Multi-receiving-array synthetic aperture sonar imaging method and system

Abstract

The invention provides a multi-receiving-array synthetic aperture sonar imaging method and system, and the multi-receiving-array synthetic aperture sonar is in the motion direction of the sonar, the receiving array is in the front, and the transmitting array is in the rear. The method comprises the following steps: carrying out approximate processing on two-way time, and carrying out fourth-order Taylor expansion on a slant range process; distance direction and azimuth direction Fourier transformation is carried out on a baseband signal to enable the baseband signal to be in a two-dimensional frequency domain, then an accurate two-dimensional frequency spectrum is obtained by applying a Lagrange inversion theorem and a stationary phase principle, the accurate two-dimensional frequency spectrum is expanded into an azimuth direction frequency and distance direction frequency series expansion form, and meanwhile, azimuth direction and range direction matched filtering functions are obtained; and based on the precise two-dimensional frequency spectrum, carrying out matched filtering processing on the two-dimensional frequency domain signal in the range and azimuth to obtain the synthetic aperture sonar simulation image focused in the range and azimuth. The method has the advantages that the imaging calculation efficiency is high, and good imaging precision and quality are achieved at different distances; and the requirement of full-scanning-band high-resolution imaging can be met.

Description

Technical Field

[0001] This application belongs to the technical field of image processing, and specifically relates to a multi-receiver array synthetic aperture sonar imaging method and system. Background Art

[0002] Synthetic Aperture Sonar (SAS) improves the azimuth resolution and mapping efficiency by virtually synthesizing a large-aperture array through the uniform linear motion of a single small element, enabling it to play a significant role in civilian and military fields such as undersea mineral resource development, topographic and geomorphic surveying, engineering quantity assessment, underwater engineering (revetment engineering, underwater pipelines, etc.) exploration, sunken object salvage, underwater archaeology, malicious throwing monitoring of solid waste, underwater explosive detection and identification, security prevention of bases and ships, underwater operation monitoring, and terrain matching navigation. The use of multiple sub-arrays has further promoted the engineering application of SAS technology but has also made signal processing more complex. The range history of synthetic aperture sonar has a complex double square root (DSR) form, which makes it difficult to find the analytical solution of the stationary phase point (PSP). Therefore, it is difficult to obtain the analytical expression of the point target reference spectrum (PTRS) in the two-dimensional frequency domain through the stationary phase principle. Since the imaging algorithms based on the fast Fourier transform are all based on PTRS, the single-station processing algorithm cannot be directly applied. To solve this problem, approximate methods are usually adopted. So far, for multi-receiver SAS systems, there are usually two main methods to obtain the two-dimensional spectrum. The first method is to numerically solve the two-dimensional spectrum of each receiver separately. Although this method can obtain accurate images in the case of wide beams, it requires multiple iterations to solve the stationary phase point (PSP) of each receiver separately, and the computational efficiency is relatively low compared with other analysis methods. The second method is to use the Displaced Phase Center Aperture (DPCA) technique to process the multi-receiver SAS data into single-base SAS equivalent data, and then directly use the single-base SAS imaging algorithm. Using DPCA, the DSR range history can be converted into the sum of a single square root (SSR) range history and an error term. These methods usually involve complex links such as interpolation and spatially varying phase correction, which can lead to edge blurring, especially in the case of wide beams. Summary of the Invention

[0003] The purpose of this application is to overcome the defects of low technical efficiency and edge blurring in the prior art.

