A method and system for multi-receiver synthetic aperture sonar imaging

Abstract

The application provides a multi-receiving array synthetic aperture sonar imaging method and system, the multi-receiving array synthetic aperture sonar is along the movement direction of the sonar, the receiving array is in front, and the transmitting array is in back; the method comprises the following steps: approximating the two-way time, and performing four-order Taylor expansion on the slant range history; performing distance and azimuth Fourier transform on the baseband signal to make it in two-dimensional frequency domain, then applying Lagrange inversion theorem and stationary phase principle to obtain accurate two-dimensional spectrum, and expanding it into azimuth and distance frequency series expansion form, and simultaneously obtaining azimuth and distance matching filter functions; based on the accurate two-dimensional spectrum, performing distance and azimuth matching filter processing on the two-dimensional frequency domain signal to obtain the synthetic aperture sonar simulation image with azimuth and distance focusing. The application has the advantages that: the imaging calculation efficiency is high, the imaging precision and quality are good at different distances; and the requirement of full scanning with high resolution imaging can be met.

Description

Technical Field

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

[0002] Synthetic Aperture Sonar (SAS) improves azimuth resolution and mapping efficiency by virtually synthesizing a large-aperture array through the uniform linear motion of individual small primitives. This has led to its significant role in both civilian and military applications, including seabed mineral resource development, topographic surveying and engineering quantity assessment, underwater engineering (bank protection, underwater pipelines, etc.) exploration, sunken object salvage, underwater archaeology, monitoring of malicious solid waste dumping, underwater explosive detection and identification, base and ship security, underwater operation monitoring, and terrain-matching navigation. The use of multiple subarrays has further promoted the engineering applications of SAS technology, but it has also increased the complexity of signal processing. The range history of synthetic aperture sonar has a complex double square root (DSR) form, making it difficult to find an analytical solution for the stationary phase point (PSP). Therefore, it is difficult to obtain an analytical expression for the point target reference spectrum (PTRS) in the two-dimensional frequency domain using the stationary phase principle. Since fast Fourier imaging algorithms are based on PTRS, single-station processing algorithms cannot be directly applied. Approximate methods are typically used to address this problem. To date, there are generally two main methods for acquiring two-dimensional spectra for multi-receiver SAS systems. The first method is to numerically solve the two-dimensional spectrum for each receiver separately. While this method can yield accurate images in wide-beam situations, it requires multiple iterations to solve for the stationary phase point (PSP) of each receiver, making it computationally inefficient compared to other analysis methods. The second method utilizes the Displaced Phase Center Aperture (DPCA) technique to process the multi-receiver SAS data into equivalent monostatic SAS data, and then directly applies the monostatic SAS imaging algorithm. DPCA converts the DSR range history into a sum of the single square root (SSR) range history and error terms. These methods typically involve complex steps such as interpolation and spatially variable phase correction, which can lead to edge blurring, especially in wide-beam situations. Summary of the Invention

[0003] The purpose of this application is to overcome the shortcomings of existing technologies, such as low technical efficiency and blurred edges.

[0004] To achieve the above objectives, this application proposes a multi-receiver array synthetic aperture sonar imaging method, wherein the multi-receiver array synthetic aperture sonar is configured such that, along the direction of motion of the sonar, the receiving array is in front and the transmitting array is behind; the method includes:

[0005] Step 1: Approximate the two-way time by expressing the two-way distance in the form of double square roots as a cosine form and performing a fourth-order Taylor expansion on the slant distance history.

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

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

[0008] Step 4: Expand the precise two-dimensional spectrum into azimuth and range frequency series expansions, and obtain the azimuth and range matched filter functions simultaneously;

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

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

[0011] Will Approximately Where c represents the speed of sound, η represents the azimuth time dilation, v represents the velocity of the sonar, and d represents the velocity of the sonar. 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.

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

[0013]

[0014] Among them, the intermediate variable R Tcen =r, intermediate variable sinθ T =0, intermediate variable and intermediate variables R T R represents the signal path distance from the transmitting array to the ideal point target; R This represents the signal backhaul distance from the point target to the i-th receiving array element.

