CN108169732A - A kind of transform domain Beamforming Method based on extension aperture sonar - Google Patents
A kind of transform domain Beamforming Method based on extension aperture sonar Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO 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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
- G01S7/539—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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Abstract
The invention discloses a kind of transform domain Beamforming Methods based on extension aperture sonar, belong to field of underwater acoustic signal processing.The present invention includes：According to sonar system index request, according to the equivalent array element phase center principle of extension aperture sonar, i.e. one transmitting array element receives array element with one and forms a module, and the phase center of this module is located at the geometric center of two array element, reasonable Arrangement transmitting battle array, the position for receiving battle array；Formation is received according to the transmitting of arrangement, at transmitting basic matrix end, transmitting battle array emits mutually orthogonal waveform simultaneously；Receive the reflection signal that battle array receives target, i.e. echo-signal；It carries out reception Wave beam forming processing respectively in transform domain to echo-signal, carries out transform domain filtering and receive Wave beam forming；The signal after Wave beam forming processing is received to transform domain, to different transmitting formation into delay inequality compensated with Wave beam forming, and then obtain the distance of extension aperture sonar to angle to sound spectrogram.
Description
Technical field
The invention belongs to field of underwater acoustic signal processing, and in particular to a kind of transform domain wave beam shape based on extension aperture sonar
Into method.
Background technology
In recent years, multi-beam image sonar technology is in seafloor topography mapping, oil pipeline detection and submarine target
Field of detecting is widely used, in order to obtain high-definition sonar image, need to improve simultaneously sonar image away from
Descriscent resolution ratio and angle are to resolution ratio.
In wideband signaling system, distance resolution is usually determined by the effective bandwidth of reception signal, and angular resolution
Usually determined by the effective aperture of receiving array and reception signal frequency.In practical applications, image sonar is specifically being applied
In field, changing its specific operating frequency range will cause its detection performance to decline, and therefore, usually select and expand sonar system
Improve angular resolution in the effective receiving array aperture of system.
In order not to increase array sizes, the hardware cost of transducer array is reduced, virtual extended aperture sonar may be used
Angle is improved to resolution ratio, operation principle is that orthogonal waveforms are penetrated in different transmitting paroxysm, receiving terminal by matched filtering into
Row transmitting Signal separator, then does reception and launching beam is formed, and achievees the purpose that the practical receiving array aperture of extension.But in work
In Cheng Yingyong, completely orthogonal signal is not present, then distance will be led to side by emitting the high cross correlation between signal
Valve is raised, and reduces the distance of sonar image to clarity.
Invention content
The invention is realized in this way：
A kind of transform domain Beamforming Method based on extension aperture sonar, which is characterized in that comprise the steps of：
Step 1 is according to sonar system index request, according to the equivalent array element phase center principle of extension aperture sonar, i.e.,
One transmitting array element receives array element with one and forms a module, and the phase center of this module is located in the geometry of two array element
The heart, reasonable Arrangement transmitting battle array, the position for receiving battle array；If sonar receiving array is one-dimensional array, two transmitting battle array cloth are placed on
Receive the both ends of battle array, if sonar receiving array is two-dimensional planar array, orientation and pitching to being required for extending, then receive it is flat
Four transmitting battle arrays are laid around the array of face；If a uniform rectilinear receiving array, adjacent array element spacing be half-wavelength, element number of array
For M, two transmitting battle arrays are arranged at array both ends, then the angle for extending aperture sonar is expressed as to beam angle
In formula, BW be angle to beam angle, unit is radian, and λ is transmitting signal wavelength, and d is adjacent reception array element
Spacing,For wave beam offset angle, setting
If a uniform two dimensional surface receiving array, adjacent array element spacing be half-wavelength, horizontal direction element number of array be L, pitching
It is Q to element number of array, four emission arrays are arranged in four angles of receiving plane battle array, then horizontal direction beam angle and pitching are to wave beam
Width is：
Wherein, BWθFor horizontal direction beam angle,It is pitching to beam angle, dθFor the adjacent array element spacing of horizontal direction,It is pitching to adjacent array element spacing；
Step 2 receives formation according to the transmitting of arrangement, and at transmitting basic matrix end, transmitting battle array emits mutually orthogonal waveform simultaneously,
In practice there is no completely orthogonal signal, design emits the signal different signal of feature in the transform domain as illustrated, with one-dimensional reception battle array
