A method, system and medium for optimizing the arrangement of a passive sonar buoy

Abstract

The application discloses a passive sonar buoy array optimization method and system, and a medium. The method comprises the following steps: determining a search area, determining a sonar laying position set E s and a submarine position set E t , randomly generating a plurality of positions for laying passive sonar buoys from E s as a laying position set, performing iteration on the laying position set: for each laying position s, calculating repulsive force F e (s) of the passive sonar buoy and attractive force F k (s) between the passive sonar buoy and the submarine, calculating resultant force F(s) according to the repulsive force F e (s) and the attractive force F k (s), calculating moving distance DS(s) according to F(s), and updating the laying position s in the laying position set according to the direction of the resultant force F(s) and DS(s). The application fully considers main influencing factors in an underwater acoustic environment and target characteristics based on sonar working processes and detection mechanisms, so that the array optimization of the passive sonar buoy can be realized, and the submarine detection efficiency of the passive sonar buoy can be ensured.

Description

Technical Field

[0001] This invention relates to the field of underwater target search technology, specifically to a method, system, and medium for optimizing the deployment of passive sonar buoys. Background Technology

[0002] Submarines operate underwater, possessing extremely high stealth capabilities and posing a significant threat to all types of surface ships. Their long-range attack weapons can effectively strike strategic targets deep within land. Anti-submarine warfare (ASW) by air, as a crucial countermeasure against submarines, offers advantages such as high mobility, high detection efficiency, and stealth.

[0003] Deploying a large-scale sonar buoy array over the target sea area based on the submarine's location is one of the main search methods for anti-submarine warfare (ASW). However, in real-world ASW environments, the marine environment significantly impacts the performance of sonar buoys. Sound waves, during propagation, are affected by the distribution of the seawater medium and the surface and seabed, resulting in refraction, scattering, reflection, interference, and attenuation, directly affecting the sonar buoy's effective range and measurement accuracy. Furthermore, the sonar buoy's technical parameters and the target's radiated noise intensity also directly influence the sonar buoy's detection effectiveness.

[0004] Currently, passive sonar buoy deployment mainly employs two methods. The first method relies on the subjective judgment of decision-makers, selecting from classic formations such as circular, square, triangular, and fan-shaped arrays, and setting the buoy placement and spacing based on experience. The second method utilizes computer-aided decision-making techniques, employing genetic algorithms and Monte Carlo algorithms to optimize buoy placement. The second method often achieves better submarine detection performance compared to the first. However, in its implementation, the sonar buoy's detection range is often simplified and modeled as a fixed shape such as a circle or sphere. While this approach is simple to implement, easy to understand, and computationally efficient, it neglects the impact of the marine environment on sonar detection performance. On one hand, the detection probability within the shape is not consistent; on the other hand, the detection probability outside the shape is not zero. Furthermore, the second method typically calculates the submarine distribution probability at the time of sonar buoy deployment based on the sonar buoy array configuration. In practical applications, the continuous operating time of sonar buoys is usually several hours, and the submarine distribution probability during monitoring is not constant but changes over time. Therefore, due to the above problems, the second type of method often suffers from inaccurate prediction of search probability in complex underwater acoustic environments, making it difficult to guarantee the search potential efficiency. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method, system and medium for optimizing the deployment of passive sonar buoys, based on the sonar working process and detection mechanism, and fully considering the main influencing factors in the underwater acoustic environment and target characteristics. This invention can optimize the deployment of passive sonar buoys and ensure the search-for-submarine efficiency of passive sonar buoys.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for optimizing the deployment of passive sonar buoys includes:

[0008] S1, Determine the search area, determine the set of sonar deployment locations E s and submarine location set E t From the set of sonar deployment locations E s Multiple locations for placing passive sonar buoys are randomly generated as a set of deployment positions, and the loop variable c is initialized. r ;

[0009] S2, for each deployment location s in the set of deployment locations, calculate the repulsive force F between the passive sonar buoys. e (s), based on the submarine location set E t Calculating the submarine's position using the gravitational force F between the passive sonar buoy and the submarine. k (s), based on the mutual repulsion force F e (s) and gravitational force F k (s) Calculate the resultant force F(s) on the passive sonar buoy at the deployment position s, calculate the distance DS(s) that the passive sonar buoy moves under the action of the resultant force F(s) based on the resultant force F(s), and update the deployment position s in the deployment position set based on the direction of the resultant force F(s) and the distance DS(s).

