CN110118962B - Radiation noise simulation method for underwater sound target maneuvering state - Google Patents

Abstract

The invention discloses a radiation noise simulation method of an underwater sound target maneuvering state, which comprises the following steps: the first step is as follows: establishing a target radiation noise continuous spectrum model and setting target basic parameters; the second step: calculating a continuous spectrum part changing along with the speed based on the target noise continuous spectrum model and the basic parameters; the third step: calculating the signal modulation frequency changing along with the speed according to the basic parameters, and calculating the modulation spectrum component in the target radiation noise; the fourth step: calculating a stationary line spectrum part of the target radiation noise; the fifth step: calculating a target radiation noise line spectrum part which changes along with the speed; and a sixth step: and overlapping and splicing the three parts obtained by calculation in the step to finally obtain the radiation noise simulation signal of the underwater sound target maneuvering state.

Description

A Radiated Noise Simulation Method for Underwater Acoustic Target Maneuvering State

technical field

The invention belongs to the field of signal processing, and in particular relates to a simulation method of radiated noise in the maneuvering state of an underwater acoustic target.

Background technique

Due to the limited conditions, the cost of obtaining the actual underwater acoustic target radiation noise signal is relatively high. Therefore, the underwater acoustic target radiation signal simulation is often used to research the signal characteristic analysis and signal processing algorithm of the underwater acoustic target. The radiated noise under the maneuvering state of the target includes the characteristic quantities that change with time. Model and simulate the acoustic characteristics of the underwater acoustic target when the maneuver changes, and simulate and generate the target radiated noise that can reflect the characteristics of the noise change when the underwater acoustic target maneuvers. It is of great significance to the detection and identification of underwater acoustic targets.

In the traditional underwater acoustic target radiation noise simulation method, it is generally assumed that the target is in a static state or a state of uniform motion. In practice, if the underwater acoustic target is in a maneuvering state, the acceleration or deceleration process of the target will bring some parameters of the underwater acoustic target radiated noise, such as noise spectrum level change, line spectrum frequency shift, modulation depth change and so on. Due to the lack of comprehensive consideration and design of signal parameters related to the target speed change such as noise spectrum level, line spectrum frequency, modulation depth, etc. in the traditional simulation method of target radiated noise, it is difficult to adapt to the radiated noise simulation under the target maneuvering state.

SUMMARY OF THE INVENTION

Purpose of the invention: In view of the above problems in the prior art, the present invention proposes a radiation noise simulation method for the maneuvering state of an underwater acoustic target. The simulation method simulates the radiation noise of the target changing with the speed according to the provided basic parameters of the target and the target motion curve. . The radiation noise of maneuvering target includes three parts: continuum spectrum, modulation spectrum and line spectrum. The method uses empirical formulas to establish a target continuum model that varies with speed, and then calculates the parameters of the shaping filter. The modulation spectrum and line spectrum parameters of the target radiated noise are associated with the target velocity profile. The target radiation noise generated by the simulation method of the present invention comprehensively considers the influence of the target speed on the radiation noise characteristics, and is closer to the actual radiation noise of the underwater acoustic target under the maneuvering state.

Technical solution: In order to achieve the above purpose, the technical solution adopted in the present invention is: a radiated noise simulation method for the maneuvering state of an underwater acoustic target, and the simulation method includes the following steps:

Step 1: Obtain or set the motion speed sequence v[i] of underwater acoustic targets such as fishing boats, merchant ships, naval destroyers, etc., i=0, 1, ..., N-1, i is the speed sampling time sequence number, N is the speed sequence length, the speed sampling time interval is T _v ; set the sampling interval of the simulation signal sequence as T _s , T _s and T _v satisfy T _v =M×T _s , and M is a natural number greater than 1; set the target propeller rotational speed coefficient and speed adjustment coefficients K, b, the number of underwater acoustic target blades N _d and the modulation depth parameters λ, μ; set N _c stable line spectrum frequencies f_c[k _c ] and line spectrum strengths g_c[k _c ], k _c =0,1, ..., N _c -1; set Ne time-varying line spectrum frequency initial values _{f_e[ke ]} and line spectrum intensity initial value _{g_e} [ _ke ], _ke = 0, 1, ..., Ne -1; Set the target displacement as DT, and use Equation (1) or Equation (2) to calculate the total noise level sequence SLA[i] above 100Hz:

Set the maximum speed of the target movement as v _max , where v _max is a real number greater than 0, and calculate the position f ₀ [i] of the continuous spectrum component of the target radiation noise power spectrum by formula (3):

Set K ₀ and K ₁ to be real numbers greater than 0 and less than 20, and calculate the power spectrum level SL _i (f) of the continuous spectrum component of the target radiation noise power spectrum by formula (4):

In the formula, f is a real variable not less than zero, which represents the signal frequency of the continuous spectrum component.

