CN108169732B - Transform domain beam forming method based on extended aperture sonar - Google Patents
Transform domain beam forming method based on extended 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
Abstract
The invention discloses a transform domain beam forming method based on extended aperture sonar, and belongs to the field of underwater acoustic signal processing. The invention comprises the following steps: according to the index requirements of a sonar system and the principle of equivalent array element phase centers of extended-aperture sonar, namely, a transmitting array element and a receiving array element form a module, the phase center of the module is positioned at the geometric center of the two array elements, and the positions of the transmitting array and the receiving array are reasonably arranged; according to the arranged transmitting and receiving array types, at the transmitting base array end, the transmitting array simultaneously transmits mutually orthogonal waveforms; a receiving array receives a reflected signal of a target, namely an echo signal; respectively carrying out receiving beam forming processing on the echo signals in a transform domain, and carrying out transform domain filtering receiving beam forming; and (3) compensating the time delay difference formed by different transmitting arrays by using beam forming for the signals after the beam forming processing is carried out on the transform domain receiving beam, and further acquiring a range-direction angle-direction sound diagram of the extended aperture sonar.
Description
Technical Field
The invention belongs to the field of underwater acoustic signal processing, and particularly relates to a transform domain beam forming method based on extended aperture sonar.
Background
In recent years, the multi-beam image sonar technology is widely applied to the fields of submarine topography mapping, petroleum pipeline detection and underwater target detection, and in order to acquire a high-definition sonar image, the distance resolution and the angle resolution of the sonar image need to be improved simultaneously.
In wideband signal systems, range resolution is typically determined by the effective bandwidth of the received signal, while angular resolution is typically determined by the effective aperture of the receive array and the received signal frequency. In practical applications, in a specific application field, changing a specific operating frequency range of the image sonar will cause the detection performance to be degraded, and therefore, the effective receiving array aperture of the sonar system is usually selected to be enlarged to improve the angular resolution.
In order to reduce the hardware cost of the transducer array without increasing the size of the array, virtual extended aperture sonar can be adopted to improve the angular resolution, the working principle is that different transmitting arrays transmit orthogonal waveforms, a receiving end separates transmitting signals through matched filtering, and then receiving and transmitting wave beam forming are carried out, so that the purpose of extending the actual receiving array aperture is achieved. However, in engineering applications, completely orthogonal signals do not exist, and high cross-correlation between the transmitted signals will cause the range to be raised to the side lobe, thereby reducing the range definition of the sonar image.
Disclosure of Invention
The invention is realized by the following steps:
a transform domain beam forming method based on extended aperture sonar is characterized by comprising the following steps:
according to the index requirements of a sonar system and the principle of equivalent array element phase centers of extended-aperture sonar, namely, a transmitting array element and a receiving array element form a module, the phase center of the module is positioned at the geometric center of the two array elements, and the positions of the transmitting array and the receiving array are reasonably arranged; if the sonar receiving array is a one-dimensional array, two transmitting arrays are arranged at two ends of the receiving array, and if the sonar receiving array is a two-dimensional plane array, the azimuth direction and the elevation direction need to be expanded, four transmitting arrays are arranged around the receiving plane array; setting a uniform linear receiving array, the distance between adjacent array elements is half-wavelength, the number of array elements is M, two transmitting arrays are arranged at two ends of the array, and the width of the angle-direction wave beam of the extended aperture sonar is expressed as
Wherein BW is the wave beam width in the angle direction, the unit is radian, lambda is the wavelength of the transmitted signal, d is the distance between adjacent receiving array elements,
for beam offset angle, setting
If an even two-dimensional plane receiving array is established, adjacent array element interval is half wavelength, and the level is L to array element number, and the every single move is Q to array element number, and four transmission arrays arrange four angles at the receiving area array, then the level is to beam width and every single move to beam width and be:
wherein, BWθIn order to be the horizontal beam width,
for beam width in elevation, dθThe spacing between adjacent array elements is horizontal,
the pitch is the distance between adjacent array elements;
