Quality improvement method for high-resolution image

Abstract

The invention relates to a quality improvement method for a high-resolution image. The method comprises the following steps: obtaining an equal-target two-way slope distance; calculating a distance error; calculating a two-dimensional frequency spectrum; calculating a truncation phase error; obtaining data of each receiving array element after micro-Doppler phase error compensation; obtaining all receiving array element data after micro-range migration error correction; obtaining data of the class receiving and transmitting combined synthetic aperture sonar; obtaining N data blocks after truncation phase error compensation; obtaining multi-receiving array element synthetic aperture sonar data; filtering to obtain filtered data; obtaining the data after the nonlinear frequency modulation processing; calculating an accurate phase; obtaining a system frequency modulation rate after second-order Taylor series approximation; calculating a coefficient of the expression of the delay time and the distance direction frequency; solving an undetermined coefficient; performing high-order phase error compensation; and a high-resolution synthetic aperture sonar image is obtained. According to the method, the reconstruction performance can be effectively improved under the conditions of larger transmission signal bandwidth and larger accumulated beam angle.

Description

A method for improving the quality of high-resolution images Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology, and in particular to a method for improving the quality of high-resolution images. Background Technology

[0002] Synthetic aperture sonar is a high-resolution imaging sonar. Its range resolution is related to the bandwidth of the transmitted signal, while its azimuth resolution is related to the cumulative beam angle of the array elements or the synthetic aperture time. In other words, to achieve high two-dimensional resolution, a wide-bandwidth signal must be transmitted, along with a large cumulative beam angle; this presents a significant challenge to image reconstruction algorithms. Linear frequency modulation (LFM) scaling image reconstruction algorithms are highly efficient and have good phase preservation, making them popular among users. However, traditional LFM scaling algorithms approximate the phase of the two-dimensional spectrum with respect to the range frequency using a second-order Taylor series, neglecting terms of third order and above, which leads to significant errors. Similarly, nonlinear frequency modulation (NFM) scaling image reconstruction algorithms approximate the phase of the two-dimensional spectrum with respect to the range frequency using a third-order Taylor series, neglecting terms of fourth order and above, still resulting in significant errors. This severely degrades the image reconstruction performance of the system under wideband or ultra-wideband transmitted signal conditions. On the other hand, current synthetic aperture sonars all employ multi-element receiver arrays. The spatial separation of the transmitting and receiving elements renders traditional image reconstruction algorithms based on combined transmitting and receiving synthetic aperture sonars unsuitable. The phase center approximation method, after compensating for the approximation error of the multi-element receiver array data, transforms it into data similar to that of combined transmitting and receiving synthetic aperture sonars, making it a highly regarded and widely used method in most current systems. However, the traditional phase center approximation method does not consider the azimuth spatial variability of the approximation error during the approximation error compensation process. This has a small or even negligible impact when the cumulative beam angle is small, but it introduces significant errors when the cumulative beam angle is large, thus affecting image reconstruction performance. Currently, some researchers attempt to address this issue by using high-order approximations of the precise signal propagation time. However, this precise propagation time is calculated only for a single point target in space and does not possess azimuth spatial variability. In other words, the result of high-order approximation cannot reduce the range approximation error when the cumulative beam angle is large. Based on the one-to-one mapping relationship between azimuth Doppler frequency and side view, some methods have emerged to solve the azimuth spatial variation of approximation error. However, they lack rigorous theoretical proof, which means that these methods can reduce the error at long distances, but cannot effectively reduce the distance approximation error at close distances.

[0003] To address these issues, this invention, based on the triangle cosine theorem, precisely calculates the distance approximation error caused by the phase center approximation method from a rigorous theoretical perspective. Compared to traditional methods, it can simultaneously reduce errors at both near and far distances, which is beneficial for improving the underwater acoustic image reconstruction performance under conditions of large cumulative beam angles. On the other hand, this invention abandons the traditional algorithm's approach of only considering the first, second, and third order Taylor expansion terms of the phase of the two-dimensional spectrum with respect to the range frequency, and instead considers the fourth order Taylor expansion term of the phase of the two-dimensional spectrum with respect to the range frequency in the algorithm, which is beneficial for improving the underwater acoustic image reconstruction performance under conditions of transmitting broadband signals with large bandwidths. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for improving the quality of high-resolution images under conditions of large transmit signal bandwidth and large cumulative beam angle.

[0005] To solve the above problems, the present invention provides a method for improving the quality of high-resolution images, comprising the following steps: (1) For a subsystem composed of a single receiving element and a transmitting element, the two-way slant range between the equivalent phase center and the target is calculated according to the phase center approximation method, and expressed as a function of the side view angle and the target distance, to obtain the target two-way slant range corresponding to the equivalent phase center; (2) The precise two-way slant range history of the subsystem composed of a single receiving element and a transmitting element is calculated according to the triangle cosine theorem, and on this basis, the distance error generated by replacing the precise two-way slant range history with the target two-way slant range corresponding to the equivalent phase center in the previous step is calculated; (3) Based on the target two-way slant range corresponding to the equivalent phase center and the distance error generated by replacing the precise two-way slant range history, an approximate two-way slant range history containing only a square root expression is calculated. And calculate the echo signal of the point target, and further calculate the two-dimensional spectrum of the echo signal of the point target using the phase dwell principle; (4) For the two-dimensional spectrum of the echo signal of the point target, perform a fourth Taylor series approximation on the phase in the radical expression of the two-dimensional spectrum with respect to the range frequency to obtain a polynomial phase expression with respect to the range frequency, and calculate the truncated phase error generated by the fourth Taylor series approximation; (5) Based on the polynomial phase expression with respect to the range frequency in step (4), extract the micro-Doppler phase error; For the echo of each receiving array element, perform a Fourier transform in the azimuth direction to obtain the data in the range-Doppler domain, and compensate for the micro-Doppler phase error in the range-Doppler domain to obtain the data of each receiving array element after micro-Doppler phase error compensation; (6) Based on the polynomial phase expression of the range frequency in step (4), the micro range migration error is extracted; for the data of each receiving array element after micro-Doppler phase error compensation, the delay time error corresponding to the micro range migration error is corrected by interpolation in the range-Doppler domain, thus obtaining all receiving array data after micro range migration error correction; (7) for all receiving array data after micro range migration error correction, inverse Fourier transform is performed in the azimuth direction to obtain two-dimensional time domain data, and the data is arranged in the two-dimensional time domain according to the spatial sampling order to obtain a transceiver composite. (8) For the synthetic aperture sonar data obtained in the previous step, divide it into N data blocks in the range direction; for the N data blocks in the range direction, perform two-dimensional frequency domain transformation respectively; based on the truncation phase error in step (4), calculate the truncation phase error at the reference range in each data block; for any data block in the N data blocks, compensate the truncation phase error of the entire data block by the truncation phase error at the reference range in each data block, and transform the data of the compensated data block to the range-Doppler domain to obtain N data blocks after truncation phase error compensation;(9) For the N data blocks after phase error compensation, arrange them sequentially in the range-Doppler domain according to the target's range in ascending order, so as to recombine the scattered N data blocks into complete multi-receiver array synthetic aperture sonar data; (10) For the recombinated complete multi-receiver array synthetic aperture sonar data, perform Fourier transform in the range direction and perform third and fourth phase filtering in the two-dimensional frequency domain to obtain the data after third and fourth phase filtering; (11) For the data after third and fourth phase filtering, perform third and fourth nonlinear frequency modulation processing in the range-Doppler domain to obtain the data after third and fourth nonlinear frequency modulation processing; (12) (13) Based on the phase dwell principle, the data after the third and fourth nonlinear frequency modulation processing in the previous step is transformed to the two-dimensional frequency domain to obtain two-dimensional frequency domain data, and the accurate phase of the two-dimensional frequency domain data is calculated; (14) For the accurate phase of the two-dimensional frequency domain data obtained in the previous step, the system modulation frequency that depends on the two-dimensional frequency and the target distance and integrates the second distance compression and the transmission signal modulation frequency is extracted, and the second-order Taylor series approximation is performed with respect to the delay time to obtain the system modulation frequency after the second-order Taylor series approximation; (15) The system modulation frequency after the second-order Taylor series approximation is substituted into the phase of the two-dimensional spectrum after being transformed to the two-dimensional frequency domain in step (12), and the power of the phase with respect to the product of the delay time and the distance frequency is calculated. The formula is organized and the coefficients of the expressions for delay time and range frequency are calculated precisely: the expression for delay time squared and range frequency squared, the expression for delay time squared and range frequency squared, the expression for delay time squared and range frequency squared, and the expression for delay time squared and range frequency cubicd; (15) Let the coefficients of the expression for delay time and range frequency squared be the reciprocal of the curvature factor to eliminate the spatial variation of range migration; let the coefficients of the expression for delay time squared and range frequency squared, the expression for delay time squared and range frequency squared, and the expression for delay time squared and range frequency cubicd, the expression for delay time squared, the expression for range frequency squared, the expression for delay time squared, the expression for range frequency squared, the expression for delay time squared, the expression for range frequency cubic ... The coefficients of the expressions for the first power of the time delay and the cubic power of the range frequency are set to zero to eliminate the dependence on the range; these five equations are solved simultaneously to solve for the undetermined coefficients in the cubic and quadratic phase filtering and cubic and quadratic nonlinear frequency modulation processes; (16) for the two-dimensional frequency domain data obtained in step (12), range pulse compression, range migration consistency correction, and high-order phase error compensation are performed in the two-dimensional frequency domain; (17) for the data processed in the previous step, inverse Fourier transform is performed in the range direction, and azimuth pulse compression, azimuth migration correction, and residual phase error compensation are performed in the range-Doppler frequency domain. The data is then transformed to the two-dimensional time domain to obtain the reconstructed high-resolution synthetic aperture sonar image.

