CN110687538A - Near-field focusing-based super-beam forming method - Google Patents

Near-field focusing-based super-beam forming method Download PDF

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CN110687538A
CN110687538A CN201911031089.7A CN201911031089A CN110687538A CN 110687538 A CN110687538 A CN 110687538A CN 201911031089 A CN201911031089 A CN 201911031089A CN 110687538 A CN110687538 A CN 110687538A
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focusing
array
super
beam forming
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王升凤
夏梦月
费玉杰
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Haiying Enterprise Group Co Ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S15/00Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
    • G01S15/88Sonar systems specially adapted for specific applications
    • G01S15/89Sonar systems specially adapted for specific applications for mapping or imaging
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/52Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
    • G01S7/523Details of pulse systems
    • G01S7/526Receivers

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Acoustics & Sound (AREA)
  • Measurement Of Velocity Or Position Using Acoustic Or Ultrasonic Waves (AREA)

Abstract

The invention discloses a super-beam forming method based on near-field focusing, and belongs to the technical field of sonar signal processing. Receiving array element domain data; calculating a focusing ring coefficient; applying a focal ring number to the super-beamforming; and performing imaging processing on the beam domain data after the beam forming processing. The method has the advantages of narrow main lobe of the ultra-beam and low side lobe, can effectively improve the detection performance of the sonar system, reduce the false alarm probability and improve the estimation precision of the target azimuth; the adoption of the sectional focusing super-beam forming technology can carry out focusing compensation on the phase in the near-field range, thereby making up the problem of image blurring caused by phase mismatch.

