Underwater sound image reconstruction method based on angle error compensation

Abstract

The invention relates to an underwater acoustic image reconstruction method based on angle error compensation, which comprises the following steps of: (1) calculating space coordinate information and a two-way slant range course of a transmitting array element and a receiving array element for each subsystem consisting of the receiving array element and the transmitting array element; (2) calculating a two-way slant range course after phase center approximation; (3) calculating a system function of a distance-Doppler domain; (4) calculating a Doppler phase error; (5) dividing the data into # imgabs0 data blocks which are not overlapped with one another, and compensating micro-range migration errors caused by range errors; (6) obtaining a signal after distance delay error compensation; (7) performing differential range migration correction processing, range pulse compression, secondary range pulse compression and consistent range migration correction processing; (8) carrying out azimuth focusing processing, residual phase error compensation operation and azimuth walking correction processing; and (9) performing coherent fusion processing and inverse Fourier transform to obtain a final high-resolution image. According to the method, the image can be quickly reconstructed, and the real-time processing requirement can be met.

Description

Technical Field

[0001] The present invention relates to the field of intelligent manufacturing technology, and in particular to an underwater acoustic image reconstruction method based on angle error compensation. Background Art

[0002] Sound waves are the only energy carrier discovered by humans so far that can carry out long-distance propagation underwater, and the underwater acoustic transducer based on sound waves is a common tool for underwater detection and mapping. After the synthetic aperture technology is applied to the field of underwater acoustics, it becomes an underwater high-resolution imaging device. Its basic principle is to use small aperture array elements and rely on signal processing to synthesize a virtual large aperture array to improve the resolution in azimuth. The resolution of underwater synthetic aperture detection equipment is improved by about an order of magnitude compared to traditional side-scan equipment, and it has a wide range of applications in military and civilian fields. In the military, it is mainly used for detection of sunken or suspended explosives, matching navigation, high-resolution reconnaissance of important sea areas, etc. In the civilian field, it is mainly used for underwater topography and geomorphology mapping, seabed exploration, archaeological search and rescue, salvage of sunken objects, and dredging of waterways.

[0003] The image reconstruction of synthetic aperture technology is based on the difference in the acoustic path of each transmission and reception obtained by solving the geometric relationship. When the motion error exceeds one-eighth of the wavelength, it will affect the quality of image reconstruction. Therefore, it is necessary to accurately estimate and compensate for the change in the acoustic path during the movement. In the actual application of synthetic aperture technology, factors such as wind and waves and ship maneuverability will cause the hydroacoustic equipment platform to deviate from the ideal track. In addition, factors such as the fluctuation and multipath of the propagation medium will also affect the quality of the image, resulting in a deterioration in the focusing effect of the hydroacoustic image. Therefore, high-resolution synthetic aperture hydroacoustic equipment must take motion compensation measures to reduce or even eliminate the influence of motion errors.

[0004] Generally speaking, navigation equipment can provide accurate motion information such as yaw and pitch (such as ring laser gyroscopes), and can also provide robust acceleration information in the roll and heading directions (such as accelerometers). If the motion attitude information is not used, and the image reconstruction is directly performed using the method published by Ma Mengbo and other authors in the "Journal of Huazhong University of Science and Technology (Natural Science Edition)" entitled "Multi-receiver Array Synthetic Aperture Sonar CZT Imaging Algorithm", the image reconstruction result will greatly reduce the performance. If the motion attitude information is used and the image reconstruction is performed using the method published by Ma Mengbo and other authors in the "Journal of Huazhong University of Science and Technology (Natural Science Edition)" entitled "Multi-receiver Subarray SAS Motion Compensation Based on Inertial Navigation System", a more precise image reconstruction result can be obtained. However, this point-by-point image reconstruction algorithm combined with attitude compensation has a very large amount of calculation, which makes this method unable to meet the system's timeliness processing requirements. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide an underwater acoustic image reconstruction method based on angle error compensation which can quickly reconstruct images and meet the real-time processing requirements.

[0006] In order to solve the above problems, the present invention provides an underwater acoustic image reconstruction method based on angle error compensation, comprising the following steps:

[0007] (1) For each subsystem composed of receiving array elements and transmitting array elements, the spatial coordinate information of the transmitting array elements and the receiving array elements is calculated in the presence of angle errors, and the two-way slant range history corresponding to any transmitting and receiving array element subsystem is calculated to obtain the two-way slant range history between the subsystem composed of the i-th receiving array element and the transmitting array element and the point target;

[0008] (2) According to the phase center approximation method, calculate the two-way slant range history after the phase center approximation;

[0009] ⑶ According to the two-way slant range history after the phase center is approximated, calculate the system function of each transceiver array element subsystem in the range-Doppler domain;

[0010] (4) For the Doppler phase error caused by the distance delay error in the phase center approximation processing, calculate the Doppler phase error caused by the distance error compensation in the two-dimensional time domain;

[0011] (5) Divide the data into N non-overlapping data blocks in the range direction, and compensate for the micro-range migration error caused by the range error in the frequency domain of any data block in the range direction;

[0012] (6) For all the data blocks after micro-distance migration compensation, arrange them in the order of the data blocks in the distance time domain to obtain the signal after distance delay error compensation;

[0013] ⑺For each receiving array element after range delay error compensation, differential range migration correction processing is performed in the range-Doppler domain in turn, and range pulse compression, secondary range pulse compression, and consistent range migration correction processing are completed while filtering operations are performed in the two-dimensional frequency domain;

[0014] ⑻For each receiving array element, after the data has been processed by range pulse compression, secondary range pulse compression, and consistent range migration correction, azimuth focusing, residual phase error compensation, and azimuth movement correction are performed while filtering in the range-Doppler domain;

[0015] ⑼ For the data after azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing of all receiving array elements, coherent fusion processing is performed in the range-Doppler domain, and azimuth inverse Fourier transform is performed to obtain the final high-resolution image.