[0004] To achieve the above purpose, this application proposes a multi-receiver array synthetic aperture sonar imaging method. The multi-receiver array synthetic aperture sonar has the receiving array in front and the transmitting array behind along the movement direction of the sonar. The method includes:

[0005] Step 1: Approximate the two-way time, represent the two-way distance in the form of a double square root as a cosine form, and perform a fourth-order Taylor expansion on the slant range history;

[0006] Step 2: Perform a range Fourier transform on the baseband signal to obtain a range-frequency - azimuth-time domain signal, and then perform an azimuth Fourier transform to place the range-frequency - azimuth-time domain signal in the two-dimensional spectrum and obtain the integrand;

[0007] Step 3: Based on the Taylor expansion of the slant range history and the approximate time in Step 1, apply the Lagrange inversion theorem and the stationary phase principle to obtain the exact two-dimensional spectrum;

[0008] Step 4: Expand the exact two-dimensional spectrum into a series expansion form of azimuth frequency and range frequency, and at the same time obtain the azimuth and range matched filtering functions;

[0009] Step 5: Based on the azimuth and range matched filtering functions, perform azimuth and range matched filtering processing on the two-dimensional frequency domain signal to obtain a synthetic aperture sonar simulation image focused in the azimuth and range directions.

[0010] As an improvement of the above method, the approximation processing of the two-way time is as follows:

[0011] Approximate as where c represents the sound speed, η represents the azimuth slow time; v represents the motion speed of the sonar; d i represents the distance between the transmitting array and the i-th receiving array; r represents the distance from the ideal point target to the center of the sub-array.

[0012] As an improvement of the above method, the cosine form is:

[0013]

[0014] where the intermediate variable R Tcen = r, the intermediate variable sinθ T = 0, the intermediate variable and the intermediate variable R T represents the signal outgoing distance from the transmitting array to the ideal point target; R R represents the signal return distance from the point target to the i-th receiving array element.

[0015] As an improvement of the above method, the fourth-order Taylor expansion of the slant range history includes:

[0016] The fourth-order Taylor expansion formula is:

[0017]

[0018] Among them, represents the fourth-order Taylor expansion of the slant range history; E5(η) represents the fourth-order Taylor expansion error.

[0019] As an improvement to the above method, the baseband signal s(τ, η; r) is:

[0020]

[0021] Among them, A is a constant term; λ is the wavelength corresponding to the center frequency; w a (·) and w r (·) are the azimuth envelope and range envelope respectively; η represents the azimuth slow time; r represents the distance from the ideal point target to the center of the subarray; τ represents the range fast time; R(η; r) represents the slant range history; j represents the imaginary unit.

[0022] As an improvement to the above method, the expansion of the accurate two-dimensional spectrum into the form of azimuth frequency and range frequency series expansions includes:

[0023]

[0024] Among them, θ(f τ , f η ) represents the range frequency domain - azimuth time domain signal; f τ is the range frequency; f η is the azimuth frequency; W1 = 0; W2 = 2πc / [4K2(f c + f τ )]; W3 = 2πK3c 2 / [8(K2) 3 (f c + f τ ) 2 ; W4 = 2πc 3 (9(K3) 2 - 4K2K4) / [64(K2) 5 (f c + f τ ) 3 ; n = 1, 2, 3, 4.

[0025] As an improvement to the above method, step 3 includes:

[0026] Construct the cubic phase compensation function cubic(f τ,η ; r):

[0027]

[0028] Among them, r ref is the reference distance; Ym(f η ) is the error after cubic phase compensation;

[0029] Phase compensation is performed by multiplying a cubic compensation function in the two-dimensional frequency domain:

[0030] SS(f τ ,f η ; r) = W r (f τ )W a (f η ) × exp[jθ(f τ ,f η )] · H cubic (f τ ,f η ; r)

[0031] where SS(f τ ,f η ; r) represents the phase compensation result;

[0032] Perform a range Fourier transform on SS(f τ ,f η ; r), and then perform a non-linear CS scaling transformation:

[0033]

[0034] where sS cs (τ,f η ; r) is the result of first performing an inverse range Fourier transform on SS(f τ ,f η ; r), and then performing a non-linear CS scaling transformation; represents the inverse range Fourier transform; q2 = Km(f η ,r ref ) × (α - 1), α = γ(f η ,r) / γ(f ηc ,r), γ(f η ,r) = 2 / K γ (f η ,r), f ηc is the Doppler center frequency, Km(f η ,r ref ) represents the changed range modulation frequency, R rd (f η ,r) represents the round-trip distance in the RD domain;

[0035]