[0006] In step (1), for a subsystem consisting of a single receiving element and a transmitting element, the two-way slant range between the equivalent phase center and the target is calculated using the phase center approximation method, and expressed as a function of the side view angle and the target distance, thus obtaining the two-way slant range of the target corresponding to the equivalent phase center; where the m-th equivalent phase center is a virtual transceiver array element located at the center position between the transmitting element and the m-th receiving element, and the two-way slant range between this phase center and the target is... Represented as: Here, r is the target range, v is the sonar tow speed, μ is the azimuth time dilation, and C is the speed of sound in water; L m Let m be the real aperture between the m-th receiving element and the transmitting element. The angle between the equivalent phase center and the target's line of sight on the horizontal axis, and the distance to the target, is called the side angle; the two-way slant distance between the phase center and the target. It can also be expressed as a function of the side view and the target distance, with the following expression: The subscript m is the index of the receiving array element.

[0007] In step (2), the precise two-way slant range history of the subsystem composed of a single receiving element and a transmitting element is calculated according to the triangle cosine theorem. Based on this, the distance error caused by replacing the precise two-way slant range history with the target two-way slant range corresponding to the equivalent phase center in the previous step is calculated. Among them, in the triangle formed by the transmitting element, the target, and the equivalent phase center, the precise transmission slant range history R between the transmitting element and the target is calculated using the cosine theorem. E (μ;r), its expression is: Here, r is the target distance, v is the sonar tow speed, and C is the speed of sound in water; L m This represents the real aperture between the m-th receiving element and the transmitting element; The angle between the equivalent phase center and the target's line of sight and the target's distance on the x-axis is called the side angle; μ is the azimuth time delay; in the triangle formed by the m-th receiver element, the target, and the equivalent phase center, the precise receiving slant range history R between the m-th receiver element and the target is calculated using the law of cosines. R,m (μ;r), the expression is: Here, the subscript m represents the index of the receiving element; based on the precise slant range history between the transmitting element and the target, and the precise slant range history between the m-th receiving element and the target, the range error caused by replacing the precise two-way slant range history with the target two-way slant range corresponding to the equivalent phase center is calculated, and the expression is: .

[0008] In step (3), based on the target two-way slant range corresponding to the equivalent phase center and the distance error generated by replacing the exact two-way slant range history, an approximate two-way slant range history containing only a square root expression is calculated, and the echo signal of the point target is calculated. Furthermore, the two-dimensional spectrum of the point target echo signal is calculated using the phase dwell principle; wherein, the target slant range obtained by combining the equivalent phase center... and its corresponding distance error ΔR m This yields an approximate two-way slant distance history R containing only a single square root expression. m for: Here, r is the target distance, v is the sonar tow speed, and C is the speed of sound in water; L m Let be the real aperture between the m-th receiving element and the transmitting element; The angle between the equivalent phase center and the target's line of sight and the target distance on the x-axis is called the side view angle; μ is the azimuth slow time; the subscript m indicates the index of the receiving array element; in the total slant range history R m Based on this, the echo signal s of the point target with two-dimensional coordinates (r,0) in the range and azimuth directions is... m The expression for (t,μ) is: Here, t represents the range-fast time, μ represents the azimuth-slow time, f0 represents the center frequency of the transmitted linear frequency modulated signal g(t), and j 2 = -1 represents the imaginary unit; define f t f μ Let represent the range frequency and azimuth Doppler frequency corresponding to the range-fast time t and azimuth-slow time μ, respectively; calculate the point target echo signal s based on the phase dwell principle. m The two-dimensional spectrum S of (t,μ) m (f t ,f μ ), whose expression S m (f t ,f μ )for: Here G(f) t Let Ψ be the spectrum of the linear frequency modulated signal g(t), and let Ψ be the phase. m (f t ,f μ The expression for ;r) is: Side view here The expression in the azimuth-directed Doppler domain is: .

[0009] In step (4), for the two-dimensional spectrum of the echo signal of the point target, the phase in the radical expression of the two-dimensional spectrum is approximated by a fourth Taylor series with respect to the range frequency to obtain a polynomial phase expression with respect to the range frequency. At the same time, the truncation phase error caused by the fourth Taylor series approximation is calculated. After the fourth Taylor series approximation of the phase in the radical expression, the phase of the two-dimensional spectrum is: Here, the zeroth, first, second, third, and fourth order coefficients of the fourth-order Taylor series approximation are respectively... The second-order coefficient β2 incorporates the modulation frequency k of the transmitted linear frequency modulated signal; r is the target distance, v is the sonar tow speed, and C is the underwater acoustic speed; L m The real aperture between the m-th receiving element and the transmitting element, and the side viewing angle. The expression in the azimuth-directed Doppler domain is: f0 is the center frequency of the linear frequency modulated signal, f t f μ Here, represents the range frequency (fast range time t) and azimuth frequency (slow azimuth time μ), respectively; the subscript m is the receiver element index; Δ is the truncated phase error generated by the fourth Taylor series approximation, and its expression is: .

[0010] In step (5), based on the polynomial phase expression for the range frequency from step (4), the micro-Doppler phase error is extracted; for the echo of each receiving element, a Fourier transform is performed in the azimuth direction to obtain the range-Doppler domain data, and the micro-Doppler phase error is compensated in the range-Doppler domain to obtain the data of each receiving element after micro-Doppler phase error compensation; wherein, the micro-Doppler phase error extracted from step (4) is ; Compensation function Λ for compensating micro-Doppler phase errors in the range-Doppler domain m for: Here ΔR m The distance error corresponding to the target slant range obtained from the equivalent phase center; C represents the underwater acoustic speed; f0 represents the center frequency of the transmitted linear frequency modulated signal; the subscript m represents the index of the receiving array element.

[0011] In step (6), based on the polynomial phase expression of the range-direction frequency from step (4), the micro-range migration error is extracted; for the data of each receiving array element after micro-Doppler phase error compensation, the delay time error corresponding to the micro-range migration error is corrected by interpolation in the range-Doppler domain, thus obtaining all receiving array data after micro-range migration error correction; wherein, the micro-range migration error extracted from step (4) is ΔR m The corresponding delay time error Δtm for: Here ΔR m The distance error corresponding to the target slant range obtained at the equivalent phase center, which has been derived in step (2); C represents the underwater acoustic speed; the subscript m represents the index of the receiving array element.

[0012] In step (7), for all received array data after micro-range migration error correction, an inverse Fourier transform is performed in the azimuth direction to obtain two-dimensional time-domain data, which is then arranged in the two-dimensional time domain according to the spatial sampling order to obtain data similar to a transceiver combined synthetic aperture sonar; assuming there are a total of M receiving array elements, the echoes of the 1st, 2nd, 3rd...Mth receiving array elements corresponding to the first pulse are represented as [ss 1,1 ,ss 1,2 ,…,ss 1,M The echoes corresponding to the 1st, 2nd, 3rd...Mth receiving elements of the second pulse are represented as [ss]. 2,1 ,ss 2,2 ,…,ss 2,M The echoes corresponding to the 1st, 2nd, 3rd...Mth receiving array elements of the Pth pulse are represented as [ss]. P,1 ,ss P,2 ,…,ss P,M Therefore, the expression for the sequential arrangement of the pulse sampling data is as follows: .

[0013] In step (8), the synthetic aperture sonar data obtained in the previous step is divided into N data blocks in the range direction; a two-dimensional frequency domain transformation is performed on each of the N data blocks in the range direction; based on the truncation phase error in step (4), the truncation phase error at the reference range in each data block is calculated; for any data block among the N data blocks, the truncation phase error of the entire data block is compensated by the truncation phase error at the reference range in each data block, and the data of the compensated data block is transformed to the range-Doppler domain to obtain N data blocks after truncation phase error compensation; if the number of sampling points along the range direction is W, then the number of sampling points Nsub in each data block is: We choose Nsub, which is divisible by W; the expression for the truncation phase error at the reference distance of the nth data block is Δn, and the corresponding phase compensation function Hsub,n is: H sub,n = exp{jΔ n}Here Δ n =Δ| r=rn This indicates that the distance of the spatial variation in the truncated phase error is measured using the reference distance r of the nth data block. n An approximation is made to eliminate the spatial variability of the distance error.

[0014] In step (9), the N data blocks after truncation phase error compensation are sequentially arranged in the range-Doppler domain according to the target's range in ascending order, so as to recombine the data of the dispersed N data blocks into complete multi-receiver array synthetic aperture sonar data; assuming the N data blocks are represented as A1, A2, A3, …, A N Therefore, the expression for data block reorganization is: .

[0015] In step (10), for the recombined multi-receiver array element synthetic aperture sonar data, a Fourier transform is performed in the range direction, and third and fourth phase filtering is performed in the two-dimensional frequency domain to obtain the third and fourth phase filtered data; wherein, the filtering function H1(f t ,f μ ;r0) is: Here Y(f) μ ) and Z(f μ ) represents the third and fourth order filter coefficients, r0 represents the reference distance corresponding to the entire mapping strip; f t ,f μ These represent the range frequency and azimuth Doppler frequency corresponding to the range fast time t and azimuth slow time μ, respectively.

[0016] In step (11), the data after third and fourth phase filtering are subjected to third and fourth nonlinear frequency modulation processing in the range-Doppler domain to obtain the data after third and fourth nonlinear frequency modulation processing; wherein, the function H2(t,f) of the nonlinear frequency modulation processing is... μ ;r) is: Here q2(f) μ ), q3(f μ ), q4(f μ () represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes; Represents the center distance r s The distance migration of the target; t is the distance-major time; f μ The value represents the Doppler frequency of the corresponding azimuth direction at slow time μ; r is the target distance; v is the sonar towing speed; C is the underwater acoustic speed; and f0 is the center frequency of the linear frequency modulated signal.