[0016] The three-dimensional space coordinates of the transmitting array element in step (1) are:

[0017]

[0018] Where: v represents the platform movement speed, in meters per second; t represents the slow time in the azimuth direction, in seconds; x t represents the azimuth coordinate of the transmitting array element at time t, in meters; t represents the coordinate of the transmitting array element at time t in meters; z t It represents the coordinate of the transmitting array element at the time t in meters;

[0019] The three-dimensional space coordinates of the i-th receiving array element are:

[0020]

[0021] Where: i (1≤i≤I) represents the index of the receiving array element; I represents the total number of receiving array elements; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; represents the rotation vector, θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw angle error in degrees; x i represents the coordinate of the i-th receiving array element along the azimuth at time t, in meters; i represents the coordinate of the i-th receiving array element along the ground distance at time t, in meters; z i represents the coordinate of the i-th receiving array element along the height at time t, in meters; It represents the distance that the ith receiving element moves along the azimuth direction from the time when the transmitting element transmits the signal to the time when the ith receiving element receives the target echo signal, in meters; c represents the speed of sound in water, in meters per second;

[0022] The two-way slant range from the subsystem composed of the i-th receiving array element and the transmitting array element to the point target is:

[0023]

[0024] in: represents the slant range of the i-th receiving array element in the case of angle error, in meters; t represents the slow time in azimuth, in seconds; r represents the closest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane, in meters; h represents the height of the hydroacoustic transducer from the bottom of the water, in meters; θ represents the slant angle of the hydroacoustic transducer, in degrees; the three-dimensional coordinates of the point target in azimuth, ground distance, and height are 0, rsinθ, h, all in meters; c represents the speed of sound in water, in meters / second; v represents the platform speed of the hydroacoustic transducer, in meters / second; u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

[0025] The calculation formula of the two-way slant range history after the phase center is approximated in step (2) is:

[0026]

[0027] Where: u i represents the distance between the i-th (1≤i≤I) receiving array element and the transmitting array element, in meters; I represents the total number of receiving array elements; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; ΔR i Represents the distance delay error after phase center approximation, in meters, ΔR i The specific expression is:

[0028]

[0029] in: represents the slant range of the i-th receiving array element in the case of angle error, in meters; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; h represents the height of the underwater acoustic transducer from the bottom of the water, in meters; θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

[0030] The calculation formula of the system function of each transceiver array element subsystem in the range-Doppler domain in step (3) is:

[0031]

[0032] Where: sS i (τ,f a ; r) represents the system function of the i-th receiving array element in the range-Doppler domain, Represents the window function of the transmitted signal, Wa (f a -f dc ) represents the joint directivity function of the receiving and transmitting array elements; j 2 =-1 represents the imaginary unit; τ represents the time from distance to speed, in seconds; c represents the speed of sound in water, in meters per second; ΔR i It represents the distance delay error after phase center approximation, in meters; f a Indicates the azimuth Doppler frequency in Hertz; f dc represents the Doppler center frequency caused by the squint of the hydroacoustic transducer, in Hertz; r represents the closest distance between the target and the receiving array on the slant range plane, in meters; θ i (τ,f a ; r) represents the phase of the system function, and the specific expression is:

[0033]

[0034] Where: u i represents the distance between the i-th (1≤i≤I) receiving array element and the transmitting array element, in meters; I represents the total number of receiving array elements; f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; v represents the movement speed of the underwater acoustic transducer platform, in meters per second; K m It represents the range modulation frequency considering the coupling of azimuth and distance, in Hertz / second. The specific expression is:

[0035]

[0036] Where: K r Indicates the frequency of the transmitted linear frequency modulation signal, in Hertz / second; D(f a )The physical meaning is that there is coupling between the azimuth and the distance, which is called the distance bending factor. The specific expression is:

[0037]

[0038] In step (4), the Doppler phase error caused by compensating the distance error in the two-dimensional time domain is calculated as follows:

[0039]

[0040] in: represents the Doppler phase error, f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; ΔR i It represents the distance delay error after phase center approximation, in meters; c represents the speed of sound in water, in meters per second.

[0041] The width Δr of each data block in step (5) is determined by the following formula:

[0042]

[0043] Among them: abs means taking the absolute value operation, express The distance between the center of the nth data block is r = r n,c The value at express At the edge distance of the nth data block r = r n,c The value at -0.5Δr; r n,c Represents the center distance of the nth data block in meters; the expression (r n,c -0.5Δr) represents the edge distance of the nth data block, in meters; Δr represents the width of the data block, in meters;

[0044] The total number of data blocks N is:

[0045]

[0046] Where: r max Indicates the maximum distance that the underwater acoustic transducer can detect, in meters; r min Indicates the minimum distance detected by the underwater acoustic transducer, in meters; ceil means rounding up to an integer;

[0047] The compensation function of the nth data block is:

[0048]

[0049] Where: Ω i (t,f r ,n) represents the compensation function of the micro-distance migration error in the nth data block, f r represents the instantaneous frequency in the distance direction, in Hertz; c represents the speed of sound in water, in meters per second; ΔR i,n Represents the distance delay error ΔR after phase center approximation i The distance between the center of the nth data block is r = r n,c The error value at , in meters, is expressed as:

[0050]

[0051] Where: u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; Represents the value of the i-th receiving array element at the center distance of the n-th data block based on the angle error, in meters; r n,crepresents the value at the center distance of the nth data block, in meters; h represents the height of the underwater acoustic transducer from the bottom of the water, in meters; θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

[0052] The method of arranging the data blocks in the time domain in the distance direction in step (6) is as follows:

[0053]

[0054] in: represents the data after micro-distance migration compensation for the first data block of the i-th receiving array element, and so on. represents the data after micro-distance migration compensation for the nth data block of the i-th receiving array element, and the subscript n (1≤n≤N) represents the index of the i-th receiving array element data block. It represents the signal after all N data blocks of the i-th receiving element are arranged in sequence.

[0055] The filtering function of step (7) when performing differential range migration correction processing in the range-Doppler domain is:

[0056]

[0057] Where: i (τ,f a ) represents the filter function for performing differential range migration correction processing on the i-th receiving array element in the range-Doppler domain, j 2 =-1 represents the imaginary unit, K m It represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at the point where c represents the speed of sound in water in meters per second; r ref represents the reference distance in meters; τ represents the distance acceleration time in seconds;

[0058] The filter function for completing range pulse compression, secondary range pulse compression, and consistent range migration correction is:

[0059]

[0060] Where: H i (f r ,f a ; r ref) represents the filtering function for performing range pulse compression, secondary range pulse compression, and consistent range migration correction on the i-th receiving array element in the two-dimensional frequency domain, D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at K m represents the modulation frequency when the fusion azimuth and distance are coupled, in Hz / s; f r Represents the instantaneous frequency in distance, in Hertz; r ref represents the reference distance in meters; c represents the speed of sound in water in meters per second.

[0061] The compensation function for performing azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing in step (8) is:

[0062]

[0063] Where: i (τ,f a ) represents the compensation function for azimuth focusing, residual phase error compensation and azimuth motion correction in the range-Doppler domain, D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; K m represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; f a Indicates the azimuth Doppler frequency in Hertz; r ref represents the reference distance in meters; r represents the shortest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane in meters; c represents the speed of sound in water in meters per second.

