Active sonar processing method and system based on COSTAS waveform

Abstract

This invention discloses an active sonar processing method and system based on the COSTAS waveform. It generates the COSTAS waveform signal by adjusting the frequency interval and the number of frequency jumps; performs frequency-domain beamforming based on steering vectors and Fast Fourier Transform, improving the signal-to-noise ratio (SNR) of the received signal and increasing azimuth information; achieves normalized matched filtering by selecting the maximum frequency modulus and estimating noise; and obtains the azimuth history map through approximate coherent weighted fusion. This invention effectively overcomes channel frequency-selective fading and significantly improves signal detection performance. Furthermore, by fully utilizing the coherent components in each frequency and combining them with an SNR-weighted fusion method, it effectively improves the echo gain in the azimuth history map, enhancing the accuracy and reliability of detection.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic signal generation and processing, and in particular to an active sonar processing method and system based on COSTAS waveforms. Background Technology

[0002] Active sonar detects and locates underwater targets by using echo localization. The underwater acoustic channel, as the transmission channel for acoustic signals, has a complex structure and is affected by many factors: low propagation speed, transmission loss increasing with frequency, and high ocean noise are all unfavorable conditions for the underwater acoustic channel. Furthermore, the underwater acoustic channel is characterized by strong time-varying properties and complex multipath propagation (M. Stojanovic and J. Preisig, "Underwater acoustic communication channels: Pro-pagation models and statistical characterization," in IEEE Communications Magazine, vol.47, no.1, pp.84-89, January 2009.). When sound waves pass through the underwater acoustic channel, severe signal distortion occurs, which is detrimental to the subsequent processing of the detected echo. The most obvious phenomena are frequency-selective fading and time-selective fading, which further exacerbate the signal distortion and place higher demands on the processing of the detected and received signals.

[0003] Traditional active sonar generally uses single-frequency waves for detection, combined with narrowband filtering, fast Fourier transform, and pulse compression techniques for echo processing. In recent years, several new types of active sonar signals have emerged, such as Linear Frequency Modulation (LFM), Hyperbolic Frequency Modulation (HFM), Pulse Code Modulation (PCM), Pseudo-Random (PR), Interpulse Modulated (IM), and composite signals. These signals each have their own characteristics, but their various performance characteristics are often contradictory, such as the relationship between velocity estimation capability and time delay estimation capability; and the relationship between measurement accuracy, different target resolution capabilities, and multi-valued ambiguity (Zhang Yao. Research on Several Methods of Active Sonar Target Detection under Shallow Sea Conditions [D]. Harbin Engineering University, 2013.). In long-range target detection, velocity and resolution are generally not the primary objectives; detecting the echo is the main objective. Therefore, there is an urgent need for an active sonar signal and related processing methods that can be used in time-varying, frequency-selective fading underwater acoustic channels. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide an active sonar processing method and system based on COSTAS waveform to improve the gain of traditional COSTAS waveform processing, in order to address the shortcomings of the existing technology.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: an active sonar processing method based on COSTAS waveforms, comprising the following steps:

[0006] S1. Beamforming is performed on the multi-channel data of the receiving array. Frequency domain beamforming results are obtained using frequency domain beamforming methods. Combined with the steering vector, beamforming in a single beam direction is achieved. By modifying the steering vector, beamforming in other directions is achieved.

[0007] S2. Select the maximum spectral line after beamforming to obtain the matched filtering result;

[0008] S3. Divide the matched filter result of single direction, single frequency hopping, and single snapshot by the estimated noise standard deviation to obtain the updated output result;

[0009] S4. For L snapshots and M beam directions, repeat steps S1 to S3. All updated output results constitute the complex azimuth history diagram of the nth hop frequency; 0≤n≤N-1, where N is the length of the COSTAS coded sequence.

