Sea-air cross-domain unmanned cluster guard and formation planning method

Abstract

The invention relates to a sea-air cross-domain unmanned cluster protection and formation planning method, and the method comprises the steps: forming an omnibearing situation awareness model through a plurality of sensors in a formation, and carrying out the fusion to generate a detection probability for potential threats; meanwhile, an initial formation scheme is formed by combining the sensing model with friend or foe combat information; then, constructing a strike model in a firepower coverage area according to the formation weapon equipment, and fusing to generate a damage probability of an incoming attack target; next, considering the data fusion of the detection probability and the damage probability, determining a threat angle, and estimating the interception success probability of attacks in the threat angle in real time; and finally, based on the predicted attack direction, the initial formation scheme is adjusted, so that the interception efficiency of the unmanned surface vehicle and the unmanned aerial vehicle in the formation on the incoming attack target is improved. A simulation result shows that the interception defense capability of the formation can be accurately estimated and unmanned cluster formation planning is realized through detection of external invasion and fusion of damage probabilities of perception and attack equipment.

Description

Technical Field

[0001] The invention relates to a sea-air cross-domain unmanned cluster escort and formation planning method. Firstly, a formation's all-round perception model and a multi-angle strike model are respectively constructed based on perception and weapon equipment to solve the detection probability and the damage probability. Secondly, the information fusion of the perception model and the strike model is considered to determine the fan-shaped threat angle of the anti-ship missile and calculate the successful interception probability within the threat angle. Finally, according to the predicted attack direction, the formation plan of the formation is adjusted to improve the interception efficiency of the formation on the incoming target. The invention belongs to the field of automatic control. Background Art

[0002] During the voyage of the fleet at sea, relying on the affiliated sea and air unmanned clusters to build a solid air defense system to deal with external attacks is a key factor in ensuring the safety of our personnel, ships, and equipment; it is an important technology to establish an advanced information acquisition system based on sensing equipment to fully grasp the environment and provide reliable information, and then pass the information to the weapon firepower system to complete effective interception and strike, which can greatly improve the survivability of the ship. According to the combat situation, reasonable and real-time formations should be adopted, and correct decisions should be made to achieve the purpose of resisting attacks and preserving oneself. With the development of cutting-edge technologies of unmanned boats and drones and the increasingly complex external dangers, higher requirements are placed on the perception, damage, interception, and formation building capabilities of unmanned cluster formations.

[0003] With the development of unmanned systems, unmanned surface boats have received widespread attention in the military and civilian fields, and are often used in scenarios such as ship escort, marine search and rescue, and resource exploration. In recent years, the escort and formation planning of unmanned boats against external attacks by enemies at sea have also been extensively studied. For example, the network fire system [Zhang Yao, Yan Yan, Gu Xin, et al. A review of the development of network fire missile weapon systems [J]. Cruise Missiles, 2016 (02): 39-42], this method uses patrol attack missiles and precision attack missiles in a coordinated manner, and achieves high-level environmental reconnaissance and powerful target strikes through joint combat modes such as precise navigation and positioning, network data link communication, and multi-functional precision attack; for example, the damage effectiveness evaluation based on Bayesian network [Teng T, Yu Q, Wang F, et al. Airport functional damage assessment and prediction based on Bayesian network [C]. International Conference on Information Sciences, Machinery, Materials and Energy, 2015], this method integrates the information detected by multiple sensors to determine the prior probability of damage to the target, and then calculates the membership degree of the damage index corresponding to the damage effectiveness level, establishes a fuzzy decision information matrix, and uses Bayesian network decision theory to evaluate the damage effectiveness level. However, when the damage information is expressed as more sophisticated intuitive fuzzy group decision information provided by multiple experts, the complicated calculation of the Bayesian network greatly affects the evaluation effect. Summary of the invention

[0004] Purpose of the invention: In order to address the deficiencies in the prior art, the present invention provides a sea-air cross-domain unmanned cluster escort and formation planning method to respond to invasive attacks initiated by the external environment. The sea-air cross-domain formation composed of unmanned boats and unmanned aerial vehicle clusters is used to obtain accurate sea-air cross-domain unmanned cluster perception, damage, and effective interception probability data, enhance maritime confrontation effectiveness, and can adopt adaptable formations to improve combat capabilities and ensure the safety of our important ships and equipment.

[0005] Technical solution: To achieve the above-mentioned purpose of the invention, the present invention provides a sea-air cross-domain unmanned cluster escort and formation planning method, comprising the following steps:

[0006] Step 1: Based on the actual situation, considering the superposition of the perception capabilities of all detection equipment in the formation, the multi-sensor fusion calculates the detection probability of our formation against external anti-ship attacks;

[0007] Preferably, the process of generating detection probability by multi-sensor fusion has the following steps:

[0008] Step 11, establish a radar polar coordinate system with the center of the radar antenna as the origin of the polar coordinates, the detection distance as the radial vector, and the elevation angle as the polar angle, and perform grid division on the detection space according to the radar distance and angle resolution;

[0009] Step 12, correct the radar lobe according to the accumulated radar detection data, draw the shielding angle diagram and the through-view diagram around the radar position, and establish the (θ, h, α, r) vertical lobe diagram shielding situation database according to the corresponding shielding object altitude h, shielding angle α and horizontal distance r from the shielding object to the radar antenna in the θ azimuth;

[0010] Step 13: For a class of radar lobes with no more than 3 significant side lobes and symmetry on a specified measurement plane, a lobe curve function R(ε) is obtained by using a function approximation method; if the function cannot be used for approximation, the vertical lobe curve is discretized to obtain the distance R corresponding to different elevation angles, and a (ε, R) lobe database is established;

[0011] Step 14, obtain the azimuth, elevation and distance of the center of the undetected flight data grid relative to the radar. Search the shielding situation database. If there is shielding, the detection probability is 0. If there is no shielding, the detection distance and detection probability at the corresponding elevation angle are found from the lobe curve database, and the detection probability of the grid center is calculated according to the undulation type of the target;

[0012] Step 15, performing the operation of step 14 on each grid at the same altitude layer to obtain a detection probability distribution map of the altitude layer;

[0013] Step 16, using a single radar detection probability calculation method for each radar in the network to obtain a spatial distribution of detection probability;

[0014] Step 17: From the probability knowledge, we know that if multiple radars in the radar network have detection probabilities P di If the target is found, then the probability of the radar network finding this target is Based on this formula, the detection probability of each grid in the overlapping area between radars is obtained;

[0015] Step 18, combining the detection probability distribution of each overlapping area with the detection probability distribution of a single radar to obtain the detection probability distribution of the radar network;

[0016] Considering the superposition of the perception capabilities of all detection devices on multiple ships, that is, the probability of multi-device collaborative perception, suppose there are n detection devices on the kth, k=1,…,mth ship, and their respective perception ranges are Ω i , the probability of finding the target is P zj , j = 1, ..., n, select a point (x, y) in space that the missile passes through, and use the set Λ (x,y) ={i|(x,y)∈Ωi , i=1,…,n} to indicate which radars (x,y) are in the sensing range at the same time, and To express the detection probability of point (x, y) at the superposition point. When generalizing from a single ship to multiple ships, that is, formation perception, first define the perception range of the kth ship as Γ k , select a point (x, y) in space where the missile passes, and the number of the ship that the point (x, y) belongs to at the same time is represented by the set Δ (x,y) ={k|(x,y)∈Γ k ,k=1,…,m} means that the formation detection probability is

