阅读说明：本技术 一种基于最大边际收益的循环否决目标分配方法 (Cyclic veto target allocation method based on maximum marginal profit ) 是由 陈万春 陈中原 于琦 于 2021-08-05 设计创作，主要内容包括：本发明提供了一种基于最大边际收益的循环否决目标分配方法,包括以下步骤：步骤一：建立拦截器对目标拦截概率模型,计算各拦截器对各目标的拦截概率；步骤二：建立高级最大边际收益算法寻优模型,根据各拦截器对各目标的拦截概率,通过寻找武器目标对使指标函数的边界收益最大,从而找到一个性能较优的次优解；步骤三：建立邻域搜索模型,使用循环否决方法进行次优解附近的邻域搜索,提高解的最优性,解决目标分配问题。该方法提高了全局收敛性,在求解最优性上相对于遗传算法等近年来发展的算法均有较大优势,无论是大规模还是小规模的目标分配,本发明得到的次优解都具有相对更高的边际收益。(The invention provides a cyclic veto target allocation method based on maximum marginal profit, which comprises the following steps: the method comprises the following steps: establishing a target interception probability model of the interceptors, and calculating the interception probability of each interceptor to each target; step two: establishing an advanced maximum marginal benefit algorithm optimizing model, and finding out a suboptimal solution with better performance by finding weapon target pairs to maximize the marginal benefit of the index function according to the interception probability of each interceptor to each target; step three: and establishing a neighborhood searching model, and performing neighborhood searching near a suboptimal solution by using a cyclic veto method, so that the optimality of the solution is improved, and the problem of target allocation is solved. The method improves the global convergence, has great advantages in solving optimality compared with algorithms developed in recent years such as genetic algorithms, and the like, and the suboptimal solution obtained by the method has relatively higher marginal benefits no matter large-scale or small-scale target distribution.)

1. A cyclic veto target allocation method based on maximum marginal profit is characterized in that: the method comprises the following steps:

the method comprises the following steps: establishing a target interception probability model of the interceptors, and calculating the interception probability of each interceptor to each target;

step two: establishing an advanced maximum marginal benefit algorithm optimizing model, and finding out a suboptimal solution with better performance by finding weapon target pairs to maximize the marginal benefit of the index function according to the interception probability of each interceptor to each target;

step three: and establishing a neighborhood searching model, and performing neighborhood searching near a suboptimal solution by using a cyclic veto method, so that the optimality of the solution is improved, and the problem of target allocation is solved.

2. The method for cyclic veto target allocation based on maximum marginal profit according to claim 1, characterized in that: the target interception probability model of the interceptor comprises the probability of reliable flight of the interceptor, the probability of successful last guidance shift change in the interceptor and the zero control interception probability of the interceptor on the target; the probability of successful terminal guidance shift switching in the interceptor comprises the probability that a target falls into a terminal guidance seeker view field when the terminal guidance shift switching is performed and the probability that the terminal guidance seeker successfully completes target detection when the terminal guidance shift switching is performed; three quantitative indexes including zero control miss amount, residual flight time and line-of-sight angular rate are mainly considered for the zero control interception probability of the interceptor on the target, and each index has complex influence on the zero control interception probability.

3. The method for cyclic veto target allocation based on maximum marginal profit according to claim 1, characterized in that: the interceptor intercepts the target with a probability model:

wherein, P_ijThe interception probability of the ith interceptor to the jth target;the probability of reliable flight for the ith interceptor;the probability of successful shift change of the last guidance in the ith interceptor is obtained;and the zero control interception probability of the ith interceptor on the target.

4. The method for cyclic veto target allocation based on maximum marginal profit according to claim 1, characterized in that: probability of successful terminal guidance shift change in interceptor:

whereinThe probability that the target falls into the field of view of the last guidance seeker during the middle and last guidance shift change is obtained;the probability that the middle guidance and the end guidance seeker successfully complete target detection is achieved.

5. The method for cyclic veto target allocation based on maximum marginal profit according to claim 1, characterized in that: the zero control interception probability of the interceptor to the target is defined as:

wherein, P_ZEM(i,j)、Andrespectively zero control interception probability, beta, corresponding to zero control miss distance, residual flight time and line-of-sight angular rate_ZEM、Andis a weighted value and satisfies:

6. the method for cyclic veto target allocation based on maximum marginal profit according to claim 1, characterized in that: the advanced maximum marginal profit algorithm optimizing model comprises the selection of a maximum weapon target pair and the calculation of a benefit matrix R; selecting a maximum weapon target pair from undistributed weapons, selecting a weapon target pair with the largest element in the benefit matrix R, and setting the corresponding position of the distribution matrix X as 1; the elements in the benefit matrix R are:

r(i,j)＝p(i,j)v(j)q(j) (5)

wherein: p (i, j) and V (j) are elements in the interception probability matrix P and the target threat weight vector V, respectively, i ∈ {1, …, m }, j ∈ {1, …, n }, and m and n are weapons, respectivelyNumber and target number;where X (i, j) is an element in the assignment matrix X.