[0010] S5. Calculate the signal-to-noise ratio (SNR) of the complex azimuth history map for each hop frequency. Based on the SNR, perform a time-delay weighted summation on the complex azimuth history maps for each hop frequency, transforming the 1-L snapshot data corresponding to the complex azimuth history map into 1+ΔL-L+ΔL snapshot data, thus obtaining the complex azimuth history map matrix Q; L is the number of snapshot data, ΔL=(n-1)T sp / T L ,T L T represents the time interval between snapshots. sp The duration of a single COSTAS symbol;

[0011] S6. Squaring the modulus of each element in the complex azimuth history matrix Q yields the azimuth history matrix E.

[0012] This invention fully utilizes the spatial array gain and time gain of the received data to improve the received signal-to-noise ratio and effectively combat the Doppler effect. At the same time, this invention utilizes the coherence of the complex azimuth history diagrams of each hopping frequency, so that the signal-to-noise ratio after weighted summation is higher than that of traditional incoherent processing methods, thereby improving the gain of traditional COSTAS processed waveforms.

[0013] In step S1, the frequency domain beamforming result R of the m-th beam direction, the p-th spectral line, and the l-th snapshot is... m,p,l Represented as: R m,p,l =g p (A m,p ,Fr l ); where r l Let F represent the matrix consisting of the l-th snapshot data received by the D channels of the receiving array, with a size of P*D, where P is the number of sampling points in each snapshot; F represents the Fourier transform matrix of size P*P, where the (k,u)-th element of F is denoted as... 1≤k≤P, 1≤u≤P; A m,p Let A be a 1*D matrix representing the steering vector corresponding to the m-th beam direction and the p-th spectral line, where 1≤m≤M, 1≤p≤P, and A m,p The (1,k)th element is d is the spacing between the elements of the linear array, θ m Let f(p) be the angle of the m-th beam direction, c be the speed of sound, and f(p) be the frequency corresponding to the p-th spectral line. f(p) = (p-1)·f s / P;g p (A m,p ,Fr l ) indicates that Fr l The pth row and A m,p Perform inner product operations.

[0014] In step S2, the matched filtering results for the m-th direction, the n-th frequency hopping, and the l-th snapshot are... Represented as:

[0015]

[0016] Here, complexmax{·} represents the operation of finding the element with the largest modulus among all elements in the matrix. R m,p,l This represents the frequency domain beamforming result for the m-th beam direction, the p-th spectral line, and the l-th snapshot. For the m-th beam direction, the p-th beam direction 1,n Root spectral line, frequency domain beamforming results of the l-th snapshot, For the m-th beam direction, the p-th beam direction 2,n Root spectral line, frequency domain beamforming result of the l-th snapshot, p 1,n ~p 2,n f n -f window to f n +f window The spectral line number corresponding to the frequency range, f n f is the frequency of the single-frequency signal corresponding to the nth symbol after COSTAS sequence modulation, i.e., the nth frequency hopping. window To set the frequency.

[0017] The above processing method can handle the Doppler effect caused by moving targets, thereby effectively detecting frequency-shifted echoes.

[0018] In step S4, the complex azimuth history of the nth hop frequency is plotted using matrix Q. n Represented as:

[0019]

[0020] Where M is the number of beam directions, This is the updated output for the m-th direction, the n-th frequency hopping, and the l-th snapshot.

[0021] In step S5, the signal-to-noise ratio (SNR) of the nth hop frequency. n The calculation formula is: Among them, Q n (i,j) represents matrix Q n The element in the i-th row and j-th column of the array.

[0022] In step S5, the expression for the complex azimuth history matrix Q is: SNR nLet be the signal-to-noise ratio at the nth hop frequency, and delay(·) denotes the delay operation. Through the delay-weighted summation operation in the above steps, on the one hand, the coherence between various frequencies is fully utilized, improving the signal-to-noise ratio of the fusion processing; on the other hand, the reliability of detection is also improved, transforming unreliable single-hop detection into reliable multi-hop detection.

[0023] The present invention also provides an active sonar processing system based on COSTAS waveforms, comprising:

[0024] One or more processors;

[0025] A memory having stored one or more programs that, when executed by one or more processors, cause the one or more processors to implement the steps of the method described above.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] 1) Based on the traditional active sonar processing flow, this invention proposes an active sonar processing flow based on the COSTAS waveform. Traditional single-frequency processing is difficult to resist time-varying and fading effects. This invention can effectively resist channel-selective fading through the COSTAS waveform, thereby improving the reliability of detection under noise and channel constraints.