[0017] Step 2: Considering the two attack methods of short-range missiles and long-range missiles, when the external attack missile enters our fire coverage area from the launch point, the killing capabilities of the two weapons and equipment in the incommunicable killing area are integrated, and the damage probability of different locations in the area is calculated according to the attack direction of the attack missile;

[0018] As a preference, the strike effects of a single boat and a group of boats are considered separately, specifically including:

[0019] The coordinate origin O of the plane rectangular coordinate system represents the center of mass of the enemy target, and two mutually perpendicular horizontal and vertical coordinate axes OY and OZ are drawn. A large number of air defense missile shooting tests have shown that the two coordinate components OY and OZ of the impact point on the target surface obey a two-dimensional normal distribution, and its probability density function is:

[0020]

[0021] Where ρ is the correlation coefficient in the OY and OZ directions. Variables Y and Z are independent of each other, so ρ = 0, m y 、m z is the systematic deviation of the impact point, σ y , σ z is the mean square error, y and z are the coordinates of the impact point, and the probability density function can be transformed into

[0022]

[0023] In the formula, m y 、m z is the systematic deviation of the impact point, σ y , σ z is the mean square error, y and z are the coordinates of the impact point,

[0024] Calculate the probability of damage caused by a single boat's counterattack:

[0025] When calculating the hit probability of air defense missiles, the ammunition usually hits the circular domain or equivalent rectangular domain. The enemy missile compartments can be divided into different rectangles (narrow areas). When calculating the hit probability of air defense missiles, the probability of the impact point falling into the rectangular domain is selected. Assuming that the rectangular domain D is {(y,z)|a≤y≤b,c≤z≤d}, the probability P of the air defense missile hitting the enemy missile equivalent rectangular domain is B for

[0026] P B (y,z)=P((y,z)∈D)=∫∫ D f(y,z)dydz

[0027] Where P B (y,z) is the probability of the air defense missile hitting the enemy missile equivalent rectangular domain, that is, the hit probability P((y,z)∈D) in the equivalent rectangular domain D, which is equal to the integral of the hit probability density function f(y,z) at each point in the region in the equivalent rectangular domain D.

[0028] Substituting into the calculation:

[0029]

[0030] In the formula, m y 、m z is the systematic deviation of the impact point, σ y , σ z is the mean square error, y and z are the coordinates of the impact point, a and b are the lower and upper limits of the horizontal axis of the equivalent rectangular domain of the enemy missile, and c and d are the lower and upper limits of the vertical axis. Since the above formula cannot be expressed by elementary functions, it can be found through a numerical integral table, and the hit probability is

[0031]

[0032] In the formula, a and b are the lower and upper limits of the horizontal axis of the enemy missile equivalent rectangular domain, c and d are the lower and upper limits of the vertical axis, Φ is the cumulative distribution function of the standard normal distribution. The cumulative probability calculation of the standard normal distribution is performed to determine the systematic deviation m of the impact point in the above formula: y 、m z and mean square error σ y , σ z The value of determines the value of the hit probability. Based on the parameter sample, these parameter values ​​are estimated by the Bayesian inference method.

[0033] In the time period t, the hit probability of multiple air defense missiles is

[0034]

[0035] Where P Bis the probability of an air defense missile hitting the enemy missile equivalent rectangular domain, N(t) is the number of air defense missile launches in time period t,

[0036] Calculate the probability of damage caused by the group of boats' counterattack:

[0037] First, define the damage range of the kth ship as Γ k , select a point (y, z) on the trajectory of the enemy anti-ship missile in space, then the joint destruction probability of the formation is

[0038]

[0039] Where Δ={k|(y,z)∈Γ k , k=1,...,m} is the set of serial numbers of all unmanned boats that belong to the damage range at the point (y,z), Q AB is the probability of multiple missile damage to a single unmanned boat.

[0040] Step 3: Using the detection probability and damage probability data, the spatial distribution of the enemy missile interception success probability can be estimated in real time, and the probability of interception success within the threat angle can be deeply integrated;

[0041] As a preferred method, the range of the anti-ship missile's sector threat angle is first determined according to the enemy's attack direction and range, and then the probability of successful interception within the threat angle is considered to be more scientific and reasonable, including:

[0042] Calculate the threat angle:

[0043] Assuming that the enemy's only attack target is an important ship that our fleet is protecting, record this core ship as the attack point. The enemy launches a missile at the edge of the attack range of our drone formation, record it as the bombing point. Assuming that the attack point and the bombing point are the two foci of the ellipse, and the maximum range of the anti-ship missile is equal to the major axis of the ellipse, an ellipse can be drawn, and the line connecting any point on the ellipse and the two foci is the possible flight trajectory of the anti-ship missile.

[0044] Then, the range of the strike model of our unmanned boat formation is drawn. The strike model range overlaps with the ellipse, where the intersection of the strike model and the upper half of the ellipse is recorded as point A, and the intersection of the strike model and the lower half of the ellipse is recorded as point B. Connect point A to the two focal points, and connect point B to the two focal points. At this time, the largest angle formed by "point A-strike point-point B" is the threat angle of the enemy's anti-ship missile, recorded as α.

[0045] Calculate the intercept probability of a single target threat:

[0046] Considering the scenario where perception capability and damage capability work together, the probability of a single missile intercepting an enemy target can be described as follows: the perception equipment first detects the enemy target, and then our weapon fires once. The damage probability after our missile is fired will change as follows:

[0047] P s,n =1-(1-P s,n-1 )(1-P·P n ).

[0048] Where P is the detection probability of our combat unit, P n is the hit probability of launching only the nth missile, P s,n-1 is the probability of destruction P after the n-1th missile is fired s,n-1 .

[0049] After the weapon firing frequency is given, according to the above iteration, the cumulative damage probability P of any point on the line segment from the enemy missile entering our defense zone to hitting our target can be calculated: s , which is the probability of eventually intercepting the attack.

[0050] In addition, the probability of local missiles appearing is higher within the threat angle and lower outside the threat angle. The failure of enemy missiles to appear is also considered a successful defense. If enemy missiles appear, our perception model needs to be able to detect enemy targets, open fire after detection, and destroy enemy missiles, then the defense is successful. Specifically, for the fan-shaped threat area, there are two situations when our defense is successful: one is that the missile appears in the fan-shaped area and is sensed and hit, and the other is that the missile does not appear in the fan-shaped area. According to the classical probability model, the probabilities of these two situations can be calculated. For other areas outside the fan-shaped area, similar solutions can be obtained. Taking into full consideration the probability of enemy appearance, the probability of target detection, and the probability of target damage, the final probability P of our combat unit's defense success against enemy anti-ship missiles is S for:

[0051]

[0052] Where P s is the probability of intercepting a missile under the combined influence of perception and destructive capabilities, and taking into account the cumulative effect of weapon firing, P α is the probability that the anti-ship missile appears in the area corresponding to the threat angle α.

[0053] Calculate the interception probability of multi-target threats:

[0054] Considering a multi-missile attack scenario, define P v The probability that the unmanned boat fleet can successfully intercept all attacks and protect our important ships and equipment from any damage when facing multiple external threats.

[0055]

[0056] In the formula, it is assumed that there are N anti-ship missiles attacking, P i It is the probability of successfully intercepting a missile coming from a certain direction.