The second step: using the power spectrum spectrum level SL _i (f) obtained in the first step, calculate the discrete sampling value of the power spectrum by formula (5), and perform equal interval sampling p _i [n]:

Calculate the discrete inverse Fourier transform of pi[ _n ] using IFFT to get Ri[ _n ].

Set p to be a natural number greater than 0 and less than 20 and solve the following equation:

Get a _i [1], a _i [2], ..., a _i [p] and b _i .

By generating the Gaussian white noise w _i [n] of unit variance, the continuum part x _i [n] of the radiated noise of the underwater acoustic target can be solved by formula (7):

The third step: According to the target propeller speed coefficient and speed adjustment coefficient K, b set in the first step, the underwater acoustic target blade number N _d and the modulation depth parameter λ, μ, calculate the underwater acoustic target propeller speed Rs by formula (8). [i]:

Rs[i]=Kv[i]+b (8)

The modulation frequency is calculated by equation (9) as f _i [k _d ], and the modulation depth _gi [k _d ] is calculated by equation (10), where k _d =1, 2, . . . , N _d +1.

After determining the modulation frequency f _i [k _d ] and the modulation depth g _i [k _d ], the modulation function sequence _mi [n] is generated:

为调制线谱相位，f_s为采样率。where g _i [k _d ] is the modulation depth that changes with the speed, f _i [k _d ] is the modulation frequency,

is the modulation line spectrum phase, and f _s is the sampling rate.

Then multiply m _i [n] with the continuous spectrum signal generated in the previous step to get the continuous signal containing the modulation spectrum component:

y _i [n] = (1+m _i [n]) x _i [n], n = 1, 2, ... M (12)

In the formula, x _i [n] is the part of the radiation noise continuum of the underwater acoustic target generated in the second step that changes with the speed, m _i [n] is the modulation function sequence generated by formula (11), and y _i [n] is A continuum signal that ultimately includes modulated spectral components.

The fourth step: for the line spectrum signal that is not related to the speed, set the number of line spectrum N _c and the amplitude g_c[k _c ] of each line spectrum, k _c =0, 1, . . . , N _c -1 and frequency f_c[k _c ] is calculated to generate a stable line spectrum signal, the method is as follows:

为线谱相位，f_s为采样率。In the formula, g_c[k _c ] is the line spectrum amplitude, f_c[k _c ] is the line spectrum frequency,

is the line spectrum phase, and f _s is the sampling rate.

The fifth step: for the line spectrum signal related to the speed, set the line spectrum number Ne, the line spectrum initial frequency _{f_e} [ _ke ], _ke = 0, 1, . . . , _Ne -1 and the line spectrum frequency and The correlation coefficient K ₃ of the target speed, by f_e _i [ _ke ]=f _e [ _ke ]+K ₃ v[i], solve the frequency curve f_e _i [ _ke ] of the signal changing with the speed;

Finally, the line spectrum signal is generated by f_e _i [ _ke ] and g_e[ _ke ], namely:

为取值大于等于0且小于2π的实数，f_s为采样率。In the formula,

is a real number whose value is greater than or equal to 0 and less than 2π, and f _s is the sampling rate.

The sixth step is to superimpose the continuous spectrum signal y _i [n], the line spectrum signal lc _i [n], and the velocity-related line spectrum le _i [n] to obtain the radiation noise z _i [n] generated by the underwater acoustic target maneuvering state ],Methods as below:

z _i [n]=y _i [n]+lc _i [n]+le _i [n], n=1, 2, ... M (15)

The M-long sequence _zi [n] obtained above is the radiation noise when the velocity is v[ _i ]. Sequentially splicing to obtain s[j], j=0, 1, ..., MN-1, s[j] is the radiated noise simulation signal sequence of the maneuvering state of the underwater acoustic target.