Example, two transmitting battle arrays, the sinusoidal signal of two different frequencies of transmitting are classified as, and the frequency response curve -3dB of two signals is without weight
Folded, i.e., frequency is without intersection, then the frequecy characteristic of this two transmitting signals is different；For another example believe in the positive negative frequency modulation of different center frequency
Number, then two transmitting signals have different characteristics in STFT time-frequency domains, you can it is orthogonal letter to think that two transmitting paroxysms are penetrated
Number；
s1(t)=cos (2 π f1t+K1πt2)
s2(t)=cos (2 π f2t+K2πt2)
In formula, s1(t), s2(t) orthogonal signalling penetrated for the transmitting paroxysm at both ends, the transmission center frequency values of a transmitting battle array
For f1, frequency change rate K1, t is time point, and the transmission center frequency values of another transmitting battle array are f2, frequency change rate K2,
The centre frequency of two signals is different, and frequency change rate is different；
Step 3 receives the reflection signal that battle array receives target, i.e. echo-signal, contains multiple Orthogonal injections in echo-signal
The superposition of the target echo of signal, it is right with reference to transmitting orthogonal signalling in the different feature of transform domain to realize waveform separation
Echo-signal carries out receiving Wave beam forming processing in transform domain respectively, carries out transform domain filtering and receives Wave beam forming；
If receiving array is one dimensional linear array, two transmitting signal transmitting different frequency signals, two signals are in the spy of frequency domain
Sign is different, then carries out reception Wave beam forming in different frequency respectively；If the frequency modulation up and down of two transmitting signal transmitting different frequencies
Signal since two class signals have different characteristics in not same order Fourier Transform of Fractional Order domain, becomes according to fractional order Fourier
Change with extraction multi -components chirp signal parameters ability, then using respectively different rank Fourier Transform of Fractional Order domain into
Row receives Wave beam forming processing；
The docking collection of letters number carries out a Fourier Transform of Fractional Order for not same order respectively, i.e.,
In formula, x (t) is the target echo received,For p1The Fourier Transform of Fractional Order kernel function of rank,For the corresponding p of x (t)1The Fourier Transform of Fractional Order domain function of rank,For p2The Fourier Transform of Fractional Order of rank
Kernel function,For the corresponding p of x (t)2The Fourier Transform of Fractional Order domain function of rank；
Step 4 inverse transform domain converts, and launching beam is formed；The signal after Wave beam forming processing is received to transform domain, into
Row inverse transform domain converts, and transforms to Beam Domain time-domain signal, according to the delay inequality that different transmitting battle arrays reflects to form target,
Time domain carry out launching beam formation processing, i.e., to it is different transmitting formation into delay inequality compensated with Wave beam forming, and then obtain expand
The distance of aperture sonar is opened up to angle to sound spectrogram.
Compared with prior art, the beneficial effects of the present invention are：
1st, proposition method of the invention can reduce the influence that transmitted waveform high correlation is adjusted the distance to high secondary lobe, realize and expand
The sound spectrogram distance of aperture sonar is opened up to high-resolution map.
2nd, proposition method of the invention can select to realize in multiple transform domains, realize that flow is simple, it is easy to accomplish.
Description of the drawings
Fig. 1 is one-dimensional array extension aperture principle schematic of the present invention；
Fig. 2 is two-dimensional planar array extension aperture sonar transducer array arrangement schematic diagram of the present invention；
Fig. 3 is invention implementing procedure block diagram；
Fig. 4 is that receiving array aperture beams figure of the present invention compares.
Specific embodiment
Invention is described in more detail below in conjunction with the accompanying drawings：
The present invention relates to a kind of transform domain Beamforming Method based on extension aperture sonar, due to virtual extended aperture sound
It receives in system, emits the incomplete orthogonal of signal, reduce the distance of sonar image to clarity, which is connect using transform domain
Receiving Beamforming Method realizes the distance of virtual extended aperture sonar to fine definition.The inventive method is first according to virtual extended
Aperture is theoretical, reasonable Arrangement emission array receiving array, and then each transmitting basic matrix transmitting orthogonal waveforms, reception basic matrix receive more
The target echo signal of a orthogonal waveforms superposition, it is different in transform domain feature according to different orthogonal waveform, it is directed in transform domain
Multigroup orthogonal waveforms do reception array beamforming, and do inverse transform domain transformation respectively, finally carry out transmitting array beam in time domain
It is formed.This method do not need to using matched filtering carry out orthogonal waveforms Signal separator, using orthogonal signalling transform domain feature
Difference receives Wave beam forming using transform domain, solves in practical application distance caused by orthogonal time-domain waveform high correlation to height
Secondary lobe, obtained while angular resolution is improved distance to fine definition, integrally improve sonar image quality.