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

[0016] The fourth-order Taylor expansion is:

[0017]

[0018] in, E5(η) 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] Where A is a constant term; λ is the wavelength corresponding to the center frequency; w a (·) and w r (·) represents 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.

[0022] As an improvement to the above method, the step of expanding the precise two-dimensional spectrum into a series expansion of azimuth and range frequencies includes:

[0023]

[0024] Where, θ(f) τ ,f η ) represents the range-frequency domain-azimuth time domain signal; f τ For range-direction frequency; f η 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 a cubic phase compensation function cubic(f) τ,η ;r):

[0027]

[0028] Where, r ref For reference distance; Ym(f η The error is the result of three phase compensations.

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

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

[0032] For SS(f) τ ,f η ;r) Perform a distance-to-Fourier transform, followed by a nonlinear CS scaling transform:

[0033]

[0034] Among them, sS cs (τ,f η ;r) is for first SS(f) τ ,f η The result of performing a distance-to-inverse Fourier transform and then a nonlinear CS scaling transform; This represents the inverse Fourier transform of the 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 Km(f) is the center frequency of the Doppler wave. η ,r ref R represents the changed range-modulated frequency. rd (f η ,r) represents the two-way distance over the RD domain;

[0035]

[0036] For sS cs (τ,fη Perform a distance-to-Fourier transform on r), then use a matched filter H. r (f η ,f τ ;r ref Perform range-directed 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] Among them, SS rd (f η ,f τ ;r) indicates that for sS cs (τ,f η ;r) The result of performing range-directed Fourier transform and range-directed matched filtering; FFT r [·] indicates the distance-to-Fourier transform; γ is γ(f η abbreviation of ,r);

[0040] For SS rd (f η ,f τ Perform a distance-to-inverse Fourier transform on r), then use a matched filter H a (f η ;r) Perform azimuth matched filtering, and finally multiply by an additional phase compensation function H e (f η ;r) Complete azimuth matched filtering:

[0041]

[0042] Among them, sS rd2 (τ,f η ;r) indicates that SS rd (f η ,f τ ;r) The result of azimuth matched filtering; Δτ=2(rr ref ) / (cγ(f η ,r));

[0043] Finally, regarding sS rd2(τ,f η Perform an inverse Fourier transform in the azimuth direction to obtain a synthetic aperture sonar simulation image ss(τ,η;r) focused in the azimuth and range directions:

[0044]

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

[0046] The fourth-order Taylor expansion module is used to approximate the two-way time, representing the two-way distance in the form of double square roots as a cosine form, and performing a fourth-order Taylor expansion on the slant distance history.

[0047] The module for obtaining the integrand is used to perform range-to-Fourier transform on the baseband signal to obtain the range-frequency domain-azimuth-time domain signal. Then, the azimuth-to-Fourier transform makes the range-frequency domain-azimuth-time domain signal in a two-dimensional spectrum and obtains the integrand.

[0048] A module for obtaining accurate two-dimensional spectrum is used to obtain accurate two-dimensional spectrum based on the Taylor expansion of slant range history and approximate time, applying the Lagrange inversion theorem and the principle of stationary phase.

[0049] The module for obtaining azimuth and range matched filter functions is used to expand the precise two-dimensional spectrum into azimuth and range frequency series expansions, and simultaneously obtain the azimuth and range matched filter functions.

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

[0051] Compared with existing technologies, the advantages of this application are:

[0052] 1. The method described in this application has high imaging computational efficiency;

[0053] 2. The method described in this application exhibits good imaging accuracy and quality at various distances;

[0054] 3. Under the parameters of a wide-beam SAS system, the method of this application can meet the requirements of high-resolution imaging across the entire scan band. Attached Figure Description

[0055] Figure 1 The diagram shows the flowchart of the multi-receiver array synthetic aperture sonar imaging method.

[0056] Figure 2 The image shown is a geometry of the multi-receiver array (SAS) imaging system.