[0017] In step (12), based on the phase dwell principle, the data after the third and fourth nonlinear frequency modulation processing in the previous step is transformed into two-dimensional frequency domain data to obtain two-dimensional frequency domain data, and the precise phase of the two-dimensional frequency domain data is calculated; wherein, the two-dimensional spectral phase The expression is: here This refers to the new frequency modulation (FM) after further incorporating azimuth and range secondary coupling factors based on the transmitted signal FM; this is called the system FM. q2, q3, and q4 are respectively q2(f μ ), q3(f μ ), q4(f μ (abbreviation) The distance r represents the relative center distance of the surveying zone. s The delay time between the target's distance and its migration. This represents the distance migration of a target at any given distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ f represents the Doppler frequency for the slow time μ in the corresponding direction. t This represents the range frequency corresponding to the range time t. This represents the coefficient of the new cubic term after third-order filtering, which incorporates the azimuth and range cubic coupling factors. This represents the coefficient of the new fourth-order term after fourth-order filtering, which incorporates the fourth-order coupling factors of the azimuth and range directions.

[0018] In step (13), for the precise phase of the two-dimensional frequency domain data obtained in the previous step, the system modulation frequency, which integrates the second-order range compression and the transmit signal modulation frequency and depends on the two-dimensional frequency and the target range, is extracted, and a second-order Taylor series approximation is performed with respect to the delay time to obtain the system modulation frequency after the second-order Taylor series approximation; wherein the system modulation frequency The expression for the delay time after approximation using a second-order Taylor series is as follows: here The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s Distance migration of the target; k0, k s k2 represents the zeroth, first, and second order coefficients after Taylor series approximation; C represents the underwater acoustic speed; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the tow speed of the sonar; f μ f represents the slow-time μ-Doppler frequency in the corresponding direction; t This represents the range frequency corresponding to the range time t.

[0019] In step (14), the system modulation frequency approximated by the second-order Taylor series is substituted into the phase of the two-dimensional spectrum after transformation to the two-dimensional frequency domain in step (12). The phase is rearranged with respect to the power of the product of delay time and range frequency, and the coefficients of the expressions for the first power of both delay time and range frequency, the second power of delay time and the first power of range frequency, the first power of delay time and the second power of range frequency, the second power of delay time and the second power of range frequency, the second power of both delay time and the second power of range frequency, and the first power of delay time and the third power of range frequency are calculated precisely. The calculated results are expressed as follows: Here O(Y,Z,q2,q3,q4,f) μ ,Δt 2 ,Δt 3 ,Δt 4 ) indicates the range-direction frequency f t Irrelevant terms, B(Y,Z,q2,q3,q4,f) μ ) is Δtf t The coefficient term, D(Y,Z,q2,q3,q4,f) μ ) is Δt 2 f t The coefficient term, E(Y,Z,q2,q3,q4,f) μ ) is Δtf t 2 The coefficient term, F(Y,Z,q2,q3,q4,f μ ) is Δt 2 f t 2 The coefficient term, J(Y,Z,q2,q3,q4,f) μ ) is Δtf t 3 The coefficient term, Q(Y,Z,q2,q3,q4,f) μ ,f t ,f t 2 ,f t 3 ,f t 4 ) represents terms that are independent of Δt; The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ f represents the Doppler frequency for the corresponding slow time μ in the direction; tThis represents the range-direction frequency corresponding to a distance and a time interval t.

[0020] In step (15), the coefficients of the expressions for both delay time and range frequency as first powers are set to the reciprocal of the curvature factor to eliminate the spatial variation of range migration; the coefficients of the expressions for delay time squared and range frequency first powers, delay time first power and range frequency squared, delay time squared and range frequency cubic powers are set to zero to eliminate the dependence on distance; these five equations are solved simultaneously to obtain the undetermined coefficients in the cubic and quaternary phase filtering and cubic and quaternary nonlinear frequency modulation processes; the expressions of the five equations are as follows: B(Y,Z,q2,q3,q4,f μ ) is Δtf in step (14) t The coefficient term, D(Y,Z,q2,q3,q4,f) μ ) is Δt in step (14) 2 f t The coefficient term, E(Y,Z,q2,q3,q4,f) μ ) is Δtf in step (14) t 2 The coefficient term, F(Y,Z,q2,q3,q4,f μ ) is Δt in step (14) 2 f t 2 The coefficient term, J(Y,Z,q2,q3,q4,f) μ ) is Δtf in step (14) t 3 The coefficient term; The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ f represents the Doppler frequency for the corresponding slow time μ in the direction; t This represents the range-direction frequency corresponding to a distance of time t; here... The bending factor is represented by the equation; the result of solving the above five equations is expressed as follows: Here q2(f) μ ), q3(fμ ), q4(f μ ) represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes mentioned above, while q2, q3, and q4 are respectively the coefficients of q2(f μ ), q3(f μ ), q4(f μ abbreviation of ); k0, k s and k2 represent the zeroth, first, and second order coefficients of the system frequency modulation after a second-order Taylor series approximation with respect to the delay time; here Y(f μ ) and Z(f μ ) represents the aforementioned third-order and fourth-order filter coefficients, while Y and Z are Y(f μ ) and Z(f μ (abbreviation of ).

[0021] In step (16), for the two-dimensional frequency domain data obtained in step (12), range pulse compression, range migration consistency correction, and higher-order phase error compensation are performed in the two-dimensional frequency domain; wherein the compensation function is: here The distance r represents the center distance of the surveying zone. s Migration at the distance from the target. This represents the azimuth Doppler center frequency f. dc And the center distance of the surveying zone is r s The target distance migration at that time; the Doppler center frequency of the front-view system is zero, i.e., f dc = 0; C represents the speed of sound in water; f t Indicates the corresponding distance and time. The range-direction frequency; f μ q2(f) represents the Doppler frequency of the corresponding slow time μ in the direction; v represents the sonar towing speed; f0 represents the center frequency of the emitted linear frequency modulated signal; here q2(f) μ ), q3(f μ ), q4(f μ ) represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes mentioned above, while q2, q3, and q4 are respectively the coefficients of q2(f μ ), q3(f μ ), q4(f μ The abbreviation for Y(f); here Y(f μ ) and Z(f μ ) represents the aforementioned third-order and fourth-order filter coefficients, while Y and Z are Y(f μ ) and Z(f μ (abbreviation of ); k0 represents the zero-order coefficient of the system frequency modulation after approximating the delay time with a second-order Taylor series.

[0022] In step (17), the data processed in the previous step is subjected to an inverse range Fourier transform. In the range-Doppler frequency domain, azimuth pulse compression, azimuth travel correction, and residual phase error compensation are performed. The data is then transformed to the two-dimensional time domain to obtain the reconstructed high-resolution synthetic aperture sonar image. The expression for the compensation function is: here k0 represents the residual phase; k0 represents the system modulation frequency. The zeroth-order coefficients after approximating the delay time using a second-order Taylor series; C represents the underwater acoustic velocity; f μ The doppler frequency corresponding to the slow time μ in the corresponding direction; β0 represents the zero-order coefficient of the phase in the aforementioned two-dimensional spectral radical formula for the point target echo, after a fourth Taylor series approximation of the range-direction frequency; side view. The expression in the azimuth-directed Doppler domain is: ;q2(f μ ), q3(f μ ), q4(f μ ) represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes mentioned above, while q2, q3, and q4 are respectively the coefficients of q2(f μ ), q3(f μ ), q4(f μ (abbreviation) The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ f represents the Doppler frequency for the corresponding slow time μ in the direction; t This represents the range-direction frequency corresponding to a distance and a time interval t.

[0023] Compared with existing technologies, this invention has the following advantages: It can process multi-element synthetic aperture sonar data under traditional narrow-band transmit signal bandwidth and small cumulative beam angle conditions, achieving reconstruction performance slightly better than traditional image reconstruction methods. Furthermore, under conditions of larger transmit signal bandwidth and larger cumulative beam angle, it can obtain reconstruction results with even better performance than traditional image reconstruction methods. In other words, compared with traditional methods, this invention has a wider range of applications and can greatly support the performance improvement of underwater two-dimensional high-resolution acoustic equipment. Attached Figure Description

[0024] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0025] Figure 1 shows the flow chart of the image reconstruction method of the present invention. Wherein: the range FT represents performing a Fourier transform in the range direction; the range IFT represents performing an inverse Fourier transform in the range direction; the azimuth FT represents performing a Fourier transform in the azimuth direction; and the azimuth IFT represents performing an inverse Fourier transform in the azimuth direction.

[0026] Figure 2 shows the two-dimensional geometry of the multi-receiver array element synthetic aperture sonar in this invention.

[0027] Figure 3 shows the phase error of the method of the present invention.

[0028] Figure 4 shows the phase error of the traditional phase center approximation method that considers the spatial variation of distance error.

[0029] Figure 5 shows the phase error of the traditional phase center approximation method that does not consider the spatial variation of distance error.

[0030] Figure 6 shows the error of the traditional series inversion method.

[0031] Figure 7 shows the spatial layout of the four ideal point targets.

[0032] Figure 8 shows the image reconstruction results of the method of the present invention.

[0033] Figure 9 shows the reconstruction results of the nonlinear frequency modulation scale image reconstruction method based on the traditional phase center approximation method that considers the spatial variation of distance error.

[0034] Figure 10 shows the reconstruction results of the nonlinear frequency modulation scale image reconstruction method based on the traditional phase center approximation method that does not consider the spatial variation of distance approximation error.