[0064] The coherent fusion processing method in step (9) is:

[0065]

[0066] in: It represents the result of coherent fusion of each receiving array data in the range-Doppler domain. represents the result of azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing for the i-th receiving array data in the range-Doppler domain, the subscript i (1≤i≤I) represents the index of the receiving array element, and I represents the total number of receiving array elements;

[0067] The final high-resolution image is obtained as follows:

[0068]

[0069] Where: IFFT represents inverse Fourier transform, and ff(τ,t) represents the final high-resolution image.

[0070] Compared with the prior art, the present invention has the following advantages:

[0071] The present invention utilizes the angle error of navigation data and integrates the correction of the angle error in each processing step of the fast image reconstruction method to compensate for the adverse effects of the underwater acoustic equipment system's deviation from non-uniform linear motion on the image, thereby improving both the performance of the image reconstruction method and the efficiency of image reconstruction, and providing great support for the real-time processing of underwater high-performance acoustic equipment. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0073] Figure 1 This is the image reconstruction method flow of the present invention. Among them: range FFT means Fourier transform in the range direction; range IFFT means inverse Fourier transform in the range direction; azimuth FFT means Fourier transform in the azimuth direction; azimuth IFFT means inverse Fourier transform in the azimuth direction.

[0074] Figure 2 The present invention discloses the two-dimensional image reconstruction geometry of multi-subarray synthetic aperture underwater acoustic equipment with angle error.

[0075] Figure 3 It is the coordinate system of the linear array formed by the transceiver array elements in the present invention.

[0076] Figure 4 is the system approximate error under different angle errors in the present invention. Among them: (a) the pitch angle is 0.5° and the yaw angle is 1°; (b) the pitch angle is 1° and the yaw angle is 2°; (c) the pitch angle is 3° and the yaw angle is 4°; (d) the pitch angle is 5° and the yaw angle is 6°.

[0077] Figure 5It is the system approximate error of the underwater acoustic transducer under different beam widths when the pitch angle is 2° and the yaw angle is 3° in the present invention. Among them: (a) beam width is 3°; (b) beam width is 6°; (c) beam width is 9°; (d) beam width is 12°.

[0078] Figure 6 is the angle error recorded by the navigation device in the present invention, wherein: (a) yaw angle error; (b) pitch angle error.

[0079] Figure 7 The processing results of the measured data at sea in the present invention include: (a) no angle error compensation; (b) only pitch error compensation; (c) only yaw error compensation; (d) both yaw and pitch errors compensation. DETAILED DESCRIPTION

[0080] like Figure 1 As shown, a method for underwater acoustic image reconstruction based on angle error compensation includes the following steps:

[0081] ⑴ For each subsystem composed of receiving array elements and transmitting array elements, the spatial coordinate information of the transmitting array elements and the receiving array elements is calculated in the presence of angle errors, and the two-way slant range history corresponding to any transmitting and receiving array element subsystem is calculated to obtain the two-way slant range history between the subsystem composed of the i-th receiving array element and the transmitting array element and the point target.

[0082] Among them: The three-dimensional space coordinates of the transmitting array element are:

[0083]

[0084] Where: v represents the platform movement speed, in meters per second; t represents the slow time in the azimuth direction, in seconds; x t represents the azimuth coordinate of the transmitting array element at time t, in meters; t represents the coordinate of the transmitting array element at time t in meters; z t It represents the height coordinate of the transmitting array element at time t, in meters.

[0085] The three-dimensional space coordinates of the i-th receiving array element are:

[0086]

[0087] Where: i (1≤i≤I) represents the index of the receiving array element; I represents the total number of receiving array elements; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; represents the rotation vector, θpitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw angle error in degrees; x i represents the coordinate of the i-th receiving array element along the azimuth at time t, in meters; i represents the coordinate of the i-th receiving array element along the ground distance at time t, in meters; z i represents the coordinate of the i-th receiving array element along the height at time t, in meters; It represents the distance that the ith receiving element moves along the azimuth direction from the time when the transmitting element transmits the signal to the time when the ith receiving element receives the target echo signal, in meters; c represents the speed of sound in water, in meters per second;

[0088] The two-way slant range from the subsystem composed of the i-th receiving array element and the transmitting array element to the point target is:

[0089]

[0090] in: represents the slant range of the i-th receiving array element in the case of angle error, in meters; t represents the slow time in azimuth, in seconds; r represents the closest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane, in meters; h represents the height of the hydroacoustic transducer from the bottom of the water, in meters; θ represents the slant angle of the hydroacoustic transducer, in degrees; the three-dimensional coordinates of the point target in azimuth, ground distance, and height are 0, rsinθ, h, all in meters; c represents the speed of sound in water, in meters / second; v represents the platform speed of the hydroacoustic transducer, in meters / second; u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

[0091] (2) According to the phase center approximation method, the two-way slant range history after phase center approximation is calculated as follows:

[0092]

[0093] Where: u i represents the distance between the i-th (1≤i≤I) receiving array element and the transmitting array element, in meters; I represents the total number of receiving array elements; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; ΔR i Represents the distance delay error after phase center approximation, in meters, ΔR i The specific expression is:

[0094]

[0095] in: represents the slant range of the i-th receiving array element in the case of angle error, in meters; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; h represents the height of the underwater acoustic transducer from the bottom of the water, in meters; θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

[0096] ⑶ According to the two-way slant range history after the phase center is approximated, the system function of each transceiver array subsystem in the range-Doppler domain is calculated. The calculation formula is:

[0097]

[0098] Where: sS i (τ,f a ; r) represents the system function of the i-th receiving array element in the range-Doppler domain, Represents the window function of the transmitted signal, W a (f a -f dc ) represents the joint directivity function of the receiving and transmitting array elements; j 2 =-1 represents the imaginary unit; τ represents the time from distance to speed, in seconds; c represents the speed of sound in water, in meters per second; ΔR i It represents the distance delay error after phase center approximation, in meters; f a Indicates the azimuth Doppler frequency in Hertz; f dc represents the Doppler center frequency caused by the squint of the hydroacoustic transducer, in Hertz; r represents the closest distance between the target and the receiving array on the slant range plane, in meters; θ i (τ,f a ; r) represents the phase of the system function, and the specific expression is:

[0099]

[0100] Where: u i represents the distance between the i-th (1≤i≤I) receiving array element and the transmitting array element, in meters; I represents the total number of receiving array elements; f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; v represents the movement speed of the underwater acoustic transducer platform, in meters per second; K m It represents the range modulation frequency considering the coupling of azimuth and distance, in Hertz / second. The specific expression is:

[0101]

[0102] Where: K r Indicates the frequency of the transmitted linear frequency modulation signal, in Hertz / second; D(f a )The physical meaning is that there is coupling between the azimuth and the distance, which is called the distance bending factor. The specific expression is:

[0103]

[0104] (4) For the Doppler phase error caused by the distance delay error in the phase center approximation process, the Doppler phase error caused by the distance error compensation in the two-dimensional time domain is calculated as follows:

[0105]

[0106] in: represents the Doppler phase error, f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; ΔR i It represents the distance delay error after phase center approximation, in meters; c represents the speed of sound in water, in meters per second.