[0057] Step 4: Generate an initial formation plan and predict the direction of the enemy's attack through the perception model built by radar networking and sensor fusion technology; adjust the formation plan of the unmanned boat formation according to the predicted direction of the attack, so that the formation's interception efficiency against the incoming target is improved.

[0058] Preferably, the formation optimization function has the following form:

[0059]

[0060] In the formula, J k is the formation optimization function in each direction, n is the number of attack directions of enemy anti-ship missiles, N k is the number of incoming missiles in each direction, and N is the total number of incoming missiles.

[0061] Based on the same inventive concept, the present invention provides a sea-air cross-domain unmanned cluster escort and formation planning system, comprising:

[0062] The probability model building module is used to determine the fan-shaped threat angle of the anti-ship missile and calculate the probability of successful interception within the threat angle. It includes the formation perception model and strike model constructed by the perception and weapon equipment carried by the unmanned cluster, respectively, to solve the detection probability and damage probability.

[0063] And, the formation plan planning module is used to simulate different enemy attack directions based on the data of the perception model before the fleet moves at sea, generate the best formation deployment strategy, and ensure that the formation has a certain defense capability in a possible threat environment. At the same time, during the air defense interception process, when the enemy launches an attack, the formation plan is adjusted through optimization theory to improve the interception efficiency. The specific form of this problem can be written as:

[0064]

[0065] In the formula, n represents the number of enemy attack directions, N k is the number of missiles in each direction, J is the total formation optimization function, and the formation optimization function in each direction is recorded as Each unmanned boat C i The position is (m i ,l i ), UAV F j The position of (p j ,q j ), Q is the combat area set, and there are (m i ,l i )∈Q,(p j ,q j )∈Q, is the set of real numbers, d(C i,H) is the distance between our combat unit and the protected ship, d(C i ,C i′ ) is the distance between any two unmanned boats of our side, d(H,F j ) is the distance between our protected ship and the drone, d(F j ,F j′ ) is the distance between any two of our drones, d L is the safe distance between any two UAVs, any two UAVs, and any UAV and the core ship. The distance between any UAV and the core ship must be greater than the minimum value d s , less than the maximum value d t In addition to the important ships in the fleet, there are Unmanned boats, A drone.

[0066] Based on the same inventive concept, the present invention provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the steps of sea and air cross-domain unmanned cluster escort and formation planning are implemented.

[0067] Beneficial effect: The sea-air cross-domain unmanned cluster escort and formation planning method proposed by the present invention first generates the detection probability of potential threats through the all-round situational awareness model formed by multiple sensors in the formation; at the same time, the perception model is combined with enemy and friendly combat information to form an initial formation plan; then, a strike model is constructed in the fire coverage area according to the formation's weapons and equipment, and the damage probability of incoming targets is generated through fusion; next, data fusion is performed based on the detection probability and damage probability, and the probability of successful interception of the attack can be estimated in real time; finally, based on the predicted attack direction, the initial formation plan of the formation is adjusted, so that the interception efficiency of the formation against the incoming target is improved. The simulation results show that through the fusion of the detection and damage probability of external attacks by the perception and strike equipment, the present invention can provide accurate invasion assessment and early warning, so that the formation can detect potential threats in time, and at the same time, reasonably organize the deployment of air defense weapons, so that the formation escort area is effectively covered by firepower, thereby scientifically and accurately estimating the formation's interception and defense capabilities, and realizing the prediction of the threat direction, and adjusting the unmanned cluster formation planning plan in a targeted manner. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is an overall structural diagram of the method of the embodiment of the present invention,

[0069] Figure 2 This is the formation and threat angle diagram of our team in this embodiment.

[0070] Figure 3This is the target probability distribution diagram discovered by the perception model of this embodiment.

[0071] Figure 4 This is the probability distribution diagram of the target destroyed by the strike model in this embodiment.

[0072] Figure 5 This is the interception defense success probability distribution diagram of this embodiment,

[0073] Figure 6 This is our formation planning diagram for this embodiment. DETAILED DESCRIPTION

[0074] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only 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 ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0075] Example: By Figure 1 As shown, the sea-air cross-domain unmanned cluster escort and formation planning method disclosed in the embodiment of the present invention, first, through the all-round situation awareness model formed by multiple sensors in the formation, the detection probability of potential threats is generated by fusion; at the same time, the perception model is combined with enemy and friendly combat information to form an initial formation plan; then, according to the formation weapons and equipment in the firepower coverage area, a strike model is constructed to generate the probability of damage to the incoming target by fusion; next, based on the detection probability and damage probability, data fusion is performed to estimate the probability of successful interception of the attack in real time; finally, based on the predicted attack direction, the initial formation plan of the formation is adjusted to improve the interception efficiency of the formation against the incoming target. Specifically, considering that a single device is more likely to have errors due to its own performance limitations, a multi-device collaborative estimation probability is adopted; considering the diversity of the attack direction, the formation faces targets from different directions, and a formation optimization function is constructed to find the optimal position and attack angle of the formation.

[0076] The following takes an example in which an important ship and a sea and air unmanned cluster escort formation of our side are attacked by an enemy anti-ship missile during navigation to illustrate the detailed implementation process of the embodiment of the present invention, including the following specific steps:

[0077] S1, perception model construction and detection probability estimation;

[0078] Consider the perception capabilities of enemy missiles by warning radar and infrared equipment respectively.

[0079] S11, radar perception probability calculation;

[0080] The aerial target is flying in a state of constant vibration and turbulence, and the target's perspective relative to the radar is constantly changing. Therefore, the target's radar cross-section is fluctuating. Considering the complexity of the target, the four fluctuation models proposed by Swerling are used to describe it. Among them, the echo amplitude of Swerling 1 and 2 type targets is a Rayleigh distributed random variable, and the echo amplitude of Swerling 3 and 4 type targets is a principal Rayleigh distributed random variable.

[0081] Assume that the radar transmission power is P t , the maximum gain of the radar antenna is G t , the wavelength of the electromagnetic wave radiated by the radar is λ, the radar cross-sectional area of ​​the target is S, the distance from the radar is R, and the loss of electromagnetic wave propagation and reception is L a , the anti-interference improvement factor of the radar system using anti-interference measures is F aj , then the signal-to-noise ratio in the radar receiver is:

[0082]

[0083] Where P n =kT0F n B r is the internal noise power of the receiver. When the radar detects a moving target, the probability of detecting the target is

[0084]

[0085] Where n(t) is the actual pulse accumulation number of the radar, Y0 is the detection threshold when the constant false alarm is on, S N is the signal-to-noise ratio of a single pulse.

[0086] Relative calculation method of detection probability: Since the radar antenna is directional, the concentration of energy in each elevation direction in the lobe is different. Therefore, even if the target radar cross-sectional area is constant and the straight-line distance from the radar is the same, the signal-to-noise ratio obtained in different elevation directions is different. However, the signal-to-noise ratio of the same target at different distances in the same elevation direction has a relative relationship. When the background conditions are the same, the relationship between different detection distances R1, R2 in the same elevation direction and the required average signal-to-noise ratio SNR1, SNR2 is:

[0087]

[0088] Define the distance R0 corresponding to the average signal-to-noise ratio of 1. From the radar equation, we know that R0 is a constant under the same background. Then we can know that the relationship between the signal-to-noise ratio and distance at any point within the radar detection range is:

[0089]

[0090] For Swerling 1 and 2 targets, when the false alarm probability remains unchanged, different signal-to-noise ratios SNR1 and SNR2 are related to the corresponding detection probability P. d1 , P d2 The relationship is

[0091] (SNR1+1)lnP d1 =(SNR2+1)lnP d2

[0092] For Swerling 1 and 2 targets, the above formula shows that the relative relationship between detection probability and distance is: in,

[0093] For Swerling 3 and 4 targets, when the false alarm probability remains unchanged, different signal-to-noise ratios SNR1 and SNR2 and the corresponding detection probability P d1 , P d2 The relationship is

[0094]

[0095] The false alarm probability P fa It is the probability e that the noise power exceeds the detection threshold T. -T For Swerling 3 and 4 targets, the relative relationship between detection probability and distance is:

[0096]

[0097] To sum up, for a certain type of target, under a certain false alarm probability condition, if the relative distance between the target and the radar at a certain point in space and the detection probability are known, then based on the relative relationship we can calculate the detection probability at any distance in the same elevation direction.

