A method for associating target tracks between hull sonar and towed linear array sonar

Abstract

The invention belongs to the technical field of sonars, and proposes a method for associating target tracks between a hull sonar and a towed linear array sonar. According to the problem that the target track association performance is easily reduced when only the side angle similarity is used to associate the target tracks due to the large difference in direction finding accuracy characteristics between the hull sonar and the towed linear array sonar, multi-dimensional features such as the side angle, signal-to-noise ratio, and DEMON spectrum of the target are extracted and joint association processing is performed, which can effectively increase the robustness of the target track association between the hull sonar and the towed linear array sonar, and improve the association accuracy.

Description

Technical Field

[0001] The invention belongs to the field of sonar technology, and is applicable to the technical field of associating the tracks of underwater passively detected targets by hull sonar and towed linear array sonar in submarine sonar systems and surface ship sonar systems, and mainly provides a method for associating the target tracks of hull sonar and towed linear array sonar. Background Art

[0002] Modern submarine sonar systems and surface ship sonar systems are mainly composed of hull sonar and towed linear array sonar. Compared with towed linear array sonar, hull sonar has the advantages of high installation accuracy, good formation consistency, and small direction-finding error when detecting targets, but the array aperture is limited by the platform space and is difficult to expand further; towed linear array sonar is towed to the rear of the ship, and is less affected by the platform background noise than hull sonar, and its array aperture is not limited by the platform space, which can realize the detection of long-distance targets, but the towed array is a flexible array, and it is easy to produce formation distortion during the towing process, with large direction-finding errors, and a single linear array has blurred left and right sides under non-maneuvering conditions.

[0003] An important function in generating a unified situation of underwater targets is to correlate the target tracks detected by the hull sonar with those detected by the towed linear array sonar, comprehensively manage the targets detected by different sonars, clarify the number of targets and the characteristics of the same target, and lay the foundation for the subsequent generation of a unified target situation for ships. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for associating target tracks of a hull sonar and a towed linear array sonar.

[0005] The object of the present invention is achieved by the following technical solution: A method for associating a target track between a hull sonar and a towed linear array sonar, comprising the following steps:

[0006] (1) Based on the detection frequency band, propagation loss, background noise level, and array gain set for the hull sonar and towed linear array sonar, a formula for converting the target output signal-to-noise ratio of the hull sonar and towed linear array sonar into the target normalized energy is established:

[0007] Hull sonar target energy normalization:

[0008]

[0009] Among them, the target spectrum level at 1000Hz is S 0 , center frequency f k0 Propagation loss is the propagation loss at the center frequency The difference between the propagation loss at 1000Hz and the background noise spectrum level at 1000Hz is NL k0 , the array gain at 1000Hz is DI k0 , n is a different frequency point, the shell sonar detection frequency band is [f kl ,f ku ]; the target output signal-to-noise ratio actually detected by the shell sonar is SNR k ; tran(), tran -1 () is a numerical conversion operation, tran(a)=10 (a / 10) , tran -1 (a) = 10log(a).

[0010] Towed linear array sonar target energy normalization:

[0011]

[0012] Among them, the target spectrum level at 1000Hz is S 0 , center frequency f t0 The propagation loss is is the center frequency f t0 The propagation loss is The difference between the propagation loss at 1000Hz and the background noise spectrum level at 1000Hz is NL t0 , the array gain at 1000Hz is DI t0 , m is a different frequency point, the detection frequency band of the towed linear array sonar is [f tl ,f tu ]; The target output signal-to-noise ratio actually detected by the towed linear array sonar is SNR t ;

[0013] (2) To address the problem that the direction finding accuracy characteristics between the hull sonar and the towed linear array sonar are quite different, thus affecting the correlation performance, the target tracks are divided into block sets for processing. In each batch of correlation processing, only the target tracks in the block set where the selected reference track is located and the left and right adjacent block sets are correlated.

[0014] (3) To address the problem that the direction finding accuracy characteristics between the hull sonar and the towed linear array sonar are quite different, thus affecting the correlation performance, the azimuth, energy, and DEMON multi-feature joint track correlation algorithm is used to establish the target multi-order azimuth feature state difference and the target zero-order energy feature state difference. Target zero-order DEMON spectrum characteristic state difference The target orientation correlation Γ is calculated respectively b , energy correlation Γ e and DEMON spectrum correlation Γ d, and then the multi-feature joint correlation Jointly determine the target track correlation characteristics between the hull sonar and the towed linear array sonar; where λ 1 , 2 , 3 is the correlation coefficient of each feature.