[0028] 2) By using an approximate coherent fusion method and combining it with a signal-to-noise ratio weighted fusion method, the coherent components in each frequency are effectively utilized, which improves the signal gain under the azimuth history map compared with the original incoherent processing algorithm. Attached Figure Description

[0029] Figure 1 This is a flowchart of the active sonar processing of COSTAS signals according to an embodiment of the present invention;

[0030] Figure 2 This is a cross-sectional view of the experimental equipment layout in an embodiment of the present invention;

[0031] Figures 3a to 3d This is a graph showing the results of the data processing.

[0032] Figure 3a Comparison of algorithms for data 221212104723costaFIV_001.bin0.00100;

[0033] Figure 3b Comparison of algorithms for data 221212104747costaFIV_001.bin0.00100;

[0034] Figure 3cThe results of processing each frequency segment of the data 221212104723costaFIV_001.bin0.00100 separately;

[0035] Figure 3d The results of processing each frequency segment of the data 221212104747costaFIV_001.bin0.00100 are processed separately. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] Example 1

[0038] In this embodiment, the COSTAS waveform signal is generated using parameters such as the COSTAS encoding sequence, frequency interval, and number of frequency transitions; the bandpass form of the COSTAS encoded signal is as follows:

[0039]

[0040] In the formula, Re[·] represents the operation of taking the real part of a complex number, rect(·) is a rectangular window function of unit duration, N is the length of the COSTAS encoded sequence, and T sp f is the duration of a single COSTAS symbol. n =f0+C n Δf is the frequency of the single-frequency signal corresponding to the nth symbol after COSTAS sequence modulation, also known as the nth frequency hopping, where f0 is the fixed carrier frequency, Δf is the frequency interval, and C n The COSTAS encoded sequence is used. In the experimental part of this embodiment, an 8-hop example is used, with the encoded sequence being -1, -4, 1, 2, 0, 3, -2, -3. Active sonar detects signals by transmitting the COSTAS encoded signal in a bandpass format.

[0041] The signal processing flow of conventional active sonar is generally "beamforming - matched filtering - normalization - azimuth history display" (DAAbraham and PKWillett, "Active sonar detection in shallow water using the Page test," in IEEE Journal of Oceanic Engineering, vol.27, no.1, pp.35-46, Jan.2002. or Baldacci A, Haralabus G. Signal processing for an active sonar system suitable for advanced sensor technology applications and environmental adaptation schemes[C] / / 2006 14th European Signal Processing Conference.IEEE, 2006:1-5.). The processing method for each single frequency of the COSTAS encoded signal in this embodiment of the invention is the same as that in the prior art (Baldacci A, Haralabus G. Signal processing for an active sonar system suitable for advanced sensor technology applications and environmental adaptation schemes[C] / / 2006 14th European Signal Processing Conference.IEEE, 2006:1-5.). For the fusion of multiple frequencies, the overall processing flow of COSTAS signal detection in this embodiment of the invention is as follows: Figure 1 As shown. The processing steps consist of four steps:

[0042] (1) Beamforming is performed on the D-channel data of the receiving array in M ​​directions to enhance the acoustic signal in the target direction and improve the signal-to-noise ratio of the received signal. The m-th beam direction, the p-th spectral line, and the l-th snapshot (each snapshot contains P sampling points with a sampling rate of f) are used. s The frequency domain beamforming result is as follows:

[0043] R m,p,l =g p (A m,p ,Fr l );

[0044] Where rl Let F represent the matrix consisting of the l-th snapshot data received by channel D, with a size of P*D; let F represent the Fourier transform matrix of size P*P, where the (k,u)-th element is... In practice, the Fast Fourier Transform (FFT) is used to reduce computational load; A m,p Let the steering vector corresponding to the m-th beam direction and the p-th root spectral line be a 1*D matrix, where the (1,k)-th element is... Where d is the spacing between the elements of the linear array, and θ m Let θ be the angle of the m-th beam direction (to achieve beamforming in other directions, the angles of other directions need to be replaced with θ). m Substitute into In this process, guide vectors in other directions are obtained, thereby achieving beamforming in other directions. Here, c is the speed of sound, f(p) is the frequency corresponding to the p-th spectral line, and f(p) = (p-1)·f s / P,;g p (A m,p ,Fr l ) indicates that A m,p With Fr l The inner product operation on the p-th row.