7. The method for cyclic veto target allocation based on maximum marginal profit according to claim 1, characterized in that: the cyclic veto method is a heuristic neighborhood search algorithm, which carries out veto on weapon target distribution scheme pairs obtained by utilizing local optimal thought successively to try to find out a more optimal solution from a new distribution scheme; the veto is carried out from the local optimal distribution scheme one by one, and the veto circulation is restarted directly after the index value is improved so as to find out a more optimal distribution scheme more quickly.

8. A method of cyclic overruling target allocation based on maximum marginal gain according to claim 1 or 2 or 3 or 4 or 5 or 6 or 7, wherein: in the step 1, specifically, the method comprises the steps of 1.1 to 1.3;

step 1.1, establishing a middle and last guidance shift deviation model, calculating the radius of a middle and last guidance shift deviation circle, and further calculating to obtain the probability that a target falls into the view field of an interceptorFurther, setting false alarm probabilityAnd calculating the signal-to-noise ratio S/N, and calculating to obtain the probability of realizing the middle-terminal guidance shift change and the successful completion of the target detection of the terminal guidance seekerAnd further calculating the success probability of the middle and end guidance shift change

Defining deviation circle radius perpendicular to visual field plane for middle and end guidance shiftComprises the following steps:

in the formula, σ_irThe radius of the position error circle of the ith interceptor; sigma_jrIs the position error circle radius of the jth target; sigma_ijqThe angle of the jth target relative to the seeker of the ith interceptor is adjusted; r_ijThe relative distance between the jth target and the ith interceptor during the guidance shift change at the middle and the end is shown; wherein:

in the formula, σ_irx,σ_iry,σ_irzIs the i-th interceptor position error component; sigma_irx,σ_iry,σ_irzError component of j-th target position;the high and low angles of the line of sight of the eyes are set;the direction angle of the visual line of the pineyes; therefore, the probability that the jth target falls into the view field of the ith interceptorComprises the following steps:

because the detection probability of the seeker to the target is related to the S/N requirement of a given signal-to-noise ratio, seeker frame frequency and detection time; since the interception of the target is performed outside the atmosphere, and therefore the influence of the atmosphere is not considered, the calculation formula of the signal-to-noise ratio S/N is as follows:

whereinIs the target radiation intensity; NEFD_iThe equivalent flux density of seeker noise of the ith interceptor;

let the false alarm probability beThe target detection probability is calculated as follows:

wherein σ is seeker detection noise variance; alpha is the amplitude of the detection signal; t is a detection threshold;is a standard normal distribution; f. of_nAccumulating the detection frame number; as long as the false alarm probability is givenCalculating T/sigma, and inputting f_nAnd S/N (db) obtaining target detection probability

Calculating the probability of the target falling into the view field of the interceptorAnd to achieve the intermediate productProbability of shift-leading and end-leading seeker successfully completing target detectionProbability of successful guidance shift change at later, middle and endExpressed as:

step 1.2, setting influence weight values of zero control miss distance, residual flight time and line-of-sight angular rate, calculating zero control interception probability corresponding to the three indexes by adopting a negative exponential function according to the three indexes, and further calculating the zero control interception probability of the interceptor to the target by using a weighting method

Three quantitative indexes including zero control miss amount, residual flight time and line-of-sight angular rate are considered for the zero control interception probability of the target by the interceptor, and each index has complex influence on the zero control interception probability; a negative exponential function is adopted to define the zero control interception probability;

setting the influence weight values of zero control miss distance, residual flight time and line-of-sight angular rate as beta_ZEM、Andand satisfies the following conditions:

the zero control miss amount is used for measuring the interceptionAn important index for judging whether the interceptor can hit the target is also an important index for measuring the intercepting effectiveness; thus, β_ZEMRatio of need to needAndlarger than the others;

let delta ZEM, delta T_goAndthe average values of the zero miss control amount, the remaining flight time and the line-of-sight angular rate are respectively defined as follows:

where m is the number of interceptors and n is the target number, ZEM (i, j), T_go(i, j) andrespectively setting zero control miss distance, residual flight time and line-of-sight angular rate of the ith interceptor on the jth target;

let I_aIs an intermediate variable for measuring whether the ith interceptor can intercept the jth target; the interceptor controlling the current starting-up timeTo approximate, where m_iFor the current quality of the ith interceptor,for the current mass flow of the ith interceptor, then