[0107] (5) Divide the data into N non-overlapping data blocks in the distance direction, and compensate for the micro-range migration error caused by the distance error in the frequency domain of any data block in the distance direction.

[0108] The width of each data block, Δr, is determined by the following formula:

[0109]

[0110] Among them: abs means taking the absolute value operation, express The distance between the center of the nth data block is r = r n,c The value at express At the edge distance of the nth data block r = r n,c The value at -0.5Δr; r n,c Represents the center distance of the nth data block in meters; the expression (r n,c -0.5Δr) represents the edge distance of the nth data block, in meters; Δr represents the width of the data block, in meters;

[0111] The total number of data blocks N is:

[0112]

[0113] Where: r max Indicates the maximum distance that the underwater acoustic transducer can detect, in meters; r minIndicates the minimum distance detected by the underwater acoustic transducer, in meters; ceil means rounding up to an integer;

[0114] The compensation function of the nth data block is:

[0115]

[0116] Where: Ω i (t,f r ,n) represents the compensation function of the micro-distance migration error in the nth data block, f r represents the instantaneous frequency in the distance direction, in Hertz; c represents the speed of sound in water, in meters per second; ΔR i,n Represents the distance delay error ΔR after phase center approximation i The distance between the center of the nth data block is r = r n,c The error value at , in meters, is expressed as:

[0117]

[0118] Where: u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; Represents the value of the i-th receiving array element at the center distance of the n-th data block based on the angle error, in meters; r n,c represents the value at the center distance of the nth data block, in meters; h represents the height of the underwater acoustic transducer from the bottom of the water, in meters; θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

[0119] (6) For all data blocks after micro-distance migration compensation, arrange them in sequence in the distance time domain according to the order of the data blocks to obtain the signal after distance delay error compensation.

[0120] The arrangement method is as follows:

[0121]

[0122] in: represents the data after micro-distance migration compensation for the first data block of the i-th receiving array element, and so on. represents the data after micro-distance migration compensation for the nth data block of the i-th receiving array element, and the subscript n (1≤n≤N) represents the index of the i-th receiving array element data block. It represents the signal after all N data blocks of the i-th receiving element are arranged in sequence.

[0123] ⑺For each receiving array element's signal after range delay error compensation, differential range migration correction processing is performed in the range-Doppler domain in turn, and range pulse compression, secondary range pulse compression, and consistent range migration correction processing are completed while filtering operations are performed in the two-dimensional frequency domain.

[0124] Where: The filter function for differential range migration correction in the range-Doppler domain is:

[0125]

[0126] Where: i (τ,f a ) represents the filter function for performing differential range migration correction processing on the i-th receiving array element in the range-Doppler domain, j 2 =-1 represents the imaginary unit, K m It represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at the point where c represents the speed of sound in water in meters per second; r ref represents the reference distance in meters; τ represents the distance acceleration time in seconds;

[0127] The filter function for completing range pulse compression, secondary range pulse compression, and consistent range migration correction is:

[0128]

[0129] Where: H i (f r ,f a ; r ref ) represents the filtering function for performing range pulse compression, secondary range pulse compression, and consistent range migration correction on the i-th receiving array element in the two-dimensional frequency domain, D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at K m represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; f r Represents the instantaneous frequency in distance, in Hertz; r ref represents the reference distance in meters; c represents the speed of sound in water in meters per second.

[0130] ⑻ For the data after range pulse compression, secondary range pulse compression, and consistent range migration correction processing of each receiving array element, azimuth focusing processing, residual phase error compensation operation, and azimuth movement correction processing are performed while filtering in the range-Doppler domain. The compensation function is:

[0131]

[0132] Where: i (τ,f a ) represents the compensation function for azimuth focusing, residual phase error compensation and azimuth motion correction in the range-Doppler domain, D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; K m represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; f a Indicates the azimuth Doppler frequency in Hertz; r ref represents the reference distance in meters; r represents the shortest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane in meters; c represents the speed of sound in water in meters per second.

[0133] ⑼ For the data after azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing of all receiving array elements, coherent fusion processing is performed in the range-Doppler domain, and azimuth inverse Fourier transform is performed to obtain the final high-resolution image.

[0134] The coherent fusion processing method is as follows:

[0135]

[0136] in: It represents the result of coherent fusion of each receiving array data in the range-Doppler domain. represents the result of azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing for the i-th receiving array data in the range-Doppler domain, the subscript i (1≤i≤I) represents the index of the receiving array element, and I represents the total number of receiving array elements;

[0137] The final high-resolution image is obtained as follows:

[0138]

[0139] Where: IFFT represents inverse Fourier transform, and ff(τ,t) represents the final high-resolution image.

[0140] Example

[0141] The present invention first calculates the spatial coordinate positions of the receiving and transmitting array elements under the condition of considering the angle error, and further calculates the two-way slant range history between the space target and the receiving and transmitting array elements, and then obtains the approximated two-way slant range history according to the phase center approximation method. On this basis, the system function of any receiving and transmitting array element subsystem in the range-Doppler domain is calculated. For each receiving array element after the range delay error compensation signal, differential range migration correction processing is performed in the range-Doppler domain, range pulse compression and secondary range pulse compression and consistent range migration correction processing are completed while filtering in the two-dimensional frequency domain, and azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing are realized while filtering in the range-Doppler domain. For the data after the azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing operations of all receiving array elements, coherent fusion processing is performed in the range-Doppler domain, and azimuth inverse Fourier transform is performed to obtain the final high-resolution image.