[0036] Perform on sS cs (τ,fη ; r) Perform range Fourier transform, and then use the matched filter H r (f η , f τ ; r ref ) to perform range matched filtering:

[0037] SS rd (f η , f τ ; r) = FFT r [sS cs (τ, f η ; r)] × H r (f η , f τ ; r ref )

[0038]

[0039] where SS rd (f η , f τ ; r) represents the result of performing range Fourier transform and range matched filtering on sS cs (τ, f η ; r); FFT r [·] represents range Fourier transform; γ is the abbreviation of γ(f η , r);

[0040] Perform inverse range Fourier transform on SS rd (f η , f τ ; r), and then use the matched filter H a (f η ; r) to perform azimuth matched filtering, and finally complete azimuth matched filtering by multiplying with the additional phase compensation function H e (f η ; r):

[0041]

[0042] where sS rd2 (τ, f η ; r) represents the result of completing azimuth matched filtering on SS rd (f η , f τ ; r); Δτ = 2(r - r ref ) / (cγ(f η , r));

[0043] Finally, for sS rd2(τ, f η ; r) performs azimuth inverse Fourier transform to obtain the synthetic aperture sonar simulation image ss(τ, η; r) that is focused in both azimuth and range directions:

[0044]

[0045] This application also provides a multi-receiver array synthetic aperture sonar imaging system, which is implemented based on the above method. The system includes:

[0046] A fourth-order Taylor expansion module, which is used to approximately process the two-way time, represent the two-way distance in the form of a double square root as a cosine form, and perform a fourth-order Taylor expansion on the slant range history;

[0047] An integrand acquisition module, which is used to perform range Fourier transform on the baseband signal to obtain a range frequency-domain - azimuth time-domain signal, and then perform azimuth Fourier transform to make the range frequency-domain - azimuth time-domain signal in a two-dimensional spectrum and obtain the integrand;

[0048] An accurate two-dimensional spectrum acquisition module, which is used to obtain an accurate two-dimensional spectrum based on the Taylor expansion formula of the slant range history and the approximate time, applying the Lagrange inversion theorem and the stationary phase principle;

[0049] An azimuth and range matched filtering function acquisition module, which is used to expand the accurate two-dimensional spectrum into a series expansion form of azimuth frequency and range frequency, and simultaneously obtain the azimuth and range matched filtering functions;

[0050] A simulation image acquisition module, which is used to perform azimuth and range matched filtering processing on the two-dimensional frequency-domain signal based on the azimuth and range matched filtering functions to obtain the synthetic aperture sonar simulation image that is focused in both azimuth and range directions.

[0051] Compared with the prior art, the advantages of this application are:

[0052] 1. The imaging calculation efficiency of the method in this application is high;

[0053] 2. The method in this application has good imaging accuracy and quality at different ranges;

[0054] 3. Under the parameters of a wide-beam SAS system, the method in this application can meet the requirements of high-resolution imaging in the full scan band. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Shown is the flow chart of the multi-receiver array synthetic aperture sonar imaging method;

[0056] Figure 2 Shown is the imaging geometry diagram of the multi-receiver array SAS;

[0057] Figure 3The figure shows a schematic diagram of phase error; among which, phase error: phase error; range: range; azimuth: azimuth angle;

[0058] Figure 4 The figure shows a schematic diagram of range error;

[0059] Figure 5 The figure shows a schematic diagram of the imaging result of a near-range point target;

[0060] Figure 6 The figure shows a schematic diagram of the imaging result of a medium-range point target;

[0061] Figure 7 The figure shows a schematic diagram of the imaging of a far-range point target. Detailed implementation manners

[0062] The technical solution of the present application will be described in detail below with reference to the accompanying drawings.