Beneficial effects: compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

The existing underwater acoustic target radiation noise simulation assumes that the target is in a static state or moving at a constant speed, and various parameters of the target are relatively stable at this time. However, when the underwater acoustic target is maneuvering, the characteristics of the target radiation noise will change with the speed during this period of time. The existing simulation methods do not systematically consider the influence of the noise characteristics with the speed change, and the simulated target radiation noise cannot reflect the target. The motion state of the target cannot be detected and extracted from this simulated signal. In this method, the relationship between various parameters and speed changes during target maneuvering is considered, and simulation parameters such as noise spectrum level, line spectrum frequency, modulation depth, etc. related to target speed are designed. It can support the detection and extraction of underwater acoustic target motion-related features.

Description of drawings

Fig. 1 is a flowchart of the present invention;

Figure 2-bit power spectrum model diagram;

Fig. 3 is the continuum time domain diagram that generates in the example;

Fig. 4 is the continuous spectrum frequency domain diagram that generates in the example;

Fig. 5 is the line spectrum time domain diagram that generates in the example;

6 is a frequency domain diagram of the radiated noise of the maneuvering target generated in the example;

Fig. 7 is the target linear acceleration power spectrum time-frequency diagram generated in the example;

FIG. 8 is a time-frequency diagram of the target linear acceleration demodulation spectrum generated in the example.

Detailed ways

The following will clearly and completely describe the technical solutions in the examples of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

As shown in FIG. 1 , a method for simulating radiation noise of an underwater acoustic target maneuvering state of the present invention includes the following steps:

Step 1: Get or set the underwater acoustic target motion speed sequence v[i], i=0, 1, ..., N-1, v[i] is a non-negative real number, i is the speed sampling time sequence number, and N is the length of the speed sequence , the speed sampling time interval is T _v ; the sampling interval of the simulation signal sequence is set to T _s , T _s and T _v satisfy T _v =M×T _s , and M is a natural number greater than 1; set the target propeller rotational speed coefficient and speed adjustment coefficient K, b, the number of underwater acoustic target blades N _d and the modulation depth parameters λ, μ; set N _c stable line spectrum frequencies f_c[k _c ] and line spectrum strengths g_c[k _c ], k _c =0,1,. ., N _c -1; set Ne time-varying line spectrum frequency initial values _{f_e[ke ]} and line spectrum intensity initial value _{g_e} [ _ke ], _ke = 0, 1, .., Ne -1; Set the target displacement as DT, calculate the total sound level sequence SLA[i] from the target displacement DT and the target velocity sequence v[i], and further calculate the power spectrum level SL _i of the continuum component of the radiated noise that changes with the target velocity ( f), f is a non-negative real number, indicating the frequency value;

Use Equation (1) or Equation (2) to calculate the total noise level sequence SLA[i] above 100Hz:

Set the maximum speed of target movement v _max , v _max is a real number and is greater than v[i], (i=0, 1, ..., N-1) all values in the sequence, calculate the target radiation noise power spectrum by formula (3) Continuum component spectral peak position f ₀ [i].

Set K ₀ and K ₁ to be real numbers greater than 0 and less than 20, and calculate the power spectrum level SL _i (f) of the continuous spectrum component of the target radiation noise power spectrum by formula (4):

The second step: using the power spectrum spectrum level SL _i (f) obtained in the first step, calculate the discrete sampling value of the power spectrum by formula (5), and perform equal interval sampling p _i [n],

Using IFFT to compute the discrete inverse Fourier transform of pi[ _n ], we get Ri[ _n ].

Set p to be a natural number greater than 0 and less than 20 and solve the following equation:

Get a _i [1], a _i [2], ..., a _i [p] and b _i .

By generating the Gaussian white noise w _i [n] of unit variance, the radiation noise continuum part x _i [n] of the underwater acoustic target can be solved by formula (7);

The target radiation noise continuum part is shown in Figure 3, and its power spectrum is shown in Figure 4.