Specific embodiment one：
In this example, systematic parameter：Receiving array is one dimensional linear array, and angle is 1.5 ° to beam angle, receives basic matrix
Working frequency be 60kHz, velocity of sound 1500m/s, operating distance 50m, signal sampling rate 300kHz.
1. calculating process：
Assuming that receiving array is a uniform linear array, adjacent array element spacing is the half-wavelength of receiving array working frequency,
In order to meet system perspective to beam angle requirement, can be obtained according to formula,
It then can be calculated, the element number of array in practical receiving array is designed as 36, and the both ends for receiving basic matrix lay two
Emit basic matrix.
According to the receiving array parameter calculated, emulated by Fig. 4 it is found that the beam angle for extending system after aperture is approximately
The 0.55 of practical receiving array system beam angle, improves angle to resolution ratio.
Two transmitting basic matrixs, emit mutually orthogonal signal, and signal waveform is respectively that centre frequency is 55kHz positive frequency modulation signals
It is 85kHz negative frequency modulation signals with centre frequency, transmitted signal bandwidth is 3kHz, and pulsewidth is 10ms.
Receiving array receives target echo signal, and analysis is it is found that the two emits signal in not same order fractional order Fourier
Transform domain has a different characteristics, and echo-signal carries out-1.539 rank Fourier Transform of Fractional Order first, it is known that, transmitting signal 1-
In 1.539 rank transform domains there is strong component, and carry out received wave beam and formed to obtain transform-domain signals y1While echo-signal (u),
Carry out 1.539 rank Fourier Transform of Fractional Order, it is known that, transmitting signal 2 has strong component, and carry out in 1.539 rank transform domains
It receives Wave beam forming and obtains transform-domain signals y2(u), it avoids and waveform separation is carried out using correlation function, lead to distance by height
Valve.
Then to transform-domain signals y1(u) and transform-domain signals y2(u) inverse transform domain transformation is carried out, transforms to time-domain signal
Respectively y1(t) and transform-domain signals y2(t), delay compensation progress launching beam is carried out again later to be formed.
The final distance that obtains is to fine definition and angle to high-definition picture.
Specific embodiment two：
1. first according to sonar system index request, according to the equivalent array element phase center principle of extension aperture sonar, i.e.,
One transmitting array element receives array element with one and forms a module, and the phase center of this module is located in the geometry of two array element
The heart, reasonable Arrangement transmitting battle array, the position for receiving battle array.If sonar receiving array is one-dimensional array, two transmitting battle array cloth are placed on
Receive the both ends of battle array, if sonar receiving array is two-dimensional planar array, orientation and pitching to being required for extending, then receive it is flat
Four transmitting battle arrays are laid around the array of face, respectively as depicted in figs. 1 and 2.Assuming that a uniform rectilinear receiving array, adjacent array element
Spacing is half-wavelength, element number of array M, and two transmitting battle arrays are arranged at array both ends, then the angle for extending aperture sonar is wide to wave beam
Degree is expressed as
In formula, BW be angle to beam angle, unit is radian, and λ is transmitting signal wavelength, and d is adjacent reception array element
Spacing,For wave beam offset angle, the method, settingIt is found that the beam angle of extension aperture sonar is approximately practical reception
The 0.55 of array aperture, then angle about doubled to resolution ratio.
Assuming that a uniform two dimensional surface receiving array, adjacent array element spacing is half-wavelength, and horizontal direction element number of array is L, is bowed
It is Q to face upward to element number of array, and four emission arrays are arranged in four angles of receiving plane battle array, then horizontal direction beam angle and pitching are to wave
Beam width is
Wherein, BWθFor horizontal direction beam angle,It is pitching to beam angle, dθFor the adjacent array element spacing of horizontal direction,It is pitching to adjacent array element spacing.