[0015] Furthermore, the target track is divided into block sets for processing. First, the 360° azimuth of the ship is divided into a block set every 10°, block set 1: 0°~10°, block set 2: 10°~20°, ..., block set 18: 170°~180°, block set 19: -180°~-170°, ..., block set 36: -10°~0°, a total of 36 azimuth sets; the hull sonar target track is taken as the reference track, and the towed linear array sonar target track is taken as the comparison track, and its azimuth sequence data is converted into each azimuth set sequence number, wherein the hull sonar target track can be divided into azimuth block sets 1~36, and the towed linear array sonar target track is divided into azimuth block sets 1~18, and each batch of association processing is only associated with the target tracks in the block set where the reference track is located and the left and right adjacent block sets.

[0016] Furthermore, the target orientation feature correlation is:

[0017] The track information of the hull sonar is selected as the reference track, and the track information of the towed linear array sonar is selected as the comparison track, which are recorded as and

[0018] Zero-order azimuth state difference:

[0019] First-order azimuth slope difference:

[0020] Second-order azimuth slope difference:

[0021]

[0022] Then the correlation between the reference track and the comparison track is:

[0023]

[0024] Where i is the number of the i-th target of the hull sonar, j is the number of the j-th target of the towed linear array sonar, L is the number of track sequence points, are the zero-order state difference, first-order slope difference and second-order slope difference describing the orientation similarity, Γ b is the orientation grey correlation degree.

[0025] Furthermore, the target energy feature correlation is:

[0026] The target energy characteristic sequence of the shell sonar is selected as the reference sequence, and the target energy characteristic sequence of the towed linear array sonar is selected as the comparison sequence, which are respectively denoted as and Since the target energy changes little in a short time, only the zero-order state difference is used as the comparison quantity here;

[0027] Zero-order energy state difference:

[0028] Then the correlation between the target energy reference sequence and the comparison sequence is:

[0029]

[0030] Furthermore, the target DEMON spectrum feature correlation is:

[0031] The DEMON spectrum characteristics of the hull sonar are selected as the reference sequence, and the DEMON spectrum characteristics of the towed linear array sonar are selected as the comparison sequence, which are recorded as and The target DEMON spectrum characteristics are related to the target number of blades and rotation speed, which are basically unchanged under the state of uniform speed and straight flight. Here, only the zero-order state difference is used as the comparison quantity.

[0032] Zero-order DEMON spectrum state difference:

[0033] Then the correlation between the target DEMON spectrum feature reference sequence and the comparison sequence is:

[0034]

[0035] The beneficial effects of the present invention are as follows: since there are large differences in direction-finding accuracy characteristics between the hull sonar and the towed linear array sonar, the target track association performance is likely to be reduced if only the side angle similarity is used for target track association. By extracting multi-dimensional features of the target such as the side angle, signal-to-noise ratio, and DEMON spectrum, and performing joint association processing, the robustness of the target track association between the hull sonar and the towed linear array sonar can be effectively increased, and the association accuracy can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 When the target sampling is varied at a uniform angle of 0.1° for each batch and the systematic error and random error of the hull sonar in detecting the target azimuth are both 1°, the correlation between pure azimuth correlation and multi-feature correlation changes with the azimuth error of the towed linear array sonar.

[0037] Figure 2When the target sampling is varied at a uniform angle of 1° for each batch, and the systematic error and random error of the hull sonar in detecting the target azimuth are both 1°, the correlation between pure azimuth correlation and multi-feature correlation changes with the azimuth error of the towed linear array sonar.

[0038] Figure 3 When the target sampling is varied at a uniform angle of 0.1° for each batch and the systematic error and random error of the hull sonar in detecting the target azimuth are both 2°, the correlation between pure azimuth correlation and multi-feature correlation changes with the azimuth error of the towed linear array sonar.

[0039] Figure 4 When the target sampling is varied at a uniform angle of 1° for each batch and the systematic error and random error of the hull sonar in detecting the target azimuth are both 2°, the correlation between pure azimuth correlation and multi-feature correlation changes with the azimuth error of the towed linear array sonar.

