D / S evidence theory low-slow small target threat assessment method based on CRITIC dynamic variable weight

Abstract

The invention discloses a CRITIC dynamic variable weight-based D / S evidence theory low-slow small target threat assessment method, which comprises the steps of determining index factors of a low-slow small target threat assessment system, and constructing a target membership matrix; based on the target membership value matrix, calculating an initial weight of each index factor by adopting a CRITIC method, and solving variable weight vectors of all target index factors by utilizing a variable weight theory on the basis of the initial weight; by adopting a neighbor principle, converting the membership value of each index factor of the target into a form of high, medium and low credibility distribution function values as an initial value of D / S evidence theory analysis, and carrying out matrix operation on the initial value and the variable weight vector to obtain a weighted credibility matrix; and based on the weighted credibility matrix, fusing each index factor of the target by adopting a Dempster rule, and solving a comprehensive threat value of the target through weighted sum. According to the method, the low-slow small target threat assessment precision based on the D / S evidence theory is improved.

Description

Technical Field

[0001] This invention belongs to the field of accurate assessment technology of low-altitude target threat, and more specifically, it relates to a method for assessing the threat of low-altitude, slow, and small targets based on CRITIC dynamic weighted D / S evidence theory. Background Technology

[0002] As a crucial component of fire control, the accuracy of target threat assessment directly impacts the subsequent fire allocation and deployment by command and control personnel, thereby affecting the security of our positions. Against this backdrop, comprehensively analyzing various information regarding incoming aerial targets and conducting accurate and reasonable threat assessments is of great significance for optimizing command and control.

[0003] Low-altitude, slow-speed, and small targets, also known as "low-altitude, slow-speed, and small" flying targets, generally refer to various small aircraft and airborne objects that meet all or some of the following characteristics: 1. Flight altitude not exceeding 1000m; 2. Flight speed not exceeding 200km / h; 3. Radar cross-section not exceeding 2m². 2 Low-altitude, slow-moving, and small targets typically exhibit characteristics such as low-altitude and ultra-low-altitude flight, short proximity times, and difficulty in detection, posing a significant challenge to ground-based air defense systems. Existing threat assessment models for low-altitude, slow-moving, and small targets require a large number of target parameters, are complex, have high computational costs, and cannot reasonably allocate the weights of various parameters. Furthermore, threat prediction involves many uncertainties, which existing models often cannot fully handle, thus affecting the accuracy of the assessment. Summary of the Invention

[0004] The purpose of this invention is to provide a threat assessment method for low-speed, small targets based on CRITIC dynamic weighting and D / S evidence theory.

[0005] The technical solution for realizing the present invention is as follows:

[0006] A threat assessment method for low-speed, small targets based on CRITIC dynamic weighting and D / S evidence theory includes:

[0007] Step 1: Determine the indicator factors for the threat assessment system of low, slow, and small targets, and construct the target membership matrix;

[0008] Step 2: Using the CRITIC method, the target membership matrix obtained in Step 1 is subjected to weight analysis to calculate the standard deviation within each indicator factor and the correlation coefficient between each indicator factor, and the initial weights of multiple indicator factors are obtained.

[0009] Step 3: Solve the state-variable weight vector by taking the initial weights of the multiple indicator factors obtained in Step 2 according to the membership values ​​of different objectives, thereby obtaining the variable weight vector of all objective indicator factors;

[0010] Step 4: Using the nearest neighbor principle, the membership values ​​of each indicator factor of the target are transformed into basic credibility values. The credibility distribution function values ​​of different levels of each target indicator factor are calculated, and the credibility matrix of each target is constructed. The weighted credibility matrix of each target is obtained by matrix operation with the variable weight vector obtained in Step 3.

[0011] Step 5: Based on the weighted credibility matrix, Dempster's rule is used to perform step-by-step orthogonal sum processing on each indicator factor of the target to obtain different levels of uncertain credibility threat values ​​for each target. The normalized credibility threat values ​​of different levels of the target are calculated. Finally, the comprehensive threat value of each target is obtained by weighting and summing the normalized credibility threat values.