[0098] S12, infrared device perception probability calculation;

[0099] The sensor's target acquisition performance is modeled by simplifying the sensor characteristics into a probabilistic detection statistical model, and the detector noise is treated as Gaussian white noise with a mean of μ0 and a variance of σ. 2 The probability density function of Gaussian white noise is

[0100]

[0101] At this time, the detector noise power is

[0102]

[0103] When there is a target signal, it is considered as a simple pulse point signal. Then the signal mean is μ and the target signal power can be expressed as

[0104]

[0105] Then the detector signal-to-noise ratio can be expressed as

[0106] S NR =P s / P n .

[0107] At this time, the false alarm probability In the case of , the false alarm probability is the probability that the noise power exceeds the detection threshold. fa , we can find the target detection threshold m, and the detector signal-to-noise ratio S under the threshold m NR and the target detection probability P r Relationship. At this time, the detection probability is

[0108]

[0109] Considering the superposition of the perception effects of all detection devices on multiple unmanned boats, suppose there are n detection devices on the kth, k=1,...,mth unmanned boats, and their respective perception ranges are Ω i , the probability of finding the target is P zj , j = 1, ..., n, select a point (x, y) in space that the missile passes through, and use the set Λ (x,y) ={i|(x,y)∈Ω i , i=1,...,n} to indicate which radars (x,y) are in the sensing range at the same time, and use To express the detection probability of point (x, y) at the superposition point. When generalizing from a single unmanned boat to multiple unmanned boats, that is, formation perception, first define the perception range of the kth unmanned boat as Γ k , select a point (x, y) in space where the missile passes, and the number of the ship that the point (x, y) belongs to at the same time is represented by the set Δ (x,y) ={k|(x,y)∈Γ k ,k=1,...,m} means that the formation detection probability is

[0110] S2, strike model construction and damage probability estimation;

[0111] Taking short-range air defense missiles and long-range air defense missiles into consideration, the damage probability is calculated within their respective firepower areas. Then, the strike probabilities of the two are fused to generate a strike model of a single unmanned boat. The formation strike model can be generated by fusion of the strike models of multiple single unmanned boats.

[0112] S21, construction of single unmanned boat strike model;

[0113] Assuming that a single unmanned boat is equipped with both long-range air defense missiles and short-range air defense missiles, the short-range air defense missile's near-boundary radius of the airspace is D. min , the far radius is D max , the attack area of ​​the short-range air defense missile is fan-shaped, and the circular area between the two boundaries is the effective attack range of the short-range air defense missile. The radius of the short-range air defense missile's airspace is H min The far boundary radius of the airspace that long-range air defense missiles fight is H max The circular area between the two boundaries is the effective attack range of long-range air defense missiles. According to general equipment parameters, the attack areas of short-range air defense missiles and long-range air defense missiles overlap.

[0114] According to the division of the attack area, assuming that r is the distance between the combat unit and the enemy at time t, the probability of damage by a single missile of a single unmanned boat is P AB :

[0115]

[0116] The probability of multiple missiles damaging a single unmanned boat is Q AB :

[0117]

[0118] The total area of ​​the enemy's anti-ship missile refers to the projection area of ​​the missile's physical shape on the horizontal plane, which is usually used to assess the possibility of its detection and hit during flight. Assuming the total area of ​​the enemy's anti-ship missile is S and the lethal area is Q, the average hit number ω is

[0119]

[0120] Assume that the far boundary of the airspace that the short-range air defense missile can resist is D max , the near boundary is D min , the angle range of the airspace to be attacked is Ψ, the angle between the enemy anti-ship missile and the ship is θ, when 0≤θ≤Ψ, the damage probability of a single short-range air defense missile is P A , otherwise the damage probability of a single short-range air defense missile is 0. Therefore, the damage probability of N missiles to the enemy's anti-ship missile is

[0121]

[0122] Among them, N(T k )=n×T k , n is the firing rate of short-range air defense missiles, T k is the interception time, P Ais the damage probability of a single short-range air defense missile, and ω is the average number of hits.

[0123] T k =(ΔS) / V T

[0124] Among them, V T is the target speed, and ΔS is the distance the target flies within the strike model.

[0125] The coordinate origin O of the plane rectangular coordinate system represents the center of mass of the enemy target, and two mutually perpendicular horizontal and vertical coordinate axes OY and OZ are drawn. A large number of air defense missile shooting tests have shown that the two coordinate components OY and OZ of the impact point on the target surface obey a two-dimensional normal distribution, and its probability density function is:

[0126]

[0127] Where ρ is the correlation coefficient in the OY and OZ directions. Variables Y and Z are independent of each other, so ρ = 0, m y 、m z is the systematic deviation of the impact point, σ y , σ z is the mean square error, y and z are the coordinates of the impact point, and the probability density function can be transformed into

[0128]

[0129] In the formula, m y 、m z is the systematic deviation of the impact point, σ y , σ z is the mean square error, y and z are the coordinates of the impact point.

[0130] When calculating the hit probability of air defense missiles, it is usually considered that the ammunition hits the circular domain or the equivalent rectangular domain. The enemy missile compartments can be divided into different rectangles (narrow areas). Therefore, when calculating the hit probability of air defense missiles, the probability when the impact point falls into the rectangular domain is selected. Assuming that the rectangular domain D is {(y,z)|a≤y≤b,c≤z≤d}, the probability P of the air defense missile hitting the enemy missile equivalent rectangular domain is B for

[0131] P B (y,z)=P((y,z)∈D)=∫∫ D f(y,z)dydz

[0132] Where P B (y,z) is the probability of the air defense missile hitting the equivalent rectangular domain of the enemy missile, that is, the hit probability P((y,z)∈D) in the equivalent rectangular domain D, which is equal to the integral of the hit probability density function f(y,z) at each point in the area in the equivalent rectangular domain D.

[0133] Substituting into the calculation:

[0134]

[0135] In the formula, m y 、m z is the systematic deviation of the impact point, σ y , σ z is the mean square error, y and z are the coordinates of the impact point, a and b are the lower and upper limits of the horizontal axis of the equivalent rectangular domain of the enemy missile, and c and d are the lower and upper limits of the vertical axis. Since the above formula cannot be expressed by elementary functions, it can be found through a numerical integral table, and the hit probability is

[0136]

[0137] In the formula, a and b are the lower and upper limits of the horizontal axis of the enemy missile equivalent rectangular domain, c and d are the lower and upper limits of the vertical axis, Φ is the cumulative distribution function of the standard normal distribution. The cumulative probability calculation of the standard normal distribution is performed to determine the systematic deviation m of the impact point in the above formula: y 、m z and mean square error σ y , σ z The value of determines the value of the hit probability. Based on the parameter sample, these parameter values ​​are estimated by the Bayesian inference method.