[0040] Figure 5 This is the flow chart of the joint track association algorithm of multiple features including azimuth, energy and DEMON. DETAILED DESCRIPTION

[0041] The present invention will be described in detail below with reference to the accompanying drawings and embodiments:

[0042] The present invention mainly extracts multi-dimensional features such as the target's side angle, signal-to-noise ratio, DEMON spectrum, etc. from the target detection data of the hull sonar and the towed linear array sonar for joint correlation processing, so as to solve the problem that the direction finding accuracy characteristics between the hull sonar and the towed linear array sonar are quite different, thereby affecting the correlation performance, increase the robustness of the target track correlation between the hull sonar and the towed linear array sonar, and improve the correlation accuracy.

[0043] (1) Divide the target track into blocks

[0044] The hull sonar and towed linear array sonar direction finding accuracy errors are mainly composed of systematic errors and random errors. The hull sonar direction finding system errors are mainly caused by array installation errors, inconsistency between array elements and pre-processing channels, and random errors are mainly caused by sound velocity measurement errors and heading errors; the towed linear array sonar direction finding system errors are mainly caused by array distortion, misalignment between array acoustic center and boat center, inconsistency between array elements and pre-processing channels, and random errors are mainly caused by sound velocity measurement errors, heading errors, and random swings of the array.

[0045] Considering the difference in the direction finding accuracy error between the hull sonar and the towed linear array sonar, the target track can be divided into block sets. First, the 360° azimuth of the ship is divided into a block set every 10°, block set 1: 0°~10°, block set 2: 10°~20°, ..., block set 18: 170°~180°, block set 19: -180°~-170°, ..., block set 36: -10°~0°, a total of 36 azimuth sets.

[0046] Then, the hull sonar target track is taken as the reference track, and the towed linear array sonar target track is taken as the comparison track, and its azimuth sequence data is converted into the sequence number of each azimuth set, among which the hull sonar target track can be divided into azimuth block sets 1 to 36, and the towed linear array sonar target track is divided into azimuth block sets 1 to 18. Each batch of association processing is only associated with the target tracks in the block set where the reference track is located and the left and right adjacent block sets.

[0047] (2) Introducing the target output signal-to-noise ratio feature

[0048] The target output signal-to-noise ratio of sonar detection is mainly determined by factors such as target source level, propagation loss, background noise level, array gain, and array processing frequency band. The following deduces the relationship between different sonar target output signal-to-noise ratios and these factors.

[0049] ① Shell sonar detection frequency band is [f kl ,f ku ], the target source level at different frequency points is S n , the propagation loss is TL n , the background noise level is NL n , the array gain is DI n , n∈[f kl ,f ku ], then the target output signal-to-noise ratio actually detected is SNR k :

[0050]

[0051] Among them, tran(), tran -1 () is a numerical conversion operation, tran(a)=10 (a / 10) , tran -1 (a) = 10log(a).

[0052] According to the target characteristic analysis, the target spectrum level at 1000Hz is assumed to be S 0 , and within the sonar detection frequency band, the target spectrum level decays by -6dB per octave with frequency; assuming that the propagation loss TL within the sonar detection frequency band is n The center frequency f k0 Propagation loss The transmission loss TL at 1000Hz is 0 Difference by a fixed value Hull sonar background noise level NL n It can be divided into platform noise and ocean environment noise. According to the noise characteristics analysis, the spectrum level of platform noise and ocean environment noise both decays by -6dB per octave with frequency. Assuming the background noise spectrum level at 1000Hz is NL k0 ; Hull sonar array gain DI n It is related to the effective area of ​​the array and has a quadratic relationship with the frequency. Assume that the array gain at 1000Hz is DI k0 , then the above formula can be transformed into

[0053]

[0054]

[0055] ②The detection frequency band of towed linear array sonar is [f tl ,f tu ], the center frequency f t0 The propagation loss is It is related to the propagation loss TL at 1000Hz 0 Difference by a fixed value The background noise level of the towed linear array sonar is NL m It can be divided into radiation noise, flow noise and ocean environment noise. According to the noise characteristics analysis, the spectrum level of radiation noise, flow noise and ocean environment noise all decays by -6dB per octave with frequency. Assuming the background noise spectrum level at 1000Hz is NL t0 ; Towed linear array sonar array gain DI m It is related to the number of array elements and is linearly related to the frequency. Assume that the array gain at 1000Hz is DI t0 , then the target output signal-to-noise ratio actually detected is SNR t :

[0056]

[0057] Based on the relationship between the target output signal-to-noise ratio obtained by the above-mentioned hull sonar and towed linear array sonar detection and factors such as target source level, propagation loss, background noise level, array gain, array processing frequency band, etc., the target energy detected by the hull sonar and towed linear array sonar can be normalized to eliminate the influence of factors other than the target's own characteristics and propagation characteristics.