[0142] like Figure 2 The figure shows the geometry of 2D image reconstruction of multi-subarray synthetic aperture underwater acoustic equipment with angle error. Figure 2 In the 3D image processing system, the movement direction of the underwater acoustic equipment, that is, the x-axis, is called the azimuth, the y-axis is called the ground distance, and the z-axis is called the altitude. The xyz coordinate system forms a three-dimensional rectangular coordinate system. In fact, the underwater acoustic synthetic aperture equipment is a two-dimensional imaging device that can only obtain a two-dimensional image. Its imaging plane is Figure 2 The target P in the image is composed of the x-axis. That is to say, the underwater acoustic synthetic aperture equipment projects the three-dimensional information of the target in the xyz three-dimensional rectangular coordinate system onto the two-dimensional imaging plane. Figure 2 In the figure, r represents the shortest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane. There is a linear array of integrated transmitting array elements and multiple receiving array elements on the x-axis. The black rectangle in the figure represents the transmitting array element, and the remaining rectangles represent the receiving array elements. For each subsystem composed of a receiving array element and a transmitting array element, the spatial coordinate information of the transmitting array element and the receiving array element is calculated, where the three-dimensional spatial coordinates of the transmitting array element are:

[0143]

[0144] Where: v represents the platform movement speed, in meters per second; t represents the slow time in the azimuth direction, in seconds; x t represents the azimuth coordinate of the transmitting array element at time t, in meters; trepresents the coordinate of the transmitting array element at time t in meters; z t It represents the height coordinate of the transmitting array element at time t, in meters.

[0145] The three-dimensional space coordinates of the i-th receiving array element are:

[0146]

[0147] Where: i (1≤i≤I) represents the index of the receiving array element, I represents the total number of receiving array elements; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; u i Represents the distance between the i-th receiving array element and the transmitting array element, in meters. Represents the rotation vector. pitch Indicates the pitch angle error in degrees. Figure 3 In the middle, it means around z a Angular error caused by shaft rotation. θ heading Indicates the yaw angle error in degrees. Figure 3 In the middle, it means around x a Angular error caused by shaft rotation, Figure 3 For Figure 2 The array three-dimensional direct coordinate system is established with the transmitting array element in the linear array as the coordinate origin, where O a Represents the coordinate origin, x a Indicates the direction, y a Distance from ground, z a Indicates the height direction, -z is given in the figure a , indicating the opposite direction of height. i represents the coordinate of the i-th receiving array element at time t along the azimuth upward, y i represents the coordinate of the i-th receiving array element at time t along the ground distance, z i Represents the coordinate of the i-th receiving array element along the height at time t. It represents the distance that the ith receiving element moves along the azimuth direction from the time when the transmitting element transmits the signal to the time when the ith receiving element receives the target echo signal, in meters. c represents the speed of sound in water, in meters per second.

[0148] For each subsystem composed of receiving array elements and transmitting array elements, the two-way slant range history corresponding to any receiving and transmitting array element subsystem is calculated, and the two-way slant range history between the subsystem composed of the i-th receiving array element and the transmitting array element and the point target is obtained as:

[0149]

[0150] in: represents the slant range of the i-th receiving array element in the case of angle error, in meters; t represents the slow time in azimuth, in seconds; r represents the closest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane, in meters; h represents the height of the hydroacoustic transducer from the bottom of the water, in meters; θ represents the oblique angle of the hydroacoustic transducer, in degrees. Here, the three-dimensional coordinates of the point target in azimuth, ground distance, and height are 0, rsinθ, and h, all in meters. c represents the speed of sound in water, in meters / second; v represents the platform speed of the hydroacoustic transducer, in meters / second. u i Represents the distance between the i-th receiving array element and the transmitting array element, in meters. pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

[0151] For each subsystem composed of receiving array elements and transmitting array elements, the two-way slant range history after phase center approximation is calculated, and the calculation formula is:

[0152]

[0153] Where: ΔR i It represents the distance delay error after phase center approximation, and its calculation formula is:

[0154]

[0155] where u i represents the distance between the i-th (1≤i≤I) receiving array element and the transmitting array element; I represents the total number of receiving array elements; θ represents the slant range of the i-th receiving array element in the case of angle error, in meters; r represents the closest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane, in meters; h represents the height of the hydroacoustic transducer from the bottom of the water, in meters. pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

[0156] According to the two-way slant range history between the subsystem composed of the i-th receiving array element and the transmitting array element and the point target, which is the two-way slant range history approximated with the phase center, the system approximation error can be calculated, and the expression is:

[0157]

[0158] Figure 4 System approximation error under different angle errors. Figure 4 (a) The yaw angle is 0.5° and the pitch angle is 1°. Figure 4 (b) The yaw angle is 1° and the pitch angle is 2°. Figure 4 (c) The yaw angle is 3° and the pitch angle is 4°, Figure 4 (d) The yaw angle is 5° and the pitch angle is 6°. Figure 4 It is not difficult to find that under different angle errors, the system approximation error is small and meets the requirement that the error is less than π / 4.

[0159] Figure 5 is the system approximate error of the underwater acoustic transducer under different beam widths when the yaw angle is 2° and the pitch angle is 3°. Figure 5 (a) The beam width is 3°, Figure 5 (b) beam width is 6°, Figure 5 (c) beam width is 9°, Figure 5 (d) The beam width is 12°. It is not difficult to see from the figure that under different beam width errors, the system approximation error is small and meets the requirement that the error is less than π / 4.

[0160] That is to say, taking the angle error into consideration, the two-way slant range history based on the phase center approximation provided by the present invention can better approximate the accurate two-way slant range history, which is also the premise for obtaining accurate image reconstruction results.

[0161] According to the two-way slant range history after phase center approximation, the system function of each transceiver array subsystem in the range-Doppler domain is calculated, and the calculation formula is:

[0162]

[0163] Where: sS i (τ,f a ; r) represents the system function of the i-th receiving array element in the range-Doppler domain, Represents the window function of the transmitted signal, W a (f a -f dc ) represents the joint directivity function of the receiving and transmitting array elements. τ represents the distance to the fast time, in seconds. c represents the speed of sound in water, in meters per second; ΔR i It represents the distance delay error after phase center approximation, in meters. a Indicates the azimuth Doppler frequency in Hertz; f dc represents the Doppler center frequency caused by the squint of the hydroacoustic transducer, in Hertz. r represents the closest distance between the target and the receiving array on the slant range plane, in meters. j 2 =-1 represents the imaginary unit. θ i (τ,f a ; r) represents the phase of the system function in the range-Doppler domain, and its expression is:

[0164]

[0165] Where: f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; u i K represents the distance between the i-th (1≤i≤I) receiving array element and the transmitting array element, in meters; I represents the total number of receiving array elements. m It indicates the modulation frequency when the azimuth and distance are coupled, in Hz / s.

[0166]

[0167] Where: K r Indicates the modulation frequency of the transmitted signal, in Hertz / second; D(f a )The physical meaning is that there is coupling between the azimuth and the distance, which is called the distance bending factor, and its expression is:

[0168]

[0169] Where v represents the movement speed of the hydroacoustic transducer platform in meters per second.