[0057] Figure 3The diagram shown illustrates the phase error; where phase error refers to the phase error itself; range refers to the range of values; and azimuth refers to the azimuth angle.

[0058] Figure 4 The diagram shown is a schematic of the distance error.

[0059] Figure 5 The image shown is a schematic diagram of the imaging results of a point target at close range;

[0060] Figure 6 The image shown is a schematic diagram of the imaging results of a target at an intermediate distance.

[0061] Figure 7 The image shown is a schematic diagram of a distant point target imaging. Detailed Implementation

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

[0063] Traditional SAS imaging algorithms are mostly suitable for narrowband conditions, and image quality degrades under wide-beam conditions, thus greatly limiting SAS imaging and signal processing. The multi-receiver array synthetic aperture sonar imaging method and system provided in this application first processes the two-way time, then performs a fourth-order Taylor expansion using the cosine form of the two-way distance, and then applies the Lagrange inversion theorem to obtain the accurate two-dimensional spectrum, which is then expanded into azimuth and range frequency series expansions. Through range and azimuth matched filtering, high-quality SAS simulation images with azimuth and range focusing are obtained. The specific processing flow is as follows: Figure 1 As shown.

[0064] Multi-receiver array SAS imaging geometry Figure 2 As shown, the vertical axis represents the azimuth dimension, which is also the platform's direction of motion; the horizontal axis represents the range dimension. Relative to the platform's direction of motion, the receiving array is in front, and the transmitting array is behind; and c is defined as the underwater acoustic speed. The sonar moves at a constant velocity v in one direction in the azimuth direction, and emits a linear frequency modulated signal independent of the platform's position in the other direction of the forward-looking direction. Its complex envelope is:

[0065]

[0066] Where rect(·) represents the rectangular pulse function, τ is the range fast time; T p K is the pulse signal width. r Let τ be the frequency modulation slope of the signal. Assume there exists an ideal point target with coordinates (r, 0) in the imaging scene, and the two-way propagation time τ from signal transmission to the echo received by the i-th receiving element is... * Inside, the platform moved forward by vτ. *The distance. Considering the effect of this "stop-go-stop" approximation, the launch array and its distance d. i The slant range history of the bistatic SAS subsystem composed of the receiving array elements is as follows:

[0067]

[0068] Where c represents the speed of sound, η represents the azimuth time dilation; R T R represents the signal path distance from the transmitting array to the ideal point target. R This represents the signal backhaul distance from the point target to the i-th receiving array element, considering the "stop-go-stop" approximation. The baseband signal after orthogonal demodulation is:

[0069]

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

[0071] Equation (3) shows two-way slant range histories, all of which include a double square root form. If this double square root slant range histories are directly used in fast imaging algorithms, then when applying the phase dwell principle to perform azimuth Fourier transform, a problem of solving a univariate octet equation for a slow-time azimuth direction will arise. This makes the process of solving for the phase dwell point and the 2D frequency domain analytical expression very complex. Therefore, it is necessary to make certain approximations to this double square root slant range histories. Considering τ * The complexity, To approximate τ * And the Taylor polynomial expansion of equation (3) at η = 0 is shown below:

[0072]

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

[0074]

[0075] To facilitate differentiation, R R (η) and R T (η) can be expressed in the form of the cosine formula, as shown in equations (8) and (7):

[0076]

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

[0078]

[0079] For equation (7)R T Taking the fourth derivative of the given information, we get:

[0080]

[0081] Similarly, R of the same form can be obtained. R The fourth derivative of (η):

[0082]

[0083] Therefore, we can conclude that:

[0084]

[0085] The two-dimensional frequency domain is obtained by using the Lagrange inversion theorem. By applying the stationary phase principle, the baseband signal shown in equation (4) is first subjected to a range-to-Fourier transform to obtain the range-frequency domain-azimuth time domain signal. Then, the two-dimensional spectrum is obtained by using an azimuth-to-Fourier transform, thus obtaining the integrand of the two-dimensional spectrum.