[0063] Most of the traditional SAS imaging algorithms are applicable under narrowband conditions. Under wide-beam conditions, the imaging quality will decline, resulting in great limitations on SAS imaging and signal processing. The multi-receiver array synthetic aperture sonar imaging method and system provided by the present application first processes the two-way time, then performs a fourth-order Taylor expansion through the two-way distance in the form of cosine, and then applies the Lagrange inversion theorem to obtain an accurate two-dimensional spectrum, and expands it into a series expansion form of azimuth frequency and range frequency. Through range and azimuth matching filtering processing, a high-quality SAS simulation image with azimuth and range focusing is obtained. The specific processing flow is as Figure 1 shown.

[0064] The multi-receiver array SAS imaging geometry is as Figure 2 shown, where the vertical axis is the azimuth dimension, which is also the movement direction of the platform; the horizontal axis is the range dimension. Relative to the movement direction of the platform, the receiving array is in front and the transmitting array is behind; and c is defined as the sound speed in water. The sonar moves at a constant linear speed v in the azimuth direction and emits a linear frequency modulation signal independent of the platform position towards the broadside direction at the same time. Its complex envelope is:

[0065]

[0066] Among which, rect(·) represents the rectangular pulse function, τ is the fast time in the range direction; T p is the pulse signal width; K r is the signal frequency modulation slope. Assume that there is an ideal point target with coordinates (r,0) in the imaging scene. During the two-way propagation time τ * from the signal transmission to the i-th receiving array element receiving the echo, the platform moves forward by vτ *The distance. Considering the influence of this "stop-go-stop" approximation, the slant range history of the bistatic SAS subsystem composed of the transmitting array and the receiving array element spaced d from it is as follows: i where c represents the speed of sound and η represents the slow time in the azimuth direction; R

[0067]

[0068] T represents the signal round-trip distance from the transmitting array to the ideal point target, and R R represents the signal return distance from the point target to the i-th receiving array element considering the "stop-go-stop" approximation. The baseband signal after quadrature demodulation is:

[0069]

[0070] where λ is the wavelength corresponding to the center frequency f c ; w a (·) and w r (·) are the azimuth and range envelopes respectively, and A is a constant term.

[0071] The two-way slant range history shown in Equation (3) all includes a form with a double square root. If this double square root slant range history is directly used for processing in the fast imaging algorithm, then when applying the phase stationary principle for azimuth Fourier transform, it will face the problem of solving a one-variable octic equation about the azimuth slow time, thus resulting in a very complex process of solving the phase stationary point and the two-dimensional frequency domain analytical expression. Therefore, it is necessary to make a certain approximation to this double square root slant range history. Considering the complexity of τ * , use to approximate τ * . And perform a Taylor polynomial expansion of Equation (3) at η = 0. The fourth-order Taylor expansion is as follows:

[0072]

[0073] where E5(η) represents the fourth-order Taylor expansion error. Combining Equation (3) and Equation (5), K i can be obtained through Equation (6):

[0074]

[0075] For the convenience of differentiation, express R R (η) and R T (η) in the form of cosine formulas, as shown in Equation (8) and Equation (7):

[0076]

[0077] Among them, R Tcen = r, sinθ T = 0, and

[0078]

[0079] Taking the fourth-order derivative of R in Equation (7) T yields:

[0080]

[0081] Similarly, the fourth-order derivative of R R (η) can be obtained:

[0082]

[0083] Therefore, it can be obtained:

[0084]

[0085] The two-dimensional frequency domain is obtained by the Lagrange inversion theorem. By the stationary phase principle, first perform the range Fourier transform on the baseband signal shown in Equation (4) to obtain the range frequency - azimuth time domain signal, and then perform the azimuth Fourier transform to obtain the two-dimensional spectrum, and the integrand of the two-dimensional spectrum can be obtained.

