻ axis is parallel with the ground and pointing to the cameras, and the ܼ axis is 
perpendicular to the muzzle direction and pointing to the sky. 
Muzzle direction
 
Fig. 7. World coordinate system 
The muzzle vibration displacement curve in the two dimensional coordinate shows in Fig. 8. 
1671. RESEARCH ON MEASURING METHOD OF LARGE-CALIBER GUN MUZZLE VIBRATION.  
GANG ZHAO, QIANG CHEN, YINGJUN WANG 
2234 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. AUG 2015, VOLUME 17, ISSUE 5. ISSN 1392-8716  
The three-dimensional displacement coordinate displacement curve shows in Fig. 9. 
According to the results, due to the recoil of the gun, the muzzle vibration displacement curve 
in the ܺ  axis direction is rising and constant moving backward, in the ܻ  axis direction is a 
continuous shock curve, which representing the swing shift and in the ܼ axis direction is a rising 
curve which represented the displacement in vertical direction, but the increase is far less than that 
in the ܺ axis direction. 
Fig. 8. The muzzle vibration displacement curve 
 
Fig. 9. The muzzle vibration displacement curve 
4. Conclusions 
To resolve the problem of conventional measurement methods , the paper realize the research 
and improvement on the measuring method of large caliber gun muzzle vibration, in which the 
binocular vision measurement method is applied to practice for a type of muzzle vibration 
measurement in practice. The measurement result provides meaningful original data support for 
the gun performance improvement and gun model development. 
Acknowledgement 
This is supported by the National Key Scientific Instrument Development Projects, 
No. 2013YQ470765. 
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1671. RESEARCH ON MEASURING METHOD OF LARGE-CALIBER GUN MUZZLE VIBRATION.  
GANG ZHAO, QIANG CHEN, YINGJUN WANG 
 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. AUG 2015, VOLUME 17, ISSUE 5. ISSN 1392-8716 2235 
[9] Ragulskis M., Maskeliunas R., Saunoriene L. Identification of in-plane vibrations using time 
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[10] Kalman R. E. A new approach to linear filtering and prediction problems. Journal of Basic 
Engineering, Vol. 82, Issue 1, 1960, p. 35-45. 
 
Gang Zhao received Master’s degree in Control Engineering from Nanjing University, 
Nanjing, China, in 2015. Now he works at 73906 PLA, Nanjing, China. His current 
research interests include test and control, parameter identification. 
 
Qiang Chen received Ph.D. degree in Computer Institute from Nanjing University of 
Science and Technology, Nanjing, China, in 2004. Now he works at Department of System 
and Control Engineering, Nanjing University. His current research interests include test 
and control, dynamics and pattern recognition. 
 
Yingjun Wang is studying for his Master’s degree in Department of System and Control 
Engineering, Nanjing University, Nanjing, China. His current research interests include 
test and control, parameter identification and intelligent algorithm. 
 


Research on measuring method of large-caliber gun muzzle vibration

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