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] (1) This invention uses the CRITIC method to calculate the weights of indicator factors, which can consider both the contrast intensity within the indicator factors and the correlation between indicator factors, thereby reducing information overlap. At the same time, by introducing variable weight theory analysis, it highlights the differences in the allocation of indicator factor weights to different targets, making the indicator factor weights of the target have adaptive characteristics. This improves the problem that the traditional D / S evidence theory, which makes the weights equal when different indicator factors are orthogonal, cannot highlight the threat attribute characteristics.

[0014] (2) Based on the quantitative analysis of the target's various indicator factors through membership function, this invention introduces the nearest neighbor principle, and uses the single membership value as a high, medium and low confidence value to participate in the subsequent D / S evidence theory analysis. This makes the comprehensive threat assessment of the target possible to be initially quantified by constructing membership function, and makes the acquisition of the original data of D / S evidence theory more intuitive and convenient. Attached Figure Description

[0015] Figure 1 This is a flowchart of a low-slow-small target threat assessment method based on CRITIC dynamic weighted D / S evidence theory.

[0016] Figure 2 A diagram illustrating the threat assessment index system for low-speed, small targets. Detailed Implementation

[0017] The specific implementation of this solution will be described below to facilitate understanding of the invention by those skilled in the art. Details of the design and prior art that may obscure the main points of the invention will be omitted here.

[0018] The following will combine Figure 1 , Figure 2 This paper describes the specific implementation method of the low-slow-target threat assessment method based on the CRITIC dynamic weighting D / S evidence theory. The specific implementation steps are as follows:

[0019] Step 1: Determine the influencing factors of the low, slow, and small target threat assessment system. Six indicators are selected: target type, flight speed, target distance, flight altitude, attack angle, and flight path shortcut. The low, slow, and small target threat assessment indicator system is as follows: Figure 2 As shown in the diagram. Target type refers to the type of incoming target, such as multi-rotor drones, fixed-wing drones, holographic balloons, and bionic birds; flight speed is the speed of movement of the incoming target as displayed on radar or other detection equipment; target distance is the horizontal straight-line distance between the incoming target and our position; flight altitude is the vertical height of the incoming target from our position; attack angle is the horizontal projection of the angle between the extension of the line connecting our position and the target and the target's flight direction; and flight path shortcut is the vertical distance projected horizontally from our position to the aerial target's heading. Based on the threat assessment index system, the threat level of each target type is directly quantified and assigned as its membership value. Different membership functions are constructed for the other five index factors, and a target membership matrix is ​​built based on these functions.

[0020] The construction of the membership matrix in step 1 specifically includes the following steps:

[0021] (1) Determine the membership value of the target type

[0022] Different target types have significantly different threat levels. We quantified the threat levels of four common low-altitude, slow-moving, and small targets—multi-rotor UAVs, fixed-wing UAVs, holographic spheres, and bionic birds—and used these as their membership values ​​in subsequent calculations. Multi-rotor UAVs and fixed-wing UAVs were further subdivided into reconnaissance and attack types, and the target type membership values ​​were obtained using a direct assignment method, as shown in Table 1.

[0023] Table 1. Target Type Threat Measurement Values

[0024]

[0025] (2) Determine the membership function of flight speed

[0026] The flight speed of small, slow-moving targets, such as small drones, is the most direct threat factor. Generally speaking, the faster the speed, the more difficult it is to intercept, and the greater the threat to our positions. Therefore, the membership function value of the flight speed threat level is positively correlated with the magnitude of the flight speed. The membership function T of the target flight speed threat level... v for:

[0027]

[0028] Where v∈[0,40] is the target flight speed in m / s, and α0=-0.08 is the speed influence factor.

[0029] (3) Determine the target distance membership function

[0030] Generally speaking, the closer a target is to our position, the shorter the time it takes for the target to reach our airspace, the shorter our reaction time, and the greater the threat level. Therefore, the membership function value of the threat level based on target distance is negatively correlated with the distance itself. The membership function T of target distance... d The calculations are shown in Table 2.