[0035] Figure 11 shows the reconstruction results of the line frequency modulation standard image reconstruction algorithm based on the traditional series inversion method. Detailed Implementation

[0036] As shown in Figure 1, a method for improving the quality of a high-resolution image includes the following steps: (1) For a subsystem composed of a single receiving element and a transmitting element, calculate the two-way slant range between the equivalent phase center and the target using the phase center approximation method, and express it as a function of the side view angle and the target distance to obtain the target two-way slant range corresponding to the equivalent phase center; (2) Calculate the precise two-way slant range history of the subsystem composed of a single receiving element and a transmitting element using the triangle cosine theorem, and on this basis, calculate the distance error caused by replacing the precise two-way slant range history with the target two-way slant range corresponding to the equivalent phase center in the previous step; (3) Based on the target two-way slant range corresponding to the equivalent phase center and the distance error caused by replacing the precise two-way slant range history, calculate the approximate two-way slant range history containing only a square root expression, and calculate... The echo signal of the point target is further calculated using the phase dwell principle to obtain the two-dimensional spectrum of the echo signal of the point target; (4) For the two-dimensional spectrum of the echo signal of the point target, the phase in the radical expression of the two-dimensional spectrum phase expression is approximated by a fourth Taylor series with respect to the range frequency to obtain a polynomial phase expression with respect to the range frequency, and the truncated phase error generated by the fourth Taylor series approximation is calculated at the same time; (5) Based on the polynomial phase expression with respect to the range frequency in step (4), the micro-Doppler phase error is extracted; For the echo of each receiving array element, Fourier transform is performed in the azimuth direction to obtain the range-Doppler domain data, and the micro-Doppler phase error is compensated in the range-Doppler domain to obtain the data of each receiving array element after micro-Doppler phase error compensation; (6) Based on the polynomial phase expression of the range frequency in step (4), the micro range migration error is extracted; for the data of each receiving array element after micro-Doppler phase error compensation, the delay time error corresponding to the micro range migration error is corrected by interpolation in the range-Doppler domain, thus obtaining all receiving array data after micro range migration error correction; (7) for all receiving array data after micro range migration error correction, inverse Fourier transform is performed in the azimuth direction to obtain two-dimensional time domain data, and the data is arranged in the two-dimensional time domain according to the spatial sampling order to obtain a transceiver composite. (8) For the synthetic aperture sonar data obtained in the previous step, divide it into N data blocks in the range direction; for the N data blocks in the range direction, perform two-dimensional frequency domain transformation respectively; based on the truncation phase error in step (4), calculate the truncation phase error at the reference range in each data block; for any data block in the N data blocks, compensate the truncation phase error of the entire data block by the truncation phase error at the reference range in each data block, and transform the data of the compensated data block to the range-Doppler domain to obtain N data blocks after truncation phase error compensation;(9) For the N data blocks after truncation phase error compensation, arrange them in the range-Doppler domain according to the target's range in ascending order, so as to recombine the scattered N data blocks into complete multi-receiver array synthetic aperture sonar data; (10) For the recombine complete multi-receiver array synthetic aperture sonar data, perform Fourier transform in the range direction, and perform third and fourth phase filtering in the two-dimensional frequency domain to obtain the data after third and fourth phase filtering; (11) For the data after third and fourth phase filtering, perform third and fourth nonlinear frequency modulation processing in the range-Doppler domain to obtain the data after third and fourth nonlinear frequency modulation processing; (12) Based on the phase dwell principle, transform the data after third and fourth nonlinear frequency modulation processing in the previous step to the two-dimensional frequency domain to obtain two-dimensional frequency domain data, and calculate the accurate phase of the two-dimensional frequency domain data; (13) For the accurate phase of the two-dimensional frequency domain data obtained in the previous step, extract the system frequency modulation that depends on the two-dimensional frequency and target range, which integrates the secondary range compression and the transmission signal frequency modulation, and calculate the delay. The time is approximated by a second-order Taylor series to obtain the system modulation frequency after the second-order Taylor series approximation; (14) Substitute the system modulation frequency after the second-order Taylor series approximation into the phase of the two-dimensional spectrum after the transformation to the two-dimensional frequency domain in step (12), and rearrange the power of the product of the delay time and the distance frequency, and accurately calculate the coefficients of the expressions for the first power of both the delay time and the distance frequency, the second power of the delay time and the first power of the distance frequency, the first power of the delay time and the second power of the distance frequency, the second power of both the delay time and the second power of the distance frequency, and the first power of the delay time and the third power of the distance frequency; (15) Set the coefficient of the expression for the first power of both the delay time and the distance frequency to the reciprocal of the curvature factor to eliminate the spatial variation of the distance migration; set the coefficients of the expressions for the second power of the delay time and the first power of the distance frequency, the first power of the delay time and the second power of the distance frequency, the second power of both the delay time and the second power of the distance frequency, and the first power of the delay time and the third power of the distance frequency to zero to eliminate the dependence on distance. These five equations are combined to solve for the undetermined coefficients in the third and fourth phase filtering and third and fourth nonlinear frequency modulation processes; (16) For the two-dimensional frequency domain data obtained in step (12), range pulse compression, range migration consistency correction, and high-order phase error compensation are performed in the two-dimensional frequency domain; (17) For the data processed in the previous step, inverse range Fourier transform is performed, and azimuth pulse compression, azimuth migration correction, and residual phase error compensation are performed in the range-Doppler frequency domain. The data is then transformed to the two-dimensional time domain to obtain the reconstructed high-resolution synthetic aperture sonar image.

[0037] The following will explain this embodiment in detail, with the specific steps as follows: In the two-dimensional geometry shown in Figure 2, the horizontal axis represents the range direction, the vertical axis represents the azimuth direction, the coordinate of the point target in the range direction is r, and the coordinate in the azimuth direction is 0. The black-filled rectangle represents the transmitting element, the gray-filled rectangle represents the m-th receiving element, and the orange-filled rectangle represents the equivalent phase center. L m Let be the real aperture between the m-th receiving element and the transmitting element; The angle between the equivalent phase center and the target's line of sight and the target distance on the x-axis is called the side view angle; v is the sonar tow velocity, μ is the azimuth time retarder, C is the underwater acoustic speed; the precise slant range history between the transmitting element and the target is R. E (μ;r); The precise slant range history between the m-th receiving element and the target is R. R,m (μ;r). t m Let t be the signal propagation time from transmission to reception of the target echo at the m-th receiving element. t represents the range-major time; C represents the underwater acoustic speed; f0 represents the center frequency of the transmitted linear frequency modulated signal g(t); j 2 = -1 represents the imaginary unit.

[0038] Step (1): For a subsystem consisting of a single receiving element and a transmitting element, calculate the two-way slant range between the equivalent phase center and the target using the phase center approximation method, and express it as a function of the side view angle and the target distance to obtain the two-way slant range of the target corresponding to the equivalent phase center; where the m-th equivalent phase center is a virtual transmit / receive combined element located at the center position between the transmitting element and the m-th receiving element, and the two-way slant range between this phase center and the target... Represented as: Here, r is the target range, v is the sonar tow speed, μ is the azimuth time dilation, and C is the speed of sound in water; L m Let m be the real aperture between the m-th receiving element and the transmitting element. The angle between the equivalent phase center and the target's line of sight and the target's distance on the horizontal axis is called the side angle. The two-way slant distance between the phase center and the target... It can also be expressed as a function of the side view and the target distance, with the following expression: ; Subscript This is the index of the receiving array element.

[0039] Step (2) involves calculating the precise two-way slant range history of the subsystem composed of a single receiving element and a transmitting element using the triangle cosine theorem. Based on this, the distance error caused by substituting the precise two-way slant range history with the target's two-way slant range corresponding to the equivalent phase center from the previous step is calculated. Specifically, within the triangle formed by the transmitting element, the target, and the equivalent phase center, the precise transmission slant range history R between the transmitting element and the target is calculated using the cosine theorem. E (μ;r), its expression is: Here, r represents the target distance, v represents the towed speed of the sonar, and C represents the speed of sound in water; L m This represents the real aperture between the m-th receiving element and the transmitting element; The angle between the equivalent phase center and the target's line of sight and the target's distance on the horizontal axis is called the side angle; μ is the azimuth slow time.

[0040] Within the triangle formed by the m-th receiving element, the target, and the equivalent phase center, the precise receiving slant range R between the m-th receiving element and the target is calculated using the law of cosines. R,m (μ;r), the expression is: Here, the subscript m represents the index of the receiving array element.

[0041] Based on the precise slant range history between the transmitting element and the target, and the precise slant range history between the m-th receiving element and the target, the range error caused by replacing the precise two-way slant range with the target's equivalent phase center is calculated. The expression is as follows: Step (3): Based on the target's two-way slant range corresponding to the equivalent phase center and the distance error generated by replacing the exact two-way slant range history, calculate the approximate two-way slant range history containing only a square root expression, and calculate the echo signal of the point target. Based on this, further calculate the two-dimensional spectrum of the point target's echo signal using the phase dwell principle; wherein, the target slant range obtained from the equivalent phase center... and its corresponding distance error ΔR m This yields an approximate two-way slant distance history R containing only a single square root expression. m for: Here, r is the target distance, v is the sonar tow speed, and C is the speed of sound in water; L m Let be the real aperture between the m-th receiving element and the transmitting element; The angle between the equivalent phase center and the target's line of sight and the target distance on the x-axis is called the side angle; μ is the azimuth slow time; the subscript m indicates the index of the receiving array element. In the total slant range history R... mBased on this, the echo signal s of the point target with two-dimensional coordinates (r,0) in the range and azimuth directions is... m The expression for (t,μ) is: Here, t represents the range-fast time, μ represents the azimuth-slow time, f0 represents the center frequency of the transmitted linear frequency modulated signal g(t), and j 2 = -1 represents the imaginary unit.