Description

Near-field focusing-based super-beam forming method
Technical Field
The invention relates to the technical field of sonar signal processing, in particular to a super-beam forming method based on near-field focusing.
Background
The high-frequency multi-beam sonar is an important instrument for detecting the current marine target and is mainly applied to detecting, positioning and classifying the short-distance small targets in the sea. However, the image sonar has the problems of imaging blurring and the like in a near-field working area, and the working performance of the equipment is seriously influenced. This is because the conventional beam forming method assumes a plane wave, and does not perform focus compensation on the near-field range, which causes phase mismatch, a main lobe of a beam becomes wider, and side lobes increase, which causes a reduction in azimuth resolution, and causes a serious deterioration in sonar image performance. Meanwhile, the traditional conventional beam forming has wider main lobe and higher side lobe, and is not beneficial to the resolution and identification of multiple targets.
Disclosure of Invention
The invention aims to provide a super-beam forming method based on near-field focusing, which aims to solve the problem of imaging blurring caused by the fact that a traditional beam is formed in a near-field working area.
In order to solve the above technical problem, the present invention provides a method for forming a super-beam based on near-field focusing, comprising:
receiving array element domain data;
calculating a focusing ring coefficient;
applying a focal ring number to the super-beamforming;
and performing imaging processing on the beam domain data after the beam forming processing.
Optionally, calculating the focus ring coefficient includes:
the near field condition is
Figure BDA0002250171680000011
Wherein L is the effective array length of the array, lambda is the wavelength, and D is the distance of the near field range;
the phase shift formed by the acoustic focusing phase shift wave beam is calculated according to a spherical wave rule, acoustic focusing is carried out on the acoustic wave emitted from a certain point in space, and left and right array acoustic focusing can be formed;
calculating the sound path difference or phase difference of the focusing point reaching each element of the receiving array, then compensating the sound path difference or phase difference during receiving processing, and forming signals transmitted from the receiving point after compensation to realize in-phase superposition so that the sound array focuses on the focusing point in space;
left half matrix phase difference phiiThe expression is as follows:
wherein R is0Is the focusing distance, λ is the wavelength, N is the total number of elements, i is the number of elements, d is the interval of elements, θkIs the angle of incidence;
by inserting phase shift angles psi between adjacent array elementskThen, the output corresponding to each array element is:
Figure BDA0002250171680000022
t is time, k is the beam number, j is the unit of imaginary number, ω 02 pi f t, f is the center frequency, phiihIs a phase shift, ψikIs phase compensation of which-phiik=φikThen, the above formula is rewritten as:
Figure BDA0002250171680000023
Figure BDA0002250171680000024
the phase difference is shown in the formula, and the formula is a calculation formula of a phase shift compensation angle of spherical waves;
the active sonar transmits a pulse signal to water through a transmitting transducer, the pulse signal is reflected by a target, the distance is measured by using the time difference between a received echo and the transmitted pulse signal, and the round-trip propagation time is as follows:
Figure BDA0002250171680000025
wherein R is the target distance and c is the sound velocity;
after the echo signal is sampled, the relation between the sampling point N and the distance is as follows:
Figure BDA0002250171680000026
fsthe sampling rate is used for calculating the insertion positions of the phase compensation coefficients of different focusing distances according to the formula.
Optionally, applying a focal ring number to the superbeam forming comprises:
equally dividing the receiving linear array into a left sub-array and a right sub-array, wherein the left sub-array and the right sub-array are respectively arranged according toThe base band conventional wave beam forming method is used for forming wave beams to obtain sum wave beams SLSum and difference beam SRAnd then:
sum beam SS=|SL|+|SR|
Difference beam SD=|SL-SR|
Subtracting the sum beam from the difference beam, and performing weighting calculation to obtain the super beam SHThe output is:
wherein n is the super-beam index and is within the range of 0.3-1, and is used for adjusting the main lobe width and the side lobe height of the output beam.
Optionally, the near-field model is adopted to calculate the beam, super-beam forming is performed, and a segmented focusing algorithm is adopted, so that the width of the main lobe is compressed while the side lobe is greatly reduced.
The invention provides a super-beam forming method based on near-field focusing, which receives array element domain data; calculating a focusing ring coefficient; applying a focal ring number to the super-beamforming; and performing imaging processing on the beam domain data after the beam forming processing.
The invention has the following beneficial effects:
(1) the method has the advantages of narrow main lobe of super-beam and low side lobe, can effectively improve the detection performance of the sonar system, reduce the false alarm probability and improve the estimation precision of the target azimuth;
(2) the method adopts a segmented focusing super-beam forming technology to perform focusing compensation on the phase within a near-field range, so that the problem of image blurring caused by phase mismatch is solved;
(3) the method effectively improves the resolving power of the sonar on a plurality of targets in different directions in the space, and has the advantages of quick computing power, simple structure and easy realization while the focusing super-beam forming precision is not lost.
Drawings
FIG. 1 is a schematic flow chart of a near-field focusing-based super-beam forming method provided by the invention;
FIG. 2 is a schematic diagram of left and right acoustic focusing;
FIG. 3 is a schematic diagram of a right beam focus A point;
FIG. 4 is a schematic diagram of a super-beamforming processing method;
FIG. 5 is a diagram of the effects of conventional beamforming, unfocused;
fig. 6 is a diagram showing effects of super-beamforming and near-field focusing.
Detailed Description
The super beam forming method based on near field focusing proposed by the present invention is further described in detail with reference to the accompanying drawings and specific embodiments. Advantages and features of the present invention will become apparent from the following description and from the claims. It is to be noted that the drawings are in a very simplified form and are not to precise scale, which is merely for the purpose of facilitating and distinctly claiming the embodiments of the present invention.