[0031] Table 2 Formulas for Calculating Target Distance and Threat Membership

[0032] Target distance d / m <![CDATA[Membership function calculation T d > [0,500] 1 (500,1500] <![CDATA[1-((d-600) / 600) 2 ×0.1]]> (1500,2000] <![CDATA[((10000-d) / 9000) 2 ×0.85]]> (2000,2500] <![CDATA[((10000-d) / 8000) 2 ×0.65]]> (2500,3500] <![CDATA[((10000-d) / 7500) 2 ×0.55]]> (3500,5500] <![CDATA[((10000-d) / 7000) 2 ×0.45]]> (5500,10000] <![CDATA[((10000-d) / 4500) 2 ×0.15]]> (10000,+∞) 0

[0033] Where d is the target distance, in meters.

[0034] (4) Determine the membership function of flight altitude

[0035] The lower the flight altitude of an incoming target, the easier it is for it to launch a direct attack on our positions, and the higher the threat level. Therefore, the membership function value of the threat level of target flight altitude is negatively correlated with the magnitude of the target altitude, and the membership function T of the target flight altitude... h The specific expression is:

[0036]

[0037] Where, k1 = 1 × 10 -5 , where a1 = 100 is the critical flight altitude of the target in meters, and h is the target's flight altitude in meters.

[0038] (5) Determine the attack angle membership function

[0039] The attack angle reflects the target's flight direction relative to our position and largely reflects the target's threatening intent. Generally, the larger the attack angle, the greater the threat from a low-altitude target. When the attack angle θ is 180°, the target is considered to be attacking our position directly, posing the highest threat level. The target attack angle membership function T... θ The expression is:

[0040]

[0041] Where 90≤θ≤180 represents the target's attack angle, in degrees; a2=180 is the upper limit of θ; and k2=0.0005 represents the deflection angle influence factor. When 0≤θ<90, it indicates that the target is flying away from the defensive position, and the threat membership value is 0.

[0042] (6) Determine the membership function of the route shortcut

[0043] The route shortcut can be calculated using the target distance and the route shortcut. The formula for calculating the route shortcut is:

[0044] sp=dsinθ

[0045] Where sp is the target route shortcut, in meters (m).

[0046] The smaller the shortcut of a low-altitude target, the narrower the horizontal range of the interception airspace, the greater the difficulty of interception, and the higher the threat level of the target. Therefore, the membership function value of the threat level of the target's shortcut is negatively correlated with the size of the shortcut. A membership function T for the target's shortcut is constructed. sp The specific expression is:

[0047]

[0048] Where, k3 = 5 × 10 -8 , where a3 = 0, represents the lower limit of the route shortcut, 0 ≤ sp ≤ 10000, in meters. When sp > 10000, the route shortcut is considered to exceed the maximum route shortcut range of the protected position. At this time, low, slow, and small targets pose almost no threat to our position, so T sp =0.

[0049] (7) Construct the target membership matrix U based on the membership values ​​obtained from the membership functions of the different index factors mentioned above. Its specific form is as follows:

[0050]

[0051] Among them, u mnThis represents the membership value of the nth indicator factor of the mth target obtained from the reconnaissance and detection equipment. m represents the number of incoming targets, and n is the number of indicator factors, arranged from left to right in the order of target type, flight speed, target distance, flight altitude, attack angle, and flight shortcut. Here, n = 6.

[0052] Step 2: Using the CRITIC method, perform weight analysis on the target membership matrix obtained in Step 1, calculate the standard deviation within each indicator factor and the correlation coefficient between each indicator factor, and determine the initial weights of the six indicator factors: target type, flight speed, target distance, flight altitude, attack angle, and flight shortcut. The specific steps are as follows:

[0053] (1) First, based on the target membership matrix obtained in step 1, calculate the standard deviation of each indicator factor, and define the standard deviation of the j-th indicator factor as:

[0054]

[0055] in, Let α represent the average membership value of the j-th indicator factor, m be the number of incoming low-speed, small targets, and α be the average membership value of the j-th indicator factor. j Let u be the standard deviation of the j-th indicator factor. ij This represents the membership value of the i-th objective and the j-th indicator factor.

[0056] (2) Next, calculate the correlation coefficient between the two indicator factors. The specific calculation formula is as follows:

[0057]

[0058] Where, r jk This represents the correlation coefficient between the j-th and k-th indicator factors. Generally, j ≠ k. When j = k, r is considered to be... jk =1, meaning the indicator factor is perfectly correlated with itself. ik This represents the membership value of the k-th indicator factor for the i-th objective.