It is found that after planar array extension, horizontal direction beam angle and pitching are practical reception battle array respectively to beam angle
To the 0.55 of beam angle, i.e. horizontal direction and pitching improves one to angular resolution for the horizontal direction beam angle of row and pitching
Times.
Wherein, Fig. 2 orbicular spots lay reception array element, and four corner black array elements of plane are laid to emit battle array.
2. the transmitting according to arrangement receives formation, at transmitting basic matrix end, transmitting battle array emits mutually orthogonal waveform simultaneously, practical
In there is no completely orthogonal signal, the design transmitting signal different signal of feature in the transform domain as illustrated, using one-dimensional receiving array as
Example, two transmitting battle arrays, the sinusoidal signal of two different frequencies of transmitting, and the frequency response curve -3dB of two signals is non-overlapping,
I.e. frequency is without intersection, then the frequecy characteristic of this two transmitting signals is different；For another example in the positive and negative FM signal of different center frequency,
Then two transmitting signals have different characteristics in STFT time-frequency domains, you can it is orthogonal signalling to think that two transmitting paroxysms are penetrated.
s1(t)=cos (2 π f1t+K1πt2)
s2(t)=cos (2 π f2t+K2πt2)
In formula, s1(t), s2(t) orthogonal signalling penetrated for the transmitting paroxysm at both ends, the transmission center frequency values of a transmitting battle array
For f1, frequency change rate K1, t is time point, and the transmission center frequency values of another transmitting battle array are f2, frequency change rate K2,
The centre frequency of two signals is different, and frequency change rate is different.
3. receiving the reflection signal that battle array receives target, i.e. echo-signal, contain multiple Orthogonal injection signals in echo-signal
Target echo superposition, in order to realize that waveform detaches, with reference to transmitting orthogonal signalling in the different feature of transform domain, to returning
Wave signal carries out receiving Wave beam forming processing in transform domain respectively, carries out transform domain filtering and receives Wave beam forming.
Assuming that receiving array is one dimensional linear array, two transmitting signal transmitting different frequency signals, two signals are in frequency domain
Feature is different, then carries out reception Wave beam forming in different frequency respectively；If the upper downward of two transmitting signal transmitting different frequencies
Frequency signal, since two class signals have different characteristics in not same order Fourier Transform of Fractional Order domain, according to fractional order Fourier
Ability of the variation with extraction multi -components chirp signal parameters, then use respectively in different rank Fourier Transform of Fractional Order domain
It carries out receiving Wave beam forming processing.
The docking collection of letters number carries out a Fourier Transform of Fractional Order for not same order respectively, i.e.,
In formula, x (t) is the target echo received,For p1The Fourier Transform of Fractional Order kernel function of rank,For the corresponding p of x (t)1The Fourier Transform of Fractional Order domain function of rank,For p2The Fourier Transform of Fractional Order of rank
Kernel function,For the corresponding p of x (t)2The Fourier Transform of Fractional Order domain function of rank.
4. inverse transform domain converts, launching beam is formed.The signal after Wave beam forming processing is received to transform domain, is carried out inverse
Transform domain converts, and Beam Domain time-domain signal is transformed to, according to the delay inequality that different transmitting battle arrays reflects to form target, in time domain
Carry out launching beam formation processing, i.e., to it is different transmitting formation into delay inequality compensated with Wave beam forming, and then obtain extending bore
The distance of diameter sonar is to angle to sound spectrogram.
The concrete operation method of the present invention is as follows：
1. first according to sonar system index request, according to the equivalent array element phase center principle of extension aperture sonar, i.e.,
One transmitting array element receives array element with one and forms a module, and the phase center of this module is located in the geometry of two array element
The heart, reasonable Arrangement transmitting battle array, the position for receiving battle array.If sonar receiving array is one-dimensional array, two transmitting battle array cloth are placed on
Receive the both ends of battle array, if sonar receiving array is two-dimensional planar array, orientation and pitching to being required for extending, then receive it is flat
Four transmitting battle arrays are laid around the array of face, respectively as depicted in figs. 1 and 2.Assuming that a uniform rectilinear receiving array, adjacent array element
Spacing is half-wavelength, element number of array M, and two transmitting battle arrays are arranged at array both ends, then the angle for extending aperture sonar is wide to wave beam
Degree is expressed as
In formula, BW be angle to beam angle, unit is radian, and λ is transmitting signal wavelength, and d is adjacent reception array element
Spacing,For wave beam offset angle, the method, settingIt is found that the beam angle of extension aperture sonar is approximately practical reception
The 0.55 of array aperture, then angle about doubled to resolution ratio.