Then the current remaining mobility of the interceptor, where a_maxMaximum acceleration generated for interceptor orbit control; if the remaining maneuvering capacity of the interceptor is greater than the zero control miss distance at the current moment, the target is considered to be blocked, the interception probability is a negative exponential function of the zero control miss distance, otherwise, the item is a small value, namely:

after the intermediate variables are obtained through calculation, zero control miss distance, residual flight time and zero control interception probability of the interceptor under the influence of the line-of-sight angular rate are defined in the form of a negative exponential function, and are respectively as follows:

whereinAndis an initial default value of the corresponding probability; based on the three quantitative indexes, the zero control interception probability of the interceptor to the target is calculated by using a weighting methodIs defined as:

step 1.3, the probability of reliable flight of each interceptor is givenBy calculating the reliable flight probability with step 1.1 and step 1.2Probability of success of arrival, terminal guidance and shift changeAnd zero control interception probability of interceptor to targetMultiplying and calculating to obtain the interception probability P of the space interceptor to the target_ij；

Setting probability of interceptor reliable flightIs directly given or is uniformly distributed in a certain interval; probability of reliable flight at a given interceptorThen, establishing an interception probability model of the space interceptor to the target as follows:

wherein, P_ijThe interception probability of the ith interceptor to the jth target.

9. A method of cyclic overruling target allocation based on maximum marginal gain according to claim 1 or 2 or 3 or 4 or 5 or 6 or 7, wherein: establishing an advanced maximum marginal benefit algorithm solution model in the step 2, calculating a benefit matrix R, selecting a weapon target pair with the largest element in the matrix R from undistributed weapons for distribution, and circulating until all weapons are completely distributed, and stopping to obtain a suboptimal solution of target distribution;

setting the number of weapons as m, the number of targets as n, and setting the interception probability matrix as P ∈ R^m×nThe distribution matrix is X ∈ R^m×nThe weight value of the target threat is V epsilon R^n×1The elements in the three matrices are respectively: p (i, j), x (i, j) and v (j), wherein i ∈{1,…,m}、j∈{1,…,n}；

Firstly, setting the number s of the distributed weapons to be 0, and initializing a target distribution matrix to be a zero matrix; next, a vector Q is calculated, where the elements are:

and calculating a benefit matrix R, wherein the elements are as follows:

r(i,j)＝p(i,j)v(j)q(j) (19)

wherein v (j) is the value of the jth target; further, selecting a weapon target pair with the largest element in the matrix R from the undistributed weapons, and setting the corresponding position of the distribution matrix X as 1; and finally accumulating the number s of the distributed weapons by 1, judging the size relation between the number s and the number m of the weapons, if s is equal to m, ending the solution, otherwise, recalculating the vector Q, and starting the next round of loop iteration.

10. A method of cyclic overruling target allocation based on maximum marginal gain according to claim 1 or 2 or 3 or 4 or 5 or 6 or 7, wherein: establishing a cyclic veto neighborhood search model in the step 3, and veto weapon target distribution scheme pairs obtained by using the local optimal idea one by one to try to find a better solution from a new distribution scheme, and finally realizing the rapid solution of the weapon target distribution problem;

firstly, the sub-optimal solution allocation scheme and the index value obtained in the step 2 are respectively stored as: x₀And f (X)₀) (ii) a Setting an intermediate variable k to be 1; under the condition that the distribution result of the kth round is rejected, a sub-optimal solution is found again by using a high-grade maximum marginal benefit algorithm, and the distribution scheme and the index value are respectively stored as follows: x₁And f (X)₁) (ii) a The index values f (X) of the two allocation schemes are then compared₀) And f (X)₁) If f (X)₁)＞f(X₀) Then let X₀＝X₁、f(X₀)＝f(X₁) K is 1, and the rejection searching is carried out again; if f (X)₁)≤f(X₀) Then judge againIf k is equal to m, jumping out of a loop, and terminating simulation; otherwise, let k equal to k +1 and perform the overruling optimization again.

Technical Field

The invention relates to a cyclic rejection target allocation method based on maximum marginal profit, and belongs to the field of target allocation.