[0059] (3) Finally, calculate the weight of each indicator factor, and based on the calculated standard deviation of each indicator factor and the correlation coefficient between the indicator factors, determine the information content contained in each indicator factor. The specific calculation formula is as follows:

[0060]

[0061] Among them, C j This represents the amount of information contained in the j-th indicator factor.

[0062] Based on the information content of each indicator factor, the initial weight of each indicator factor is calculated using normalization. The specific calculation formula is as follows:

[0063]

[0064] Where, ω j This represents the initial weight value of the j-th indicator factor.

[0065] Step 3: Using variable weight theory analysis, the initial weights of the six indicator factors obtained in Step 2 are weighted according to the membership values ​​of different objectives, and the state variable weight vector is calculated. Then, the variable weight vectors of all objective indicator factors are obtained. The specific steps are as follows:

[0066] (1) First, based on the target membership matrix obtained in step 1 and the initial weights of the indicator factors obtained in step 2, the state variable weight vector S of each target indicator factor is calculated. The specific calculation formula is as follows:

[0067]

[0068] Where N represents the ratio of penalty to incentive amplitude, taken as N = 1.8, k4 is the penalty threshold coefficient, taken as k4 = 0.7, S ij Let S represent the value of the state-variable weight vector for the i-th objective and the j-th indicator factor. Therefore, the state-variable weight vector S can be expressed as:

[0069]

[0070] (2) Next, the initial weight values ​​and the values ​​of the state variable weight vectors are multiplied by Hadamard to calculate the variable weight vectors of each indicator factor of the target. The specific calculation formula is as follows:

[0071]

[0072] in, Let ω represent the dynamic weighting value of the j-th indicator factor for the i-th objective. Then, the weighting vector ω for all indicators factors for all objectives... d It can be represented as:

[0073]

[0074] Step 4: Using the nearest neighbor principle, the membership values ​​of each target indicator factor are transformed into basic credibility values. The high, medium, and low credibility distribution function values ​​for each target indicator factor are calculated. Based on these values, a credibility matrix for each target is constructed. This matrix is ​​then used in matrix operations with the variable weight vector obtained in Step 3 to obtain the weighted credibility matrix for each target. The specific steps are as follows:

[0075] (1) First, based on the membership value, a threat level range is constructed according to the threat assessment index system. The threat levels are divided into three levels: high [0.7,1], medium [0.4,0.7) and low [0,0.4).

[0076] (2) Next, calculate the distance between the membership values ​​of each indicator factor of the target in each interval. The specific calculation formula is as follows:

[0077] d ijx =(|u ij -a xmin |+|u ij -a xmax |) / (a xmax -a xmin )-1

[0078] Where, d ijx This represents the distance of the membership value of the j-th indicator factor for the i-th target in the x-th threat level interval, where x = 1, 2, 3, and the values ​​from smallest to largest represent the high, medium, and low threat level intervals, respectively. xmin a represents the lower limit of the x-th threat level interval. xmax This represents the upper limit of the x-th threat level interval. Since the medium and low threat level intervals contain open intervals, the upper limit 'a' of the open interval... xmax When selecting, the open interval is treated as a closed interval, and the upper limit value is selected based on this as 'a'. xmax The value is substituted into the calculation, and it will not affect the accuracy of the result.

[0079] (3) Next, the distances between the membership values ​​of each indicator factor of the target in the three intervals are normalized to obtain the confidence distribution function value. The specific calculation formula is as follows:

[0080]

[0081] Where, m ijx d represents the confidence distribution function value of the membership degree of the i-th target and the j-th indicator factor in the x-th interval. ijy This represents the distance of the membership value of the i-th target and j-th indicator factor in the y-th threat level interval, where y = 1, 2, 3, and has the same meaning as x. g = 3 represents the number of threat level intervals.