Example one
The invention provides a near-field focusing-based super-beam forming method, the flow of which is shown in figure 1 and comprises the following steps:
receiving array element domain data;
calculating a focusing ring coefficient;
applying a focal ring number to the super-beamforming;
and performing imaging processing on the beam domain data after the beam forming processing.
Specifically, the first step: receiving data:
receiving array element domain data;
step two: calculating the focusing ring coefficient:
the near field conditions were:
wherein, L is the effective array length of the array, lambda is the wavelength, and D is the distance of the near field range.
The phase shift formed by the acoustic focusing phase shift wave beam is calculated according to the spherical wave rule, acoustic focusing is carried out on the acoustic wave emitted from a certain point in space, and left and right array sound can be formedFocusing, as shown in FIG. 2; in fig. 2, N is the number of elements, o is the geometric center of the array, d is the element spacing, Fo is the normal, and the focal length of the right beam Ao is RoRight sideLeft beam focal length Bo ═ RoLeft side ofThe included angles between Ao and Fo and between Bo and Fo are the left and right beam pointing angles, 1<i<j<N。
Firstly, the sound path difference or phase difference of the sound wave of the focusing point A (or B) reaching each element of the receiving array is calculated, then the sound path difference or phase difference is compensated during receiving processing, and after compensation, the signals transmitted from the receiving point are formed to realize in-phase superposition, so that the sound array is focused on the space A (or B). The spherical wave phase shift compensation angle calculation formula is described below. For simplicity of analysis, the right beam is taken as an example, as shown in fig. 3.
In fig. 3, the focal length of the right beam is Ro, and Ai and Aj are calculated by using the triangular pythagorean theorem: distances Ai and Aj from a focusing point A to primitives i and j, corresponding sound paths Ai-Ro and Aj-Ro and left and right half matrix phase differences phii、φj. And (4) calculating the result: phi is aiAnd phijThe expressions are identical, and the phase difference expression is:
Figure BDA0002250171680000042
wherein R is0Is the focusing distance, λ is the wavelength, N is the total number of elements, i is the number of elements, d is the interval of elements, θkIs the angle of incidence;
by inserting phase shift angles psi between adjacent array elementskThen, the output corresponding to each array element is:
t is time, k is the beam number, j is the unit of imaginary number, ω 02 pi f t, f is the center frequency, phiihIs a phase shift, ψikIs phase compensation of which-phiik=φikThen, the above formula is rewritten as:
Figure BDA0002250171680000052
φikis the phase difference, and the formula (1.4) is the calculation formula of the phase shift compensation angle of the spherical wave.
As can be known from the formula (1.4), the phase compensation coefficient formed by the focused beam in the near-field environment is a two-dimensional function of the signal incidence angle theta and the distance R between the sound source and the center of the array element. For single-point focusing, only the beam performance in the area near the focus can be guaranteed, and the beam performance will be deteriorated if targets at other positions are not accurately compensated. Therefore, the whole near field area is divided into a plurality of segments in distance, and the focus compensation is respectively carried out on the middle point of each segment in distance. The more segmentation, the smaller the beam error, the better the focusing performance, and the larger the calculation amount, the more difficult the implementation. In actual engineering, the balance between the amount of calculation and the focusing performance needs to be considered.
The active sonar transmits a pulse signal to water through a transmitting transducer, the pulse signal is reflected by a target, the distance is measured by using the time difference between a received echo and the transmitted pulse signal, and the round-trip propagation time is as follows:
wherein R is the target distance and c is the sound velocity;
after the echo signal is sampled, the relation between the sampling point N and the distance is as follows:
Figure BDA0002250171680000054
fsis the sampling rate, the insertion position of the phase compensation coefficients for different focusing distances is calculated according to equation (1.6).
Step three: focused super-beam forming:
and applying the ring focusing system number obtained in the second step to the following super-beam forming.
The super-beam forming processing method is as shown in fig. 4, the receiving linear array is equally divided into a left sub-array and a right sub-array, the left sub-array and the right sub-array are respectively subjected to beam forming according to a baseband conventional beam forming method to obtain a sum beam SLSum and difference waveBundle SRThe beam-forming algorithm, according to the definition of the superbeam algorithm,
sum beam SS=|SL|+|SR| (1.7)
Difference beam SD=|SL-SR| (1.8)
Subtracting the sum beam from the difference beam, and performing weighting calculation to obtain the super beam SHThe output is:
wherein n is the super-beam index and is within the range of 0.3-1, and is used for adjusting the main lobe width and the side lobe height of the output beam.
Step four: and (3) sending data:
and obtaining the beam domain data after the beam forming processing through the steps, and performing imaging processing. Fig. 5 adopts a far-field model to calculate a beam, and performs conventional beam forming, but does not adopt a focusing algorithm, so that it can be seen that a higher side lobe causes deterioration of near-field imaging effect, the closer the target is, the poorer the imaging effect is, and the target distance is deviated, so that the positioning is inaccurate. Fig. 6 adopts a near-field model to calculate a beam, carries out super-beam formation, adopts a sectional focusing algorithm, greatly reduces side lobes, simultaneously compresses the width of a main lobe, improves the resolution capability of sonar on a plurality of targets in the space, effectively improves the detection performance of the system, reduces the false alarm probability, improves the estimation precision of the target azimuth, and has optimal imaging effect.
The above description is only for the purpose of describing the preferred embodiments of the present invention, and is not intended to limit the scope of the present invention, and any variations and modifications made by those skilled in the art based on the above disclosure are within the scope of the appended claims.