[0042] Define f t f μ Let represent the range frequency and azimuth Doppler frequency corresponding to the range-fast time t and azimuth-slow time μ, respectively; calculate the point target echo signal s based on the phase dwell principle. m The two-dimensional spectrum S of (t,μ) m (f t ,f μ ), whose expression S m (f t ,f μ ) is: S m (f t ,f μ )=G(f t )·exp{jΨ m (f t ,f μ ;r)} Here G(f t Let Ψ be the spectrum of the linear frequency modulated signal g(t), and let Ψ be the phase. m (f t ,f μ The expression for ;r) is: Side view here The expression in the azimuth-directed Doppler domain is: .

[0043] Step (4): For the two-dimensional spectrum of the echo signal of the point target, the phase in the radical expression of the two-dimensional spectrum is approximated by a fourth Taylor series with respect to the range frequency to obtain a polynomial expression with respect to the range frequency. At the same time, the truncation phase error caused by the fourth Taylor series approximation is calculated. After the fourth Taylor series approximation of the phase in the radical expression, the phase of the two-dimensional spectrum is: Here, the zeroth, first, second, third, and fourth order coefficients (β0, β1, β2, β3, β4) of the fourth-order Taylor series approximation are respectively The second-order coefficient β2 incorporates the modulation frequency k of the transmitted linear frequency modulated signal. r is the target distance, v is the sonar tow speed, and C is the speed of sound in the water; L m The real aperture between the m-th receiving element and the transmitting element, and the side viewing angle. The expression in the azimuth-directed Doppler domain is: f0 is the center frequency of the linear frequency modulated signal, f t f μ Here, represents the range frequency (fast time t) and azimuth frequency (slow time μ), respectively; the subscript m is the receiver element index. Δ is the truncated phase error generated by the fourth Taylor series approximation, and its expression is: Step (5): For the echo of each receiving array element, perform a Fourier transform in the azimuth direction to obtain the data in the range-Doppler domain, and compensate for the micro-Doppler phase error caused by the range error in the range-Doppler domain, thus obtaining the data of each receiving array element after micro-Doppler phase error compensation; the phase micro-Doppler error compensation function Λ m for: Here ΔR m The distance error corresponding to the target slant range obtained from the equivalent phase center, as derived above; C represents the underwater acoustic speed; f0 represents the center frequency of the transmitted linear frequency modulated signal; the subscript m represents the index of the receiving array element.

[0044] Step (6): For the data of each receiving array element after micro-Doppler phase error compensation, interpolation is used in the range-Doppler domain to correct the micro-range migration error caused by the range error, thus obtaining all receiving array data after micro-range migration error correction; the delay time error Δt corresponding to the micro-range migration error to be corrected. m for: Here ΔR m The distance error corresponding to the target slant range obtained at the equivalent phase center, as derived above, is given by C; C represents the underwater acoustic speed; the subscript m represents the index of the receiving array element.

[0045] Step (7): For all received array data after micro-range migration error correction, perform inverse Fourier transform in the azimuth direction to obtain two-dimensional time-domain data, and arrange them in the two-dimensional time domain according to the spatial sampling order to obtain data similar to a transceiver combined synthetic aperture sonar; assuming there are a total of M receiving array elements, the echoes of the 1st, 2nd, 3rd...Mth receiving array elements corresponding to the first pulse are represented as [ss 1,1 ,ss 1,2 ,…,ss 1,M The echoes corresponding to the 1st, 2nd, 3rd...Mth receiving elements of the second pulse are represented as [ss]. 2,1 ,ss 2,2 ,…,ss 2,M The echoes corresponding to the 1st, 2nd, 3rd...Mth receiving array elements of the Pth pulse are represented as [ss]. P,1 ,ss P,2,…,ss P,M Therefore, the expression for the sequential arrangement of the pulse sampling data is as follows: Step (8): For the synthetic aperture sonar data obtained in the previous step, divide it into N data blocks in the range direction; for each of the N data blocks in the range direction, perform a two-dimensional frequency domain transformation; for any data block in the N data blocks, compensate for the truncation phase error of the entire data block by using the truncation phase error at the reference range in each data block, and transform the data of the compensated data block to the range-Doppler domain; after this processing, N data blocks after truncation phase error compensation are obtained; if the number of sampling points along the range direction is W, then the number of sampling points N in each data block is... sub for: Generally, we choose N that is divisible by W. sub Use; corresponding to the first The expression for the truncation phase error at the reference distance of each data block is Δ n The corresponding phase compensation function H sub,n For: H sub,n = exp{jΔ n}Here Δ n =Δ| r=rn This indicates that the distance of the spatial variation in the truncated phase error is measured using the reference distance r of the nth data block. n An approximation is made to eliminate the spatial variability of the distance error.

[0046] Step (9): For the N data blocks after truncation phase error compensation, arrange them sequentially in the range-Doppler domain according to the target's range in ascending order, so as to recombine the data of the scattered N data blocks into complete multi-receiver array element synthetic aperture sonar data; assuming the N data blocks are represented as A1, A2, A3, …, A N Therefore, the expression for data block reorganization is: Step (10): For the recombined multi-receiver array element synthetic aperture sonar data, perform Fourier transform in the range direction and perform third and fourth phase filtering in the two-dimensional frequency domain to obtain the third and fourth phase filtered data; wherein, the filtering function H1(f t ,f μ ;r0) is: Here Y(f) μ ) and Z(f μ ) represents the third and fourth order filter coefficients, r0 represents the reference distance corresponding to the entire mapping strip; ft, f μThese represent the range frequency and azimuth Doppler frequency corresponding to the range fast time t and azimuth slow time μ, respectively.

[0047] Step (11): For the data after third and fourth phase filtering, perform third and fourth nonlinear frequency modulation processing in the range-Doppler domain to obtain the data after third and fourth nonlinear frequency modulation processing; wherein, the nonlinear frequency modulation processing function H2(t,f) μ ;r) is: Here q2(f) μ ), q3(f μ ), q4(f μ () represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes; Represents the center distance r s The distance migration of the target; t is the distance-major time. f μ This represents the Doppler frequency corresponding to the azimuth direction at slow time μ. r is the target range, v is the sonar tow speed, C is the underwater acoustic speed, and f0 is the center frequency of the linear frequency modulated signal.

[0048] Step (12): Based on the phase dwell principle, the data after the third and fourth nonlinear frequency modulation processing in the previous step is transformed into two-dimensional frequency domain data to obtain two-dimensional frequency domain data, and the accurate phase of the two-dimensional frequency domain data is calculated; wherein, the two-dimensional spectral phase... The expression is: here This refers to the new frequency modulation (FM) after further incorporating azimuth and range secondary coupling factors based on the transmitted signal FM; this is called the system FM. q2, q3, and q4 are respectively q2(f μ ), q3(f μ ), q4(f μ (abbreviation) The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ ft represents the Doppler frequency at slow time μ in the corresponding direction, and ft represents the range frequency at fast time t in the corresponding range direction. This represents the coefficient of the new cubic term after third-order filtering, which incorporates the azimuth and range cubic coupling factors. This represents the coefficient of the new fourth-order term after fourth-order filtering, which incorporates the fourth-order coupling factors of the azimuth and range directions.

[0049] Step (13): Based on the precise phase of the two-dimensional frequency domain data obtained in the previous step, extract the system modulation frequency (CMFM) that integrates the secondary range compression and the transmitted signal modulation frequency, which depends on the two-dimensional frequency and the target range. Then, perform a second-order Taylor series approximation with respect to the delay time to obtain the system modulation frequency after the second-order Taylor series approximation; where the system modulation frequency... The expression for the delay time after approximation using a second-order Taylor series is as follows: here The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s Distance migration of the target; k0, k s k2 represents the zeroth, first, and second order coefficients after Taylor series approximation; C represents the underwater acoustic speed; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the tow speed of the sonar; f μ ft represents the slow-time μ Doppler frequency in the corresponding direction; ft represents the range frequency in the fast-time t direction in the corresponding range direction.

[0050] Step (14): Substitute the system modulation frequency approximated by the second-order Taylor series into the phase of the two-dimensional spectrum after transformation to the two-dimensional frequency domain in step (12). Rearrange the phase with respect to the power of the product of delay time and range frequency, and accurately calculate the coefficients of the expressions for the first power of both delay time and range frequency, the second power of delay time and the first power of range frequency, the first power of delay time and the second power of range frequency, the second power of delay time and the third power of range frequency, the second power of delay time and the third power of range frequency, and the third power of delay time and the third power of range frequency. The calculated results are expressed as follows: Here O(Y,Z,q2,q3,q4,f) μ ,Δt 2 ,Δt 3 ,Δt 4 ) indicates the range-direction frequency f t Irrelevant terms, B(Y,Z,q2,q3,q4,f) μ ) is Δtf t The coefficient term, D(Y,Z,q2,q3,q4,f) μ ) is Δt 2 f t The coefficient term, E(Y,Z,q2,q3,q4,f) μ ) is Δtf t 2 The coefficient term, F(Y,Z,q2,q3,q4,fμ ) is Δt 2 f t 2 The coefficient term, J(Y,Z,q2,q3,q4,f) μ ) is Δtf t 3 The coefficient term, Q(Y,Z,q2,q3,q4,f) μ ,f t ,f t 2 ,f t 3 ,f t 4 ) represents terms that are independent of Δt. The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ ft represents the Doppler frequency in the slow time μ direction; ft represents the range frequency in the fast time t direction.