[0082] After transforming the membership values ​​of the targets using the confidence distribution function, the confidence matrix M of the i-th target is obtained. i Its expression is as follows:

[0083]

[0084] (4) Finally, calculate the weighted confidence matrix for each target. Multiply the variable weight vector obtained in step 3 with the target confidence matrix to obtain the weighted confidence value for each target. The specific calculation formula is as follows:

[0085]

[0086] in, This represents the weighted confidence value of the j-th indicator factor for the i-th target in the x-th threat level interval. This represents the dynamic weighted value of the j-th indicator factor for the i-th objective. Therefore, the weighted credibility matrix for the i-th objective is obtained. It can be represented as:

[0087]

[0088] in, This represents the weighted credibility matrix for the i-th objective. This represents the uncertainty measure of the i-th objective and j-th indicator factor, extended to the last column of the weighted confidence matrix.

[0089] Step 5: Based on the weighted credibility matrix, using Dempster's rule, perform step-by-step orthogonal sum processing on each indicator factor of the target to obtain high, medium, low, and uncertain credibility threat values ​​for each target. Calculate the normalized credibility threat values ​​for high, medium, and low targets. Finally, by weighting and summing the normalized credibility threat values, obtain the comprehensive threat value for each target. The specific steps are as follows:

[0090] (1) First, the Dempster rule is used to fuse the four weighted confidence values ​​of high, medium, low, and uncertain for the first and second indicator factors. The calculation formula is as follows:

[0091]

[0092] Where A = {high, medium, low, uncertain}, is a set containing four confidence levels. p The values ​​of p, from smallest to largest, represent confidence subsets containing only high, medium, low, and uncertain elements, respectively. Each A... p It contains only one element. f, q, p = 1, 2, 3, 4, A f A represents a subset of confidence levels containing only any f-th confidence level (high, medium, low, uncertain). q A represents a subset of credibility that contains only any q-th credibility level. f and A q The selections between them are independent and do not interfere with each other. The fusion rule is: when f = q, A... f ∩A q=A f =A q ; when A f and A q Given two subsets of credibility (high, medium, and low) and a subset of credibility with uncertain elements, the intersection is the subset of credibility containing high, medium, and low elements. In other words, the intersection of any credibility subset and an uncertain credibility subset is considered to still be that credibility subset. For example, when f = 2 and q = 4, then A... f ∩A q =A f ; when A f and A q All are subsets of credibility containing high, medium, and low elements, and f≠q, then

[0093] at this time respectively with A f A q Correspondingly, This represents the weighted credibility value of the first indicator factor and the f-th credibility factor for the current i-th objective. The element in row 1 and column f is A again. f The weighted credibility value corresponding to the credibility subset.

[0094] This represents the weighted credibility value of the second indicator factor and the qth credibility level for the current i-th objective. and The values ​​are independent of each other. K1 represents the threat value of the p-th credibility level fused for the i-th target, which is obtained by fusing two indicator factors. K1 represents the conflict coefficient between the two indicator factors.

[0095] (2) Next, the four credibility threat values ​​obtained in the previous step are successively fused with the four weighted credibility values ​​of the third to sixth indicator factors of the target using the Dempster rule to obtain the final threat credibility value of the target. The specific calculation formula is as follows:

[0096]

[0097] Wherein, K2 represents the conflict coefficient between the credibility threat value and the indicator factors. This represents the weighted confidence value of the i-th objective, the j-th indicator factor, and the q-th confidence level (high, medium, low, and uncertain). Let r represent the threat value of the rth credibility level after incorporating the jth indicator factor for the i-th target, where r = 1, 2, 3, 4, and j starts from 3.

[0098] (3) Furthermore, based on the four credibility threat values ​​of the target obtained, the uncertainty portion is allocated to the high, medium, and low credibility threat value portions respectively, to obtain the normalized credibility threat value. The specific calculation formula is as follows:

[0099]

[0100] in, This represents the credibility threat value of the uncertain part in the i-th objective, and is also... The value when r=4, Net represents the threat value of the i-th target with the f-th credibility obtained in the previous step, after incorporating indicator factors. ir Let f represent the normalized credibility threat value of the i-th target at the r-th position, where f = 1, 2, 3 and r = 1, 2, 3. This yields the normalized credibility threat value for each target, and the normalized credibility threat matrix for the i-th target can be represented as Net. i =(Net) i1 Net i2 Net i3 The elements in the ) represent high, medium, and low normalized credibility threat values, respectively.