Claims (4)

1. A super beam forming method based on near field focusing is characterized by comprising the following steps:
receiving array element domain data;
calculating a focusing ring coefficient;
applying a focal ring number to the super-beamforming;
and performing imaging processing on the beam domain data after the beam forming processing.
2. The near-field focusing based super-beamforming method according to claim 1, wherein calculating the number of focus ring comprises:
the near field condition is
Figure FDA0002250171670000011
Wherein L is the effective array length of the array, lambda is the wavelength, and D is the distance of the near field range;
the phase shift formed by the acoustic focusing phase shift wave beam is calculated according to a spherical wave rule, acoustic focusing is carried out on the acoustic wave emitted from a certain point in space, and left and right array acoustic focusing can be formed;
calculating the sound path difference or phase difference of the focusing point reaching each element of the receiving array, then compensating the sound path difference or phase difference during receiving processing, and forming signals transmitted from the receiving point after compensation to realize in-phase superposition so that the sound array focuses on the focusing point in space;
left half matrix phase difference phiiThe expression is as follows:
Figure FDA0002250171670000012
wherein R is0Is the focusing distance, λ is the wavelength, N is the total number of elements, i is the number of elements, d is the interval of elements, θkIs the angle of incidence;
by inserting phase shift angles psi between adjacent array elementskThen, the output corresponding to each array element is:
Figure FDA0002250171670000013
t is time, k is the beam number, j is the unit of imaginary number, ω02 pi f t, f is the center frequency, phiihIs a phase shift, ψikIs phase compensation of which-phiik=φikThen, the above formula is rewritten as:
Figure FDA0002250171670000014
φikthe phase difference is shown in the formula, and the formula is a calculation formula of a phase shift compensation angle of spherical waves;
the active sonar transmits a pulse signal to water through a transmitting transducer, the pulse signal is reflected by a target, the distance is measured by using the time difference between a received echo and the transmitted pulse signal, and the round-trip propagation time is as follows:
Figure FDA0002250171670000021
wherein R is the target distance and c is the sound velocity;
after the echo signal is sampled, the relation between the sampling point N and the distance is as follows:
fsthe sampling rate is used for calculating the insertion positions of the phase compensation coefficients of different focusing distances according to the formula.
3. The near-field focusing based super beam forming method according to claim 1, wherein applying a focal ring number to super beam forming comprises:
equally dividing the receiving linear array into a left sub-array and a right sub-array, and respectively performing beam forming on the left sub-array and the right sub-array according to a baseband conventional beam forming method to obtain a sum beam SLSum and difference beam SRAnd then:
sum beam SS=|SL|+|SR|
Difference beam SD=|SL-SR|
Subtracting the sum beam from the difference beam, and performing weighting calculation to obtain the super beam SHThe output is:
Figure FDA0002250171670000023
wherein n is the super-beam index and is within the range of 0.3-1, and is used for adjusting the main lobe width and the side lobe height of the output beam.
4. The near-field focusing-based super-beam forming method of claim 3, wherein a near-field model is used for calculating a beam, super-beam forming is performed, and a segmented focusing algorithm is used for compressing the width of a main lobe while greatly reducing side lobes.
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112729742A (en) * 2020-12-25 2021-04-30 西安理工大学 Impact positioning method based on probability imaging
CN113030983A (en) * 2021-03-17 2021-06-25 中国科学院声学研究所 Near-field point-by-point focusing DOA method based on depth sounding side-scan sonar
CN113391301A (en) * 2021-05-26 2021-09-14 南京理工大学 Super-beam forming method and system based on time modulation linear array
CN114488008A (en) * 2022-01-19 2022-05-13 中国科学院声学研究所 Square ultrashort baseline positioning method
CN115902853A (en) * 2023-03-09 2023-04-04 中国科学院深海科学与工程研究所 Synthetic receiving aperture focusing beam forming method suitable for high-speed seabed surveying and mapping