step two, according to the arranged transmitting and receiving array type, at the transmitting base array end, the transmitting arrays simultaneously transmit mutually orthogonal waveforms, completely orthogonal signals do not exist in practice, signals with different characteristics of the transmitting signals in a transform domain are designed, for example, a one-dimensional receiving array is taken as an example, the two transmitting arrays transmit two sinusoidal signals with different frequencies, the frequency response curves-3 dB of the two signals are not overlapped, namely the frequencies are not crossed, and the frequency characteristics of the two transmitting signals are different; if the positive and negative frequency modulation signals with different central frequencies exist, the two transmitting signals have different characteristics in the STFT time-frequency domain, and the signals transmitted by the two transmitting arrays can be considered to be orthogonal signals;
s1(t)＝cos(2πf1t+K1πt2)
s2(t)＝cos(2πf2t+K2πt2)
in the formula, s1(t)，s2(t) is orthogonal signal transmitted by two transmitting arrays at two ends, and the transmitting center frequency of one transmitting array is f1Frequency change rate of K1T is a time point, and the transmitting center frequency of another transmitting array is f2Frequency change rate of K2The center frequencies of the two signals are different, and the frequency change rates are different;
receiving a reflection signal of a target, namely an echo signal, by a receiving array, wherein the echo signal contains superposition of target reflection signals of a plurality of orthogonal transmission signals, and in order to realize waveform separation, receiving beam forming processing is respectively carried out on the echo signal in a transform domain by combining different characteristics of the transmission orthogonal signals in the transform domain, and transform domain filtering receiving beam forming is carried out;
setting a receiving array as a one-dimensional linear array, transmitting signals with different frequencies by two transmitting signals, and respectively forming receiving beams at different frequencies if the characteristics of the two signals in frequency domains are different; if the two transmitting signals transmit upper and lower frequency modulation signals with different frequencies, because the two types of signals have different characteristics in different order fractional order Fourier transform domains, the capability of extracting multi-component chirp signal parameters is realized according to the fractional order Fourier transform, and then the receiving wave beam forming processing is carried out in the different order fractional order Fourier transform domains respectively;
by fractional Fourier transforms of different orders, i.e. on the received signal separately
Where x (t) is the received target reflection signal,
is p1A fractional order fourier transform kernel of order,
is x (t) corresponding to p1A fractional order fourier transform domain function of order,
is p2A fractional order fourier transform kernel of order,
is x (t) corresponding to p2Fractional order Fourier transform domain function of order;
step four, inverse transform domain transformation and emission beam forming are carried out; and performing inverse transform domain transformation on the signals after the transform domain receiving beam forming processing, transforming the signals into beam domain time domain signals, and performing transmitting beam forming processing in the time domain according to the time delay difference formed by the reflection of different transmitting arrays on the target, namely performing beam forming compensation on the time delay difference formed by the different transmitting arrays so as to obtain the range-direction angle-direction sound pattern of the extended aperture sonar.
Compared with the prior art, the invention has the beneficial effects that:
1. the method provided by the invention can reduce the influence of high correlation of the transmitted waveform on the distance-direction high side lobe and realize the extension of the distance-direction high-definition diagram of the acoustic diagram of the aperture sonar.
2. The method provided by the invention can be selectively realized in a plurality of transform domains, and is simple in realization process and easy to realize.
Drawings
FIG. 1 is a schematic diagram of the one-dimensional array extended aperture principle of the present invention;
fig. 2 is a schematic diagram of the two-dimensional planar array extended aperture sonar basic array layout of the present invention;
FIG. 3 is a block flow diagram of an implementation of the present invention;
fig. 4 is a comparison of receive array aperture beam patterns of the present invention.
Detailed Description
The invention is described in more detail below with reference to the accompanying drawings:
the invention relates to a transform domain beam forming method based on extended aperture sonar, which reduces the range-direction definition of sonar images due to incomplete orthogonality of transmitting signals in a virtual extended aperture sonar system. The method comprises the steps of firstly, reasonably arranging transmitting array receiving arrays according to a virtual extended aperture theory, then, transmitting orthogonal waveforms by each transmitting array, receiving target echo signals superposed by a plurality of orthogonal waveforms by the receiving arrays, carrying out receiving array beam forming on a plurality of groups of orthogonal waveforms in a transform domain according to different characteristics of different orthogonal waveforms in the transform domain, respectively carrying out inverse transform domain transform, and finally carrying out transmitting array beam forming in a time domain. The method does not need to adopt matched filtering to separate orthogonal waveform signals, utilizes the different characteristics of the orthogonal signals in a transform domain, adopts transform domain receiving beam forming, solves the problem of high distance side lobe caused by high correlation of orthogonal time domain waveforms in practical application, improves the angular resolution, obtains high distance definition at the same time, and integrally improves the quality of sonar images.