[0101] (4) Finally, the comprehensive threat value of the target is calculated. The normalized credibility threat value of the target is weighted and summed to obtain the comprehensive threat value of the target. The comprehensive weight matrix ω is then constructed. t = (1.5, 1, 0.5), and its specific calculation formula is as follows:

[0102]

[0103] Among them, Net ir Represents the normalized credibility threat value of the i-th target at the r-th time, i.e., matrix Net. i The r-th element, ω tr The matrix ω represents the overall weight value of the r-th confidence level. t The r-th element in the dataset, where r = 1, 2, 3, Th i This represents the overall threat value of the i-th target. This allows us to obtain the overall threat values ​​of the targets and their ranking.

[0104] Implementation Cases

[0105] Assume that the air defense reconnaissance system detects 6 low, slow, and small targets approaching our position. The target characteristic parameters are shown in Table 3 below, where the target numbers are represented by H1 to H6, and H1 to H4 are all unmanned aerial vehicles (UAVs).

[0106] Table 3. Raw Data Collection for Low-Speed, Small Targets

[0107]

[0108] The steps for assessing the threat level of low-speed, small targets based on target characteristic parameters detected by the air defense reconnaissance system are as follows:

[0109] Step 1: Determine the influencing factors of the low, slow and small target threat assessment system. Select six indicators as influencing factors of the low, slow and small target threat assessment system: target type, flight speed, target distance, flight altitude, attack angle, and flight path shortcut. Assign a quantitative value to the threat of the target type as its membership value. Construct different membership functions for the other five indicators and build a target membership matrix based on these functions.

[0110] Based on the membership function calculation formula for each indicator factor, the membership values ​​of each indicator factor of the target are determined, and their specific values ​​are shown in Table 4:

[0111] Table 4 Membership values ​​of target indicators

[0112]

[0113] According to Table 4, the target membership matrix U can be obtained. The specific matrix form of U is as follows:

[0114]

[0115] Step 2: Using the CRITIC method, the target membership matrix obtained in Step 1 is weighted and processed. The standard deviation within each indicator factor and the correlation coefficient between each indicator factor are calculated to determine the initial weights for six indicator factors: target type, flight speed, target distance, flight altitude, attack angle, and flight shortcut. The specific steps are as follows:

[0116] (1) First, based on the target membership matrix obtained in step 1, the standard deviation of each indicator factor is calculated. The calculated standard deviations are as follows:

[0117] α j =[0.2115,0.1198,0.3087,0.2989,0.2212,0.1747]

[0118] (2) Next, calculate the correlation coefficient between each pair of indicator factors. The calculated correlation coefficients are as follows:

[0119]

[0120] (3) Finally, the weights of each indicator factor are calculated. Based on the calculated standard deviations of each indicator factor and the correlation coefficients between the indicator factors, the information content contained in each indicator factor is obtained, and then the initial weights of each indicator factor are obtained by normalization. The calculated initial weights are as follows:

[0121] ω j =[0.1225,0.0711,0.2679,0.2224,0.2135,0.1026]

[0122] Step 3 involves using variable weighting theory to analyze the initial weights of the six indicator factors obtained in Step 2. This is done by weighting the factors according to their membership values ​​for different objectives, calculating the state variable weighting vector, and then obtaining the variable weighting vectors for all objective indicator factors. Step 3 specifically includes the following steps:

[0123] (1) First, based on the target membership matrix obtained in step 1 and the initial weights of the indicator factors obtained in step 2, the state-weighted vector of each target indicator factor is calculated. The calculated state-weighted vector is as follows:

[0124]

[0125] (2) Next, perform a Hadamard product between the initial weight vector and the state variable weight vector to calculate the variable weight vectors of each target indicator factor. The variable weight vectors of each target indicator factor obtained after the Hadamard product are as follows:

[0126]

[0127] Step 4: Using the nearest neighbor principle, the membership values ​​of each target indicator factor are transformed into basic credibility values. The high, medium, and low credibility distribution function values ​​for each target indicator factor are calculated. Based on these values, a credibility matrix for each target is constructed. This matrix is ​​then used in matrix operations with the variable weight vector obtained in Step 3 to obtain the weighted credibility matrix for each target. The specific steps are as follows:

[0128] (1) First, based on the membership value, a threat level range is constructed according to the threat assessment index system. The threat levels are divided into three levels: high [0.7,1], medium [0.4,0.7) and low [0,0.4).