[0138] Assume that the time when the enemy anti-ship missile is first detected by our perception model is t0=0, and the flight time of the enemy anti-ship missile within our detectable range is recorded as t, t=ΔS / V, where V is the target speed and ΔS is the distance the target flies within the damage range.

[0139] Ship-to-air missile switching firing time T zh Refers to the interval from pressing the missile "launch" button for conventional firing to the commander issuing the switch fire order, completing the switch fire preparation and pressing the "launch" button for the switch fire missile. zh Compared with the conventional shooting time t sj and the switching shooting preparation time t zb Related: T zh =t sj +t zb . Conventional shooting time t sj Refers to the time required from the missile launch conditions being met to the missile and the target meeting in the kill zone and completing the shooting effect evaluation: t sj =t zy +(n-1)τ+t pg , where n is the number of ship-to-air missiles fired at one time, τ is the interval between ship-to-air missile launches, and t zyis the time when the last ship-to-air missile encounters the target in a shooting, and its value depends on the shooting distance. pg To evaluate the shooting effect time, usually 1-3s is taken. After the conventional shooting is completed, the preparation time for the switching shooting is: t zb =t mz +t zd , where t mz is the target switching indication time, t zd is the rotation time of the illuminator, usually 8s. In the time period t, the hit probability of multiple air defense missiles is

[0140]

[0141] Where P B is the probability that the air defense missile hits the enemy missile equivalent rectangular domain, and N(t) is the number of air defense missile launches in time period t.

[0142] S22, formation strike model construction;

[0143] First, define the damage range of the kth ship as Γ k , select a point (y, z) on the trajectory of the enemy's anti-ship missile in space, and use the set Δ to represent all the ship numbers that belong to the damage range at the point (y, z) (y,z) ={k|(y,z)∈Γ k ,k=1,…,m}, then the formation hit probability Where Q AB is the probability of multiple missile damage to a single unmanned boat.

[0144] Taking into account the continuous firing, our probability of destroying the enemy target will be cumulative. Each time we launch a missile, the damage probability will change as follows:

[0145] Q n =1-(1-Q n-1 )(1-P n )

[0146] Among them, Q n and Q n-1 are the damage probabilities after launching the nth and n-1th missiles, respectively, P n is the damage probability of launching only the nth missile. Given the weapon firing frequency, according to the above iteration, the cumulative damage probability Q of any point on the line segment from the enemy missile entering our defense zone to hitting our target can be calculated, that is, the final result of the damage probability. According to the length of the path (excluding the area outside the defense zone) and speed of the enemy in the interception zone, the time T of the enemy in the interception zone can be obtained. Combined with the launch frequency f of our interception missiles, the number of our missiles reflected at any point on the path can be obtained.

[0147] S3, intercept probability fusion estimation;

[0148] S31, air threat sector angle calculation;

[0149] First, we need to estimate the sector threat angle based on the initial distance between the enemy and us and the enemy's attack direction. Assuming that the distance between the enemy and us is S d , the maximum range of the anti-ship missile is S max , the actual range is less than or equal to the maximum range. The minimum turning angle (the complementary angle of the turning angle) of a missile or an enemy aircraft carrying an anti-ship missile is α min , the minimum route segment distance is L min , the minimum length of the terminal route segment is D min The minimum length of the terminal route section of the "equivalent anti-ship missile" is the actual range S of the airborne anti-ship missile. dz . When the hit probability is not less than the given value P gd Under these conditions, the enemy always strives to minimize the missile range, maximize the distance between the enemy and us, and launch multi-directional attacks.

[0150] Assume that the enemy's only strike target is an important ship surrounded and protected by our unmanned boat formation, and record this core ship as the strike point. The enemy launches a missile at the edge of the attack range of our auxiliary drone formation, which is recorded as the bombing point. Assuming that the strike point and the bombing point are the two foci of the ellipse, and the maximum range of the anti-ship missile is equal to the major axis of the ellipse, an ellipse can be drawn, and the line connecting any point on the ellipse and the two foci is the possible flight trajectory of the anti-ship missile. Subsequently, draw the range of our strike model. The strike model overlaps with the ellipse, where the intersection of the strike model and the upper half of the ellipse is recorded as point A, and the intersection of the strike model and the lower half of the ellipse is recorded as point B. Connect point A to the two foci, and connect point B to the two foci. At this time, the largest angle formed by "point A-strike point-point B" is the threat angle of the enemy's anti-ship missile, recorded as α.

[0151] Assume that only one turn is made on the anti-ship missile attack route, the strike point is A, the bombing point is D, and the actual planned range is S hcz That is its maximum range S max , then the turning point F can be any point on the maximum route planning area ellipse. At the same time, its turning angle α should satisfy α≥α min Let ∠AFD=∠AF'D=α min , then the turning point can only be between the FF' arcs on the ellipse (F' is a point symmetrical to the minor axis of the ellipse). Obviously, when choosing a turning point on the FF' arc, the closer to the F point, the larger the corresponding maximum threat angle. Therefore, when ∠FAD=α min When the corresponding angle 2∠FAD is the maximum threat angle when only one turn is considered and only the steering angle limit is considered. When planning the route, the length of the last route section of the anti-ship missile should also meet the requirement of not less than the specified minimum distance D min,but

[0152] 1) When AF = D min When the angle 2∠FAD is the maximum threat angle when only one turn is made Its value is

[0153]

[0154] make The distance between us and the enemy is S d Satisfaction: S d =S ad .

[0155] 2) When AF<D min When the enemy and us are at a distance of: S d >S ad , in order to satisfy D min According to the restriction requirement, it is assumed that the turning point F moves along the ellipse toward the launch point to a point C, so that AC = D min , at this time the turning angle is greater than α min , and the corresponding threat angle is the maximum value, and its value is still

[0156]

[0157] 3) When AF>D min When the enemy and us are at a distance of: S d <S ad , and 2∠FAD is still the maximum threat angle when the missile makes only one turn, but it is not the actual maximum threat angle. Because when the maximum range requirement is met, the missile can make two turns, let the strike point be A, the bombing point be D, the first turn point be B, and the second turn point be C. In order to ensure that the missile can attack within the maximum range, even if the threat angle is the largest, the final turn angle should be α min , and ensure that the distance of the last route segment is not less than D min , that is, AC ≥ D min For missile route planning, the distance between each route segment should also meet the minimum distance L specified. min , then we know that CB ≥ L min , and the missile range is still its maximum range, then AC+CB+BD=S max According to the analysis, when AC=D min CB=L min When , the corresponding threat angle is the largest. At this time, due to ∠ACB=α min , then

[0158]

[0159] make

[0160] The maximum threat angle is:

[0161]

[0162] S32, single threat interception probability calculation;

[0163] Considering the scenario where perception capability and damage capability work together, the probability of a single missile intercepting an enemy target. The process is described as follows: the perception equipment first detects the enemy target, and then our weapon fires once. The damage probability after our launch of the nth missile will change as follows:

[0164] P s,n =1-(1-P s,n-1 )(1-P·P n )

[0165] Where P is the detection probability of our combat unit, P n is the hit probability of launching only the nth missile, P s,n-1 is the probability of destruction after the n-1th missile is fired.