[0045] (2) Perform matched filtering. Repeat step (1) to obtain the m-th beam direction, the l-th snapshot, and f. n -f window to f n +f window Frequency range (corresponding spectral line number p) 1,n ~p 2,n The frequency domain beamforming result of f window The frequency shift caused by relative motion determines f window The values ​​are no more than 5Hz, and the frequency domain beamforming results form a vector:

[0046]

[0047] Then, the complex value corresponding to the frequency with the maximum energy is selected as the output; this process is called matched filtering. Therefore, the matched filtering result for the m-th direction, the n-th frequency hopping, and the l-th snapshot is:

[0048]

[0049] The complexmax{·} operation represents finding the element with the largest modulus among all elements in the matrix.

[0050] (3) Noise Energy Normalization. The matched filtering result is divided by the estimated noise standard deviation to normalize the noise energy. The output is then updated as follows:

[0051]

[0052] The complexmean{·} operation represents the average of the moduli of all elements in the matrix.

[0053] (4) The normalized matched filtering results for a single frequency hop, a single snapshot, and a single beam direction were obtained through the above steps. By traversing L snapshots and repeatedly executing (1) to (3) in M ​​beam directions, the complex azimuth history map of the nth hop was obtained. The matrix Q was used to... n This indicates that the matrix has M rows and L columns.

[0054]

[0055] The signal-to-noise ratio (SNR) of each image is estimated, weighting coefficients are determined, and then the images are summed after time delay. The SNR is... n The method for determining it is as follows:

[0056]

[0057] Where max{·} represents the operation of finding the maximum value among all elements in the matrix, and abs(·) represents the operation of taking the modulo of the elements in the matrix, Q n (i,j) represents the element in the i-th row and j-th column of the matrix.

[0058] Based on the signal-to-noise ratio results SNR1, SNR2, ..., SNR of the complex azimuth history diagrams at each hopping frequency n ,…,SNR N Complex azimuth history diagrams for each hopping frequency Q1, Q2, ..., Q n ,…,Q N Perform a delayed weighted summation. In the following formula, delay(·) represents a delay operation, specifically, it makes Q... n The corresponding snapshot data from 1 to L becomes snapshot data from 1+ΔL to L+ΔL, where ΔL=(n-1)T sp / T L ,T L Given the time interval between snapshots, we obtain the complex orientation history matrix Q:

[0059]

[0060] Finally, the magnitude of each element in the matrix is ​​squared to obtain the azimuth history map matrix E. The azimuth history map matrix E is used to make target decisions (Baldacci A, Haralabus G. Signal processing for an activesonar system suitable for advanced sensor technology applications and environmental adaptation schemes[C] / / 2006 14th European Signal Processing Conference.IEEE,2006:1-5.), thus completing the detection.

[0061] E = Φ(Q);

[0062] Where Φ(·) represents the operation of squaring the modulus of each element in the matrix.

[0063] It is foreseeable that the embodiments of the present invention improve the processing gain and enhance the stability of the method by fusing multiple frequencies.

[0064] To verify the method proposed in the embodiments of the present invention, a lake trial experiment was conducted in December 2022. Figure 2 As shown, the probe vessel is equipped with a 4-element hydrophone array, positioned approximately 30m underwater, with the hydrophones spaced 1.5m apart. The transponder vessel has a single transducer, also positioned 30m underwater. The transponder vessel is approximately 2km away from the probe vessel. The transponder vessel transmits a weak signal via its transducer, and the probe vessel receives the signal via its hydrophones. This experimental scheme verifies the performance of Costas in an underwater acoustic environment and the gain of the method proposed in this embodiment of the invention. Using the method of this embodiment of the invention, the following analytical results were obtained:

[0065] Combination Figure 3a , Figure 3b Conventional processing methods fuse signals at each frequency of COSTAS using an equal-weighted sum of squares approach, but this does not fully extract the gain. Therefore, this embodiment of the invention uses coherent approximate fusion combined with signal-to-noise ratio weighting to process weak signal data. Figure 3a The image shows the experimental data named "221212104723costaFIV_001.bin0.00100". "221212104723" indicates the experimental time, "costaFIV_001.bin" represents the wavetable code used for detection, and "0.00100" represents the intensity (relative intensity, full power is 1) of the acoustic wave transmitted by the transponder. Figure 3a , Figure 3bThe results show that, compared with traditional methods, both approximate coherent fusion and weighted fusion can obtain better orientation history maps, with more obvious bright spots and weaker background noise.

[0066] Simultaneously, by processing multiple sets of data, the signal-to-noise ratio (PSNR) of each azimuth history map is calculated:

[0067]

[0068] Table 1 below lists the PSNR results for four sets of experimental data:

[0069] Table 1 PSNR results of four sets of experimental data

[0070]

[0071] As shown in the table above, using approximate coherent fusion and weighted fusion alone can improve the signal-to-noise ratio. Combining the approximate coherent method with weighted fusion further improves the signal-to-noise ratio of the azimuth history map.

[0072] Combination Figure 3c , Figure 3d By processing each frequency of COSTAS individually, it can be observed that under individual processing, due to channel frequency-selective fading, Figure 3c The signal-to-noise ratios of the azimuth history maps at 460Hz, 520Hz, 500Hz, 530Hz, 480Hz, and 470Hz are significantly low. If a single frequency is used for detection, it is impossible to guarantee the selection of low-fading frequencies such as 490Hz and 510Hz, thus making it difficult to achieve robust detection. Figure 3d The signal-to-noise ratios (SNRs) of the azimuth history maps at 490Hz, 460Hz, 510Hz, 520Hz, 530Hz, and 470Hz are significantly low. Using a single frequency for detection cannot guarantee the selection of low-fading frequencies such as 500Hz and 480Hz, making robust detection difficult. Therefore, robust detection cannot be achieved using a single frequency. However, by fusing multiple frequency azimuth history maps, especially through approximate coherence and weighted fusion methods, the SNR is significantly improved. This ensures a high probability of selecting low-fading frequencies and fully utilizes the coherence between frequencies (experiments show that a 10Hz frequency interval can guarantee good coherence), thus improving the SNR of the fused processing.

[0073] Active sonar echo processing faces challenges such as multipath propagation, Doppler effects, and environmental time-varying characteristics, leading to frequency-selective fading of the echo signal and rendering traditional single-frequency wave-based detection methods unreliable. This invention proposes a COSTAS-based active detection processing method that fully utilizes the coherent components at various frequencies. Combined with a signal-to-noise ratio weighted method, it effectively improves the echo gain under azimuth history maps, significantly enhancing signal detection performance. Furthermore, experiments demonstrate that the COSTAS processing method outperforms existing methods.

[0074] Example 2

[0075] Embodiment 2 of the present invention provides a terminal device corresponding to Embodiment 1 above. The terminal device can be a processing device for a client, such as a mobile phone, a laptop, a tablet computer, a desktop computer, etc., to execute the method of the above embodiments.

[0076] The terminal device in this embodiment includes a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method in Embodiment 1 described above.

[0077] In some implementations, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0078] In other implementations, the processor can be any type of general-purpose processor, such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation here.

[0079] Example 3

[0080] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to Embodiment 1 above, on which a computer program / instructions are stored. When the computer program / instructions are executed by a processor, they implement the steps of the method of Embodiment 1 above.