[0129] (2) Next, the distance between the membership values ​​of each indicator of the target in each interval is calculated. Due to the large amount of data, the first target will be used as an example for calculation and analysis. The distance between the membership values ​​of all indicator factors of the first target in the three intervals is calculated as follows:

[0130]

[0131] (3) Next, the distances between the membership values ​​of each indicator factor of the target in the three intervals are normalized to obtain the confidence distribution function value, and then the confidence matrix is ​​obtained. The confidence matrix of the first target after normalization is as follows:

[0132]

[0133] (4) Finally, calculate the weighted credibility matrix for each target. Multiply the variable weight vector obtained in step 3 with the target credibility matrix to obtain the weighted credibility matrix for each target. The weighted credibility matrix for the first target is calculated as follows:

[0134]

[0135] Step 5: Based on the weighted credibility matrix, using Dempster's rule, perform step-by-step orthogonal sum processing on each indicator factor of the target to obtain high, medium, low, and uncertain credibility threat values ​​for each target. Calculate the normalized credibility threat values ​​for high, medium, and low targets. Finally, by weighting and summing the normalized credibility threat values, obtain the comprehensive threat value for each target. Step 5 specifically includes the following steps:

[0136] (1) First, the Dempster rule is used to sequentially fuse the four weighted credibility threat values ​​of the six indicator factors: high, medium, low, and uncertain. The first target weighted credibility threat value after fusion is:

[0137]

[0138] (2) Based on the four credibility threat values ​​obtained for the target, the uncertainty portion is allocated to the high, medium, and low credibility threat value portions respectively, resulting in normalized credibility threat values. The calculated normalized credibility threat matrix for the first target is as follows:

[0139] Net1 = [0.3186, 0.4443, 0.2371]

[0140] (3) Finally, the comprehensive threat value of the target is calculated. The normalized credibility threat value of the target is weighted and processed to obtain the comprehensive threat value of the first target as Th1 = 1.0407.

[0141] Similarly, the overall threat value of the remaining targets can be calculated. Therefore, after calculation, the overall threat value of the six targets is:

[0142] Th i =[1.0407,1.1120,0.8776,1.1861,1.0054,1.0268]

[0143] Arranged in descending order, the overall threat ranking of the six low-speed, small targets is as follows:

[0144] H4 > H2 > H1 > H6 > H5 > H3

[0145] This allows for the completion of threat assessments of low-speed, small targets.

[0146] In practice, the threat assessment method can be implemented as a computer program. When importing the raw data of incoming targets, it is important to ensure that the collected values ​​meet preset boundary conditions. For example, the collection range of the target flight speed membership function requires that the speed cannot exceed 40 m / s, to ensure the accuracy of the threat assessment method.

Claims

1. A threat assessment method for low-speed, small targets based on CRITIC dynamic weighting and D / S evidence theory, characterized in that, include: Step 1: Determine the indicator factors for the threat assessment system of low, slow, and small targets, and construct the target membership matrix; Step 2: Using the CRITIC method, the target membership matrix obtained in Step 1 is subjected to weight analysis to calculate the standard deviation within each indicator factor and the correlation coefficient between each indicator factor, and the initial weights of multiple indicator factors are obtained. Step 3: Solve the state-variable weight vector by taking the initial weights of the multiple indicator factors obtained in Step 2 according to the membership values ​​of different objectives, thereby obtaining the variable weight vector of all objective indicator factors; Step 4: Using the nearest neighbor principle, the membership values ​​of each indicator factor of the target are transformed into basic credibility values. The credibility distribution function values ​​of different levels of each target indicator factor are calculated, and the credibility matrix of each target is constructed. The weighted credibility matrix of each target is obtained by matrix operation with the variable weight vector obtained in Step 3. Step 5: Based on the weighted credibility matrix, Dempster's rule is used to perform step-by-step orthogonal sum processing on each indicator factor of the target to obtain different levels of uncertain credibility threat values ​​for each target. The normalized credibility threat values ​​of different levels of the target are calculated. Finally, the comprehensive threat value of each target is obtained by weighting and summing the normalized credibility threat values.