Assuming that a uniform two dimensional surface receiving array, adjacent array element spacing is half-wavelength, and horizontal direction element number of array is L, is bowed
It is Q to face upward to element number of array, and four emission arrays are arranged in four angles of receiving plane battle array, then horizontal direction beam angle and pitching are to wave
Beam width is
It is found that after planar array extension, horizontal direction beam angle and pitching are practical reception battle array respectively to beam angle
To the 0.55 of beam angle, i.e. horizontal direction and pitching improves one to angular resolution for the horizontal direction beam angle of row and pitching
Times.
Wherein, Fig. 2 orbicular spots lay reception array element, and four corner black array elements of plane are laid to emit battle array.
2. the transmitting according to arrangement receives formation, at transmitting basic matrix end, transmitting battle array emits mutually orthogonal waveform simultaneously, practical
In there is no completely orthogonal signal, the design transmitting signal different signal of feature in the transform domain as illustrated, using one-dimensional receiving array as
Example, two transmitting battle arrays, the sinusoidal signal of two different frequencies of transmitting, and the frequency response curve -3dB of two signals is non-overlapping,
I.e. frequency is without intersection, then the frequecy characteristic of this two transmitting signals is different；For another example in the positive and negative FM signal of different center frequency,
Then two transmitting signals have different characteristics in STFT time-frequency domains, you can it is orthogonal signalling to think that two transmitting paroxysms are penetrated.
s1(t)=cos (2 π f1t+K1πt2)
s2(t)=cos (2 π f2t+K2πt2)
In formula, s1(t), s2(t) orthogonal signalling penetrated for the transmitting paroxysm at both ends, the transmission center frequency values of a transmitting battle array
For f1, frequency change rate K1, t is time point, and the transmission center frequency values of another transmitting battle array are f2, frequency change rate K2,
The centre frequency of two signals is different, and frequency change rate is different.
3. receiving the reflection signal that battle array receives target, i.e. echo-signal, contain multiple Orthogonal injection signals in echo-signal
Target echo superposition, in order to realize that waveform detaches, with reference to transmitting orthogonal signalling in the different feature of transform domain, to returning
Wave signal carries out receiving Wave beam forming processing in transform domain respectively, carries out transform domain filtering and receives Wave beam forming.
Assuming that receiving array is one dimensional linear array, two transmitting signal transmitting different frequency signals, two signals are in frequency domain
Feature is different, then carries out reception Wave beam forming in different frequency respectively；If the upper downward of two transmitting signal transmitting different frequencies
Frequency signal, since two class signals have different characteristics in not same order Fourier Transform of Fractional Order domain, according to fractional order Fourier
Ability of the variation with extraction multi -components chirp signal parameters, then use respectively in different rank Fourier Transform of Fractional Order domain
It carries out receiving Wave beam forming processing.
The docking collection of letters number carries out a Fourier Transform of Fractional Order for not same order respectively, i.e.,
In formula, x (t) is the target echo received,For p1The Fourier Transform of Fractional Order kernel function of rank,For the corresponding p of x (t)1The Fourier Transform of Fractional Order domain function of rank,For p2The Fourier Transform of Fractional Order of rank
Kernel function,For the corresponding p of x (t)2The Fourier Transform of Fractional Order domain function of rank.
4. pair transform domain receives the signal after Wave beam forming processing, inverse transform domain transformation is carried out, when transforming to Beam Domain
According to the delay inequality that transmitting battle array reflects to form target, transmitting terminal Wave beam forming processing is carried out, and then obtain in time domain for domain signal
The distance of aperture sonar is extended to angle to sound spectrogram.