The first embodiment is as follows:
in this example, the system parameters: the receiving array is a one-dimensional linear array, the width of an angular beam is 1.5 degrees, the working frequency of the receiving array is 60kHz, the sound velocity is 1500m/s, the acting distance is 50m, and the signal sampling rate is 300 kHz.
1. And (3) calculating:
assuming that the receiving array is a uniform linear array, the distance between adjacent array elements is half wavelength of the working frequency of the receiving array, in order to meet the requirement of the beam width in the angle direction of the system, according to the formula,
the calculation can be carried out, the number of the array elements in the actual receiving array is designed to be 36, and two transmitting matrixes are distributed at two ends of the receiving matrix.
From the calculated receiving array parameters, as can be seen from the simulation of fig. 4, the beam width of the system after aperture expansion is about 0.55 of the beam width of the actual receiving array system, and the angular resolution is improved.
The two transmitting matrixes transmit mutually orthogonal signals, the signal waveforms are respectively a positive frequency modulation signal with the center frequency of 55kHz and a negative frequency modulation signal with the center frequency of 85kHz, the bandwidth of the transmitting signals is 3kHz, and the pulse width is 10 ms.
The receiving array receives the target echo signal, and the analysis shows that the two transmitting signals have different characteristics in different order fractional order Fourier transform domains, firstly, the echo signal is subjected to-1.539 order divisionThe Fourier transform of several orders shows that the transmitting signal 1 has strong component in the transform domain of-1.539 orders, and the receiving beam is formed to obtain the transform domain signal y1(u) simultaneously, the echo signals are subjected to fractional Fourier transform of 1.539 order, so that the transmitting signals 2 have strong components in the transform domain of 1.539 order, and receiving wave beams are formed to obtain transform domain signals y2And (u) avoiding the adoption of correlation functions for waveform separation, which leads to high distance side lobes.
Then to the transform domain signal y1(u) and transform domain signal y2(u) inverse transform domain transformation is performed to transform the time domain signals to y1(t) and transform domain signal y2And (t) then performing time delay compensation to perform transmitting beam forming.
Finally, the distance direction high definition and angle direction high resolution images are obtained.
The second embodiment is as follows:
1. firstly, according to the requirement of sonar system indexes, according to the principle of equivalent array element phase center of extended aperture sonar, namely, a transmitting array element and a receiving array element form a module, the phase center of the module is positioned at the geometric center of the two array elements, and the positions of the transmitting array and the receiving array are reasonably arranged. If the sonar receiving arrays are one-dimensional arrays, two transmitting arrays are arranged at two ends of the receiving arrays, and if the sonar receiving arrays are two-dimensional plane arrays, the azimuth direction and the elevation direction need to be expanded, four transmitting arrays are arranged around the receiving plane arrays, which are respectively shown in fig. 1 and fig. 2. Assuming a uniform linear receiving array, the distance between adjacent array elements is half wavelength, the number of the array elements is M, two transmitting arrays are arranged at two ends of the array, and the width of the angle-direction wave beam of the extended aperture sonar is expressed as
Wherein BW is the wave beam width in the angle direction, the unit is radian, lambda is the wavelength of the transmitted signal, d is the distance between adjacent receiving array elements,
for the beam offset angle, the method sets
It can be seen that the beam width of the extended-aperture sonar is about 0.55 of the actual receiving array aperture, which doubles the angular resolution.
Assuming a uniform two-dimensional plane receiving array, the distance between adjacent array elements is half wavelength, the number of horizontal array elements is L, the number of pitch array elements is Q, four transmitting arrays are arranged at four corners of the receiving area array, and the width of horizontal beam and the width of pitch beam are
Wherein, BWθIn order to be the horizontal beam width,
for beam width in elevation, dθThe spacing between adjacent array elements is horizontal,
the pitch is the pitch of adjacent array elements.