2. The method for assessing the threat of low-speed, small targets based on CRITIC dynamic weighted D / S evidence theory according to claim 1, characterized in that, The initial weight of the j-th indicator factor is: Where C j α represents the amount of information contained in the j-th indicator factor. j Let r be the standard deviation of the j-th indicator factor. jk Let m represent the correlation coefficient between the j-th and k-th indicator factors, where m is the target number.

3. The low-slow-speed, small-target threat assessment method based on CRITIC dynamic weighting and D / S evidence theory according to claim 2, characterized in that, The correlation coefficient between the j-th indicator factor and the k-th indicator factor is: The standard deviation of the j-th indicator factor is: u ij This represents the membership value of the j-th indicator factor for the i-th objective. u represents the average membership value of the j-th indicator factor. ik This represents the membership value of the k-th indicator factor for the i-th objective.

4. The method for assessing the threat of low-speed, small targets based on CRITIC dynamic weighting and D / S evidence theory according to claim 1, characterized in that, The dynamic weighting value of the i-th objective and j-th indicator factor in the weighting vector is: S ij ω represents the value of the state-variable weight vector for the i-th objective and the j-th indicator factor. j represents the initial weight value of the j-th indicator factor, n is the number of indicator factors, N represents the ratio of penalty to incentive magnitude, and k4 is the penalty threshold coefficient.

5. The method for assessing the threat of low-speed, small targets based on CRITIC dynamic weighting and D / S evidence theory according to claim 1, characterized in that, The weighted credibility matrix is ​​represented as follows: in, This represents the weighted credibility matrix for the i-th objective. Let m represent the uncertainty measure of the i-th objective and the j-th indicator factor. ijx Let represent the confidence distribution function value of the membership degree of the i-th objective and the j-th indicator factor in the x-th interval. denoted by , represents the dynamic weighted value of the j-th indicator factor for the i-th target, and g represents the number of threat level intervals.

6. The method for assessing the threat of low-speed, small targets based on CRITIC dynamic weighted D / S evidence theory according to claim 5, characterized in that, The confidence distribution function value of the membership degree of the i-th objective and the j-th indicator factor in the x-th interval is: d ijx =(|u ij -a xmin |+|u ij -a xmax |) / (a xmax -a xmin )-1 d ijx d represents the distance of the membership value of the j-th indicator factor for the i-th target within the x-th threat level interval. ijy a represents the distance of the membership value of the j-th indicator factor for the i-th target within the y-th threat level interval. xmin a represents the lower limit of the x-th threat level interval. xmax u represents the upper limit of the x-th threat level interval. ij denoted by , represents the membership value of the i-th target and the j-th indicator factor, and g represents the number of threat level intervals.

7. The method for assessing the threat of low-speed, small targets based on CRITIC dynamic weighted D / S evidence theory according to claim 1, characterized in that, The overall threat value of the i-th target is: Where ω tr Net represents the overall weight value of the r-th confidence level. ir This represents the normalized credibility threat value of the i-th target at the r-th time. This represents the credibility threat value of the uncertain part in the i-th objective. This represents the threat value of the r-th credibility level for the i-th target after incorporating the j-th indicator factor. This represents the threat value of the f-th credibility level of the i-th target after incorporating the j-th indicator factor.

8. The method for assessing the threat of low-speed, small targets based on CRITIC dynamic weighting and D / S evidence theory according to claim 7, characterized in that, The threat value of the i-th target with the r-th credibility after incorporating the j-th indicator factor is: Where K2 represents the conflict coefficient between the credibility threat value and the indicator factors. A represents the weighted credibility value of the ith target, the j-th indicator factor, and the q-th credibility factor. p According to the values ​​of p, from smallest to largest, they represent confidence subsets containing only different levels of uncertain elements, A f A represents a subset of credibility that contains only any f-th credibility level. q A represents a subset of credibility that contains only any q-th credibility level. f and A q The values ​​are independent of each other. This represents the weighted confidence value of the first indicator factor for the current i-th objective, and the f-th confidence level. This represents the weighted confidence value of the qth confidence level of the second indicator factor for the i-th objective. and The values ​​are independent of each other. K1 represents the threat value of the p-th credibility level fused for the i-th target, which is obtained by fusing two indicator factors. K1 represents the conflict coefficient between the two indicator factors.

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