[0086]

[0087] Among them, f τ is the range frequency, f η is the azimuth frequency. Let the derivative of the integral phase be 0 to obtain the stationary point:

[0088]

[0089] According to Equation (14), it can be known that f η is a function of η. According to the Lagrange inversion theorem, the inverse function η(f η ) of f can be obtained: η )

[0090]

[0091] According to Equations (5) and (11), it can be obtained:

[0092]

[0093] Therefore, it can be obtained:

[0094]

[0095] Substituting Equations (15), (16), and (17) into the phase in Equation (12) gives:

[0096]

[0097] Among them, W1 = 0, W2 = 2πc / [4K2(f c +f τ )], W3 = 2πK3c 2 / [8(K2) 3 (f c +f τ ) 2 , W4 = 2πc 3 (9(K3) 2 -4K2K4) / [64(K2) 5 (f c +f τ ) 3 . Expand Equation (18)

[0098] into the Taylor expansion of f η . In order to apply it under the wide beam condition, retain up to the cubic term:

[0099]

[0100] Among them, Some important parameters and phases required for algorithmic imaging can be obtained from Equation (20), where θ(0, f η ) is the azimuth modulation term, θ′(0, f η ) is the range migration term, is the range frequency modulation term, is the second-order range compression term, is the third-order coupling term of range and azimuth. The range modulation frequency Kr will be changed by the coupling of range and azimuth in the received signal. The changed range modulation frequency Km varies with range. The changed range modulation frequency Km and the exact two-way range equation R rd in the RD domain can be obtained from Equations (21) and (22). Through the two-dimensional spectrum, we can obtain the phase function and important parameters required for imaging. We can obtain the complete SAS image as long as we perform two-dimensional space-variant matched filtering.

[0101]

[0102] Based on the phase function shown in Equation (19), perform two-dimensional phase compensation on the two-dimensional frequency domain signal. First, construct a cubic phase compensation function:

[0103]

[0104] Among them, r ref is the reference range, generally the center of the mapping bandwidth. Ym(f η ) is the error after cubic phase compensation. Phase compensation is performed by multiplying a cubic compensation function in the two-dimensional frequency domain.

[0105] SS(f τ ,f η ; r) = W r (f τ )W a (f η ) × exp[jθ(f τ ,f η )] · H cubic (f τ ,f η ; r) (24)

[0106] where W r and W a are the azimuth and range frequency domain envelopes respectively. Perform an inverse Fourier transform in the range direction on SS(f τ ,f η ; r) to make it in the range-Doppler domain. Then perform a non-linear CS scaling transformation:

[0107]

[0108] H cs (τ, f τ ) = exp[-jπq2(τ - τ ref ) 2 -j2πq3(τ - τ ref ) 3 / 3] (26)

[0109] Let then q2 = Km(f η , r ref ) × (α - 1),

[0110] α = γ(f η , r) / γ(f ηc , r), γ(f η , r) = 2 / K γ (f η , r), where f ηc

[0111] is the Doppler center frequency. Then perform a Fourier transform in the range direction on sS cs (τ, f η ; r) to make the signal in the two-dimensional frequency domain, and then perform range-direction matched filtering. The matched filter is H r (f η , fτ ; r ref )。

[0112]

[0113] SS rd (f η , f τ ; r) = FFT r [sS cs (τ, f η ; r)] × H r (f η , f τ ; r ref ) (28)

[0114] Next, perform a range inverse Fourier transform on SS rd (f η , f τ ; r) to place the signal in the range-Doppler domain, then perform azimuth matched filtering. The matched filter is H a (f η ; r), and finally complete the azimuth matched filtering by multiplying with the additional phase compensation function H e (f η ; r).

[0115]

[0116] Among them, Δτ = 2(r - r ref ) / (cγ(f η , r)), and finally perform an azimuth inverse Fourier transform on sS rd2 (τ, f η ; r) to obtain the SAS image focused in both the azimuth and range directions.