Background

With the continuous development of bait technology, the task of distinguishing real objects from baits becomes increasingly difficult for intercepting missile guides. Under the condition that the probability of identifying the target by the missile is gradually reduced, the interception effect of a kinetic energy interceptor carried by the traditional interception missile is greatly weakened. In order to improve the reliability of an interceptor system outside the atmosphere, researchers put forward the concept of a multi-target killer, aiming at not distinguishing real targets and baits in a space and reducing the requirement on the identification performance of a seeker. When the multi-target killer is subjected to guidance shift change at the middle and the end, each interceptor needs to be assigned with a specific target, which is called a weapon target assignment problem. The goal of solving the weapon target assignment problem is to be able to maximize weapon performance. The target distribution criteria generally include the maximum probability of interception of a target group, the maximum residual value of intercepting targets with fewer weapons, and protecting a defense area.

The target assignment algorithm can be divided into an exact algorithm and a heuristic method. The precise algorithms for solving the target distribution are only a few, mainly because the target distribution problem is a complex NP complete problem and is difficult to solve. For the static target allocation problem, if there are m weapons, n targets, a possible allocation scheme is n, assuming that all weapons must be allocated^mAnd (4) seed preparation. As the number of weapons and targets increases, the possible solutions will grow exponentially, and searching all solutions will face a huge computational burden. The accurate algorithm for target allocation is mainly a branch-and-bound method, researchers use the method to solve the nonlinear target allocation problem and can find the optimal solution of the small-scale problem of 10 weapons and 10 targets, however, with the increase of the problem scale, the method may not find the solution within 7 days. In order to accelerate the solution efficiency of the large-scale target distribution problem, researchers convert the nonlinear target distribution problem into a linear problem and then find the optimal solution by utilizing a linear integer programming technology. The search range is also reduced by the researchers developing an algorithm that finds the most profitable weapon-target assignment pairs to solve the optimal solution, using a joint ammunition efficacy manual, specifying the minimum efficacy of each weapon-target assignment pair.

However, due to the computational complexity of the target distribution problem, heuristic algorithms are increasingly widely applied to the target distribution problem, especially random optimization methods based on bionic ideas, such as ant colony algorithms, bee colony algorithms, genetic algorithms, and the like. The genetic algorithm is a parallel computing method for simulating the species evolution thought by using the bionics principle, and has the advantages that: the method can represent feasible solutions of various problems due to the coding characteristics, has good group search characteristics, has certain expandability and the like. However, the genetic algorithm still has partial defects: constraints that do not easily represent optimization problems; the convergence rate is too slow and is easy to converge to a local optimal solution; and because the optimization result has certain randomness, the analysis on the reliability and the calculation complexity is not intuitive. Although the optimization effect of the genetic algorithm is improved to a certain extent after suboptimal solution or neighborhood search improvement, due to the large-scale parallel search characteristic of the genetic algorithm, the calculation time is increased sharply when the population scale is increased, and when the calculation time is increased to a point that the real-time calculation requirement cannot be met, a new target distribution solving algorithm which mainly emphasizes the real-time performance and considers the solving quality is required to be considered.

Disclosure of Invention

Objects of the invention

The invention mainly aims to provide a cyclic rejection target allocation method based on maximum marginal profit, which can obtain suboptimal solution or even optimal solution in a short time and improve the solution quality of a target allocation problem.

(II) technical scheme

The present invention is directed to a method for cyclic veto target allocation based on maximum marginal profit, so as to solve at least the above problems.

The invention provides a cyclic veto target allocation method based on maximum marginal profit, which comprises the following steps: the method comprises the following steps: establishing a target interception probability model of the interceptors, and calculating the interception probability of each interceptor to each target; step two: establishing an advanced maximum marginal benefit algorithm optimizing model, and finding out a suboptimal solution with better performance by finding weapon target pairs to maximize the marginal benefit of the index function according to the interception probability of each interceptor to each target; step three: and establishing a neighborhood searching model, and performing neighborhood searching near a suboptimal solution by using a cyclic veto method, so that the optimality of the solution is improved, and the problem of target allocation is solved.

Further, the probability model for intercepting the target by the interceptor comprises the probability of reliable flight of the interceptor, the probability of successful terminal guidance shift change in the interceptor and the zero control interception probability of the interceptor on the target.

Further, the probability that the last guidance shift in the interceptor succeeds comprises the probability that the target falls into the view field of the last guidance seeker during the middle and last guidance shift and the probability that the middle and last guidance shift is achieved and the last guidance seeker succeeds in completing target detection.