[0166] After the weapon firing frequency is given, according to the above iteration, the cumulative damage probability P of any point on the line segment from the enemy missile entering our defense zone to hitting our target can be calculated: s , which is the probability of eventually intercepting the attack.

[0167] In addition, the probability of local missiles appearing is higher within the threat angle and lower outside the threat angle. The failure of enemy missiles to appear is also considered a successful defense. If enemy missiles appear, our perception model needs to be able to detect enemy targets, open fire after detection, and destroy enemy missiles, then the defense is successful. Specifically, for the fan-shaped threat area, there are two situations when our defense is successful: one is that the missile appears in the fan-shaped area and is sensed and hit, and the other is that the missile does not appear in the fan-shaped area. According to the classical probability model, the probabilities of these two situations can be calculated. For other areas outside the fan-shaped area, similar solutions can be obtained. Taking into full consideration the probability of enemy appearance, the probability of target detection, and the probability of target damage, the final probability P of our combat unit's defense success against enemy anti-ship missiles is S for:

[0168]

[0169] Among them, P s is the probability of intercepting a missile under the combined influence of the perception and strike models and taking into account the cumulative effect of weapon firing, P α is the probability that the anti-ship missile appears in the area corresponding to the threat angle α.

[0170] S33, multi-threat interception probability calculation;

[0171] Based on the construction of our strike model, considering the multi-missile attack scenario, we build a strike model under multi-angle attack:

[0172]

[0173] Among them, suppose there are N anti-ship missiles attacking, P v is the interception success probability of our formation when multiple missiles attack from multiple directions, P i is the probability of successfully intercepting a missile coming from a certain direction. v It is defined as the probability that our fleet can successfully implement all-round interception when responding to anti-ship missile threats from multiple directions, ensuring that our important ships and equipment are not hit in any way.

[0174] S4, under certain constraints, adjust the formation planning of the unmanned boat formation according to the predicted direction of attack, so that the unmanned boat formation can effectively intercept the incoming target.

[0175] Take the strike point as the origin of coordinates and establish a coordinate system. Note that our important ships are H and the combat units in the unmanned boat formation are C. i , the aerial drone combat unit is F j , assuming that in addition to the important ships in the fleet Unmanned boats, have drone, i.e. Assume that each unmanned boat C i The position of (x i ,y i ), the attack direction is Drone F j The position of (x j ,y j ), the attack direction is Our fleet may be attacked by multiple batches of missiles in a short period of time with high density. Therefore, it is assumed that the enemy anti-ship missiles are predicted to have n attack directions, recorded as θ = {θ1,θ2,…,θ n}, the number of enemy incoming missiles in each direction is recorded as N1, N2, ..., N n , the total number of incoming missiles is

[0176] The purpose of formation optimization is to enhance the probability of successful defense of the combat system, that is, to adjust the position and attack direction of the combat unit to reduce the survival probability of the enemy missile. The overall formation optimization function of the formation is defined as

[0177]

[0178] In the formula, J kis the formation optimization function in each direction, n is the number of attack directions of enemy anti-ship missiles, N k is the number of incoming missiles in each direction, and N is the total number of incoming missiles.

[0179] For sea and air unmanned cluster formations, it is necessary to protect the safety of important ships as much as possible. Therefore, important ships are generally deployed at the core position of the formation, and escort unmanned boats are deployed around the important ships to perform cover tasks.

[0180] In addition, the formation optimization problem also needs to meet the following constraints:

[0181] 1) Assume that the combat area is a set Q. The positions of all our combat units (i.e. important ships, unmanned boats, and drones) need to be within the combat area, i.e. (x i ,y i )∈Q,(x j ,y j )∈Q;

[0182] 2) The distance between any two of our unmanned boats and the distance between any unmanned boat and an important ship must meet the relative safety distance d L , otherwise there will be a risk of collision; similarly, the distance between any two drones must also meet the safety distance d L ;

[0183] 3) Our drone has the constraints of maximum flight distance and minimum safety distance, that is, the distance between the drone and the important ship must be greater than the minimum value d s Less than the maximum value d t .

[0184] The specific form of the formation plan generation problem can be written as:

[0185]

[0186] in, is the set of real numbers, d(C i ,H) is the distance between our combat units and important ships, d(C i ,C i′ ) is the distance between any two unmanned boats of our side, d(H,F i ) is the distance between our important ship and the drone, d(F j ,F j′ ) is the distance between any two of our drones. The detailed expression of the above constraints is given using Euclidean distance:

[0187]

[0188] When the enemy missile has only one attack direction, k = n = 1, and the number of enemy missiles is N, the above model has the following form:

[0189]

[0190] Figure 2 This is a schematic diagram of the formation and threat angle of our important ships and the escort unmanned cluster formation in this embodiment. The enemy anti-ship missile (blue ×) is launched at (250, 0), and the attack target is our important unit (red asterisk) at (0, 0). The total number of our formation is set to 7, including one important ship and 6 escort unmanned boats (diamonds). The specific positions of each ship are (0, 0), (-10, 10), (-10, -10), (30, 30), (30, -30), (80, 20) and (80, -20). After the formation of our formation and the launch position of the enemy are determined, the scene of our formation and threat fan angle can be obtained.

[0191] The perception devices used in the simulation are radar and infrared detection equipment. The pulse transmission period of the radar is 0.01, the target speed is 1, and the transmission power calculation formula is 0.001*dis^4, where dis is the maximum perception distance, which is 15, 70, 70, 15, 15, 15 and 15 respectively. The maximum gain is 100, the radar wavelength is 1, the target cross-sectional area is 5, the loss is 0.1, the anti-interference improvement factor is 10, the internal noise power is 1, the detection threshold is 10, the infrared noise mean is 0.1, the signal mean is 1, the noise standard deviation is 1, the noise power is 1.01, the specific calculation formula of the signal power is 0.99, the signal-to-noise ratio is 0.98, the detection threshold is 1, and the perception distances are 10, 10, 10, 10, 10, 10 and 10 respectively. By integrating the two types of equipment, the detection probability of anti-ship missiles can be obtained, such as Figure 3 shown.

[0192] The attack equipment consists of air defense missiles and short-range interceptor missiles. The air defense missiles are responsible for long-range strikes, while the short-range missiles are responsible for close-range interception of targets. The launch cycles of the long-range air defense missiles are 1.5, 2, 4, 3, 3, 2, and 2.5, and the launch cycles for the far-end strikes are 15, 60, 40, 15, 15, 15, and 15, and the launch cycles for the close-end strikes are 10, 10, 10, 10, 10, 10, and 10; the launch cycles of the short-range air defense missiles are 1.5, 2, 4, 3, 3, 2, and 2.5. The launch cycles for the far-end strikes are 5, 5, 5, 5, 5, and 2, 2, 2, 2, 2, 2, and 2 for the close-end strikes. The probability of the interceptor missile damaging the enemy within the range is, for example, Figure 4 shown.

[0193] Based on the enemy's attack and defense forms, the probability of the perception model finding the target, and the probability of the strike model destroying the target, the probability of successful interception within the threat angle can be calculated, such as Figure 5 shown.

[0194] like Figure 6 As shown in the figure, the red dotted line indicates that the enemy missile is predicted to attack from the northeast. In order to protect an important ship (red asterisk) in our formation, the four escort unmanned boats (diamonds) closer to the core ship quickly responded, and each ship moved to its respective target position at a relatively small distance cost, approached the core ship, and was closely protected in the direction around the important ship. The remaining two unmanned boats suddenly moved to the predicted attack direction (black dotted line), and with the cooperation of four drones (triangles), they coordinated to prepare for the enemy's combat. The distribution of each combat unit is the result of the sea and air cluster formation formation plan formed by our side based on the predicted attack direction.