[0170] For each subsystem composed of receiving array elements and transmitting array elements, the Doppler phase error caused by the distance error is compensated in the two-dimensional time domain:

[0171]

[0172] in represents the Doppler phase error, f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; ΔR i It represents the distance delay error after phase center approximation, in meters; c represents the speed of sound in water, in meters per second.

[0173] For each subsystem composed of a receiving array element and a transmitting array element, the data is divided into N non-overlapping data blocks in the range direction, and the width Δr of each data block is determined by the following formula:

[0174]

[0175] Where abs means taking the absolute value operation. express The distance between the center of the nth data block is r = r n,c The value at express At the edge distance of the nth data block r = r n,c The value at -0.5Δr, r n,c Represents the center distance of the nth data block in meters; the expression (r n,c-0.5Δr) represents the edge distance of the nth data block, in meters; Δr represents the width of the data block, in meters. Therefore, the total number of data blocks is:

[0176]

[0177] where r max Indicates the maximum distance that the hydroacoustic equipment can detect, in meters; r min It indicates the minimum detection distance of the underwater acoustic equipment, in meters; ceil means rounding up to an integer.

[0178] For any data block of the subsystem data composed of each receiving array element and transmitting array element, the micro-range migration error caused by the range error is compensated in the range frequency domain. The compensation function of the nth data block is:

[0179]

[0180] Where Ω i (t,f r ,n) represents the compensation function of the micro-distance migration error in the nth data block, f r represents the instantaneous frequency in the distance direction, in Hertz; c represents the speed of sound in water, in meters per second; ΔR i,n Represents the distance delay error ΔR after phase center approximation i The distance between the center of the nth data block is r = r n,c The error value at , in meters, is calculated as follows:

[0181]

[0182] where u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; Represents the value of the i-th receiving array element at the center distance of the n-th data block based on the angle error, in meters; r n,c Represents the value at the center distance of the nth data block, in meters; h represents the height of the underwater acoustic transducer from the bottom of the water, in meters. pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

[0183] All data blocks after micro-range migration compensation of each subsystem composed of receiving array elements and transmitting array elements are arranged in sequence in the range time domain according to the order of the data blocks. The arrangement method is as follows:

[0184]

[0185] in represents the data after micro-distance migration compensation for the first data block of the i-th receiving array element, and so on. represents the data after micro-distance migration compensation for the nth data block of the i-th receiving array element, and the subscript n (1≤n≤N) represents the index of the i-th receiving array element data block. It represents the signal after all N data blocks of the i-th receiving element are arranged in sequence.

[0186] For the signal after all data blocks of each receiving array element are arranged in sequence, differential range migration correction processing is performed in the range-Doppler domain, and its filter function is:

[0187]

[0188] where Γ i (τ,f a ) represents the filter function for performing differential range motion correction processing on the i-th receiving array element in the range-Doppler domain, j 2 =-1 represents the imaginary unit, K m It represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at the point where c represents the speed of sound in water in meters per second; r ref represents the reference distance in meters per second; τ represents the distance-to-speed time in seconds.

[0189] For the data after differential range motion correction processing of each receiving array element, a filtering operation is performed in the two-dimensional frequency domain to simultaneously complete range pulse compression, secondary range pulse compression, and consistent range motion correction processing. The filtering function is:

[0190]

[0191] Among them, H i (f r ,f a ; r ref ) represents the filtering function for performing range pulse compression, secondary range pulse compression, and consistent range migration correction on the i-th receiving array element in the two-dimensional frequency domain, D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at K mrepresents the modulation frequency when the azimuth and distance are coupled, in Hz / s; f r Represents the instantaneous frequency in distance, in Hertz; r ref represents the reference distance in meters; c represents the speed of sound in water in meters per second.

[0192] For the data after range pulse compression, secondary range pulse compression, and consistent range migration correction processing of each receiving array element, azimuth focusing processing, residual phase error compensation operation, and azimuth movement correction processing are performed in the range-Doppler domain. The compensation function is:

[0193]

[0194] where Λ i (τ,f a ) represents the compensation function for azimuth focusing, residual phase error compensation and azimuth motion correction in the range-Doppler domain, D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; K m represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; f a Indicates the azimuth Doppler frequency in Hertz; r ref represents the reference distance in meters; r represents the shortest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane in meters; c represents the speed of sound in water in meters per second.

[0195] For all the receiving array elements, the data after azimuth focusing, residual phase error compensation and azimuth movement correction are processed, and coherent fusion processing is performed in the range-Doppler domain. The processing method is as follows:

[0196]

[0197] in It represents the result of coherent fusion of each receiving array data in the range-Doppler domain. It represents the result of azimuth focusing, residual phase error compensation and azimuth motion correction in the range-Doppler domain for the i-th receiving array data. The subscript i (1≤i≤I) represents the index of the receiving array element, and I represents the total number of receiving array elements.

[0198] For the data after coherent fusion of all receiving array elements, the inverse Fourier transform in azimuth is performed to obtain the final high-resolution image. The processing method is as follows:

[0199]

[0200] Where IFFT represents inverse Fourier transform, and ff(τ,t) represents the final high-resolution image.

