A reentry glider trajectory prediction method based on minimum cost criterion

Abstract

The application discloses a reentry gliding vehicle trajectory prediction method based on a minimum cost criterion, and relates to the technical field of reentry gliding vehicle trajectory prediction. The application divides a target guidance task, constructs a time-varying parameter prediction model set matched with the task, reduces redundancy of a lateral parameter model, and guarantees rapid implementation of a prediction algorithm; an intention cost function with an adaptive cost coefficient is proposed by comprehensively considering the target maneuvering capability, guidance intention and battlefield situation, and the accuracy of guidance intention cost estimation is improved; the target attack intention and parameter model are inferred based on the Bayes theory and the minimum cost criterion, and error accumulation in the prediction process is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of reentry gliding vehicle trajectory prediction, in particular to a reentry gliding vehicle trajectory prediction method based on minimum cost criterion. BACKGROUND

[0002] As a global rapid strike weapon, the reentry gliding vehicle has the characteristics of fast speed, strong penetration ability and wide strike range in the long flight of near space. At the same time, it poses new challenges to the early warning, detection, tracking and interception of the defense party, so the trajectory prediction research of reentry gliding target has important significance.

[0003] Unlike ballistic targets, reentry gliding targets will perform large-scale high-speed maneuvers during reentry gliding. In order to reduce the maneuvering overload of the interceptor and improve the combat effectiveness of the defense weapon, the defense party usually adopts a zero-control interception strategy based on the predicted hit point after obtaining the target trajectory information, which puts high requirements on the trajectory prediction accuracy and prediction length of the reentry gliding target.

[0004] From the prediction mechanism, the trajectory prediction technology for reentry gliding targets mainly includes two categories of trajectory prediction methods based on data analysis and model. The first method predicts by analyzing the historical tracking data of the target trajectory, which has the characteristics of high short-term prediction accuracy and simple method implementation. Yang Chunwei et al. used attention mechanism and LSTM (Long Short Term Memory) structure to input the state information and attack angle of the target, and realized a Seq2Seq trajectory prediction method; Han Chunyao et al. used the prediction idea of decomposition and integration, and realized high-precision short-term prediction of the target by predicting the trend item, periodic item and random item of the target trajectory sequence respectively; Hu Xingzhi et al. statistically analyzed the motion trajectory of the target by Gaussian process regression, which has good prediction effect on the target trajectory with the same data distribution, but lacks the support of the target motion model, and the constraint of trajectory prediction is not strong. The above methods directly process the shallow information of the target, lack deep model constraints, and are difficult to meet the demand of high-precision, medium-and long-term trajectory prediction.

[0005] In addition, the second method is mainly divided into three types of parameter estimation, pattern recognition and intention inference from the perspective of prediction mechanism. Among them, parameter estimation regards the reentry gliding target as a non-cooperative target, integrates the unknown information such as target mass, force area and aerodynamic coefficient into a parameter, and realizes the iterative prediction of the target by means of the dynamic model. In the case of insufficient prior information, determining the appropriate and easy-to-predict parameter is the key to this method. Wang Lu et al. realized the trajectory prediction by estimating the lift-drag ratio of the target, and the prediction effect was better when the lift-drag ratio changed linearly; Zhai Daoliang et al. gave a set of aerodynamic parameters under high-altitude high-speed environment and target attitude approximately linear, and combined with the least square fitting to realize the long-time trajectory prediction of the reentry gliding target; Li Shijie et al. constructed a set of control variables suitable for trajectory prediction on the basis of the literature, and realized the trajectory prediction of the target under different maneuvering modes; Li Mingjie et al. combined the control parameters and aerodynamic parameters with LSTM network respectively, and the simulation showed that the control parameters had superiority in the trajectory prediction of reentry target. The above methods only predict the target trajectory by parameter estimation, which is suitable for the case of simple parameter variation law, and has great limitations. However, the target will change the movement law in real time according to the specific maneuvering mode or the predetermined attack intention during reentry, at this time the method of parameter estimation is no longer applicable. Based on this, many scholars have made very beneficial exploration on the trajectory prediction method based on pattern recognition and intention inference of reentry gliding vehicles.