[0195] Based on the same inventive concept, an embodiment of the present invention discloses a sea-air cross-domain unmanned cluster escort and formation planning method, including: a probability model construction module, used to determine the fan threat angle of the anti-ship missile and calculate the probability of successful interception within the threat angle, including a perception model and a strike model of the unmanned boat formation constructed by perception and weapon equipment respectively, to solve the detection probability and the damage probability; and a formation scheme planning module, used to simulate different enemy strike directions based on the data of the perception model before the fleet moves at sea, to generate the best formation deployment strategy, to ensure that the formation has a certain defense capability in a possible threat environment, and at the same time, during the air defense interception process, when the enemy launches an attack, the formation formation plan is adjusted through optimization theory to improve the interception efficiency.

[0196] The specific working process of each module described above can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here. The module division is only a logical function division, and there may be other division methods in actual implementation, such as multiple modules can be combined or integrated into another system.

[0197] Based on the same inventive concept, an embodiment of the present invention discloses a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the steps of the sea and air cross-domain unmanned cluster escort and formation planning method are implemented.

[0198] Those skilled in the art can understand that the technical solution of the present invention, in essence or in other words, the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for enabling a computer system (which may be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in the embodiment of the present invention. The storage medium includes: various media that can store computer programs, such as a USB flash drive, a mobile hard disk, a read-only memory ROM, a random access memory RAM, a magnetic disk or an optical disk.

[0199] The above is only one of the embodiments of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A sea-air cross-domain unmanned swarm escort and formation planning method, characterized in that: The steps include: Step 1: Based on the actual situation, considering the superposition of the perception capabilities of all detection equipment in the formation, the multi-sensor fusion is used to calculate the detection probability of our unmanned boat formation against external anti-ship attacks; Step 2: Consider the two attack methods of short-range missiles and long-range missiles. When the external attack missile enters our fire coverage area from the launch point, the killing capabilities of the two weapons and equipment in the non-killing area are combined, and the damage probability of different locations in the area is calculated according to the attack direction of the attack missile; Step 3: Using the detection probability and damage probability data, the spatial distribution of the enemy missile interception success probability can be estimated in real time, and the probability of interception success within the threat angle can be deeply integrated; Step 4: Generate an initial formation plan and predict the direction of the enemy's attack through the perception model constructed by radar networking and sensor fusion technology; adjust the formation plan according to the predicted direction of the attack, so that the formation's interception efficiency against the incoming target is improved.

2. The sea-air cross-domain unmanned cluster escort and formation planning method according to claim 1 is characterized in that: In step 1, multi-sensor data fusion is considered, including: Step 11, establish a radar polar coordinate system with the center of the radar antenna as the origin of the polar coordinates, the detection distance as the radial vector, and the elevation angle as the polar angle, and perform grid division on the detection space according to the radar distance and angle resolution; Step 12, correct the radar lobe according to the accumulated radar detection data, draw the shielding angle diagram and the through-view diagram around the radar position, and establish the (θ, h, α, r) vertical lobe diagram shielding situation database according to the corresponding shielding object altitude h, shielding angle α and horizontal distance r from the shielding object to the radar antenna in the θ azimuth; Step 13: For a class of radar lobes with no more than 3 significant side lobes and symmetry on a specified measurement plane, a lobe curve function R(ε) is obtained by using a function approximation method; if the function cannot be used for approximation, the vertical lobe curve is discretized to obtain the distance R corresponding to different elevation angles, and a (ε, R) lobe database is established; Step 14, obtain the azimuth, elevation and distance of the center of the undetected flight data grid relative to the radar, search the shielding situation database, if there is shielding, the detection probability is 0, if there is no shielding, find the detection distance and detection probability at the corresponding elevation angle from the lobe curve database, and calculate the detection probability of the grid center according to the undulation type of the target; Step 15, performing the operation of step 14 on each grid at the same altitude layer to obtain a detection probability distribution map of this altitude layer; Step 16, using a single radar detection probability calculation method for each radar in the network to obtain a spatial distribution of detection probability; Step 17: From the probability knowledge, we know that if multiple radars in the radar network have detection probabilities P di If the target is found, then the probability of the radar network finding this target is Based on this formula, the detection probability of each grid in the overlapping area between radars is obtained; Step 18, combining the detection probability distribution of each overlapping area with the detection probability distribution of a single radar to obtain the detection probability distribution of the radar network; Considering the superposition of the perception capabilities of all detection devices on multiple unmanned boats, that is, the probability of multi-device collaborative perception, suppose there are n detection devices on the kth, k=1,...,mth ship, and their respective perception ranges are Ω i , the probability of finding the target is P zj , j = 1, ..., n, select a point (x, y) in space that the missile passes through, and use the set Λ (x,y) ={i|(x,y)∈Ω i , i=1,...,n} to indicate which radars (x,y) are in the sensing range at the same time, and use To express the detection probability of point (x, y) at the superposition point, when generalizing from a single ship to multiple ships, that is, formation perception, first define the perception range of the kth ship as Γ k , select a point (x, y) in space where the missile passes, and the number of the ship that the point (x, y) belongs to at the same time is represented by the set Δ (x,y) ={k|(x,y)∈Γ k ,k=1,...,m} means that the formation detection probability is 3. The sea-air cross-domain unmanned cluster escort and formation planning method according to claim 1 is characterized in that: In step 2, the strike effects of a single boat and a group of boats are considered separately, including: The origin O of the plane rectangular coordinate system represents the center of mass of the enemy target, and two mutually perpendicular horizontal and vertical axes OY and OZ are drawn. A large number of air defense missile shooting tests show that the two coordinate components OY and OZ of the impact point on the target surface obey a two-dimensional normal distribution, and its probability density function is: Where ρ is the correlation coefficient in the OY and OZ directions. Variables Y and Z are independent of each other, so ρ = 0, m y 、m z is the systematic deviation of the impact point, σ y , σ z is the mean square error, y and z are the coordinates of the impact point, and the probability density function can be transformed into In the formula, m y 、m z is the systematic deviation of the impact point, σ y , σ z is the mean square error, y and z are the coordinates of the impact point, Calculate the probability of damage caused by a single boat's counterattack: When calculating the hit probability of air defense missiles, the ammunition usually hits the circular domain or equivalent rectangular domain. The enemy missile compartments can be divided into different rectangles (narrow areas). When calculating the hit probability of air defense missiles, the probability of the impact point falling into the rectangular domain is selected. Assuming that the rectangular domain D is {(y,z)|a≤y≤b,c≤z≤d}, the probability P of the air defense missile hitting the enemy missile equivalent rectangular domain is B for P B (y,z)=P((y,z)∈D)=∫∫ D f(y,z)dydz Where P B (y,z) is the probability of the air defense missile hitting the enemy missile equivalent rectangular domain, that is, the hit probability P((y,z)∈D) in the equivalent rectangular domain D, which is equal to the integral of the hit probability density function f(y,z) at each point in the region in the equivalent rectangular domain D. Substituting into the calculation: In the formula, m y 、m z is the systematic deviation of the impact point, σ y , σ z is the mean square error, y and z are the coordinates of the impact point, a and b are the lower and upper limits of the horizontal axis of the equivalent rectangular domain of the enemy missile, and c and d represent the lower and upper limits of the vertical axis. Since the above formula cannot be expressed by elementary functions, it can be found through a numerical integral table, and the hit probability is In the formula, a and b represent the lower and upper limits of the horizontal axis of the enemy missile equivalent rectangular domain, c and d represent the lower and upper limits of the vertical axis, and Φ is the cumulative distribution function of the standard normal distribution. The cumulative probability calculation of the standard normal distribution is performed to determine the systematic deviation m of the impact point in the above formula: y 、m z and mean square error σ y , σ z The value of the damage probability is determined. Based on the parameter samples, these parameter values ​​are estimated by the Bayesian inference method. In the time period t, the damage probability of multiple air defense missiles is Where P B is the probability of an air defense missile hitting the enemy missile equivalent rectangular domain, N(t) is the number of air defense missile launches in time period t, Calculate the probability of damage caused by the group of boats' counterattack: First, define the damage range of the kth ship as Γ k , select a point (y, z) on the trajectory of the enemy anti-ship missile in space, then the joint destruction probability of the formation is Where Δ={k|(y,z)∈Γ k , k=1,...,m} is the set of serial numbers of all unmanned boats that belong to the damage range at the point (y,z), Q AB is the probability of multiple missile damage to a single unmanned boat.