[0010] S3, Update loop variable c r Count the loop variable c. r Equal to the preset maximum number of iterations c max If the condition is met, output the final set of placement positions, end the process, and exit; otherwise, proceed to step S2.

[0011] Optionally, the search area determined in step S1 is a cylinder, and its cylindrical surface is the maximum dispersion radius d of the submarine throughout the entire submarine search process, with the initial detection position (x0, y0) of the submarine as the center. e The cylinder forms a circular region, and its height is equal to the maximum sea depth r of that circular region. z And there are:

[0012] d e =v m *(tarr +t w ),

[0013] Among them, v m For the submarine's maximum speed, t arr Let t be the time from the moment the submarine is detected to the time when the anti-submarine aircraft arrives at the initial detection position (x0, y0) of the submarine. w This is the maximum operating time for a passive sonar buoy.

[0014] Optionally, the set E of sonar deployment locations determined in step S1 s for:

[0015]

[0016] In the above formula, (x, y, z) are the coordinates of the candidate sonar buoy deployment position, (x0, y0) is the center of the search area, and d x and s y These are the longitude and latitude distance conversion parameters, respectively, d e d represents the maximum dispersion radius of the submarine during the anti-submarine search process. sm The maximum operating depth of the passive sonar buoy; the set of submarine positions E determined in step S1. t for:

[0017]

[0018] In the above formula, (x, y, z) are the coordinates of the submarine's position, (x0, y0) is the center of the search area, and d x and d y These are the longitude and latitude distance conversion parameters, respectively, d e d represents the maximum dispersion radius of the submarine during the anti-submarine search process. tm This is the maximum diving depth of the submarine.

[0019] Optionally, in step S2, the repulsive force F e The expression for the computation function of (s) is:

[0020]

[0021] In the above formula, α is a constant, and d si This represents the straight-line distance between the position s of one passive sonar buoy and the position i of another passive sonar buoy.

[0022] Optionally, in step S2, the submarine location set E is used as a reference. t Calculating the submarine's position using the gravitational force F between the passive sonar buoy and the submarine. k (s) includes:

[0023] S201, Calculate the submarine's position set Et At any position j in the equation, the underwater acoustic signal emitted by the submarine propagates to the set of candidate sonar buoy deployment positions E. s Signal margin SE at any position i ij and the detection probability DP ij ;

[0024] S202, based on the submarine's location set E t The probability H(j) of any position j in the array is given by the detection probability DP. ij The submarine's location set E is obtained by cumulative calculation. t The cumulative detection probability DR(i) of a passive sonar buoy at position i when the object is at position j.

[0025] S203, calculate the gravitational force F between the passive sonar buoy and the submarine according to the following formula. k (s):

[0026]

[0027] In the above formula, β is a constant, and E t Given a set of passive sonar buoys, DR(i) represents the submarine's position set E. t The cumulative detection probability d of a passive sonar buoy at position i when the object is at position j. si This represents the straight-line distance between the position s of one passive sonar buoy and the position i of another passive sonar buoy.

[0028] Optionally, in step S201, the signal margin SE ij The expression for the computation function is:

[0029] SE = SL-TL-NL + DI-DT

[0030] In the above formula, SE represents the calculated signal margin, SL is the target sound source level, NL is the marine ambient noise level, TL is the propagation loss, DI is the receiver directivity index, and DT is the detection threshold; the detection probability DP ij The expression for the computation function is:

[0031]

[0032] In the above formula, SE ij The signal margin is σ, and the standard deviation is σ. The calculation function expression for the cumulative detection probability DR(i) is:

[0033]

[0034] In the above formula, E tLet H(j) be the set of submarine locations, and H(j) be the probability that a submarine is located at position j within the set of submarine locations. DP ij For detection probability.

[0035] Optionally, the calculation function expression for the resultant force F(s) in step S2 is:

[0036] F(s)=F e (s)+F k (s),

[0037] In the above formula, F e (s) represents the repulsive force, F k (s) represents gravity.

[0038] Optionally, the calculation function expression for the moving distance DS(s) in step S2 is:

[0039]

[0040] In the above formula, F(s) is the resultant force F(s), and γ is the maximum single movement distance of the passive sonar buoy.

[0041] In addition, the present invention provides a passive sonar buoy deployment optimization system, including a microprocessor and a memory interconnected thereto, the microprocessor being programmed or configured to execute the passive sonar buoy deployment optimization method.