Furthermore, three quantitative indexes including zero control miss distance, residual flight time and line-of-sight angular rate are mainly considered for the zero control interception probability of the interceptor on the target, and each index has complex influence on the zero control interception probability.

Further, the interceptor intercepts the target with a probability model:

wherein, P_ijThe interception probability of the ith interceptor to the jth target;the probability of reliable flight for the ith interceptor;the probability of successful shift change of the last guidance in the ith interceptor is obtained;and the zero control interception probability of the ith interceptor on the target.

Further, the probability of successful terminal guidance shift change in the interceptor:

whereinThe probability that the target falls into the field of view of the last guidance seeker during the middle and last guidance shift change is obtained;the probability that the middle guidance and the end guidance seeker successfully complete target detection is achieved.

Further, the zero control interception probability of the interceptor on the target can be defined as:

wherein, P_ZEM(i,j)、Andrespectively zero control interception probability, beta, corresponding to zero control miss distance, residual flight time and line-of-sight angular rate_ZEM、Andis a weighted value and satisfies:

further, the advanced maximum marginal profit algorithm optimizing model mainly comprises selection of a maximum weapon target pair and calculation of a benefit matrix R. The selection of the largest weapon target pair is to select the weapon target pair with the largest element in the benefit matrix R from the unassigned weapons and set the corresponding position of the assignment matrix X to 1. The elements in the benefit matrix R are:

r(i,j)＝p(i,j)v(j)q(j) (5)

wherein: p (i, j) and V (j) are elements in the interception probability matrix P and the target threat weight vector V, respectively, i ∈ {1, …, m }, j ∈ {1, …, n }, and m and n are the number of weapons and the number of targets, respectively.Where X (i, j) is an element in the assignment matrix X.

Further, the circular veto method is a heuristic neighborhood search algorithm that serially veto pairs of weapon target distribution schemes derived using local optimality to try to find a better solution from the new distribution schemes. The scheme starts to reject from the local optimal distribution scheme one by one and directly restarts a rejection loop after the index value is improved so as to find a more optimal distribution scheme more quickly. Compared with the traditional ED element heuristic neighborhood searching method, the method provided by the invention has the advantages that the execution times are less, and the number of the interceptors cannot exceed m times at most; the scheme provided by the invention is simple to execute, does not need to calculate an index matrix, does not need to design a threshold value to determine a rejection scheme, and has more obvious operability; the scheme provided by the invention has higher optimization efficiency.

(III) advantages and Effect of the invention

By applying the technical scheme of the invention, a method for rapidly solving the target distribution problem is designed and provided, the method improves the global convergence, has greater advantages in solving optimality compared with algorithms developed in recent years such as genetic algorithm and the like, and suboptimal solutions obtained by the algorithm of the invention have relatively higher marginal benefits no matter large-scale or small-scale target distribution. In addition, the algorithm of the invention can obtain suboptimal solution or even optimal solution in a short time, the advantage is more obvious in the problem of large-scale target distribution, and the requirement of real-time index can be met under the typical battle condition.

Drawings

FIG. 1 is a flow chart of an advanced maximum marginal gain algorithm;

FIG. 2 is a flow chart of a loop veto method;

FIG. 3 is a diagram of the results of the allocation of six interceptors to six targets.

Detailed Description

The following further describes the method for allocating cyclic veto targets based on maximum marginal profit according to the present invention as follows:

step 1, establishing a model of interception probability of the interceptors on the targets, and calculating the interception probability of each interceptor on each target, specifically comprising the steps 1.1 to 1.3.

Step 1.1, establishing a middle and last guidance shift deviation model, calculating the radius of a middle and last guidance shift deviation circle, and further calculating to obtain the probability that a target falls into the view field of an interceptorFurther, setting false alarm probabilityAnd calculating the signal-to-noise ratio (S/N), and calculating to obtain the probability of realizing the middle-terminal guidance shift change and the successful completion of the target detection of the terminal guidance seekerAnd further calculating the success probability of the middle and end guidance shift change

Probability of success of terminal guidance shift change in the calculation of completion step 1.1Then, in order to establish a zero control interception probability model of the interceptor on the target, the method enters step 1.2, influence weight values of zero control miss distance, residual flight time and line-of-sight angular rate are set, according to the three indexes, zero control interception probabilities corresponding to the three indexes are calculated by adopting a negative exponential function, and further, a weighting method is used for calculating the zero control interception probability of the interceptor on the target