Claims (1)
1. a kind of transform domain Beamforming Method based on extension aperture sonar, which is characterized in that comprise the steps of：
Step 1 is according to sonar system index request, according to the equivalent array element phase center principle of extension aperture sonar, i.e., one
Emit array element and receive array element one module of composition with one, the phase center of this module is located at the geometric center of two array element, closes
Removing the work puts transmitting battle array, the position for receiving battle array；If sonar receiving array is one-dimensional array, two transmitting battle array cloth are placed on reception battle array
Both ends, if sonar receiving array is two-dimensional planar array, orientation and pitching to being required for extending, then in receiving plane array
Around lay four transmitting battle arrays；If a uniform rectilinear receiving array, adjacent array element spacing be half-wavelength, element number of array M, battle array
It arranges both ends and arranges two transmitting battle arrays, then the angle for extending aperture sonar is expressed as to beam angle
In formula, BW be angle to beam angle, unit is radian, and λ is transmitting signal wavelength, and d is adjacent reception array element spacing,For wave beam offset angle, setting
If a uniform two dimensional surface receiving array, adjacent array element spacing is half-wavelength, and horizontal direction element number of array is L, and pitching is to battle array
First number is Q, and four emission arrays are arranged in four angles of receiving plane battle array, then horizontal direction beam angle and pitching are to beam angle
For：
Wherein, BWθFor horizontal direction beam angle,It is pitching to beam angle, dθFor the adjacent array element spacing of horizontal direction,To bow
It faces upward to adjacent array element spacing；
Step 2 receives formation according to the transmitting of arrangement, and at transmitting basic matrix end, transmitting battle array emits mutually orthogonal waveform simultaneously, practical
In there is no completely orthogonal signal, the design transmitting signal different signal of feature in the transform domain as illustrated, using one-dimensional receiving array as
Example, two transmitting battle arrays, the sinusoidal signal of two different frequencies of transmitting, and the frequency response curve -3dB of two signals is non-overlapping,
I.e. frequency is without intersection, then the frequecy characteristic of this two transmitting signals is different；For another example in the positive and negative FM signal of different center frequency,
Then two transmitting signals have different characteristics in STFT time-frequency domains, you can it is orthogonal signalling to think that two transmitting paroxysms are penetrated；
s1(t)=cos (2 π f1t+K1πt2)
s2(t)=cos (2 π f2t+K2πt2)
In formula, s1(t), s2(t) orthogonal signalling penetrated for the transmitting paroxysm at both ends, the transmission center frequency values of a transmitting battle array are f1,
Frequency change rate is K1, t is time point, and the transmission center frequency values of another transmitting battle array are f2, frequency change rate K2, two
The centre frequency of signal is different, and frequency change rate is different；
Step 3 receives the reflection signal that battle array receives target, i.e. echo-signal, contains multiple Orthogonal injection signals in echo-signal
Target echo superposition, to realize waveform separation, with reference to transmitting orthogonal signalling in the different feature of transform domain, to echo
Signal carries out receiving Wave beam forming processing in transform domain respectively, carries out transform domain filtering and receives Wave beam forming；
If receiving array be one dimensional linear array, two transmitting signals transmitting different frequency signals, two signals frequency domain feature not
Together, then reception Wave beam forming is carried out in different frequency respectively；If the FM signal up and down of two transmitting signal transmitting different frequencies,
Since two class signals have different characteristics in not same order Fourier Transform of Fractional Order domain, had according to fractional order Fourier variation
The ability of multi -components chirp signal parameters is extracted, then uses and is received respectively in different rank Fourier Transform of Fractional Order domain
Wave beam forming processing；
The docking collection of letters number carries out a Fourier Transform of Fractional Order for not same order respectively, i.e.,
In formula, x (t) is the target echo received,For p1The Fourier Transform of Fractional Order kernel function of rank,
For the corresponding p of x (t)1The Fourier Transform of Fractional Order domain function of rank,For p2The Fourier Transform of Fractional Order core letter of rank
Number,For the corresponding p of x (t)2The Fourier Transform of Fractional Order domain function of rank；
Step 4 inverse transform domain converts, and launching beam is formed；The signal after Wave beam forming processing is received to transform domain, is carried out inverse
Transform domain converts, and Beam Domain time-domain signal is transformed to, according to the delay inequality that different transmitting battle arrays reflects to form target, in time domain
Carry out launching beam formation processing, i.e., to it is different transmitting formation into delay inequality compensated with Wave beam forming, and then obtain extending bore
The distance of diameter sonar is to angle to sound spectrogram.
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| CN108761433A (en) * | 2018-08-02 | 2018-11-06 | 西北工业大学 | A kind of high-resolution imaging method handled using MIMO sonar difference combined arrays |
| CN113702978A (en) * | 2021-08-04 | 2021-11-26 | 中国科学院声学研究所 | Submarine pipeline detection positioning method and system based on forward-looking sonar |
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