Step 3: Calculate the underwater acoustic target propeller speed Rs[i] by formula (8);

Rs[i]=Kv[i]+b (8)

The modulation frequency is calculated by formula (9) as f _i [k _d ], and the modulation depth g _i [k _d ] is calculated by formula (10), where k _d =1, 2,..., N _d +1;

After determining the modulation frequency f _i [k _d ] and the modulation depth g _i [k _d ], the modulation function sequence _mi [n] is generated:

为调制线谱相位，f_s为采样率；where g _i [k _d ] is the modulation depth that changes with the speed, f _i [k _d ] is the modulation frequency,

is the modulation line spectrum phase, f _s is the sampling rate;

Then multiply m _i [n] with the continuous spectrum signal generated in the previous step to get the continuous signal containing the modulation spectrum component:

y _i [n]=(1+m _i [n]) x _i [n] (12)

In the formula, x _i [n] is the continuous spectrum time-domain signal generated by the random signal through the shaping filter in the second step, m _i [n] is the modulation function generated by equation (11), and y _i [n] is the final A continuum signal that modulates spectral components.

Step 4: Divide the underwater acoustic target line spectrum into two types, namely the line spectrum signal related to the speed and the line spectrum signal not related to the speed. For line spectrum signals that are not related to velocity, the set number of line spectra N _c and the amplitude g_c[k _c ] of each line spectrum, k _c =0, 1, . . . , N _c -1 and frequency f_c[k _c ] is calculated to generate a stable line spectrum signal, the method is as follows:

为线谱相位，f_s为采样率。其时域图如图5所示。In the formula, g_c[k _c ] is the line spectrum amplitude, f_c[k _c ] is the line spectrum frequency,

is the line spectrum phase, and f _s is the sampling rate. Its time domain diagram is shown in Figure 5.

The fifth step: for the line spectrum signal related to the speed, set the line spectrum number Ne, the line spectrum initial frequency _{f_e} [ _ke ], _ke = 0, 1, . . . , _Ne -1 and the line spectrum frequency and The correlation coefficient K ₃ of the target speed, by f_e _i [ _ke ]=f _e [ _ke ]+K ₃ v[i], solve the frequency curve f_e _i [ _ke ] of the signal changing with the speed;

Finally, the line spectrum signal is generated by f_e _i [ _ke ] and g_e[ _ke ], namely:

为取值大于等于0且小于2π的实数，f_s为采样率。In the formula,

is a real number whose value is greater than or equal to 0 and less than 2π, and f _s is the sampling rate.

Step 6: Superimpose the continuous spectrum signal y _i [n], the line spectrum signal lc _i [n], and the velocity-related line spectrum le _i [n] to obtain the radiation noise z _i [n] generated under the maneuvering state of the underwater acoustic target ],Methods as below:

z _i [n]=y _i [n]+lc _i [n]+le _i [n], n=1, 2, ... M (15)

The M-long sequence _zi [n] obtained above is the radiation noise when the velocity is v[ _i ]. After splicing, s[j], j=0, 1, ..., MN-1, s[j] is the radiated noise simulation signal sequence of the underwater acoustic target maneuvering state. An example is given below.

Example

An existing surface ship has a displacement of 3,000 tons, and it accelerates linearly at 0.03 knots per second on the water surface, and the maximum speed of the ship is 30 knots. The velocity curve is sampled at a sampling rate of 32000Hz.

First, the total sound level that changes with the speed is solved according to the formula (1), and the continuous spectrum component model is obtained by bringing the formula (3) and formula (4) into it. In this example, K ₀ =0.5 and K ₁ =6.

Next, the inverse Fourier transform of the model is solved, and the Levinson-Durbin is used to recursively solve equation (6) to obtain the shaping filter coefficients of the continuum model. The filter is excited with unit white noise to obtain the target noise continuum part.

Then, according to the set modulation spectrum parameters into formula (9), formula (10), formula (11), the signal superposed by the continuous spectrum and the modulation spectrum can be obtained.

Then, according to the set stable line spectrum frequency and amplitude and formula (13), the signal is solved, and then according to the set line spectrum parameters that change with the speed, it is brought into formula (14) to obtain the line spectrum signal.

Finally, by superimposing and splicing the signals obtained above as in equations (15) and (16), the radiation noise of the target velocity curve change can be obtained. The time-frequency diagram of the signal is shown in Figure 7, and the time-frequency diagram of the demodulation spectrum is shown in Figure 7. 8 shown.