[0051] Step (15): Set the coefficients of the expressions for both delay time and range-frequency to the first power to the reciprocal of the curvature factor to eliminate the spatial variation of range migration; set the coefficients of the expressions for delay time quadratic and range-frequency first power, delay time first power and range-frequency quadratic, delay time and range-frequency quadratic, and delay time first power and range-frequency cubic power to zero to eliminate the dependence on distance. Solve these five equations simultaneously to find the undetermined coefficients in the cubic and quaternary phase filtering and cubic and quaternary nonlinear frequency modulation processes. The expressions of the five equations are as follows: B(Y,Z,q2,q3,q4,f μ ) is Δtf in step (14) t The coefficient term, D(Y,Z,q2,q3,q4,f) μ ) is Δt in step (14) 2 f t The coefficient term, E(Y,Z,q2,q3,q4,f) μ ) is Δtf in step (14) t 2 The coefficient term, F(Y,Z,q2,q3,q4,fμ ) is Δt in step (14) 2 f t 2 The coefficient term, J(Y,Z,q2,q3,q4,f) μ ) is Δtf in step (14) t 3 The coefficient term; The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ ft represents the Doppler frequency corresponding to the slow time μ in the corresponding direction; ft represents the range frequency corresponding to the fast time t in the corresponding range direction; here Let represent the bending factor. The result of solving the above five equations is expressed as: Here q2(f) μ ), q3(f μ ), q4(f μ ) represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes mentioned above, while q2, q3, and q4 are respectively the coefficients of q2(f μ ), q3(f μ ), q4(f μ abbreviation of ) . k0, k s Let k2 represent the zeroth, first, and second-order coefficients of the system frequency modulation after a second-order Taylor series approximation with respect to the delay time. Here, Y(f μ ) and Z(f μ ) represents the aforementioned third-order and fourth-order filter coefficients, while Y and Z are Y(f μ ) and Z(f μ (abbreviation of ).

[0052] Step (16): For the two-dimensional frequency domain data obtained in step (12), range pulse compression, range migration consistency correction, and higher-order phase error compensation are performed in the two-dimensional frequency domain; where the compensation function is: here The distance r represents the center distance of the surveying zone. s Migration at the distance from the target. This represents the azimuth Doppler center frequency f. dc And the center distance of the surveying zone is r s The target distance migration at that time; the Doppler center frequency of the front-view system is zero, i.e., fdc = 0. C represents the speed of sound in water; f t f represents the range-direction frequency corresponding to a distance time t; μ q2(f) represents the Doppler frequency of the corresponding slow time μ in the direction; v represents the sonar towing speed; f0 represents the center frequency of the emitted linear frequency modulated signal; here q2(f) μ ), q3(f μ ), q4(f μ ) represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes mentioned above, while q2, q3, and q4 are respectively the coefficients of q2(f μ ), q3(f μ ), q4(f μ The abbreviation for Y(f). μ ) and Z(f μ ) represents the aforementioned third-order and fourth-order filter coefficients, while Y and Z are Y(f μ ) and Z(f μ (abbreviation of ) . k0 represents the zeroth-order coefficient of the system frequency modulation after approximating the delay time with a second-order Taylor series.

[0053] Step (17): For the data processed in the previous step, perform an inverse range Fourier transform. Then, perform azimuth pulse compression, azimuth travel correction, and residual phase error compensation in the range-Doppler frequency domain. Transforming the data to the two-dimensional time domain yields the reconstructed high-resolution synthetic aperture sonar image. The expression for the compensation function is: here Represents the residual phase. k0 represents the system modulation frequency. The zeroth-order coefficients are obtained by approximating the delay time using a second-order Taylor series. C represents the speed of sound in the water; f μ The doppler frequency corresponding to the slow time μ in the corresponding direction; β0 represents the zero-order coefficient of the phase in the aforementioned two-dimensional spectral radical formula for the point target echo, after a fourth Taylor series approximation of the range-direction frequency; side view. The expression in the azimuth-directed Doppler domain is: q2(f μ ), q3(f μ ), q4(f μ ) represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes mentioned above, while q2, q3, and q4 are respectively the coefficients of q2(f μ ), q3(f μ ), q4(f μ (abbreviation of ). The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ f represents the Doppler frequency for the corresponding slow time μ in the direction; t This represents the range-direction frequency corresponding to a distance and a time interval t.

[0054] Assume the center frequency of the linear frequency modulated signal emitted by the sonar is 110 kHz, and the bandwidth is 40 kHz. There are a total of 67 receiving elements, each with an aperture of 3 cm along the azimuth direction. The sonar tow speed is 2.01 m / s, and the pulse repetition period is 0.5 s. Based on these parameters, using the phase of the two-dimensional spectrum obtained by numerical calculation as a reference, the phase error of each receiving element at a fixed distance is calculated. The maximum value of this phase error is then extracted, thereby eliminating the dependence of the phase error on the two-dimensional frequency. The phase error calculated according to this method is shown in Figure 3. Figure 4 shows the phase error of the traditional phase center approximation method considering the spatial variation of range error. Figure 5 shows the phase error of the traditional phase center approximation method not considering the spatial variation of range error. Figure 6 shows the error of the traditional series inversion method. From the comparison, it is easy to see that the error of the method of this invention is very small.

[0055] Assuming there are four ideal point targets in space, the spatial layout is shown in Figure 7. Figure 8 shows the image reconstruction result of the method of the present invention; Figure 9 shows the reconstruction result of the nonlinear frequency modulation scaling image reconstruction method based on the traditional phase center approximation method considering the spatial variation of range error; Figure 10 shows the reconstruction result of the nonlinear frequency modulation scaling image reconstruction method based on the traditional phase center approximation method without considering the spatial variation of range approximation error; and Figure 11 shows the reconstruction result of the line frequency modulation scaling image reconstruction algorithm based on the traditional series inversion method. From the results shown in Figures 8, 9, 10, and 11, it is easy to see the superiority of the method of the present invention in processing wide-range transmitted signals and synthetic aperture sonar data with a large coherence accumulation angle.

[0056] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for improving the quality of a high-resolution image, comprising the following steps: (1) For a subsystem consisting of a single receiving element and a transmitting element, calculate the two-way slant range between the equivalent phase center and the target using the phase center approximation method, and express it as a function of the side view angle and the target distance to obtain the target two-way slant range corresponding to the equivalent phase center; (2) Calculate the precise two-way slant range history of the subsystem consisting of a single receiving element and a transmitting element using the triangle cosine theorem, and on this basis, calculate the distance error caused by replacing the precise two-way slant range history with the target two-way slant range corresponding to the equivalent phase center in the previous step; (3) Based on the target two-way slant range corresponding to the equivalent phase center and the distance error caused by replacing the precise two-way slant range history, calculate the approximate two-way slant range history containing only a square root expression, and calculate the echo signal of the point target. Based on this, the phase dwell principle is further used to calculate the two-dimensional spectrum of the echo signal of the point target; (4) For the two-dimensional spectrum of the echo signal of the point target, the phase in the radical expression of the two-dimensional spectrum phase expression is approximated by a fourth Taylor series with respect to the range frequency to obtain a polynomial phase expression with respect to the range frequency, and the truncated phase error generated by the fourth Taylor series approximation is calculated at the same time; (5) Based on the polynomial phase expression with respect to the range frequency in step (4), the micro-Doppler phase error is extracted; For the echo of each receiving array element, Fourier transform is performed in the azimuth direction to obtain the range-Doppler domain data, and the micro-Doppler phase error is compensated in the range-Doppler domain to obtain the data of each receiving array element after micro-Doppler phase error compensation; (6) Based on the polynomial phase expression of the range frequency in step (4), extract the micro range migration error; for the data of each receiving array element after micro Doppler phase error compensation, use interpolation in the range-Doppler domain to correct the delay time error corresponding to the micro range migration error, and obtain all receiving array data after micro range migration error correction; (7) for all receiving array data after micro range migration error correction, perform inverse Fourier transform in the azimuth direction to obtain two-dimensional time domain data, and arrange them in the two-dimensional time domain according to the order of spatial sampling to obtain data of a transceiver combined synthetic aperture sonar; (8) For the synthetic aperture sonar data obtained in the previous step, divide it into N data blocks in the range direction; perform two-dimensional frequency domain transformation on each of the N data blocks in the range direction; calculate the truncation phase error at the reference range in each data block based on the truncation phase error in step (4); for any data block in the N data blocks, compensate the truncation phase error of the entire data block by the truncation phase error at the reference range in each data block, and transform the data of the compensated data block to the range-Doppler domain to obtain N data blocks after truncation phase error compensation. (9) For the N data blocks after truncation phase error compensation, arrange them in the range-Doppler domain according to the target's range in ascending order, so as to recombine the scattered N data blocks into complete multi-receiver array synthetic aperture sonar data; (10) For the recombine complete multi-receiver array synthetic aperture sonar data, perform Fourier transform in the range direction and perform third and fourth phase filtering in the two-dimensional frequency domain to obtain the data after third and fourth phase filtering; (11) For the data after third and fourth phase filtering, perform third and fourth nonlinear frequency modulation processing in the range-Doppler domain to obtain the data after third and fourth nonlinear frequency modulation processing. (12) Based on the phase dwell principle, the data after the third and fourth nonlinear frequency modulation processing in the previous step is transformed to the two-dimensional frequency domain to obtain two-dimensional frequency domain data, and the accurate phase of the two-dimensional frequency domain data is calculated; (13) For the accurate phase of the two-dimensional frequency domain data obtained in the previous step, the system modulation frequency that depends on the two-dimensional frequency and the target distance and is integrated with the second-order range compression and the transmission signal modulation frequency is extracted, and a second-order Taylor series approximation is performed with respect to the delay time to obtain the system modulation frequency after the second-order Taylor series approximation; (14) The system modulation frequency after the second-order Taylor series approximation is substituted into step (12) to transform to the two-dimensional frequency domain. In the phase of the two-dimensional spectrum after the frequency domain, the power of the product of the delay time and the distance frequency of the phase is rearranged, and the coefficients of the expressions for the first power of both the delay time and the distance frequency, the second power of the delay time and the first power of the distance frequency, the first power of the delay time and the second power of the distance frequency, the second power of both the delay time and the distance frequency, and the first power of the delay time and the third power of the distance frequency are calculated precisely; (15) Let the coefficient of the expression for the first power of both the delay time and the distance frequency be the reciprocal of the curvature factor to eliminate the spatial variation of the distance migration. Set the coefficients of the expressions for the square of the delay time and the first power of the range frequency, the first power of the delay time and the square of the range frequency, the expressions for the square of both the delay time and the range frequency, and the expressions for the first power of the delay time and the cubic of the range frequency to zero to eliminate the dependence on distance. (16) Solve the five equations together to solve the undetermined coefficients in the third and fourth phase filtering and third and fourth nonlinear frequency modulation processes; (17) Perform range pulse compression, range migration consistency correction and high-order phase error compensation on the two-dimensional frequency domain data obtained in step (12); (18) Perform range inverse Fourier transform on the data processed in the previous step, perform azimuth pulse compression, azimuth migration correction and residual phase error compensation on the range-Doppler frequency domain, and transform the data to the two-dimensional time domain to obtain the reconstructed high-resolution synthetic aperture sonar image.

2. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (1) involves calculating the two-way slant range between the equivalent phase center and the target for a subsystem consisting of a single receiving element and a transmitting element, using the phase center approximation method. This slant range is then expressed as a function of the side view angle and the target distance, yielding the two-way slant range corresponding to the equivalent phase center. The m-th equivalent phase center is a virtual transceiver array element located at the center between the transmitting element and the m-th receiving element. The two-way slant range between this phase center and the target is... Represented as: Here, r is the target range, v is the sonar tow speed, μ is the azimuth time dilation, and C is the speed of sound in water; L m Let m be the real aperture between the m-th receiving element and the transmitting element. The angle between the equivalent phase center and the target's line of sight on the horizontal axis, and the distance to the target, is called the side angle; the two-way slant distance between the phase center and the target. It can also be expressed as a function of the side view and the target distance, with the following expression: ; Subscript This is the index of the receiving array element.

3. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (2) calculates the precise two-way slant range history of the subsystem composed of a single receiving element and a transmitting element according to the triangle cosine theorem. Based on this, the distance error caused by replacing the precise two-way slant range history with the target two-way slant range corresponding to the equivalent phase center in the previous step is calculated. Among them, in the triangle formed by the transmitting element, the target, and the equivalent phase center, the precise transmission slant range history R between the transmitting element and the target is calculated using the cosine theorem. E (μ;r), its expression is: Here, r represents the target distance, v represents the towed speed of the sonar, and C represents the speed of sound in water; L m This represents the real aperture between the m-th receiving element and the transmitting element; The angle between the equivalent phase center and the target's line of sight and the target's distance on the x-axis is called the side angle; μ is the azimuth slow time; in the triangle formed by the m-th receiving element, the target, and the equivalent phase center, the precise receiving slant range history R between the m-th receiving element and the target is calculated using the law of cosines. R,m (μ;r), the expression is: Here, the subscript m represents the index of the receiving element; based on the precise slant range history between the transmitting element and the target, and the precise slant range history between the m-th receiving element and the target, the range error caused by replacing the precise two-way slant range history with the target two-way slant range corresponding to the equivalent phase center is calculated, and the expression is: 。 4. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (3) calculates an approximate two-way slant range history containing only a square root expression based on the target two-way slant range corresponding to the equivalent phase center and the distance error generated by replacing the exact two-way slant range history. It also calculates the echo signal of the point target and further uses the phase dwell principle to calculate the two-dimensional spectrum of the point target's echo signal. The target slant range obtained from the equivalent phase center is considered as a whole. and its corresponding distance error ΔR m This yields an approximate two-way slant distance history R containing only a single square root expression. m for: Here, r is the target distance, v is the sonar tow speed, and C is the speed of sound in water; L m Let be the real aperture between the m-th receiving element and the transmitting element; The angle between the equivalent phase center and the target's line of sight and the target distance on the x-axis is called the side view angle; μ is the azimuth slow time; the subscript m indicates the index of the receiving array element; in the total slant range history R m Based on this, the echo signal s of the point target with two-dimensional coordinates (r,0) in the range and azimuth directions is... m The expression for (t,μ) is: Here, t represents the range-fast time, μ represents the azimuth-slow time, f0 represents the center frequency of the transmitted linear frequency modulated signal g(t), and j 2 = -1 represents the imaginary unit; define f t f μ Let represent the range frequency and azimuth Doppler frequency corresponding to the range-fast time t and azimuth-slow time μ, respectively; calculate the point target echo signal s based on the phase dwell principle. m The two-dimensional spectrum S of (t,μ) m (f t ,f μ ), whose expression S m (f t ,f μ ) is: S m (f t ,f μ )=G(f t )·exp{jΨ m (f t ,f μ ;r)} Here G(f t Let Ψ be the spectrum of the linear frequency modulated signal g(t), and let Ψ be the phase. m (f t ,f μ The expression for ;r) is: Side view here The expression in the azimuth-directed Doppler domain is: 。 5. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: In step (4), for the two-dimensional spectrum of the echo signal of the point target, the phase in the radical expression of the two-dimensional spectrum is approximated by a fourth Taylor series with respect to the range frequency to obtain a polynomial phase expression with respect to the range frequency. At the same time, the truncation phase error caused by the fourth Taylor series approximation is calculated. After the phase in the radical expression is approximated by a fourth Taylor series, the phase of the two-dimensional spectrum is: Here, the zeroth, first, second, third, and fourth order coefficients of the fourth-order Taylor series approximation are respectively... The second-order coefficient β2 incorporates the modulation frequency k of the transmitted linear frequency modulated signal; r is the target distance, v is the sonar tow speed, and C is the underwater acoustic speed; L m The real aperture between the m-th receiving element and the transmitting element, and the side viewing angle. The expression in the azimuth-directed Doppler domain is: f0 is the center frequency of the linear frequency modulated signal, f t f μ Here, represents the range frequency (fast range time t) and azimuth frequency (slow azimuth time μ), respectively; the subscript m is the receiver element index; Δ is the truncated phase error generated by the fourth Taylor series approximation, and its expression is: 。 6. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (5) extracts the micro-Doppler phase error based on the polynomial phase expression for the range frequency obtained in step (4); for the echo of each receiving element, a Fourier transform is performed in the azimuth direction to obtain the range-Doppler domain data, and the micro-Doppler phase error is compensated in the range-Doppler domain to obtain the data of each receiving element after micro-Doppler phase error compensation; wherein, the micro-Doppler phase error extracted from step (4) is ; Compensation function Λ for compensating micro-Doppler phase errors in the range-Doppler domain m for: Here ΔR m The distance error corresponding to the target slant range obtained from the equivalent phase center, as derived above; C represents the underwater acoustic speed; f0 represents the center frequency of the transmitted linear frequency modulated signal; the subscript m represents the index of the receiving array element.

7. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (6) extracts the micro-range migration error based on the polynomial phase expression of the range-direction frequency obtained in step (4). For the data of each receiving array element after micro-Doppler phase error compensation, the delay time error corresponding to the micro-range migration error is corrected by interpolation in the range-Doppler domain, thus obtaining all receiving array data after micro-range migration error correction. Among them, the micro-range migration error extracted from step (4) is ΔR. m The corresponding delay time error Δt m for: Here ΔR m The distance error corresponding to the target slant range obtained at the equivalent phase center, which has been derived in step (2); C represents the underwater acoustic speed; the subscript m represents the index of the receiving array element.

8. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (7) involves performing an inverse Fourier transform in the azimuth direction on all received array data after micro-range migration error correction to obtain two-dimensional time-domain data. This data is then arranged in the two-dimensional time domain according to the spatial sampling order to obtain data similar to a transceiver combined synthetic aperture sonar. Assuming there are a total of M receiving array elements, the echoes of the 1st, 2nd, 3rd...Mth receiving array elements corresponding to the first pulse are represented as [ss...]. 1,1 ,ss 1,2 ,…,ss 1,M The echoes corresponding to the 1st, 2nd, 3rd...Mth receiving elements of the second pulse are represented as [ss]. 2,1 ,ss 2,2 ,…,ss 2,M The echoes corresponding to the 1st, 2nd, 3rd...Mth receiving array elements of the Pth pulse are represented as [ss]. P,1 ,ss P,2 ,…,ss P,M Therefore, the expression for the sequential arrangement of the pulse sampling data is as follows: 。 9. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (8) involves dividing the synthetic aperture sonar data obtained in the previous step into N data blocks along the range direction; performing two-dimensional frequency domain transformation on each of the N data blocks along the range direction; calculating the truncation phase error at the reference range in each data block based on the truncation phase error in step (4); compensating the truncation phase error of the entire data block for any data block in the N data blocks using the truncation phase error at the reference range in each data block, and transforming the data of the compensated data block to the range-Doppler domain to obtain N data blocks after truncation phase error compensation; if the number of sampling points along the range direction is W, then the number of sampling points N in each data block is... sub for: We choose N that is divisible by W. sub Used; the expression for the truncation phase error corresponding to the reference distance of the nth data block is Δ n The corresponding phase compensation function H sub,n For: H sub,n = exp{jΔ n }Here Δ n =Δ| r=rn This indicates that the distance of the spatial variation in the truncated phase error is measured using the reference distance r of the nth data block. n An approximation is made to eliminate the spatial variability of the distance error.

10. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (9) involves sequentially arranging the N data blocks after truncation and phase error compensation in the range-Doppler domain according to the target's range in ascending order, so as to recombine the data of the dispersed N data blocks into complete multi-receiver array synthetic aperture sonar data; assuming the N data blocks are represented as A1, A2, A3, …, A N Therefore, the expression for data block reorganization is: 。 11. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (10) involves performing a Fourier transform in the range direction on the reassembled multi-receiver array element synthetic aperture sonar data, and performing third and fourth phase filtering in the two-dimensional frequency domain to obtain the third and fourth phase filtered data; wherein, the filtering function H1(f t ,f μ ;r0) is: Here Y(f) μ ) and Z(f μ ) represents the third- and fourth-order filter coefficients, r0 represents the reference distance corresponding to the entire mapping strip; f t f μ These represent the range frequency and azimuth Doppler frequency corresponding to the range fast time t and azimuth slow time μ, respectively.

12. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (11) involves performing third and fourth nonlinear frequency modulation processing on the data after third and fourth phase filtering in the range-Doppler domain to obtain the data after third and fourth nonlinear frequency modulation processing; wherein, the nonlinear frequency modulation processing function H2(t,f) μ ;r) is: Here q2(f) μ ), q3(f μ ), q4(f μ () represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes; Represents the center distance r s The distance migration of the target; t is the distance-major time; f μ The value represents the Doppler frequency of the corresponding azimuth direction with slow time μ; r is the target distance; v is the sonar towing speed; C is the underwater acoustic speed; and f0 is the center frequency of the linear frequency modulated signal.

13. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (12) is based on the phase dwell principle. It transforms the data processed by the third and fourth nonlinear frequency modulation steps in the previous step into a two-dimensional frequency domain to obtain two-dimensional frequency domain data, and calculates the precise phase of the two-dimensional frequency domain data; wherein, the two-dimensional spectral phase... The expression is: here This refers to the new frequency modulation (FM) after further incorporating azimuth and range secondary coupling factors based on the transmitted signal FM; this is called the system FM. q2, q3, and q4 are respectively q2(f μ ), q3(f μ ), q4(f μ (abbreviation) The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any given distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ f represents the Doppler frequency for the slow time μ in the corresponding direction. t Indicates the corresponding distance to fast time The distance to the frequency; This represents the coefficient of the new cubic term after third-order filtering, which incorporates the azimuth and range cubic coupling factors. This represents the coefficient of the new fourth-order term after fourth-order filtering, which incorporates the fourth-order coupling factors of the azimuth and range directions.

14. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (13) involves extracting the system modulation frequency (CMFM), which is dependent on the two-dimensional frequency and target distance and incorporates secondary range compression and transmit signal frequency modulation, based on the precise phase of the two-dimensional frequency domain data obtained in the previous step. A second-order Taylor series approximation is then performed with respect to the delay time to obtain the approximated CMFM. The expression for the delay time after approximation using a second-order Taylor series is as follows: here The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any given distance. The distance r represents the center distance of the surveying zone. s Distance migration of the target; k0, k s k2 represents the zeroth, first, and second order coefficients after Taylor series approximation; C represents the underwater acoustic speed; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the tow speed of the sonar; f μ f represents the slow-time μ-Doppler frequency in the corresponding direction; t This represents the range frequency corresponding to the range time t.

15. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: In step (14), the system modulation frequency approximated by the second-order Taylor series is substituted into the phase of the two-dimensional spectrum after transformation to the two-dimensional frequency domain in step (12). The phase is rearranged with respect to the power of the product of delay time and range frequency, and the coefficients of the expressions for the first power of both delay time and range frequency, the second power of delay time and the first power of range frequency, the first power of delay time and the second power of range frequency, the second power of delay time and the third power of range frequency, the second power of both delay time and the second power of range frequency, and the first power of delay time and the third power of range frequency are calculated precisely. The calculated results are expressed as follows: Here O(Y,Z,q2,q3,q4,f) μ ,Δt 2 ,Δt 3 ,Δt 4 ) indicates the range-direction frequency f t Irrelevant terms, B(Y,Z,q2,q3,q4,f) μ ) is Δtf t The coefficient term, D(Y,Z,q2,q3,q4,f) μ ) is Δt 2 f t The coefficient term, E(Y,Z,q2,q3,q4,f) μ ) is Δtf t 2 The coefficient term, F(Y,Z,q2,q3,q4,f μ ) is Δt 2 f t 2 The coefficient term, J(Y,Z,q2,q3,q4,f) μ ) is Δtf t 3 The coefficient term, Q(Y,Z,q2,q3,q4,f) μ ,f t ,f t 2 ,f t 3 ,f t 4 ) represents terms that are independent of Δt; The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any given distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ f represents the Doppler frequency for the corresponding slow time μ in the direction; t This represents the range-direction frequency corresponding to a distance and a time interval t.

16. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (15) sets the coefficients of the expression for both the delay time and the range frequency to the first power to the reciprocal of the curvature factor to eliminate the spatial variation of the range migration. Set the coefficients of the expressions for the square of the delay time and the first power of the range frequency, the first power of the delay time and the square of the range frequency, the expressions for the square of both the delay time and the range frequency, and the expressions for the first power of the delay time and the cubic of the range frequency to zero to eliminate the dependence on distance. These five equations are used to solve for the undetermined coefficients in the third and fourth phase filtering and third and fourth nonlinear frequency modulation processes; the expressions for the five equations are as follows: B(Y,Z,q2,q3,q4,f μ ) is Δtf in step (14) t The coefficient term, D(Y,Z,q2,q3,q4,f) μ ) is Δt in step (14) 2 f t The coefficient term, E(Y,Z,q2,q3,q4,f) μ ) is Δtf in step (14) t 2 The coefficient term, F(Y,Z,q2,q3,q4,f μ ) is Δt in step (14) 2 f t 2 The coefficient term, J(Y,Z,q2,q3,q4,f) μ ) is Δtf in step (14) t 3 The coefficient term; The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any given distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ f represents the Doppler frequency for the corresponding slow time μ in the direction; t This represents the range-direction frequency corresponding to a distance of time t; here... The bending factor is represented by the equation; the result of solving the above five equations is expressed as follows: Here q2(f) μ ), q3(f μ ), q4(f μ ) represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes mentioned above, while q2, q3, and q4 are respectively the coefficients of q2(f μ ), q3(f μ ), q4(f μ abbreviation of ); k0, k s and k2 represent the zeroth, first, and second order coefficients of the system frequency modulation after a second-order Taylor series approximation with respect to the delay time; here Y(f μ ) and Z(f μ ) represents the aforementioned third-order and fourth-order filter coefficients, while Y and Z are Y(f μ ) and Z(f μ (abbreviation of ).

17. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (16) performs range pulse compression, range migration consistency correction, and higher-order phase error compensation on the two-dimensional frequency domain data obtained in step (12); wherein the compensation function is: here The distance r represents the center distance of the surveying zone. s Migration at the distance from the target. This represents the azimuth Doppler center frequency f. dc And the center distance of the surveying zone is r s The target distance migration at that time; the Doppler center frequency of the front-view system is zero, i.e., f dc = 0; C represents the speed of sound in water; f t f represents the range-direction frequency corresponding to a distance time t; μ q2(f) represents the Doppler frequency of the corresponding slow time μ in the direction; v represents the sonar towing speed; f0 represents the center frequency of the emitted linear frequency modulated signal; here q2(f) μ ), q3(f μ ), q4(f μ ) represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes mentioned above, while q2, q3, and q4 are respectively the coefficients of q2(f μ ), q3(f μ ), q4(f μ The abbreviation for Y(f); here Y(f μ ) and Z(f μ ) represents the aforementioned third-order and fourth-order filter coefficients, while Y and Z are Y(f μ ) and Z(f μ (abbreviation of ); k0 represents the zero-order coefficient of the system frequency modulation after approximating the delay time with a second-order Taylor series.

18. The method for improving the quality of a high-resolution image as described in claim 1, characterized in that: Step (17) involves performing an inverse range Fourier transform on the data processed in the previous step, performing azimuth pulse compression, azimuth travel correction, and residual phase error compensation in the range-Doppler frequency domain, and transforming the data to the two-dimensional time domain to obtain the reconstructed high-resolution synthetic aperture sonar image; wherein, the expression of the compensation function is: here k0 represents the residual phase; k0 represents the system modulation frequency. The zeroth-order coefficients after approximating the delay time using a second-order Taylor series; C represents the underwater acoustic velocity; f μ The doppler frequency corresponding to the slow time μ in the corresponding direction; β0 represents the zero-order coefficient of the phase in the aforementioned two-dimensional spectral radical formula for the point target echo, after a fourth Taylor series approximation of the range-direction frequency; side view. The expression in the azimuth-directed Doppler domain is: ;q2(f μ ), q3(f μ ), q4(f μ ) represents the coefficients of the second, third, and fourth nonlinear frequency modulation processes mentioned above, while q2, q3, and q4 are respectively the coefficients of q2(f μ ), q3(f μ ), q4(f μ (abbreviation) The relative distance r between the centers of the surveying zone s The delay time between the target's distance and its migration. This represents the distance migration of a target at any distance. The distance r represents the center distance of the surveying zone. s The distance migration of the target; C represents the speed of underwater acoustics; f0 represents the center frequency of the emitted linear frequency modulated signal; v represents the towed speed of the sonar; f μ f represents the Doppler frequency for the corresponding slow time μ in the direction; t This represents the range-direction frequency corresponding to a distance and a time interval t.

Images