[0086]

[0087] Among them, f τ For the range frequency, f η Given the azimuth frequency, the dwell point can be obtained by setting the derivative of the integral phase to zero:

[0088]

[0089] According to equation (14), f η It is a function of η, and according to the Lagrange inversion theorem, f can be obtained. η The inverse function η(f) η ):

[0090]

[0091] According to equations (5) and (11), we can obtain:

[0092]

[0093] Therefore, we can conclude that:

[0094]

[0095] Substituting equations (15), (16), and (17) into the phase in equation (12), we can obtain:

[0096]

[0097] in, 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 [Regarding equation (18)]

[0098] Expand into f η The Taylor expansion, to be applied under wide-beam conditions, retains the terms down to the cubic level:

[0099]

[0100] in, Equation (20) provides some important parameters and phase required for the algorithmic imaging, where θ(0,f) η ) represents the azimuth modulation term, θ′(0,f η ) represents the distance migration term. For distance frequency modulation, This is a quadratic distance compression term. This is a third-order coupling term for range and azimuth. The range-directed modulation frequency (MDC) Kr is altered by the range and azimuth coupling in the received signal. The altered MDC Km varies with the range. The altered MDC Km and the exact two-way range equation R in the RD domain... rd It 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 only need to perform two-dimensional spatially varied matched filtering to obtain the complete SAS image.

[0101]

[0102] Based on the phase function shown in equation (19), two-dimensional phase compensation is performed on the two-dimensional frequency domain signal. First, a cubic phase compensation function is constructed:

[0103]

[0104] Where, r ref This is a reference distance, typically the center of the survey bandwidth. Ym(f η The error is represented by 3x3 phase compensation. Phase compensation is performed in the two-dimensional frequency domain by multiplying by a three-dimensional compensation function.

[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] Among them, W r and W a These are the frequency domain envelopes for the azimuth and range directions, respectively, for SS(f τ ,f η ;r) Perform an inverse Fourier transform to the range direction to place it in the range-Doppler domain. Then perform a nonlinear CS scaling transform:

[0107]

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

[0109] make 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] The center frequency of the Doppler wave is given. Then, for sS... cs (τ,f η Perform a range-to-Fourier transform on the signal to place it in the two-dimensional frequency domain, and then perform range-to-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, SS rd (f η ,f τ Perform a range-direction inverse Fourier transform (r) to place the signal in the range-Doppler domain, then perform azimuth-direction matched filtering. The matched filter is H. a (f η ;r), and finally multiplied by the additional phase compensation function H e (f η ;r) complete the azimuth matched filtering.

[0115]

[0116] in, Δτ=2(rr ref ) / (cγ(f η ,r)), finally for sS rd2 (τ,f η By performing an inverse Fourier transform in the azimuth direction, SAS images focused in both the azimuth and range directions can be obtained.

[0117]

[0118] To verify the effectiveness and accuracy of the method proposed in this application, we conducted a multi-point target simulation experiment. Point targets were set at close range, intermediate range, and long range, respectively. The close-range targets were mainly distributed at around 50m, the intermediate-range targets were mainly distributed at around 150m, and the long-range targets were mainly distributed at around 250m. The simulation parameters are shown in Table 1. Figure 5 This is the imaging result for a close-range point target. Figure 6 This is the imaging result of a target at an intermediate distance. Figure 7The results show the imaging results for distant point targets. The impulse response width (IRW), peak sidelobe ratio (PSLR), and integral sidelobe ratio (ISLR) of the range 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 -10dB, and the IRW is less than 0.5m, indicating that the algorithm has good imaging accuracy and quality at different distances. Figure 3 The phase error when r = rc is shown, and it is easy to see that the maximum phase error is 0.0146 (rad), which is less than π / 4. Therefore, under the parameters of a wide-beam SAS system, the method proposed in this paper can achieve accurate focusing in both the azimuth and range directions, meeting the requirements for high-resolution imaging across the entire scan band. Figure 4 The distance error using a fourth-order Taylor expansion is shown, and it can be seen that the distance 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 comprising:

[0125] The fourth-order Taylor expansion module is used to approximate the two-way time, representing the two-way distance in the form of double square roots as a cosine form, and performing a fourth-order Taylor expansion on the slant distance history.