[0058] Hull sonar target energy normalization:

[0059]

[0060] Towed linear array sonar target energy normalization:

[0061]

[0062] (3) Introducing DEMON spectrum features

[0063] Due to differences in array design and functional design, the operating frequency bands of hull sonars and towed linear array sonars are mainly concentrated in the medium and high frequencies (above 1000 Hz), while the operating frequency bands of towed linear array sonars are mainly in the low frequency bands (below 1000 Hz). The overlap of the commonly used operating frequency bands of the two is small, resulting in differences in the frequency spectrum information of the detected targets. The DEMON spectrum is obtained by demodulating the received broadband signal to obtain the low-frequency envelope spectrum, and then obtain the low-frequency physical characteristics of the target such as the shaft frequency and blade frequency. For different arrays, although the processing frequency band range is different, low-frequency DEMON spectrum information can be obtained at the same time. The DEMON spectrum information of the same target obtained by different arrays, that is, the DEMON spectrum information of the target beam, can achieve the purpose of improving the quality of target track association and the correct degree of association.

[0064] (4) Track fitting

[0065] Due to differences in array aperture, background noise, etc., hull sonar and towed linear array sonar have different ranges for targets such as surface ships and submarines. Towed linear array sonar can detect farther than hull sonar. If the target is at the boundary of the detectable distance of the hull sonar, it is easy for the towed linear array sonar to detect the target track to be stable, while the hull sonar to detect the target track to be intermittent. At this time, if the track correlation processing is directly performed, the correlation calculation cannot accurately reflect the similarity between the tracks due to the influence of data breakpoints. Therefore, it is necessary to fit the target track before the correlation calculation. When breakpoint data appears, the track data at that moment can be directly recursively obtained through the fitting algorithm to ensure track continuity.

[0066] Surface ships, submarines and other targets generally cruise in a uniform linear motion state, so the target is set to move in a uniform linear motion relative to this platform.

[0067] The target azimuth is

[0068] Among them, r x0 、r y0 is the initial position of the target relative to the platform, and v x 、v y are the horizontal and vertical coordinate values ​​of the target's speed relative to the platform, and t is the time.

[0069] when And r y0 ≠0, then

[0070] It can be concluded that under the condition of uniform linear motion, when t is small, the target azimuth tangent value is linearly related to time, and the target azimuth track can be fitted based on this relationship.

[0071] (5) Multi-feature joint correlation

[0072] ① Target orientation feature correlation

[0073] The track information of the hull sonar is selected as the reference track, and the track information of the towed linear array sonar is selected as the comparison track, which are recorded as and

[0074] Zero-order azimuth state difference:

[0075] First-order azimuth slope difference:

[0076] Second-order azimuth slope difference:

[0077]

[0078] Then the correlation between the reference track and the comparison track is:

[0079]

[0080] Where i is the number of the i-th target of the hull sonar, j is the number of the j-th target of the towed linear array sonar, L is the number of track sequence points, are the zero-order state difference, first-order slope difference and second-order slope difference describing the orientation similarity, Γ b is the orientation grey correlation degree.

[0081] ②Target energy feature correlation

[0082] The target energy characteristic sequence of the shell sonar is selected as the reference sequence, and the target energy characteristic sequence of the towed linear array sonar is selected as the comparison sequence, which are respectively denoted as and Since the target energy changes little in a short time, only the zero-order state difference is used as the comparison quantity here.

[0083] Zero-order energy state difference:

[0084] Then the correlation between the target energy reference sequence and the comparison sequence is:

[0085]

[0086] ③ Target DEMON spectrum feature correlation

[0087] The DEMON spectrum characteristics of the hull sonar are selected as the reference sequence, and the DEMON spectrum characteristics of the towed linear array sonar are selected as the comparison sequence, which are recorded as and The target DEMON spectrum characteristics are related to the target number of blades and rotation speed, which are basically unchanged under the state of uniform speed and straight flight. Here, only the zero-order state difference is used as the comparison quantity.