[0042] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program for being programmed or configured by a microprocessor to execute the array optimization method for the passive sonar buoy.

[0043] Compared with the prior art, the present invention has the following main advantages: The method of the present invention includes determining the search area and determining the set of sonar deployment positions E. s and submarine location set E t From E s Multiple locations for placing passive sonar buoys are randomly generated as a set of deployment locations. The set of deployment locations is iterated over: for each deployment location s, the repulsive force F of the passive sonar buoys is calculated. e (s) and the gravitational force F between the submarine k (s), according to F e (s gravity F) k (s) Calculate the resultant force F(s), calculate the moving distance DS(s) based on F(s), and update the deployment position s in the deployment position set based on the direction of the resultant force F(s) and DS(s). This invention, starting from the sonar working process and detection mechanism, fully considers the main influencing factors in the underwater acoustic environment and target characteristics, enabling optimized deployment of passive sonar buoys and ensuring their search-for-submarine effectiveness. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the basic process of the method in an embodiment of the present invention.

[0045] Figure 2 This is a schematic diagram of the calculation results in an embodiment of the present invention. Detailed Implementation

[0046] The following section will provide a detailed description of the implementation of the technical solution of the present invention through practical examples.

[0047] like Figure 1 As shown, this embodiment provides a method for optimizing the deployment of passive sonar buoys, including:

[0048] S1, Determine the search area, determine the set of sonar deployment locations E s and submarine location set E t From the set of sonar deployment locations E s Multiple locations for placing passive sonar buoys are randomly generated as a set of deployment positions, and the loop variable c is initialized. r ;

[0049] S2, for each deployment location s in the set of deployment locations, calculate the repulsive force F between the passive sonar buoys. e (s), based on the submarine location set E t Calculating the submarine's position using the gravitational force F between the passive sonar buoy and the submarine. k (s), based on the mutual repulsion force F e (s) and gravitational force F k (s) Calculate the resultant force F(s) on the passive sonar buoy at the deployment position s, calculate the distance DS(s) that the passive sonar buoy moves under the action of the resultant force F(s) based on the resultant force F(s), and update the deployment position s in the deployment position set based on the direction of the resultant force F(s) and the distance DS(s).

[0050] S3, Update loop variable c r Count the loop variable c. r Equal to the preset maximum number of iterations c max If the condition is met, output the final set of placement positions, end the process, and exit; otherwise, proceed to step S2.

[0051] The search area is generally a circular region. However, considering the effects of sound reflection, scattering, and refraction, the geographical extent of the calculation area needs to be expanded. Specifically, in this embodiment, the expansion is in the vertical direction. Since underwater sound propagation is affected by the sea surface and seabed, the depth range needs to be extended to [0, r]. z ], where rz The maximum sea depth is defined as the circular area centered at (x0, y0). Specifically, in step S1 of this embodiment, the search area is a cylinder, and its cylindrical surface is defined as the maximum dispersion radius d of the submarine throughout the entire search process, centered at the initial detection position (x0, y0) of the submarine. e The cylinder forms a circular region, and its height is equal to the maximum sea depth r of that circular region. z And there are:

[0052] d e =v m *(t arr +t w ),

[0053] Among them, v m For the submarine's maximum speed, t arr Let t be the time from the moment the submarine is detected to the time when the anti-submarine aircraft arrives at the initial detection position (x0, y0) of the submarine. w This is the maximum operating time for a passive sonar buoy.

[0054] For example, as a specific illustration, in this embodiment, the maximum speed of the submarine is set to v. m The speed is 30 knots, and the initial detection position is (112°E, 11°N), i.e., x0 = 112°E, y0 = 11°N. The time t from the moment the submarine is detected to the time the anti-submarine aircraft reaches the initial detection position is... arr The maximum working time of the sonar buoy is t, which is 1 hour. w If the search lasts for 4 hours, then the maximum dispersion radius d of the submarine during the entire search process is... e =v m *(t arr +t w The search area is defined as a circular sea area centered at (112°E, 11°N) with a radius of 9.26 km. The maximum depth r within this circular sea area is... z The height is 4200 meters. Therefore, in this embodiment, the cylinder is a cylinder centered at (112°E, 11°N), with a radius of 9.26 km and a height of 4200 meters, pointing downwards from the sea surface.