4. The sea-air cross-domain unmanned cluster escort and formation planning method according to claim 1 is characterized in that: In step 3, the interception probability fusion estimation problem is considered, which includes: Calculate the threat angle: Assuming that the enemy's only attack target is an important ship that our fleet is protecting, the core ship is recorded as the attack point. The enemy launches a missile at the edge of the attack range of the drone cluster sent by our side, which is recorded as the bombing point. Assuming that the attack point and the bombing point are the two foci of the ellipse, and the maximum range of the anti-ship missile is equal to the major axis of the ellipse, an ellipse can be drawn. The line connecting any point on the ellipse and the two foci is the possible flight trajectory of the anti-ship missile. Then, draw the range of our unmanned boat formation's strike model. The strike model range overlaps with the ellipse. The intersection of the strike model and the upper half of the ellipse is recorded as point A, and the intersection of the strike model and the lower half of the ellipse is recorded as point B. Connect point A to the two foci, and connect point B to the two foci. At this time, the largest angle formed by "point A-strike point-point B" is the threat angle of the enemy's anti-ship missile, recorded as α. Calculate the intercept probability of a single target threat: Considering the scenario where perception capability and damage capability work together, the probability of a single missile intercepting an enemy target can be described as follows: the perception equipment first detects the enemy target, and then our weapon fires once. The damage probability after our missile is fired will change as follows: P s,n =1-(1-P s,n-1 )(1-P·P n ) Where P is the detection probability of our combat unit, P n is the hit probability of launching only the nth missile, P s,n-1 is the probability of destruction after the n-1th missile is fired, After the weapon firing frequency is given, according to the above iteration, the cumulative damage probability P of any point on the line segment from the enemy missile entering our defense zone to hitting our target is calculated s , that is, the probability of eventually intercepting the attack, In addition, the probability of enemy missiles appearing within the threat angle is higher, and lower outside the threat angle. The non-appearance of enemy missiles is also regarded as a successful defense. If enemy missiles appear, our perception model needs to be able to detect enemy targets, open fire after detection, and destroy enemy missiles, then the defense is successful. Specifically, for the fan-shaped threat area, our defense is successful in two cases: one is that the missile appears in the fan-shaped area and is sensed and hit, and the other is that the missile does not appear in the fan-shaped area. According to the classical probability model, the probability of these two situations is calculated, taking into full consideration the probability of enemy appearance, the probability of target detection, and the probability of target damage. Finally, the probability of our combat unit's defense success against enemy anti-ship missiles P S for: Where P s is the probability of intercepting a missile under the combined influence of perception and destructive capabilities, and taking into account the cumulative effect of weapon firing, P α is the probability that the anti-ship missile appears in the area corresponding to the threat angle α, Calculate the intercept probability of multi-target threats: Considering a multi-missile attack scenario, define P v The probability that the unmanned boat fleet can successfully intercept all attacks and protect our important ships and equipment from any damage when facing multiple external threats. In the formula, it is assumed that there are N anti-ship missiles attacking, P i It is the probability of successfully intercepting a missile coming from a certain direction.

5. The sea-air cross-domain unmanned cluster escort and formation planning method according to claim 1 is characterized in that: In step 4, when the formation initially enters the sea environment, it uses the perception model to generate an initial formation plan and predict the attack direction of the enemy missile, and adjusts the formation according to the predicted direction. Take the strike point as the origin of coordinates and establish a coordinate system. Note that our important ships are H and the unmanned boat combat units in the formation are C. i , the drone is F j , assuming that in addition to the important ships in the fleet Unmanned boats, have drone, i.e. Assume that each unmanned boat C i The position of (x i ,y i ), the attack direction is Drone F j The position of (x j ,y j ), the attack direction is Our fleet may be attacked by multiple batches of missiles in a short period of time with high density. Therefore, it is assumed that the enemy anti-ship missiles are predicted to have n attack directions, recorded as θ = {θ1,θ2,…,θ n }, the number of enemy missiles in each direction is recorded as N1, N2, ..., N n , the total number of incoming missiles is The purpose of formation optimization is to enhance the success probability of the formation's defense, that is, to adjust the position and attack direction of the combat units to reduce the survival probability of the enemy's missiles. The overall formation optimization function of the formation is defined as In the formula, J k is the formation optimization function in each direction, n is the number of attack directions of enemy anti-ship missiles, N k is the number of incoming missiles in each direction, and N is the total number of incoming missiles.

6. A sea-air cross-domain unmanned swarm escort and formation planning system, characterized in that: Used to implement the sea-air cross-domain unmanned cluster escort and formation planning method described in any one of claims 1-5, include: The probability model building module is used to determine the sector threat angle of the anti-ship missile and calculate the probability of successful interception within the threat angle. It includes the perception model and attack model of the unmanned boat formation constructed by the perception and weapon equipment respectively, and solves the detection probability and damage probability. In addition, the formation planning module is used to simulate different enemy attack directions based on the data of the perception model before the fleet moves at sea, generate the best formation deployment strategy, and ensure that the formation has a certain defense capability in a possible threat environment. At the same time, during the air defense interception process, when the enemy launches an attack, the formation plan is adjusted through optimization theory to improve the interception efficiency. The specific form is as follows: In the formula, n represents the number of enemy attack directions, N k is the number of missiles in each direction, J is the total formation optimization function, and the formation optimization function in each direction is recorded as Each unmanned boat C i The position is (m i ,l i ), UAV F j The position of (p j ,q j ), Q is the combat area set, and there are (m i ,l i )∈Q,(p j ,q j )∈Q, is the set of real numbers, d(C i ,H) is the distance between our combat unit and the protected ship, d(C i ,C i′ ) is the distance between any two unmanned boats of our side, d(H,F j ) is the distance between our protected ship and the drone, d(F j ,F j′ ) is the distance between any two of our drones, d L is the safe distance between any two UAVs, any two UAVs, and any UAV and the core ship. The distance between any UAV and the core ship must be greater than the minimum value d s , less than the maximum value d t In addition to the important ships in the fleet, there are Unmanned boats, A drone.

7. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is loaded into the processor, the steps of the sea-air cross-domain unmanned cluster escort and formation planning method according to any one of claims 1-5 are implemented.

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