[0081] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0082] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0083] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0084] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0085] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0086] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. An active sonar processing method based on COSTAS waveforms, characterized in that, Includes the following steps: S1. Beamforming is performed on the multi-channel data of the receiving array. Frequency domain beamforming results are obtained using frequency domain beamforming methods. Combined with the steering vector, beamforming in a single beam direction is achieved. By modifying the steering vector, beamforming in other directions is achieved. S2. Select the maximum spectral line after beamforming to obtain the matched filtering result; S3. Divide the matched filter result of single direction, single frequency hopping, and single snapshot by the estimated noise standard deviation to obtain the updated output result; S4. For L snapshots and M beam directions, repeat steps S1 to S3. All updated output results constitute the complex azimuth history diagram of the nth hop frequency; 0≤n≤N-1, where N is the length of the COSTAS coded sequence. S5. Calculate the signal-to-noise ratio (SNR) of the complex azimuth history map for each hop frequency. Based on the SNR, perform a time-delay weighted summation on the complex azimuth history maps for each hop frequency, transforming the 1-L snapshot data corresponding to the complex azimuth history map into 1+ΔL-L+ΔL snapshot data, thus obtaining the complex azimuth history map matrix Q; L is the number of snapshot data, ΔL=(n-1)T sp / T L ,T L T represents the time interval between snapshots. sp The duration of a single COSTAS symbol; S6. Squaring the modulus of each element in the complex azimuth history matrix Q yields the azimuth history matrix E.

2. The active sonar processing method based on COSTAS waveforms according to claim 1, characterized in that, In step S1, the frequency domain beamforming result R of the m-th beam direction, the p-th spectral line, and the l-th snapshot is... m,p,l Represented as: R m,p,l =g p (A m,p ,Fr l ); where r l Let F represent the matrix consisting of the l-th snapshot data received by the D channels of the receiving array, with a size of P*D, where P is the number of sampling points in each snapshot; F represents the Fourier transform matrix of size P*P, where the (k,u)-th element of F is denoted as... 1≤k≤P, 1≤u≤P; A m,p Let A be a 1*D matrix representing the steering vector corresponding to the m-th beam direction and the p-th spectral line, where 1≤m≤M, 1≤p≤P, and A m,p The (1,k)th element is d is the spacing between the elements of the linear array, θ m Let f(p) be the angle of the m-th beam direction, c be the speed of sound, and f(p) be the frequency corresponding to the p-th spectral line. f(p) = (p-1)·f s / P;g p (A m,p ,Fr l ) indicates that Fr l The pth row and A m,p Perform inner product operations.

3. The active sonar processing method based on COSTAS waveforms according to claim 1, characterized in that, In step S2, the matched filtering results for the m-th direction, the n-th frequency hopping, and the l-th snapshot are... Represented as: Here, complexmax{·} represents the operation of finding the element with the largest modulus among all elements in the matrix. R m，p，l This represents the frequency domain beamforming result for the m-th beam direction, the p-th spectral line, and the l-th snapshot. For the m-th beam direction, the p-th beam direction 1,n Root spectral line, frequency domain beamforming results of the l-th snapshot, For the m-th beam direction, the p-th beam direction 2,n Root spectral line, frequency domain beamforming result of the l-th snapshot, p 1,n ~p 2,n f n -f window to f n +f window The spectral line number corresponding to the frequency range, f n f is the frequency of the single-frequency signal corresponding to the nth symbol after COSTAS sequence modulation, i.e., the nth frequency hopping. window To set the frequency.

4. The active sonar processing method based on COSTAS waveforms according to claim 1, characterized in that, In step S4, the complex azimuth history of the nth hop frequency is plotted using matrix Q. n Represented as: Where M is the number of beam directions, This is the updated output for the m-th direction, the n-th frequency hopping, and the l-th snapshot.

5. The active sonar processing method based on COSTAS waveforms according to claim 4, characterized in that, In step S5, the signal-to-noise ratio (SNR) of the nth hop frequency. n The calculation formula is: Among them, Q n (i,j) represents matrix Q n The element in the i-th row and j-th column of the array.

6. The active sonar processing method based on COSTAS waveform according to claim 4, characterized in that, In step S5, the expression for the complex azimuth history matrix Q is: SNR n Let n be the signal-to-noise ratio of the nth hop frequency, and delay(·) represents the delay operation.

7. An active sonar processing system based on COSTAS waveforms, characterized in that, include: One or more processors; A memory having stored one or more programs that, when executed by one or more processors, cause the one or more processors to perform the steps of the method according to any one of claims 1 to 6.

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