[0117]

[0118] To verify the effectiveness and accuracy of the method of this application, we conducted a multi-point target simulation experiment. Point targets were set at close range, medium range, and long range respectively. The close-range targets were mainly distributed around 50 m, the medium-range target points were mainly distributed near 150 m; the long-range targets were mainly distributed near 250 m. The simulation parameters are shown in Table 1. Figure 5 is the imaging result of the close-range point target, Figure 6 is the imaging result of the medium-range point target, Figure 7This is the imaging result of a long-distance point target. The pulse response widths (IRW), peak sidelobe ratios (PSLR), and integrated sidelobe ratios (ISLR) of the range slices and azimuth slices of these three point targets were measured. The results are shown in Table 2. It can be seen that the PSLR and ISLR in both the azimuth and range directions are less than -10 dB, and the IRW is less than 0.5 m, indicating that the proposed algorithm has good imaging accuracy and quality at different ranges. Figure 3 The phase error at r = rc is shown. It is not difficult to find that the maximum value of the phase error is 0.0146 (rad), which is less than π / 4. Therefore, under the parameters of the wide-beam SAS system, the method proposed in this paper can achieve accurate focusing in both the azimuth and range directions, meeting the requirements of high-resolution imaging in the full scan band. Figure 4 The range error using the fourth-order Taylor expansion is shown. It can be seen that the range error is less than 0.2λ.

[0119] Table 1 System Parameters

[0120]

[0121] Table 2 Measurement of Imaging Quality Parameters

[0122]

[0123]

[0124] This application also provides a multi-receiver array synthetic aperture sonar imaging system implemented based on the above method. The system includes:

[0125] A fourth-order Taylor expansion module for approximately processing the two-way time, representing the two-way distance in the form of a double square root as a cosine form, and performing a fourth-order Taylor expansion on the slant range history;

[0126] An integrand acquisition module for performing a range Fourier transform on the baseband signal to obtain a range frequency-domain - azimuth time-domain signal, and then performing an azimuth Fourier transform to place the range frequency-domain - azimuth time-domain signal in a two-dimensional spectrum and obtain the integrand;

[0127] An accurate two-dimensional spectrum acquisition module for obtaining an accurate two-dimensional spectrum based on the Taylor expansion formula of the slant range history and the approximate time, applying the Lagrange inversion theorem and the stationary phase principle;

[0128] An azimuth and range matched filtering function acquisition module for expanding the accurate two-dimensional spectrum into a series expansion form of azimuth frequency and range frequency, and simultaneously obtaining the azimuth and range matched filtering functions;

[0129] A simulation image acquisition module is configured to perform azimuth and range matched filtering on the two-dimensional frequency domain signal based on the azimuth and range matched filtering functions, so as to obtain a synthetic aperture sonar simulation image with azimuth and range focusing.

[0130] The present application may also provide a computer device, including: at least one processor, a memory, at least one network interface, and a user interface. Each component in the device is coupled together through a bus system. It can be understood that the bus system is used to realize the connection and communication between these components. In addition to the data bus, the bus system further includes a power bus, a control bus, and a status signal bus.

[0131] Among them, the user interface may include a display, a keyboard, or a pointing device. For example, a mouse, a trackball, a touchpad, or a touch screen, etc.

[0132] It can be understood that the memory in the disclosed embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchlink dynamic random access memory (SLDRAM), and direct rambus random access memory (DRRAM). The memory described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0133] In some embodiments, the memory stores the following elements, executable modules, or data structures, or subsets thereof, or extended sets thereof: an operating system and an application program.

[0134] Among them, the operating system includes various system programs, such as the framework layer, the core library layer, the driver layer, etc., which are used to implement various basic services and handle hardware-based tasks. The application programs include various application programs, such as Media Player, Browser, etc., which are used to implement various application services. The program for implementing the method of the embodiments of the present disclosure may be included in the application programs.

[0135] In the above embodiments, the program or instruction stored in the memory may also be called. Specifically, it may be the program or instruction stored in the application program. The processor is used for:

[0136] Executing the steps of the above method.

[0137] The above method may be applied to the processor or implemented by the processor. The processor may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method may be completed by the integrated logic circuit in the hardware of the processor or the instruction in the form of software. The above processor may be a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps and logic block diagrams disclosed above. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. Combining the steps of the above disclosed method may be directly embodied as being executed and completed by the hardware decoding processor, or executed and completed by the combination of the hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0138] It can be understood that these embodiments described in the present application can be implemented by hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more Application Specific Integrated Circuits (ASICs), Digital Signal Processors (DSPs), DSP Devices (DSPDs), Programmable Logic Devices (PLDs), Field-Programmable Gate Arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in the present application, or a combination thereof.