Calculating the zero control interception probability of the interceptor to the target after finishing the step 1.2Then, in order to establish an interception probability model of the space interceptors for the target, the step 1.3 is carried out, and the probability of reliable flight of each interceptor is givenThe reliable flight probability and the middle and end guidance shift-switching success probability calculated in the step 1.1 and the step 1.2 are used for obtainingAnd zero control interception probability of interceptor to targetMultiplying, calculating to obtain the interception probability P of the space interceptor to the target_ij。

Calculating the interception probability P of the space interceptor to the target at the completion of step 1.3_ijAnd then, distributing suboptimal solutions to the targets, entering the step 2, establishing a high-grade maximum marginal profit algorithm solving model, calculating a benefit matrix R, selecting weapon target pairs with the largest elements in the matrix R from the undistributed weapons for distribution, and circulating until all weapons are completely distributed, and stopping to obtain the suboptimal solutions of target distribution.

After the calculation of the suboptimal solution of the target distribution in the step 2 is completed, in order to improve the optimality of the result, the step 3 is entered, a cyclic rejection neighborhood search model is established, the weapon target distribution scheme pair obtained by utilizing the local optimal idea is rejected successively to try to find a more optimal solution from a new distribution scheme, and finally the rapid solution of the weapon target distribution problem is realized.

For further understanding of the present invention, the following describes the maximum marginal profit-based cyclic veto target allocation method according to the present invention in detail with reference to fig. 1 to 2.

Step 1.1, establishing a Chinese-style powder preparationCalculating the radius of the middle and last guidance shift deviation circle by the guidance shift deviation model, and further calculating to obtain the probability that the target falls into the view field of the interceptorFurther, setting false alarm probabilityAnd calculating the signal-to-noise ratio (S/N), and calculating to obtain the probability of realizing the middle-terminal guidance shift change and the successful completion of the target detection of the terminal guidance seekerAnd further calculating the success probability of the middle and end guidance shift change

Defining deviation circle radius perpendicular to visual field plane for middle and end guidance shiftComprises the following steps:

in the formula, σ_irThe radius of the position error circle of the ith interceptor; sigma_jrIs the position error circle radius of the jth target; sigma_ijqThe angle of the jth target relative to the seeker of the ith interceptor is adjusted; r_ijIs the relative distance between the jth target and the ith interceptor during the middle and last guidance shift change. Wherein:

in the formula, σ_irx,σ_iry,σ_irzIs the i-th interceptor position error component; sigma_irx,σ_iry,σ_irzError component of j-th target position;the high and low angles of the line of sight of the eyes are set;is the direction angle of the visual line of the pinball. Therefore, the probability that the jth target falls into the view field of the ith interceptorComprises the following steps:

since the probability of detection of a target by a seeker is related to a given signal-to-noise ratio S/N requirement, seeker frame rate, and detection time. Since the interception of the target is performed outside the atmosphere, and therefore the influence of the atmosphere is not considered, the calculation formula of the signal-to-noise ratio S/N is as follows:

whereinIs the target radiation intensity; NEFD_iThe seeker noise equivalent flux density for the ith interceptor.

Let the false alarm probability beThe target detection probability is calculated as follows:

wherein σ is seeker detection noise variance; alpha is the amplitude of the detection signal; t is a detection threshold;is a standard normal distribution; f. of_nTo accumulate the number of detected frames. As long as the false alarm probability is givenT/sigma can be calculated and f is input_nAnd S/N (db) can obtain the target detection probability

Calculating the probability of the target falling into the view field of the interceptorAnd the probability that the middle guidance and the end guidance shift change and the end guidance seeker successfully completes target detection is realizedProbability of successful guidance shift change at later, middle and endCan be expressed as:

step 1.2, setting influence weight values of zero control miss distance, residual flight time and line-of-sight angular rate, calculating zero control interception probability corresponding to the three indexes by adopting a negative exponential function according to the three indexes, and further calculating the zero control interception probability of the interceptor to the target by using a weighting method

Three quantitative indexes including zero control miss amount, residual flight time and line-of-sight angular rate are mainly considered for the zero control interception probability of the interceptor on the target, and each index has complex influence on the zero control interception probability. Taking the angular rate of view as an example, for a particular initial angular rate of view, the greater relative distance R_ijIt is beneficial to correct the initial course angle error and improve the zero control intercept probability, but increases the remaining flight time. When the relative distance R_ijWhen small, the interceptor may not be able to enter the collision triangle and miss the target. Therefore, the three indexes for measuring the zero control interception probability can influence each other. In order to maximize the combat efficiency, each index needs to be compromised, which also indicates that the multiple interceptors need to be used for cooperative combat. In the terminal guidance process, the smaller the three index values for measuring the zero control interception probability, the larger the zero control interception probability of the interceptor on the target. The method combines three quantization indexes and adopts a negative exponential function to define the zero control interception probability.