It can be seen that after the planar array is expanded, the horizontal beam width and the elevation beam width are respectively 0.55 of the horizontal beam width and the elevation beam width of the actual receiving array, i.e. the horizontal and elevation angular resolutions are improved by one time.
In fig. 2, the receiving array elements are arranged in the circular dots, and the black array elements at four corners of the plane are arranged as the transmitting array.
2. According to the arranged transmitting and receiving array type, at the transmitting base array end, the transmitting arrays simultaneously transmit mutually orthogonal waveforms, completely orthogonal signals do not exist in practice, the signals with different characteristics of the transmitting signals in a transform domain are designed, for example, a one-dimensional receiving array is taken as an example, two transmitting arrays transmit two sinusoidal signals with different frequencies, the frequency response curves-3 dB of the two signals are not overlapped, namely the frequencies are not crossed, and the frequency characteristics of the two transmitting signals are different; if the positive and negative frequency modulation signals with different center frequencies exist, the two transmitting signals have different characteristics in the STFT time-frequency domain, and the signals transmitted by the two transmitting arrays can be considered as orthogonal signals.
s1(t)＝cos(2πf1t+K1πt2)
s2(t)＝cos(2πf2t+K2πt2)
In the formula, s1(t)，s2(t) is orthogonal signal transmitted by two transmitting arrays at two ends, and the transmitting center frequency of one transmitting array is f1Frequency change rate of K1T is a time point, and the transmitting center frequency of another transmitting array is f2Frequency change rate of K2The center frequencies of the two signals are different, and the frequency change rates are different.
3. The receiving array receives a reflection signal of a target, namely an echo signal, the echo signal comprises superposition of target reflection signals of a plurality of orthogonal transmitting signals, and in order to realize waveform separation, the echo signal is respectively subjected to receiving beam forming processing in a transform domain by combining different characteristics of the transmitting orthogonal signals in the transform domain, and then is subjected to transform domain filtering receiving beam forming.
Assuming that the receiving array is a one-dimensional linear array, two transmitting signals transmit different frequency signals, and the characteristics of the two signals in the frequency domain are different, receiving wave beam formation is respectively carried out at different frequencies; if the two transmitting signals transmit upper and lower frequency modulation signals with different frequencies, because the two types of signals have different characteristics in different order fractional order Fourier transform domains, the capability of extracting multi-component chirp signal parameters is realized according to the fractional order Fourier transform, and then the receiving wave beam forming processing is carried out in the different order fractional order Fourier transform domains respectively.
By fractional Fourier transforms of different orders, i.e. on the received signal separately
Where x (t) is the received target reflection signal,
is p1A fractional order fourier transform kernel of order,
is x (t) corresponding to p1A fractional order fourier transform domain function of order,
is p2A fractional order fourier transform kernel of order,
is x (t) corresponding to p2Fractional order fourier transform domain function of order.
4. Inverse transform domain transform, transmit beamforming. And performing inverse transform domain transformation on the signals after the transform domain receiving beam forming processing, transforming the signals into beam domain time domain signals, and performing transmitting beam forming processing in the time domain according to the time delay difference formed by the reflection of different transmitting arrays on the target, namely performing beam forming compensation on the time delay difference formed by the different transmitting arrays so as to obtain the range-direction angle-direction sound pattern of the extended aperture sonar.
The specific operation method of the invention is as follows:
1. firstly, according to the requirement of sonar system indexes, according to the principle of equivalent array element phase center of extended aperture sonar, namely, a transmitting array element and a receiving array element form a module, the phase center of the module is positioned at the geometric center of the two array elements, and the positions of the transmitting array and the receiving array are reasonably arranged. If the sonar receiving arrays are one-dimensional arrays, two transmitting arrays are arranged at two ends of the receiving arrays, and if the sonar receiving arrays are two-dimensional plane arrays, the azimuth direction and the elevation direction need to be expanded, four transmitting arrays are arranged around the receiving plane arrays, which are respectively shown in fig. 1 and fig. 2. Assuming a uniform linear receiving array, the distance between adjacent array elements is half wavelength, the number of the array elements is M, two transmitting arrays are arranged at two ends of the array, and the width of the angle-direction wave beam of the extended aperture sonar is expressed as
Wherein BW is the wave beam width in the angle direction, the unit is radian, lambda is the wavelength of the transmitted signal, d is the distance between adjacent receiving array elements,
for the beam offset angle, the method sets
It can be seen that the beam width of the extended-aperture sonar is about 0.55 of the actual receiving array aperture, which doubles the angular resolution.