[0088] Zero-order DEMON spectrum state difference:

[0089] Then the correlation between the target DEMON spectrum feature reference sequence and the comparison sequence is:

[0090]

[0091] ④Multi-feature joint correlation

[0092] The multi-feature joint correlation is composed of the target orientation feature correlation, the target energy feature correlation and the target DEMON spectrum feature correlation.

[0093]

[0094] Among them, λ 1 , 2 , 3 is the correlation coefficient of each feature, which is related to the role of each feature in the joint correlation.

[0095] Example:

[0096] Suppose a moving target moves at a uniform angle (0.1° or 1° for each batch of sampling) at 90° from the observation point. The system error and random error of the hull sonar when detecting the target azimuth are both 1° or 2°. The system error and random error of the towed linear array sonar when detecting the target azimuth vary from 1° to 10°. The maximum energy fluctuation of the hull sonar and towed linear array sonar when detecting the target is 30%, which obeys the uniform distribution. The maximum error of DEMON spectrum feature extraction is 1Hz, which obeys the uniform distribution. The comparison of pure bearing association and bearing, energy, and DEMON multi-feature joint track association algorithm is shown in the figure below. Figure 1-4 described.

[0097] As can be seen from the figure, in order to solve the problem that the direction-finding accuracy characteristics between the hull sonar and the towed linear array sonar are quite different, thus affecting the correlation performance, the azimuth, energy, and DEMON multi-feature joint track correlation algorithm can effectively improve the correlation degree compared to the pure azimuth track correlation algorithm. When the correlation judgment threshold ε remains unchanged, the correlation accuracy of the same target can be improved.

[0098] (1) Setting the detection frequency band of hull sonar and towed array sonar ([fkl ,f ku ]、[f tl ,f tu ]), passively detect the target;

[0099] (2) Continuously receive omnidirectional pre-beamed data output by hull sonar and towed linear array sonar When a target appears, the operator performs tracking processing and outputs tracking target information (SG k (t), SG t (t)) and beam data

[0100] (3) Extracting the target’s azimuth and trajectory from the hull sonar tracking target information and beam data and DEMON spectral feature sequences Extract the target output signal-to-noise ratio sequence SNR from the tracking target beam data and the omnidirectional pre-beam data k (k), k = 1, 2, ..., l; Extract the target azimuth track from the towed linear array sonar tracking target information and beam data and DEMON spectral feature sequences Extract the target output signal-to-noise ratio sequence SNR from the tracking target beam data and the omnidirectional pre-beam data t (k), k = 1, 2, ..., L;

[0101] (4) According to the linear relationship between the tangent value of the azimuth and time, tanθ=at+b, the target azimuth track is fitted;

[0102] (5) Receive environmental parameters input from the external system, and calculate the difference between the propagation loss at the center frequency point and at 1000 Hz based on the detection frequency band set by the shell sonar and towed linear array sonar. Background noise level at 1000Hz (NL k0 NL t0 ), array gain at 1000Hz (DI k0 ,DI t0 ), according to the shell sonar energy calculation formula and the energy calculation formula of towed linear array sonar The target detection energy of hull sonar and towed linear array sonar is normalized to eliminate the influence of factors other than the target's own characteristics and propagation characteristics.

[0103] (6) The 360° azimuth of the ship is divided into a block set every 10°, block set 1: 0°~10°, block set 2: 10°~20°, ..., block set 36: 350°~360°, for a total of 36 azimuth sets. The sonar detected target azimuth sequence data is converted into the sequence number of each azimuth set. Each batch of association processing is only performed on the target track in the block set where the selected reference track is located and the left and right adjacent block sets.

[0104] (7) Select the target azimuth, energy, and DEMON spectrum information of the shell sonar as the reference value, and the target azimuth, energy, and DEMON spectrum information of the towed linear array sonar as the comparison value to calculate the azimuth zero-order state difference. First-order slope difference and the second-order slope difference Energy zero-order state difference DEMON spectrum zero-order state difference

[0105] (8) Use the grayscale correlation algorithm to calculate the orientation feature correlation between different targets Calculate energy feature correlation Correlation with DEMON spectrum features

[0106] (9) Determine the contribution of target azimuth characteristics, target energy characteristics, and target DEMON spectrum characteristics to target association based on different types of sonar systems of submarines and surface ships, and determine the correlation coefficient λ of each characteristic 1 , 2 , 3 ,Depend on Calculate the joint correlation of multiple features;

[0107] (10) Set the correlation decision threshold ε, when Γ(α i ,β j )≥ε, the hull sonar track α i Tracks with towed array sonar β j If yes, then no.