Setting the influence weight values of zero control miss distance, residual flight time and line-of-sight angular rate as beta_ZEM、Andand satisfies the following conditions:

generally speaking, the zero miss control amount is an important index for measuring whether the interceptor can hit the target, and is also an important index for measuring the interception effectiveness. Thus, β_ZEMRatio of need to needAndslightly larger.

Let delta ZEM, delta T_goAndthe average values of the zero miss control amount, the remaining flight time and the line-of-sight angular rate are respectively defined as follows:

where m is the number of interceptors and n is the target number, ZEM (i, j), T_go(i, j) andrespectively is the zero control miss distance, the residual flight time and the line-of-sight angular rate of the ith interceptor on the jth target.

Let I_aIs an intermediate variable that measures whether the ith interceptor can intercept the jth target. The current startup time of the interceptor rail control is availableTo approximate, where m_iFor the current quality of the ith interceptor,for the current mass flow of the ith interceptor, thenThen the current remaining mobility of the interceptor, where a_maxThe maximum acceleration that can be generated is tracked for the interceptor. If the remaining maneuvering capacity of the interceptor is greater than the zero control miss distance at the current moment, the target is considered to be blocked, the interception probability is a negative exponential function of the zero control miss distance, otherwise, the item is a small value, namely:

after the intermediate variables are obtained through calculation, zero control miss distance, residual flight time and zero control interception probability of the interceptor under the influence of the line-of-sight angular rate are defined in the form of a negative exponential function, and are respectively as follows:

whereinAndis an initial default value for the corresponding probability. Based on the three quantitative indexes, the zero control interception probability of the interceptor to the target is calculated by using a weighting methodCan be defined as:

step 1.3, the probability of reliable flight of each interceptor is givenThe reliable flight probability and the middle and end guidance shift-switching success probability calculated in the step 1.1 and the step 1.2 are used for obtainingAnd zero control interception probability of interceptor to targetMultiplying, calculating to obtain the interception probability P of the space interceptor to the target_ij。

Probability of interceptor reliable flightCan be obtained by means of a reliability analysis, but it is outside the scope of the present invention, in which we consider the probability of reliable flight of the interceptorAre directly given or are evenly distributed within a certain interval. Reliable flight at a given interceptorProbability of (2)Then, an interception probability model of the space interceptor to the target can be established as follows:

wherein, P_ijThe interception probability of the ith interceptor to the jth target.

And 2, establishing an advanced maximum marginal profit algorithm solution model, calculating a benefit matrix R, selecting a weapon target pair with the largest element in the matrix R from undistributed weapons for distribution, and circulating until all the weapons are completely distributed, and stopping to obtain a suboptimal solution of target distribution.

The high-level maximum marginal profit algorithm solving model is to find out a suboptimal solution with better performance by finding out the weapon target pair to maximize the marginal profit of the index function. The solving flow chart of the algorithm is shown in fig. 1. Assuming that the number of weapons is m, the number of targets is n, and the interception probability matrix is set to be P e R^m×nThe distribution matrix is X ∈ R^m×nThe weight value of the target threat is V epsilon R^n×1The elements in the three matrices are respectively: p (i, j), x (i, j), and v (j), where i ∈ {1, …, m }, j ∈ {1, …, n }.

First, the number s of the allocated weapons is set to 0, and the target allocation matrix is initialized to zero. Next, a vector Q is calculated, where the elements are:

and calculating a benefit matrix R, wherein the elements are as follows:

r(i,j)＝p(i,j)v(j)q(j) (19)

where v (j) is the value of the jth target. Further, selecting a weapon target pair with the largest element in the matrix R from the undistributed weapons, and setting the corresponding position of the distribution matrix X to be 1. And finally accumulating the number s of the distributed weapons by 1, judging the size relation between the number s and the number m of the weapons, if s is equal to m, ending the solution, otherwise, recalculating the vector Q, and starting the next round of loop iteration.

And 3, establishing a cyclic veto neighborhood search model, and gradually veto weapon target distribution scheme pairs obtained by using the local optimal idea to try to find a better solution from a new distribution scheme, thereby finally realizing the rapid solution of the weapon target distribution problem.