[0055] The positions within a cylinder are theoretically infinite. Therefore, in order to reduce the number of points on the cylinder, and to determine the set E of sonar deployment positions... s and submarine location set E t The location of the cylinder is used for sampling. In this embodiment, after determining the search area, the search area is rasterized to determine the location. In this embodiment, the maximum longitude x of the circular area centered at (112°E, 11°N) with a radius of 9.26km is defined. max The latitude is 112.436°E, with the maximum latitude being y. maxIt is 11.083°N, with the minimum longitude x min The minimum latitude is 111.564°E. min The value is 10.917°N. Set the rasterization parameters for the computational region, including the raster granularity s in the longitude direction. x The latitudinal grid granularity is 0.008°, s. y The depth direction grid granularity is 0.002°. z The distance is 50 meters. Based on the above parameters, the calculation area is rasterized, where the longitude direction is uniformly divided into... The latitudinal direction is uniformly divided into (ymax-ymin) / sy=(11.083°-10.917°) / 0.002°=83 segments, and the depth direction is uniformly divided into... After the region is rasterized, the position of each grid point within the region is represented by a triplet (x, y, z), where x is longitude, y is latitude, and z is depth. There are a total of 109 × 83 × 84 = 759948 three-dimensional grid points. One three-dimensional grid point is equivalent to a location within the search region. For any location s, the three-dimensional coordinates are (x, y, z). s ,y s ,z s ), where x s For longitude, y s For latitude, z s For depth.

[0056] Based on this, marine environmental data, including temperature, salinity, surface wind, sea depth, and seabed sediment, can be loaded onto each 3D grid point. Temperature and salinity are 3D data, which, after interpolation, yield data corresponding to each grid point in the rasterized computational area. Surface wind, sea depth, and seabed sediment are 2D data, which, after interpolation, yield data corresponding to each latitude and longitude grid point in the rasterized computational area. For example, using the empirical formula for ocean sound speed, the sound speed *c* at each 3D grid point's location can be calculated using the temperature, salinity, and depth data.

[0057] c = 1449.2 + Δc T +Δc TS +Δc z ,

[0058] In the above formula, Δc T Δc TS and Δc z It is an intermediate variable, and has Δc T =4.6T - 0.55T 2 +0.00029T 3 , Δc TS=(1.34-0.01T)(S-35), Δc z =0.016z. Where T is the temperature value in degrees Celsius, S is the salinity value in thousands, and z is the depth value in meters. In addition, based on the sea depth and seabed sediment type, the average acoustic parameters of the seabed sediment layer at each two-dimensional grid point location on the seabed were calculated using the Hamiltonian geoacoustic model.

[0059] In this embodiment, the set E of sonar deployment locations determined in step S1 s for:

[0060]

[0061] In the above formula, (x, y, z) are the coordinates of the candidate sonar buoy deployment position, (x0, y0) is the center of the search area, and d x and d y These are the longitude and latitude distance conversion parameters, respectively, d e d represents the maximum dispersion radius of the submarine during the anti-submarine search process. sm The maximum operating depth of the passive sonar buoy (300 meters in this embodiment); the set of submarine positions E determined in step S1. t for:

[0062]

[0063] In the above formula, (x, y, z) are the coordinates of the submarine's position, (x0, y0) is the center of the search area, and d x and d y These are the longitude and latitude distance conversion parameters, respectively, d e d represents the maximum dispersion radius of the submarine during the anti-submarine search process. tm This represents the submarine's maximum diving depth (400 meters in this embodiment). The longitude and latitude conversion parameters d... x and d y The specific search area can be determined. For example, in this embodiment, for an area centered at (112°E, 11°N) with a radius of 9.26 km, x0 = 112°E, y0 = 11°N, d e = 9.26km, longitude distance conversion parameter d x = 21.2405 km / °, latitude distance conversion parameter d y =111.3195km / °.

[0064] In this embodiment, the mutual repulsion force F in step S2 e The expression for the computation function of (s) is:

[0065]

[0066] In the above formula, α is a constant (taken as 3 in this embodiment), d si This represents the straight-line distance between the position s of one passive sonar buoy and the position i of another passive sonar buoy.

[0067] In this embodiment, step S1 involves selecting the sonar deployment location set E s Multiple locations for placing passive sonar buoys are randomly generated as a set of deployment locations, specifically from the sonar deployment location set E. s Sixteen locations are randomly generated to serve as the deployment locations for passive sonar buoys, and these 16 locations are numbered from 1 to 16.