[0201] A set of typical underwater acoustic synthetic aperture equipment system parameters are given below, and no weighting is used in the processing of range and azimuth. The center frequency of the linear frequency modulation signal is 75kHz, the pulse width is 20ms, the signal bandwidth is 20kHz, the platform speed is 2.5m / s, the pulse repetition frequency is 0.576s, the number of receiving array elements is 36, the length of the transmitting array element along the azimuth direction is 0.16m, the length of the receiving array element along the azimuth direction is 0.08m, and the height of the underwater acoustic equipment from the bottom of the water is 50m. When using typical synthetic aperture equipment system parameters, different yaw angle errors and pitch angle errors are used, and the simulated system approximate errors are as follows Figure 4 As shown, Figure 4 (a) The yaw angle is 0.5° and the pitch angle is 1°. Figure 4 (b) The yaw angle is 1° and the pitch angle is 2°. Figure 4 (c) The yaw angle is 3° and the pitch angle is 4°, Figure 4 (d) The yaw angle is 5° and the pitch angle is 6°. Figure 4 It is not difficult to find that under different angle errors, the system approximate error is small and meets the requirement that the error is less than π / 4. The system approximate error simulation results show that the method given by the present invention can solve the problem of high-precision image reconstruction under the conditions of yaw angle error and pitch angle error. When the yaw angle is 2° and the pitch angle is 3°, the system approximate error under different beam widths is as follows: Figure 5 As shown, Figure 5 (a) The beam width is 3°, Figure 5 (b) beam width is 6°, Figure 5 (c) beam width is 9°, Figure 5 (d) The beam width is 12°. It is not difficult to see from the figure that under different beam width errors, the system approximation error is small and meets the requirement that the error is less than π / 4. The system approximation error simulation results show that the method given by the present invention can solve the problem of high-precision image reconstruction under different beam widths. For equipment with the same parameter design, the angle error of a certain voyage at sea is extracted as follows Figure 6 As shown, Figure 6 (a) is the pitch angle error, Figure 6 (b) is the yaw angle error. Figure 6The angle error shown is compensated, and the image reconstruction result is as follows Figure 7 As shown in (a), most traditional image reconstruction algorithms do not consider attitude compensation. For example, the method published by Ma Mengbo et al. in the Journal of Huazhong University of Science and Technology (Natural Science Edition) entitled "Multi-receiver Array Synthetic Aperture Sonar CZT Imaging Algorithm" has a poor image reconstruction performance. Figure 7 (a) is equivalent, which will greatly affect the subsequent target detection and recognition; only Figure 6 The pitch angle error shown in (a) is compensated, and the image reconstruction result is as follows Figure 7 (b) shows that, relative Figure 7 (a) It can be found that the result after pitch angle error compensation is more accurate; Figure 6 The yaw angle error shown in (b) is compensated, and the image reconstruction result is as follows Figure 7 (c) shows that, relative Figure 7 (a) It can be found that the image reconstruction result after yaw angle error compensation is significantly improved; Figure 6 (a) Figure 6 The pitch angle error and yaw angle error shown in (b) are compensated, and the image reconstruction result is as follows Figure 7 As shown in (d), compared Figure 7 (a) Figure 7 (b) and Figure 7 The results shown in (c) show that a more refined image reconstruction effect is achieved after compensating for both the pitch angle error and the yaw angle error, which further verifies the effectiveness and reliability of the method of the present invention. It should be noted that: Figure 7 The color bar on the right side of each figure represents the dynamic range of the energy amplitude of each pixel signal in the figure. In addition, based on Matlab software, the method of the present invention is compared with the point-by-point image reconstruction algorithm based on angle error compensation to process 4000 azimuth points and 8000 range points. The image reconstruction time of the method of the present invention is about 26 seconds, and the image reconstruction time of the method published by Ma Mengbo and other authors in the "Journal of Huazhong University of Science and Technology (Natural Science Edition)" entitled "SAS Motion Compensation of Multi-receiving Subarrays Based on Inertial Navigation System" is about 7060 seconds. The image reconstruction efficiency of the method of the present invention is improved by about 272 times, which further reflects the high efficiency of the method of the present invention.

[0202] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all these improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A method for underwater acoustic image reconstruction based on angle error compensation, comprising the following steps: (1) For each subsystem composed of receiving array elements and transmitting array elements, the spatial coordinate information of the transmitting array elements and the receiving array elements is calculated in the presence of angle errors, and the two-way slant range history corresponding to any transmitting and receiving array element subsystem is calculated to obtain the two-way slant range history between the subsystem composed of the i-th receiving array element and the transmitting array element and the point target; (2) According to the phase center approximation method, calculate the two-way slant range history after the phase center approximation; ⑶ According to the two-way slant range history after the phase center is approximated, calculate the system function of each transceiver array element subsystem in the range-Doppler domain; (4) For the Doppler phase error caused by the distance delay error in the phase center approximation processing, the Doppler phase error caused by the distance error is calculated and compensated in the two-dimensional time domain; (5) Divide the data into N non-overlapping data blocks in the range direction, and compensate for the micro-range migration error caused by the range error in the frequency domain of any data block in the range direction; (6) For all the data blocks after micro-distance migration compensation, arrange them in the order of the data blocks in the distance time domain to obtain the signal after distance delay error compensation; ⑺For each receiving array element after range delay error compensation, differential range migration correction processing is performed in the range-Doppler domain in turn, and range pulse compression, secondary range pulse compression, and consistent range migration correction processing are completed while filtering operations are performed in the two-dimensional frequency domain; ⑻For each receiving array element, after the data has been processed by range pulse compression, secondary range pulse compression, and consistent range migration correction, azimuth focusing, residual phase error compensation, and azimuth movement correction are performed while filtering in the range-Doppler domain; ⑼ For the data after azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing of all receiving array elements, coherent fusion processing is performed in the range-Doppler domain, and azimuth inverse Fourier transform is performed to obtain the final high-resolution image.

2. The method for underwater acoustic image reconstruction based on angle error compensation according to claim 1, characterized in that: The three-dimensional space coordinates of the transmitting array element in step (1) are: Where: v represents the platform movement speed, in meters per second; t represents the slow time in the azimuth direction, in seconds; x t represents the azimuth coordinate of the transmitting array element at time t, in meters; t represents the coordinate of the transmitting array element at time t in meters; z t It represents the coordinate of the transmitting array element at the time t in meters; The three-dimensional space coordinates of the i-th receiving array element are: Where: i (1≤i≤I) represents the index of the receiving array element; I represents the total number of receiving array elements; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; represents the rotation vector, θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw angle error in degrees; x i represents the coordinate of the i-th receiving array element along the azimuth at time t, in meters; i represents the coordinate of the i-th receiving array element along the ground distance at time t, in meters; z i represents the coordinate of the i-th receiving array element along the height at time t, in meters; It represents the distance that the ith receiving element moves along the azimuth direction from the time when the transmitting element transmits the signal to the time when the ith receiving element receives the target echo signal, in meters; c represents the speed of sound in water, in meters per second; The two-way slant range from the subsystem composed of the i-th receiving array element and the transmitting array element to the point target is: in: represents the slant range of the i-th receiving array element in the case of angle error, in meters; t represents the slow time in azimuth, in seconds; r represents the closest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane, in meters; h represents the height of the hydroacoustic transducer from the bottom of the water, in meters; θ represents the slant angle of the hydroacoustic transducer, in degrees; the three-dimensional coordinates of the point target in azimuth, ground distance, and height are 0, rsinθ, h, all in meters; c represents the speed of sound in water, in meters / second; v represents the platform speed of the hydroacoustic transducer, in meters / second; u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