A method for simulating radiated noise in the maneuvering state of an underwater acoustic target provided by the embodiments of the present invention has been described above in detail. In this paper, specific examples are used to illustrate the principles and implementations of the present invention. The descriptions of the above embodiments are only It is used to help understand the method of the present invention and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific embodiments and application scope. The contents of the description should not be construed as limiting the present invention.

Claims (7)

1. a radiation noise simulation method of underwater acoustic target maneuvering state, is characterized in that, this simulation method comprises the following steps: Step 1: Get or set the underwater acoustic target motion speed sequence v[i], i=0, 1, ..., N-1, v[i] is a non-negative real number, i is the speed sampling time sequence number, and N is the length of the speed sequence , the speed sampling time interval is T _v , the sampling interval of the simulation signal sequence is set to T _s , T _s and T _v satisfy T _v =M×T _s , M is a natural number greater than 1; set the target propeller rotational speed coefficient and speed adjustment coefficient K, b, the number of underwater acoustic target blades N _d and the modulation depth parameters λ, μ; set N _c stable line spectrum frequencies f_c[k _c ] and line spectrum strengths g_c[k _c ], k _c =0,1,. .., N _c -1; set Ne time-varying line spectrum frequency initial values _{f_e[ke ]} and line spectrum intensity initial value _{g_e} [ _ke ], _ke = 0, 1, ..., Ne - 1; Set the target displacement as DT, calculate the total sound level sequence SLA[i] from the target displacement DT and the target velocity sequence v[i], and further calculate the power spectrum level SL of the continuum component of the radiated noise that changes with the target velocity _i (f), f is a non-negative real number, indicating the frequency value; The second step: based on SL _i (f), solve the radiation noise continuum part x _i [n] of the underwater acoustic target with velocity, n=0, 1,..., M-1; The third step: Calculate the modulation frequency f _i that changes with the speed from the target motion speed sequence v[i], the target propeller rotational speed coefficient K and the speed adjustment coefficient b, the number of underwater acoustic target blades N _d and the modulation depth parameters λ, μ [ k _d ] and modulation depth parameter g _i [k _d ], generate a modulation function sequence _mi [n], and calculate a continuous spectrum signal y _i [n] including modulation components; Step 4: Calculate and generate a stable line spectrum signal l_c _i [n] from the stable line spectrum frequency f_c[k _c ] and the line spectrum intensity g_c[k _c ]; Step 5: Calculate the frequency value f_e _i [ _ke ] of the signal changing with the speed from the target motion speed sequence v[i], the initial value of the time-varying line spectrum frequency f_e[ _ke ], and then combine the line spectrum intensity

The value g_e[ _ke ] calculates the time-varying line spectrum signal l_e _i [n]; Step 6: Superimpose the continuous spectrum signal y _i [n], the stable line spectrum signal l_c _i [n], and the time-varying line spectrum signal l_e _i [n] to obtain the radiation noise _zi [ n]; splicing all _zi [n] in sequence to obtain the radiation noise simulation signal sequence s[j] of the maneuvering state of the underwater acoustic target, j=0, 1, . . . , NM-1. 2. the radiation noise simulation method of a kind of underwater acoustic target maneuvering state according to claim 1, is characterized in that, in the first step, obtain the radiation noise power spectrum continuum component method that the target changes with speed as follows: (2.1) Use Equation (1) or Equation (2) to calculate the total noise level sequence SLA[i] above 100Hz:

(2.2) Set the maximum speed of target movement v _max , v _max is a real number and is greater than all values in the v[i] sequence, and the position f ₀ [i] of the continuous spectrum component of the target radiated noise power spectrum is calculated by formula (3). , i=0,1,...,N-1;

(2.3) Set K ₀ and K ₁ to be real numbers greater than 0 and less than 20, and calculate the power spectrum level SL _i (f) of the continuous spectrum component of the target radiation noise power spectrum by formula (4):

3. the radiated noise simulation method of a kind of underwater acoustic target maneuver state according to claim 2, is characterized in that, in the second step, based on SL _i (f) solves the radiated noise continuum that the underwater acoustic target changes with speed Part _xi [n], the method is as follows: (3.1) Using the power spectrum spectrum level SL _i (f) obtained in the first step, the discrete sampling values of the power spectrum are calculated by formula (5), and the sampling values p _i [n] are equally spaced:

Use IFFT to calculate the discrete inverse Fourier transform of p _i [n] to get R _i [n]; (3.2) Set p to be a natural number greater than 0 and less than 20, and solve the following equation:

get a _i [1], a _i [2], ..., a _i [p] and b _i ; (3.3) By generating the Gaussian white noise w _i [n] with unit variance, the radiation noise continuum part x _i [n] of the underwater acoustic target changing with the speed can be solved by formula (7);

4. the radiated noise simulation method of a kind of underwater acoustic target maneuver state according to claim 3, is characterized in that, in the 3rd step, by target motion speed sequence v[i], target propeller rotational speed coefficient and speed adjustment coefficient K, b, the number of underwater acoustic target blades N _d and the modulation depth parameters λ, μ, calculate the modulation frequency f _i [k _d ] and modulation depth parameter g _i [k _d ] that vary with the speed, and generate the modulation function sequence _mi [ n], and calculate the continuum signal y _i [n] including the modulation component as follows: (4.1) Calculate the underwater acoustic target propeller speed Rs[i] by formula (8); Rs[i]=Kv[i]+b (8) (4.2) The modulation frequency is calculated as f _i [k _d ] by the formula (9), and the modulation depth g _i [k _d ] is calculated by the formula (10), where k _d =1,2,...,N _d + 1;

(4.3) After determining the modulation frequency f _i [k _d ] and the modulation depth g _i [k _d ], generate the modulation function sequence _mi [n]:

where g _i [k _d ] is the modulation depth that changes with the speed, f _i [k _d ] is the modulation frequency,

is the modulation line spectrum phase, f _s sampling rate; (4.4) Multiply m _i [n] with the continuous spectrum signal generated in the previous step to obtain a continuous signal containing modulation spectrum components: y _i [n]=(1+m _i [n]) x _i [n] (12) In the formula, x _i [n] is the continuous spectrum time domain signal generated by the random signal through the shaping filter in the second step, m _i [n] is the modulation function generated by formula (11), and y _i [n] is the final A continuum signal that modulates spectral components. 5. the radiation noise simulation method of a kind of underwater acoustic target maneuvering state according to claim 4, is characterized in that, in the 4th step, for the line spectrum signal that is irrelevant with speed, by the set line spectrum quantity N _c And each line spectrum amplitude g_c[k _c ], k _c =0, 1, . . . , N _c -1 and frequency f_c[k _c ] are calculated to generate a stable line spectrum signal, the method is as follows:

In the formula, g_c[k _c ] is the line spectrum amplitude, f_c[k _c ] is the line spectrum frequency,

is the line spectrum phase, and f _s is the sampling rate. 6. The radiated noise simulation method of a kind of underwater acoustic target maneuver state according to claim 5, it is characterized in that, in the 5th step, for the line spectrum signal related to speed, calculate the frequency curve f_e that the signal changes with speed _i [k _e ], the time-varying line spectrum signal l_e _i [n] is obtained from this, the method is as follows: (6.1) For the line spectrum signal related to the speed, set the line spectrum number Ne, the line spectrum initial frequency _{f_e} [ _ke ], _ke = 0, 1, . . . , _Ne -1 and the line spectrum frequency and target The correlation coefficient K ₃ of the speed, by f_e _i [ _ke ]=f _e [ _ke ]+K ₃ v[i], solve the frequency curve f_e _i [ _ke ] of the signal changing with the speed; (6.2) Finally, the line spectrum signal is generated by f_e _i [ _ke ] and g_e[ _ke ], namely:

In the formula,

is a real number whose value is greater than or equal to 0 and less than 2π, and f _s is the sampling rate. 7 . The method for simulating radiation noise of underwater acoustic target maneuvering state according to claim 6 , wherein in step 6, the continuous spectrum signal y _i [n], the line spectrum signal lc _i [n] , the velocity-related line spectra le _i [n] are superimposed to obtain the radiation noise z _i [n] generated by the underwater acoustic target in the maneuvering state, the method is as follows: z _i [n]=y _i [n]+lc _i [n]+le _i [n], n=1,2,...,M (15) The M-long sequence _zi [n] obtained above is the radiation noise when the velocity is v[ _i ]. Sequentially splicing s[j], j=0, 1, ..., MN-1, s[j] is the radiated noise simulation signal sequence of the maneuvering state of the underwater acoustic target.

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