[0139] For software implementation, the technology of the present application can be implemented by executing the functional modules of the present application (such as procedures, functions, etc.). The software code can be stored in a memory and executed by a processor. The memory can be implemented inside or outside the processor.

[0140] The present application can also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, the various steps in the above method embodiments can be implemented.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit them. Although the present application has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present application does not depart from the spirit and scope of the technical solutions of the present application, and they should all be covered by the scope of the claims of the present application.

Claims

1. A multi-receiving array synthetic aperture sonar imaging method, wherein the multi-receiving array synthetic aperture sonar is along the movement direction of the sonar, with the receiving array in front and the transmitting array in the back; the method comprises: Step 1: Approximate the two-way time, express the two-way distance in double root form into cosine form, and perform a fourth-order Taylor expansion on the slant distance history; Step 2: Perform a range Fourier transform on the baseband signal to obtain a range frequency domain-azimuth time domain signal, and then perform a azimuth Fourier transform to make the range frequency domain-azimuth time domain signal in a two-dimensional spectrum and obtain the integrand; Step 3: Based on the Taylor expansion of the slant range history and the approximate time in step 1, the Lagrange inversion theorem and the stationary phase principle are applied to obtain the accurate two-dimensional spectrum; Step 4: Expand the precise two-dimensional spectrum into the azimuth frequency and the distance frequency series expansion form, and obtain the azimuth and distance matched filter functions at the same time; Step 5: Based on the azimuth and range matched filter functions, the two-dimensional frequency domain signal is processed in the azimuth and range matched filters to obtain a synthetic aperture sonar simulation image focused in the azimuth and range directions.

2. The multi-receiving array synthetic aperture sonar imaging method according to claim 1, characterized in that: The round trip time is approximated as follows: Seems to be Where c represents the speed of sound, η represents the azimuth slow time, v represents the speed of the sonar, d i represents the distance between the transmitting array and the i-th receiving array; r represents the distance from the ideal point target to the center of the subarray.

3. The multi-receiving array synthetic aperture sonar imaging method according to claim 2, characterized in that: The cosine form is: Among them, the intermediate variable R Tcen = r, intermediate variable sinθ T =0, intermediate variable and intermediate variables R T Represents the signal travel distance from the transmitting array to the ideal point target; R R Represents the signal return distance from the point target to the i-th receiving array element.

4. The multi-receiving array synthetic aperture sonar imaging method according to claim 2, characterized in that: The fourth-order Taylor expansion of the slant range history comprises: The fourth-order Taylor expansion is: in, represents the fourth-order Taylor expansion of the slant range history; E5(η) represents the fourth-order Taylor expansion error.

5. The multi-receiving array synthetic aperture sonar imaging method according to claim 3, characterized in that: The baseband signal s(τ,η;r) is: Among them, A is a constant term; λ is the wavelength corresponding to the center frequency; w a (·) and w r (·) are the azimuth and range envelopes respectively; η represents the azimuth slow time; r represents the distance from the ideal point target to the center of the subarray; τ represents the range fast time; R(η; r) represents the slant range history; j represents the complex unit.

6. The multi-receiving array synthetic aperture sonar imaging method according to claim 5, characterized in that: The step of expanding the precise two-dimensional spectrum into a frequency series expansion form in the azimuth direction and the distance direction includes: θ″′(0,f η )=[W1″′A 2 +W2″′A 3 +W3″′A 4 ]+3[2W1″BA+3BA 2 W2″+4BA 3 W3″]+6[B 2 W1′+3B 2 AW2′+6B 2 A 2 W3′]+6[B 3 W2+4B 3 AW3] Among them, θ(f τ ,f η ) represents the distance frequency domain-azimuth time domain signal; f τ is the distance frequency; f η is the azimuth frequency; W1 = 0; W2 = 2πc / [4K2(f c +f τ )]; W3 = 2πK3c 2 / [8(K2) 3 (f c +f τ ) 2 ]; W4 = 2πc 3 (9(K3) 2 -4K2K4) / [64(K2) 5 (f c +f τ ) 3 ]; n=1,2,3,4.