3. The method for underwater acoustic image reconstruction based on angle error compensation according to claim 1, characterized in that: The calculation formula of the two-way slant range history after the phase center is approximated in step (2) is: Where: u i represents the distance between the i-th (1≤i≤I) receiving array element and the transmitting array element, in meters; I represents the total number of receiving array elements; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; ΔR i Represents the distance delay error after phase center approximation, in meters, ΔR i The specific expression is: in: represents the slant range of the i-th receiving array element in the case of angle error, in meters; r represents the closest distance between the target and the motion trajectory of the underwater acoustic transducer on the slant range plane, in meters; h represents the height of the underwater acoustic transducer from the bottom of the water, in meters; θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

4. The method for underwater acoustic image reconstruction based on angle error compensation according to claim 1, characterized in that: The calculation formula of the system function of each transceiver array element subsystem in the range-Doppler domain in step (3) is: Where: sS i (τ,f a ; r) represents the system function of the i-th receiving array element in the range-Doppler domain, Represents the window function of the transmitted signal, W a (f a -f dc ) represents the joint directivity function of the receiving and transmitting array elements; j 2 =-1 represents the imaginary unit; τ represents the time from distance to speed, in seconds; c represents the speed of sound in water, in meters per second; ΔR i It represents the distance delay error after phase center approximation, in meters; f a Indicates the azimuth Doppler frequency in Hertz; f dc represents the Doppler center frequency caused by the squint of the hydroacoustic transducer, in Hertz; r represents the closest distance between the target and the receiving array on the slant range plane, in meters; θ i (τ,f a ; r) represents the phase of the system function, and the specific expression is: Where: u i represents the distance between the i-th (1≤i≤I) receiving array element and the transmitting array element, in meters; I represents the total number of receiving array elements; f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; v represents the movement speed of the underwater acoustic transducer platform, in meters per second; K m It represents the range modulation frequency considering the coupling of azimuth and distance, in Hertz / second. The specific expression is: Where: K r Indicates the frequency of the transmitted linear frequency modulation signal, in Hertz / second; D(f a )The physical meaning is that there is coupling between the azimuth and the distance, which is called the distance bending factor. The specific expression is:

5. The method for underwater acoustic image reconstruction based on angle error compensation according to claim 1, characterized in that: In step (4), the Doppler phase error caused by compensating the distance error in the two-dimensional time domain is calculated as follows: in: represents the Doppler phase error, f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; ΔR i It represents the distance delay error after phase center approximation, in meters; c represents the speed of sound in water, in meters per second.

6. The method for underwater acoustic image reconstruction based on angle error compensation according to claim 1, characterized in that: The width Δr of each data block in step (5) is determined by the following formula: Among them: abs means taking the absolute value operation, express The distance between the center of the nth data block is r = r n,c The value at express At the edge distance of the nth data block r = r n,c The value at -0.5Δr; r n,c Represents the center distance of the nth data block in meters; the expression (r n,c -0.5Δr) represents the edge distance of the nth data block, in meters; Δr represents the width of the data block, in meters; The total number of data blocks N is: Where: r max Indicates the maximum distance that the underwater acoustic transducer can detect, in meters; r min Indicates the minimum distance detected by the underwater acoustic transducer, in meters; ceil means rounding up to an integer; The compensation function of the nth data block is: Where: Ω i (t,f r ,n) represents the compensation function of the micro-distance migration error in the nth data block, f r represents the instantaneous frequency in the distance direction, in Hertz; c represents the speed of sound in water, in meters per second; ΔR i,n Represents the distance delay error ΔR after phase center approximation i The distance between the center of the nth data block is r = r n,c The error value at , in meters, is expressed as: Where: u i represents the distance between the i-th receiving array element and the transmitting array element, in meters; Represents the value of the i-th receiving array element at the center distance of the n-th data block based on the angle error, in meters; r n,c represents the value at the center distance of the nth data block, in meters; h represents the height of the underwater acoustic transducer from the bottom of the water, in meters; θ pitch Indicates the pitch angle error, in degrees; θ heading Indicates the yaw error in degrees.

7. The method for underwater acoustic image reconstruction based on angle error compensation according to claim 1, characterized in that: The method of arranging the data blocks in the time domain in the distance direction in step (6) is as follows: in: represents the data after micro-distance migration compensation for the first data block of the i-th receiving array element, and so on. represents the data after micro-distance migration compensation for the nth data block of the i-th receiving array element, and the subscript n (1≤n≤N) represents the index of the i-th receiving array element data block. It represents the signal after all N data blocks of the i-th receiving array element are arranged in sequence.

8. The method for underwater acoustic image reconstruction based on angle error compensation according to claim 1, characterized in that: The filtering function of step (7) when performing differential range migration correction processing in the range-Doppler domain is: Where: i (τ,f a ) represents the filter function for performing differential range motion correction processing on the i-th receiving array element in the range-Doppler domain, j 2 =-1 represents the imaginary unit, K m It represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at the point where c represents the speed of sound in water in meters per second; r ref represents the reference distance in meters; τ represents the distance acceleration time in seconds; The filter function for completing range pulse compression, secondary range pulse compression, and consistent range migration correction is: Where: H i (f r ,f a ; r ref ) represents the filtering function for performing range pulse compression, secondary range pulse compression, and consistent range migration correction on the i-th receiving array element in the two-dimensional frequency domain, D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at K m represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; f r Represents the instantaneous frequency in distance, in Hertz; r ref represents the reference distance in meters; c represents the speed of sound in water in meters per second.

9. The method for underwater acoustic image reconstruction based on angle error compensation according to claim 1, characterized in that: The compensation function for performing azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing in step (8) is: Where: i (τ,f a ) represents the compensation function for azimuth focusing, residual phase error compensation and azimuth motion correction in the range-Doppler domain, D(f a ) represents the distance bending factor, D(f dc ) represents the distance bending factor D(f a ) at the Doppler center f a =f dc The value at f0 represents the center frequency of the transmitted linear frequency modulation signal, in Hertz; K m represents the modulation frequency when the azimuth and distance are coupled, in Hz / s; f a Indicates the azimuth Doppler frequency in Hertz; r ref represents the reference distance in meters; r represents the shortest distance between the target and the motion trajectory of the hydroacoustic transducer on the slant range plane in meters; c represents the speed of sound in water in meters per second.

10. The method for underwater acoustic image reconstruction based on angle error compensation according to claim 1, characterized in that: The coherent fusion processing method in step (9) is: in: It represents the result of coherent fusion of each receiving array data in the range-Doppler domain. represents the result of azimuth focusing processing, residual phase error compensation operation and azimuth movement correction processing for the i-th receiving array data in the range-Doppler domain, the subscript i (1≤i≤I) represents the index of the receiving array element, and I represents the total number of receiving array elements; The final high-resolution image is obtained as follows: Where: IFFT represents inverse Fourier transform, and ff(τ,t) represents the final high-resolution image.

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