In order to avoid the algorithm from being trapped in local optimization, the invention adopts a neighborhood search strategy to further improve the optimality of the algorithm. In order to improve the convergence rate of the algorithm, the invention provides a cyclic denial method for performing neighborhood search near suboptimal solution, namely a fast suboptimal distribution method for the cyclic denial neighborhood search based on the maximum marginal profit. Because the general solution algorithm of the suboptimal solution usually selects the distribution scheme with the maximum index value in a certain step based on the local optimal thought, when the suboptimal solution is subjected to neighborhood optimization, the weapon target distribution scheme pair obtained by using the local optimal thought is rejected successively to try to find a more optimal solution from a new distribution scheme. The flow chart of the loop veto method is shown in fig. 2.

Firstly, the sub-optimal solution allocation scheme and the index value obtained in the step 2 are respectively stored as: x₀And f (X)₀). The intermediate variable k is set to 1. Under the condition that the distribution result of the kth round is rejected, a sub-optimal solution is found again by using a high-grade maximum marginal benefit algorithm, and the distribution scheme and the index value are respectively stored as follows: x₁And f (X)₁). The index values f (X) of the two allocation schemes are then compared₀) And f (X)₁) If f (X)₁)＞f(X₀) Then let X₀＝X₁、f(X₀)＝f(X₁) K is 1, and the rejection searching is carried out again; if f (X)₁)≤f(X₀) Judging the size relationship between the intermediate variable k and the weapon number m again, if k is equal to m, jumping out of the loop, and terminating the simulation; otherwise, let k equal to k +1 and perform the overruling optimization again.

In conclusion, the cyclic veto target allocation method based on the maximum marginal profit provides a suboptimal target allocation scheme meeting real-time performance, and the interception effect of the interceptor is obviously improved. The cyclic veto method provided by the invention carries out veto on weapon target distribution scheme pairs obtained by utilizing local optimal thought successively to try to find out more optimal solution from a new distribution scheme, compared with the traditional ED element heuristic neighborhood search method, the cyclic veto method has the advantages of less execution times, no need of calculating an index matrix, no need of designing a threshold value to determine the veto scheme, more obvious operability and higher optimization finding efficiency. Compared with the traditional genetic algorithm and the target allocation algorithm based on the test problem, the target allocation solving method provided by the invention has the advantage that the obtained suboptimal solution has relatively higher marginal benefits. In addition, the algorithm of the invention can obtain suboptimal solution or even optimal solution in a short time, the advantage is more obvious in the problem of large-scale target distribution, and the requirement of real-time index can be met under the typical battle condition.

Examples

In this embodiment, the scheme provided by the present invention is verified by the allocation problem of six interceptors to six targets. Probability of assuming reliable flight of ith interceptorIn [0.8,1 ]]Uniformly distributed among the layers; the position of the interceptor is provided by inertial navigation and GPS during middle and last guidance shift change, the target position can be provided by a ground radar, the average value of the measurement error is assumed to be zero, the measurement variance of the position of the interceptor is 200m, and the variance of the target position is 500 m. The line-of-sight measurement noise mean is zero and the variance is 1 μ rad. The accumulated detection frame number is 5 frames, the false alarm probability is set to be 1%, and the signal-to-noise ratio is uniformly distributed between 3 and 5. The state of the interceptor and the state of the target at the end-guidance shift change time in the interceptor are shown in tables 1 and 2 below, respectively.

TABLE 1 last shift state in interceptor

TABLE 2 target initial position velocity

According to the step 1 of the invention, the interception probability P of the ith interceptor to the jth target is calculated_ijAnd write it in matrix form as:

setting the threat weight V of the target as follows:

V＝[0.89 0.23 0.85 0.78 0.72 0.88] (21)

according to step 2 of the invention, the calculated suboptimal solution of target assignment is shown in table 3:

TABLE 3 target assignment suboptimal solution

Summing all the elements in the benefit matrix R yields a benefit of 3.1808 for this allocation scheme.

According to step 3 of the present invention, a more optimal solution of the calculated target assignment is shown in table 4 and fig. 3, where the numbers on the line of view in fig. 3 are the corresponding interception probabilities, and the numbers behind the target are the threat weights of the corresponding targets.

TABLE 4 target assignment better solution

Summing all the elements in the benefit matrix R yields a benefit of 3.2315 for this allocation scheme, with a total computation time of 0.0049 s.

The embodiment shows that the algorithm provided by the invention can well solve the weapon target distribution problem, and the scheme benefit value is obviously improved after the cyclic rejection neighborhood search of the steps; the algorithm provided by the invention has short calculation time and can meet the requirement of online distribution and use.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.