7. The multi-receiving array synthetic aperture sonar imaging method according to claim 6, characterized in that: The step 3 comprises: Constructing a cubic phase compensation function cubic (f τ,η ; r): Among them, r ref is the reference distance; Ym(f η ) is the error after three-time phase compensation; Phase compensation is performed in the two-dimensional frequency domain by multiplying by a cubic compensation function: SS(f τ ,f η ;r)=W r (f τ )W a (f η )×exp[jθ(f τ ,f η )]·H cubic (f τ ,f η ;r) Among them, SS(f τ ,f η ; r) represents the phase compensation result; For SS(f τ ,f η ; r) Perform distance Fourier transform and then perform nonlinear CS scale transform: Among them, sS cs (τ,f η ; r) is the first SS (f τ ,f η ; r) Perform distance inverse Fourier transform, and then perform nonlinear CS scale transform on the result; IFFT fτ [·] represents the inverse Fourier transform of distance; q2 = Km (f η ,r ref )×(α-1), α=γ(f η ,r) / γ(f ηc ,r),γ(f η ,r)=2 / K γ (f η ,r), f ηc is the Doppler center frequency, Km(f η ,r ref ) represents the changed range modulation frequency, R rd (f η ,r) represents the two-way distance on the RD domain; For sS cs (τ,f η ; r) Perform distance Fourier transform, and then use matched filter to H r (f η ,f τ ; r ref ) to perform distance matching filtering: SS rd (f η ,f τ ;r)=FFT r [sS cs (τ,f η ;r)]×H r (f η ,f τ ;r ref ) Among them, SS rd (f η ,f τ ; r) indicates sS cs (τ,f η ; r) the result of performing distance Fourier transform and distance matched filtering; FFT r [·] represents the distance to Fourier transform; γ is γ(f η ,r) abbreviation; To SS rd (f η ,f τ ; r) perform inverse Fourier transform to the distance, and then use the matched filter H a (f η ; r) perform azimuth matched filtering, and finally multiply by the additional phase compensation function H e (f η ; r) Complete azimuth matched filtering: sS rd2 (τ,f η ;r)=IFFT fτ [SS rd (f η ,f τ ;r)]×H a (f η ;r)×H e (f η ;r) Among them, sS rd2 (τ,f η ; r) indicates SS rd (f η ,f τ ; r) completing the result of azimuth matched filtering; Δτ=2(rr ref ) / (cγ(f η ,r)); Finally, for sS rd2 (τ,f η ; r) perform inverse Fourier transform in azimuth to obtain the synthetic aperture sonar simulation image ss(τ,η; r) focused in azimuth and range:

8. A multi-receiving array synthetic aperture sonar imaging system, implemented based on the method according to any one of claims 1 to 7, characterized in that: The system comprises: The fourth-order Taylor expansion module is used to approximate the two-way time, express the two-way distance in double root form into cosine form, and perform the fourth-order Taylor expansion on the slant distance history; An integrand obtaining module is used to perform a range Fourier transform on the baseband signal to obtain a range frequency domain-azimuth time domain signal, and then perform a range Fourier transform on the azimuth to make the range frequency domain-azimuth time domain signal in a two-dimensional spectrum, and obtain an integrand; Obtaining accurate two-dimensional spectrum module, used to obtain accurate two-dimensional spectrum based on slant range history Taylor expansion and approximate time, applying Lagrange inversion theorem and stationary phase principle; A module for obtaining azimuth and range matched filter functions is used to expand the precise two-dimensional spectrum into azimuth frequency and range frequency series expansion forms, and simultaneously obtain azimuth and range matched filter functions; and The simulation image acquisition module is used to perform matched filtering processing on the two-dimensional frequency domain signal in azimuth and range directions based on the azimuth and range matched filtering functions to obtain a synthetic aperture sonar simulation image focused in azimuth and range directions.

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