Assuming a uniform two-dimensional plane receiving array, the distance between adjacent array elements is half wavelength, the number of horizontal array elements is L, the number of pitch array elements is Q, four transmitting arrays are arranged at four corners of the receiving area array, and the width of horizontal beam and the width of pitch beam are
It can be seen that after the planar array is expanded, the horizontal beam width and the elevation beam width are respectively 0.55 of the horizontal beam width and the elevation beam width of the actual receiving array, i.e. the horizontal and elevation angular resolutions are improved by one time.
In fig. 2, the receiving array elements are arranged in the circular dots, and the black array elements at four corners of the plane are arranged as the transmitting array.
2. According to the arranged transmitting and receiving array type, at the transmitting base array end, the transmitting arrays simultaneously transmit mutually orthogonal waveforms, completely orthogonal signals do not exist in practice, the signals with different characteristics of the transmitting signals in a transform domain are designed, for example, a one-dimensional receiving array is taken as an example, two transmitting arrays transmit two sinusoidal signals with different frequencies, the frequency response curves-3 dB of the two signals are not overlapped, namely the frequencies are not crossed, and the frequency characteristics of the two transmitting signals are different; if the positive and negative frequency modulation signals with different center frequencies exist, the two transmitting signals have different characteristics in the STFT time-frequency domain, and the signals transmitted by the two transmitting arrays can be considered as orthogonal signals.
s1(t)＝cos(2πf1t+K1πt2)
s2(t)＝cos(2πf2t+K2πt2)
In the formula, s1(t)，s2(t) is orthogonal signal transmitted by two transmitting arrays at two ends, and the transmitting center frequency of one transmitting array is f1Frequency change rate of K1T is a time point, and the transmitting center frequency of another transmitting array is f2Frequency change rate of K2The center frequencies of the two signals are different, and the frequency change rates are different.
3. The receiving array receives a reflection signal of a target, namely an echo signal, the echo signal comprises superposition of target reflection signals of a plurality of orthogonal transmitting signals, and in order to realize waveform separation, the echo signal is respectively subjected to receiving beam forming processing in a transform domain by combining different characteristics of the transmitting orthogonal signals in the transform domain, and then is subjected to transform domain filtering receiving beam forming.
Assuming that the receiving array is a one-dimensional linear array, two transmitting signals transmit different frequency signals, and the characteristics of the two signals in the frequency domain are different, receiving wave beam formation is respectively carried out at different frequencies; if the two transmitting signals transmit upper and lower frequency modulation signals with different frequencies, because the two types of signals have different characteristics in different order fractional order Fourier transform domains, the capability of extracting multi-component chirp signal parameters is realized according to the fractional order Fourier transform, and then the receiving wave beam forming processing is carried out in the different order fractional order Fourier transform domains respectively.
By fractional Fourier transforms of different orders, i.e. on the received signal separately
Where x (t) is the received target reflection signal,
is p1A fractional order fourier transform kernel of order,
is x (t) corresponding to p1A fractional order fourier transform domain function of order,
is p2A fractional order fourier transform kernel of order,
is x (t) corresponding to p2Fractional order fourier transform domain function of order.
4. And performing inverse transform domain transformation on the signals subjected to the transform domain receiving beam forming processing, transforming the signals into beam domain time domain signals, performing transmitting end beam forming processing in a time domain according to time delay difference formed by reflection of a transmitting array on a target, and further acquiring a range-direction angle-direction sound diagram of the extended aperture sonar.