[0068] In this embodiment, step S2 is based on the submarine location set E t Calculating the submarine's position using the gravitational force F between the passive sonar buoy and the submarine. k (s) includes:

[0069] S201, Calculate the submarine's position set E t At any position j in the equation, the underwater acoustic signal emitted by the submarine propagates to the set of candidate sonar buoy deployment positions E. s Signal margin SE at any position i ij and the detection probability DP ij ;

[0070] S202, based on the submarine's location set E t The probability H(j) of any position j in the array is given by the detection probability DP. ij The submarine's location set E is obtained by cumulative calculation. t The cumulative detection probability DR(i) of a passive sonar buoy at position i when the object is at position j.

[0071] S203, calculate the gravitational force F between the passive sonar buoy and the submarine according to the following formula. k (s):

[0072]

[0073] In the above formula, β is a constant (taken as 3 in this embodiment), E t Given a set of passive sonar buoys, DR(i) represents the submarine's position set E. t The cumulative detection probability d of a passive sonar buoy at position i when the object is at position j. si This represents the straight-line distance between the position s of one passive sonar buoy and the position i of another passive sonar buoy.

[0074] The probability of sonar detection is closely related to the signal margin; the larger the signal margin, the higher the probability of sonar detection. For passive sonar buoys, the signal margin SE in step S201 of this embodiment... ij The expression for the computation function is:

[0075] SE = SL-TL-NL + DI-DT

[0076] In the above formula, SE represents the calculated signal margin, SL is the target sound source level, NL is the marine environmental noise level, TL is the propagation loss, DI is the receiver directivity index, and DT is the detection threshold. In this embodiment, after the passive sonar buoy and submarine models are determined, the detection threshold DT of the passive sonar buoy is set to 10dB, the receiver directivity index DI is set to 15dB, the target sound source level SL of the submarine is set to 105dB, the marine environmental noise level NL is obtained from the Wenz curve, and the propagation loss TL is calculated using a ray model based on the sound speed profile and marine environmental data, where the sound speed profile is obtained based on the sound speed at each location.

[0077] In this embodiment, the detection probability DP ij The expression for the computation function is:

[0078]

[0079] In the above formula, SE ij Let σ represent the signal margin, σ represent the standard deviation, and x represent the integral variable.

[0080] In this embodiment, the calculation function expression for the cumulative detection probability DR(i) is:

[0081]

[0082] In the above formula, E t Let H(j) be the set of submarine locations, and H(j) be the probability that a submarine is located at position j within the set of submarine locations. DP ij For detection probability.

[0083] Any set of candidate sonar buoy deployment locations E s The two forces acting at any position s in the middle include the repulsive force F between the passive sonar buoys. e (s) and the gravitational force F at the submarine's location k Therefore, the calculation function expression for the resultant force F(s) in step S2 of this embodiment is:

[0084] F(s)=F e (s)+F k (s),

[0085] In the above formula, F e (s) represents the repulsive force, Fk (s) represents gravity.

[0086] In this embodiment, the calculation function expression for the moving distance DS(s) in step S2 is:

[0087]

[0088] In the above formula, F(s) is the resultant force F(s), and γ is the maximum single movement distance of the passive sonar buoy.

[0089] In step S1 of this embodiment, the loop variable c r The initial value is 0, and the loop variable c is updated in step S3. r The count is incremented by 1. Additionally, the required initialization value and update method can be selected as needed (e.g., subtracting 1; the step size can also be other step sizes as needed). In this embodiment, the preset maximum number of iterations c... max When the value is 100000, the final output set of deployment locations contains 16 deployment locations, as shown below. Figure 2 As shown, each placement position (represented by a dot) is the final position obtained through 100,000 updates. The XOY axes represent longitude and latitude, respectively, and the Z-axis represents depth. Undoubtedly, the preset maximum number of iterations, c... max You can also choose a value based on your actual needs.

[0090] Furthermore, this embodiment also provides a passive sonar buoy deployment optimization system, including a microprocessor and a memory interconnected thereto. The microprocessor is programmed or configured to execute the aforementioned passive sonar buoy deployment optimization method. Additionally, this embodiment also provides a computer-readable storage medium storing a computer program for being programmed or configured by the microprocessor to execute the aforementioned passive sonar buoy deployment optimization method.

[0091] 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 embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. 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, create a machine for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus 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.