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104215965A (en) * 2014-09-05 2014-12-17 中国船舶重工集团公司第七一五研究所 Gear dividing method of high-frequency sonar near field focusing distance
CN109116334A (en) * 2018-10-19 2019-01-01 海鹰企业集团有限责任公司 Sonar wave beams forming method and system based on super beam weighting
CN109283536A (en) * 2018-09-01 2019-01-29 哈尔滨工程大学 A kind of multibeam echosounding sonar water body imaging beam formation algorithm
CN109581388A (en) * 2018-12-20 2019-04-05 华中科技大学 A kind of near field wide viewing angle Beamforming Method of real time three-dimensional imaging sonar
CN110235022A (en) * 2016-12-15 2019-09-13 达尔豪斯大学 For using the compound Fresnel that is concerned with to focus the system and method for carrying out Ultrasound beamforming

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104215965A (en) * 2014-09-05 2014-12-17 中国船舶重工集团公司第七一五研究所 Gear dividing method of high-frequency sonar near field focusing distance
CN110235022A (en) * 2016-12-15 2019-09-13 达尔豪斯大学 For using the compound Fresnel that is concerned with to focus the system and method for carrying out Ultrasound beamforming
CN109283536A (en) * 2018-09-01 2019-01-29 哈尔滨工程大学 A kind of multibeam echosounding sonar water body imaging beam formation algorithm
CN109116334A (en) * 2018-10-19 2019-01-01 海鹰企业集团有限责任公司 Sonar wave beams forming method and system based on super beam weighting
CN109581388A (en) * 2018-12-20 2019-04-05 华中科技大学 A kind of near field wide viewing angle Beamforming Method of real time three-dimensional imaging sonar

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
张昌: "图像声纳的聚焦波束形成技术研究及实现", 《中国优秀硕士学位论文全文数据库 基础科学辑》 *
杨东方, 《海洋出版社》 *

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112729742A (en) * 2020-12-25 2021-04-30 西安理工大学 Impact positioning method based on probability imaging
CN112729742B (en) * 2020-12-25 2023-08-22 西安理工大学 Impact positioning method based on probability imaging
CN113030983A (en) * 2021-03-17 2021-06-25 中国科学院声学研究所 Near-field point-by-point focusing DOA method based on depth sounding side-scan sonar
CN113030983B (en) * 2021-03-17 2021-12-28 中国科学院声学研究所 Near-field point-by-point focusing DOA method based on depth sounding side-scan sonar
CN113391301A (en) * 2021-05-26 2021-09-14 南京理工大学 Super-beam forming method and system based on time modulation linear array
CN114488008A (en) * 2022-01-19 2022-05-13 中国科学院声学研究所 Square ultrashort baseline positioning method
CN114488008B (en) * 2022-01-19 2024-10-11 中国科学院声学研究所 Square ultrashort baseline positioning method
CN115902853A (en) * 2023-03-09 2023-04-04 中国科学院深海科学与工程研究所 Synthetic receiving aperture focusing beam forming method suitable for high-speed seabed surveying and mapping
CN115902853B (en) * 2023-03-09 2023-05-12 中国科学院深海科学与工程研究所 Synthetic receiving aperture focusing beam forming method suitable for high-speed submarine surveying and mapping

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