[0126] The module for obtaining the integrand is used to perform range-to-Fourier transform on the baseband signal to obtain the range-frequency domain-azimuth-time domain signal. Then, the azimuth-to-Fourier transform makes the range-frequency domain-azimuth-time domain signal in a two-dimensional spectrum and obtains the integrand.

[0127] A module for obtaining accurate two-dimensional spectrum is used to obtain accurate two-dimensional spectrum based on the Taylor expansion of slant range history and approximate time, applying the Lagrange inversion theorem and the principle of stationary phase.

[0128] The module for obtaining azimuth and range matched filter functions is used to expand the precise two-dimensional spectrum into azimuth and range frequency series expansions, and simultaneously obtain the azimuth and range matched filter functions.

[0129] The simulation image acquisition module is used to perform azimuth and range matched filtering on the two-dimensional frequency domain signal based on the azimuth and range matched filtering functions to obtain a synthetic aperture sonar simulation image focused in the azimuth and range directions.

[0130] This application may also provide a computer device, including: at least one processor, memory, at least one network interface, and a user interface. The various components in this device are coupled together via a bus system. It is understood that the bus system is used to implement communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0131] The user interface can include a display, keyboard, or clicking device. Examples include a mouse, trackball, touchpad, or touchscreen.

[0132] It is understood that the memory in the embodiments disclosed in this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be 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 DRAM (SDRAM), Double Data Rate Synchronous DRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memories described herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0133] In some implementations, the memory stores elements such as executable modules or data structures, or subsets thereof, or extended sets thereof: operating systems and applications.

[0134] The operating system includes various system programs, such as the framework layer, core library layer, and driver layer, used to implement various basic business functions and handle hardware-based tasks. The application programs include various applications, such as media players and browsers, used to implement various application functions. Programs implementing the methods of the embodiments of this disclosure can be included in the application programs.

[0135] In the above embodiments, the processor can also invoke programs or instructions stored in memory, specifically programs or instructions stored in an application program, for the following purposes:

[0136] Follow the steps described above.

[0137] The above methods can be applied to or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above methods can be completed by integrated logic circuits in the processor's hardware or by software instructions. The processor can 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, or discrete hardware components. It can implement or execute the disclosed methods, steps, and logic block diagrams. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the disclosed methods can be directly implemented by a hardware decoding processor, or implemented by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0138] It is understood that the embodiments described in this application can be implemented using 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), digital signal processing 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 this application, or combinations thereof.

[0139] For software implementation, the technology of this application can be implemented by executing the functional modules (e.g., procedures, functions, etc.) of this application. The software code can be stored in memory and executed by a processor. The memory can be implemented in the processor or externally.

[0140] This application may also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, it can implement the steps in the above method embodiments.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application, and should all be covered within the scope of the claims of this application.