Claims (1)
1. A transform domain beam forming method based on extended aperture sonar is characterized by comprising the following steps:
according to the index requirements of a sonar system and the principle of equivalent array element phase centers of extended-aperture sonar, namely, a transmitting array element and a receiving array element form a module, the phase center of the module is positioned at the geometric center of the two array elements, and the positions of the transmitting array and the receiving array are reasonably arranged; if the sonar receiving array is a one-dimensional array, two transmitting arrays are arranged at two ends of the receiving array, and if the sonar receiving array is a two-dimensional plane array, the azimuth direction and the elevation direction need to be expanded, four transmitting arrays are arranged around the receiving plane array; setting a uniform linear receiving array, the distance between adjacent array elements is half-wavelength, the number of array elements is M, two transmitting arrays are arranged at two ends of the array, and the width of the angle-direction wave beam of the extended aperture sonar is expressed as
Wherein BW is the wave beam width in the angle direction, the unit is radian, lambda is the wavelength of the transmitted signal, d is the distance between adjacent receiving array elements,
for beam offset angle, setting
If an even two-dimensional plane receiving array is established, adjacent array element interval is half wavelength, and the level is L to array element number, and the every single move is Q to array element number, and four transmission arrays arrange four angles at the receiving area array, then the level is to beam width and every single move to beam width and be:
wherein, BWθIs a horizontal waveThe width of the beam is such that,
for beam width in elevation, dθThe spacing between adjacent array elements is horizontal,
the pitch is the distance between adjacent array elements;
step two, according to the arranged transmitting and receiving array type, at the transmitting base array end, the transmitting arrays simultaneously transmit mutually orthogonal waveforms, completely orthogonal signals do not exist in practice, signals with different characteristics of the transmitting signals in a transform domain are designed, for example, a one-dimensional receiving array is taken as an example, the two transmitting arrays transmit two sinusoidal signals with different frequencies, the frequency response curves-3 dB of the two signals are not overlapped, namely the frequencies are not crossed, and the frequency characteristics of the two transmitting signals are different; if the positive and negative frequency modulation signals with different central frequencies exist, the two transmitting signals have different characteristics in the STFT time-frequency domain, and the signals transmitted by the two transmitting arrays can be considered to be orthogonal signals;
s1(t)＝cos(2πf1t+K1πt2)
s2(t)＝cos(2πf2t+K2πt2)
in the formula, s1(t)，s2(t) is orthogonal signal transmitted by two transmitting arrays at two ends, and the transmitting center frequency of one transmitting array is f1Frequency change rate of K1T is a time point, and the transmitting center frequency of another transmitting array is f2Frequency change rate of K2The center frequencies of the two signals are different, and the frequency change rates are different;
receiving a reflection signal of a target, namely an echo signal, by a receiving array, wherein the echo signal contains superposition of target reflection signals of a plurality of orthogonal transmission signals, and in order to realize waveform separation, receiving beam forming processing is respectively carried out on the echo signal in a transform domain by combining different characteristics of the transmission orthogonal signals in the transform domain, and transform domain filtering receiving beam forming is carried out;
setting a receiving array as a one-dimensional linear array, transmitting signals with different frequencies by two transmitting signals, and respectively forming receiving beams at different frequencies if the characteristics of the two signals in frequency domains are different; if the two transmitting signals transmit upper and lower frequency modulation signals with different frequencies, because the two types of signals have different characteristics in different order fractional order Fourier transform domains, the capability of extracting multi-component chirp signal parameters is realized according to the fractional order Fourier transform, and then the receiving wave beam forming processing is carried out in the different order fractional order Fourier transform domains respectively;
by fractional Fourier transforms of different orders, i.e. on the received signal separately
Where x (t) is the received target reflection signal,
is p1A fractional order fourier transform kernel of order,
is x (t) corresponding to p1A fractional order fourier transform domain function of order,
is p2A fractional order fourier transform kernel of order,
is x (t) corresponding to p2Fractional order Fourier transform domain function of order;
step four, inverse transform domain transformation and emission beam forming are carried out; and performing inverse transform domain transformation on the signals after the transform domain receiving beam forming processing, transforming the signals into beam domain time domain signals, and performing transmitting beam forming processing in the time domain according to the time delay difference formed by the reflection of different transmitting arrays on the target, namely performing beam forming compensation on the time delay difference formed by the different transmitting arrays so as to obtain the range-direction angle-direction sound pattern of the extended aperture sonar.
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