[0092] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing the deployment of passive sonar buoys, characterized in that, include: S1, Determine the search area and the set of sonar deployment locations. Set up submarine positions From the sonar deployment location Multiple locations for placing passive sonar buoys are randomly generated as a set of deployment positions, and the loop variable is initialized. ; S2, for each deployment location in the deployment location set Calculate the mutual repulsion between passive sonar buoys According to the submarine location set Submarine position calculation: Gravity between passive sonar buoy and submarine According to mutual repulsion and gravity Calculate the deployment location of the passive sonar buoy The combined force on the place According to the combined force Calculate the resultant force of passive sonar buoys Distance of movement under action According to the combined force Direction and distance of movement Update the deployment locations in the deployment location set. ; S3, Update the loop variable Counting, checking the loop variable Equal to the preset maximum number of iterations If the condition is met, output the final set of placement positions, end and exit; otherwise, jump to step S2. mutual repulsion in step S2 The expression for the computation function is: ， In the above formula, It is a constant. Indicates the location of the passive sonar buoy The location of another passive sonar buoy The straight-line distance between them; In step S2, based on the submarine location set Submarine position calculation: Gravity between passive sonar buoy and submarine include: S201, Calculate the set of submarine positions. any position in At that time, the underwater acoustic signals emitted by the submarine propagate to the deployment location of the candidate sonar buoys. any position in the middle signal margin and the probability of being detected ; S202, based on the submarine's position assembly any position in probability Based on detection probability The set of submarine positions is obtained by cumulative calculation. any position in Location Cumulative detection probability of passive sonar buoy at the location ; S203, calculate the gravitational force between the passive sonar buoy and the submarine according to the following formula. : ， In the above formula, It is a constant. Given a set of passive sonar buoys, For the submarine to assemble at its location any position in Location The cumulative detection probability of passive sonar buoys at the location. Indicates the location of the passive sonar buoy The location of another passive sonar buoy The straight-line distance between them.

2. The method for optimizing the deployment of passive sonar buoys according to claim 1, characterized in that, The search area determined in step S1 is a cylinder, and its cylindrical surface is the initial detection position of the submarine. The center of the circle represents the maximum dispersion radius of the submarine throughout the entire submarine search process. The cylinder forms a circular region, and its height is equal to the maximum ocean depth of that circular region. And there are: ， in, This is the submarine's maximum speed. The time from when the submarine is detected to when the anti-submarine aircraft arrives at the initial detection position of the submarine. Time, This is the maximum operating time for a passive sonar buoy.

3. The method for optimizing the deployment of passive sonar buoys according to claim 2, characterized in that, The set of sonar deployment locations determined in step S1 for: ， In the above formula, The coordinates of the candidate sonar buoy deployment locations are ( x 0, y 0) is the center of the search area. and These are the longitude distance conversion parameters and the latitude distance conversion parameters, respectively. This represents the maximum dispersion radius of submarines during the anti-submarine search process. The maximum operating depth of the passive sonar buoy; the set of submarine positions determined in step S1. for: ， In the above formula, The coordinates of the submarine's position are ( x 0, y 0) is the center of the search area. and These are the longitude distance conversion parameters and the latitude distance conversion parameters, respectively. This represents the maximum dispersion radius of submarines during the anti-submarine search process. This is the maximum diving depth of the submarine.

4. The method for optimizing the deployment of passive sonar buoys according to claim 1, characterized in that, Signal margin in step S201 The expression for the computation function is: ， In the above formula, This represents the calculated signal margin. For the target sound source level, This is the marine environmental noise level. To spread the loss, To receive the directional index, The detection threshold; the detection probability The expression for the computation function is: ， In the above formula, This is the signal margin. The standard deviation is represented by the cumulative detection probability. The expression for the computation function is: ， In the above formula, For the collection of submarine locations, The submarine's location is within the set of submarine locations. j The probability of its location. For detection probability.

5. The method for optimizing the deployment of passive sonar buoys according to claim 1, characterized in that, Resultant force in step S2 The expression for the computation function is: ， In the above formula, As a repulsive force, It is gravity.

6. The method for optimizing the deployment of passive sonar buoys according to claim 1, characterized in that, Distance moved in step S2 The expression for the computation function is: ， In the above formula, To work together , This represents the maximum distance a passive sonar buoy can travel in a single operation.

7. A passive sonar buoy deployment optimization system, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to execute the passive sonar buoy array optimization method according to any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that, The computer program is used to be programmed or configured by a microprocessor to execute the array optimization method for passive sonar buoys according to any one of claims 1 to 6.

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