[0108] It is understandable that, for those skilled in the art, any equivalent replacement or change to the technical solution and inventive concept of the present invention should fall within the protection scope of the claims attached to the present invention.

Claims

1. A method for associating target tracks between a hull sonar and a towed linear array sonar, characterized in that: The steps include: (1) Based on the detection frequency band, propagation loss, background noise level, and array gain set for the hull sonar and towed linear array sonar, a formula for converting the target output signal-to-noise ratio of the hull sonar and towed linear array sonar into the target normalized energy is established: Hull sonar target energy normalization: Among them, the target spectrum level at 1000Hz is S0, and the center frequency f k0 Propagation loss is the propagation loss at the center frequency The difference between the propagation loss at 1000Hz and the background noise spectrum level at 1000Hz is NL k0 , the array gain at 1000Hz is DI k0 , n is a different frequency point, the shell sonar detection frequency band is [f kl ,f ku ]; the target output signal-to-noise ratio actually detected by the shell sonar is SNR k ;tran -1 () is a numerical conversion operation, tran -1 (a) = 10log(a); Towed linear array sonar target energy normalization: Among them, the target spectrum level at 1000Hz is S0, and the center frequency f t0 The propagation loss is is the center frequency f t0 The propagation loss is The difference between the propagation loss at 1000Hz and the background noise spectrum level at 1000Hz is NL t0 , the array gain at 1000Hz is DI t0 , m is a different frequency point, the detection frequency band of the towed linear array sonar is [f tl ,f tu ]; The target output signal-to-noise ratio actually detected by the towed linear array sonar is SNR t ; (2) The target track is divided into block sets for processing, and each batch of association processing is only performed on the target track in the block set where the selected reference track is located and the left and right adjacent block sets; (3) Adopt the joint track association algorithm of azimuth, energy, and DEMON multi-features to establish the target multi-order azimuth characteristic state difference and the target zero-order energy characteristic state difference. Target zero-order DEMON spectrum characteristic state difference The target orientation correlation Γ is calculated respectively b , energy correlation Γ e and DEMON spectrum correlation Γ d , and then the multi-feature joint correlation Jointly determine the target track correlation characteristics between the hull sonar and the towed linear array sonar; where λ1, λ2, and λ3 are the characteristic correlation coefficients; The target track is divided into block sets for processing. First, the 360° azimuth of the ship is divided into a block set every 10°, block set 1: 0°~10°, block set 2: 10°~20°, ..., block set 18: 170°~180°, block set 19: -180°~-170°, ..., block set 36: -10°~0°, a total of 36 azimuth sets; the hull sonar target track is taken as the reference track, and the towed linear array sonar target track is taken as the comparison track, and its azimuth sequence data is converted into each azimuth set sequence number, wherein the hull sonar target track can be divided into azimuth block sets 1~36, and the towed linear array sonar target track is divided into azimuth block sets 1~18. Each batch of association processing is only associated with the target tracks in the block set where the reference track is located and the left and right adjacent block sets; Target orientation feature correlation: Grayscale correlation algorithm is used to calculate the orientation feature correlation between different targets. Target energy feature correlation: The target energy characteristic sequence of the shell sonar is selected as the reference sequence, and the target energy characteristic sequence of the towed linear array sonar is selected as the comparison sequence, which are respectively denoted as and Since the target energy changes little in a short time, only the zero-order state difference is used as the comparison quantity here; Zero-order energy state difference: Then the correlation between the target energy reference sequence and the comparison sequence is: Target DEMON spectrum feature correlation: The DEMON spectrum characteristics of the hull sonar are selected as the reference sequence, and the DEMON spectrum characteristics of the towed linear array sonar are selected as the comparison sequence, which are recorded as and The target DEMON spectrum characteristics are related to the target blade number and rotation speed. They are basically unchanged in the state of uniform speed and straight flight. Here, only the zero-order state difference is used as the comparison quantity. Zero-order DEMON spectrum state difference: Then the correlation between the target DEMON spectrum feature reference sequence and the comparison sequence is:

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