Claims

1. A method for imaging with multi-receiver array synthetic aperture sonar, wherein the multi-receiver array synthetic aperture sonar is configured such that, along the direction of motion of the sonar, the receiving array is in front and the transmitting array is behind; the method includes: Step 1: Approximate the two-way time by expressing the two-way distance in the form of double square roots as a cosine form and performing a fourth-order Taylor expansion on the slant distance history. Step 2: Perform range-to-Fourier transform on the baseband signal to obtain the range-frequency domain-azimuth-time domain signal, and then perform azimuth-to-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 from Step 1, apply the Lagrange inversion theorem and the principle of stationary phase to obtain the accurate two-dimensional spectrum; Step 4: Expand the precise two-dimensional spectrum into azimuth and range frequency series expansions, and obtain the azimuth and range matched filter functions simultaneously; Step 5: Based on the azimuth and range matched filtering functions, perform azimuth and range matched filtering on the two-dimensional frequency domain signal to obtain the synthetic aperture sonar simulation image focused in the azimuth and range directions; Step 3 includes: Constructing a cubic phase compensation function : ； in, j Indicates the complex unit; r This represents the distance from the ideal point target to the center of the subarray; For reference distance; For the third-order coupling terms of distance and orientation, This represents the error after three phase compensations. For range-direction frequency; For azimuth frequency; Phase compensation is performed in the two-dimensional frequency domain by multiplying by a cubic compensation function: ； in, This indicates the phase compensation result; and These are the azimuth and range envelopes, respectively. Represents the range-frequency-azimuth-time domain signal; right Perform a distance-to-inverse Fourier transform, followed by a nonlinear CS scaling transform: ； in, First of all The result of performing a distance-to-inverse Fourier transform, followed by a nonlinear CS scaling transform; This represents the inverse Fourier transform of the distance; Indicates distance in advance; , , , , The center frequency of the Doppler wave. This indicates the changed range-modulated frequency. Represents the two-way distance over the RD field; , ; ; Indicates the speed of sound; right Perform a distance-to-Fourier transform, and then use a matched filter for... Perform range-directed matched filtering: ； ； in, Indicates to The results of performing range-directed Fourier transform and range-directed matched filtering; This represents a distance-to-Fourier transform. for abbreviation; ; right Perform a distance-to-inverse Fourier transform, then use a matched filter. Azimuth matched filtering is performed, and finally, the mixture is multiplied by an additional phase compensation function. Complete azimuth matched filtering: ； ； ； in, Indicates to The result of azimuth matched filtering; , ; Finally, for Perform inverse Fourier transform in the azimuth direction to obtain synthetic aperture sonar simulation images focused in the azimuth and range directions. : ； in, This indicates the inverse Fourier transform of the orientation.

2. The multi-receiver array synthetic aperture sonar imaging method according to claim 1, characterized in that, The approximation of the two-way travel time is as follows: Will Approximately ;in, Indicates direction in slow time; Indicates the velocity of the sonar; Indicates the launch array and the first i The distance between the receiving arrays.

3. The multi-receiver array synthetic aperture sonar imaging method according to claim 2, characterized in that, The cosine form is: ； Among them, intermediate variables intermediate variables intermediate variables and intermediate variables ; This indicates the signal travel distance from the transmitting array to the ideal point target; Indicates the distance from the point target to the first... The signal return distance of each receiving array element.

4. The multi-receiver array synthetic aperture sonar imaging method according to claim 2, characterized in that, The fourth-order Taylor expansion of the slant range history includes: The fourth-order Taylor expansion is: ； in, The fourth-order Taylor expansion representing the slant range history; This represents the error of the fourth-order Taylor expansion.

5. The multi-receiver array synthetic aperture sonar imaging method according to claim 3, characterized in that, The baseband signal for: ； in, For constant terms; The wavelength corresponds to the center frequency; Indicates direction in slow time; Indicates the slant distance history; j Indicates the complex unit; This represents the frequency modulation slope of the signal.

6. A multi-receiver array synthetic aperture sonar imaging system, implemented based on the method described in any one of claims 1-5, characterized in that, The system includes: The fourth-order Taylor expansion module is used to approximate the two-way time, representing the two-way distance in the form of double square roots as a cosine form, and performing a fourth-order Taylor expansion on the slant distance history. The module for obtaining the integrand is used to perform range-to-Fourier transform on the baseband signal to obtain the range-frequency domain-azimuth-time domain signal. Then, the azimuth-to-Fourier transform makes the range-frequency domain-azimuth-time domain signal in a two-dimensional spectrum and obtains the integrand. A module for obtaining accurate two-dimensional spectrum is used to obtain accurate two-dimensional spectrum based on the Taylor expansion of slant range history and approximate time, applying the Lagrange inversion theorem and the principle of stationary phase. The module for obtaining azimuth and range matched filter functions is used to expand the precise two-dimensional spectrum into azimuth and range frequency series expansions, and simultaneously obtain the azimuth and range matched filter functions; and The simulation image acquisition module is used to perform azimuth and range matched filtering on the two-dimensional frequency domain signal based on the azimuth and range matched filtering functions to obtain a synthetic aperture sonar simulation image focused in the azimuth and range directions.

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