[0006] In the aspect of target maneuver mode recognition, it has been proved to be feasible to establish the corresponding prediction model in advance according to different maneuver modes, and then to match the model through recognition technology. Chen Nanhua et al. determined the parameters of the Autoregressive Integrated Moving Average (ARIMA) model by using historical tracking data, and realized the prediction of target trajectory by combining the UKF algorithm. Wei Xiqing et al. matched the target motion law by using double-sine and function for the reentry target trajectory with periodic jump characteristics, and recursively obtained the target prediction trajectory. Cheng Yunpeng et al. generated a set of maneuver modes to train SVM according to the definition of maneuver mode, and realized the pattern recognition and prediction of target maneuver trajectory. Sun et al. composed the analytical expressions of height and velocity variables by using linear decay term and amplitude decay sinusoidal term for the target longitudinal jump glide trajectory under simplified conditions, and realized the calculation of the trajectory prediction pipeline by means of LSTM network. In the aspect of target intent inference, since the reentry guidance always has a certain purpose, the prediction result of the maneuver mode recognition method can be further improved by introducing the attack intent to correct it. Zhang Kai et al. derived the recursive formula of maneuver mode and motion state by constructing the intent cost function, and realized the trajectory prediction of target maneuver under uncertain conditions. Hu et al. transformed the trajectory prediction problem into solving the probability of the target possible passing area in the reachable region by means of the intent cost function and the Bayesian principle for the problem of maneuver mode mutation on the basis of the literature. The algorithm does not depend on the target dynamics process, has high short-term prediction accuracy, but takes a long time, which is not conducive to online prediction. Li Jialai et al. improved the intent cost function on the basis of the literature, and respectively constructed the time-varying prediction model set of the longitudinal and lateral directions, realized the multi-model and multi-intent fusion trajectory prediction of reentry glide target, but the cost coefficient needs to be given artificially, and the algorithm does not have universality. Xu et al. established the relationship between the target initial state, control quantity and flight area by means of deep neural network, improved the calculation efficiency of target attack intent inference and trajectory prediction, but the algorithm does not consider the influence of no-fly zone on target trajectory.

[0007] Therefore, a reentry glide vehicle trajectory prediction method based on the minimum cost criterion is proposed to solve the problems in the prior art. SUMMARY

[0008] The present application aims to provide a reentry glide vehicle trajectory prediction method based on the minimum cost criterion to solve the problems in the prior art.

[0009] To achieve the above object, the present application provides the following technical scheme: a reentry glide vehicle trajectory prediction method based on the minimum cost criterion, comprising the following steps:

[0010] Step1: initialize radar parameters, prediction parameters, no-fly zone and intention position information;

[0011] Step2: track the target according to the CS-UKF filtering algorithm, and obtain the control parameters The predicted

[0012] Step3: calculate the target reachable region, determine the attack intention set Θ, and execute Step4-Step6 for each possible attack intention;

[0013] Step4: judge the target guidance task, when the target task is T f , go to Step5; when the target task is T b , go to Step6;

[0014] The judgment of the target guidance task includes:

[0015] According to whether the no-fly zone affects the target trajectory, the guidance task is divided into avoiding the no-fly zone and the regular guidance, denoted as T b and T f , respectively. The judgment logic consists of angle condition and distance condition, as shown in Figure 2 , and the specific form is as follows:

[0016]

[0017] In the formula: ψ∈(ψ bmin ,ψ bmax ) is the angle condition, indicating that the velocity of the target points to the no-fly zone at this time, ψ bmin represents the minimum track angle of the target to the boundary of the no-fly zone, and ψ bmax represents the maximum track angle of the target to the boundary of the no-fly zone; is the distance condition, indicating that the target will intersect with the no-fly zone if it continues to fly at the current bank angle or the bank angle after changing sign, i.e. the no-fly zone affects the normal trajectory of the target, Γ σ , Γ -σ respectively represent the edges of the instantaneous turning circle with positive and negative signs of the bank angle, and Γ b represents the edge of the no-fly zone;

[0018] Among them, the expressions of ψ bmin and ψ bmax are as follows:

[0019]

[0020] In the formula: ψ b is the track angle of the target to the center of the no-fly zone, R b is the radius of the no-fly zone, and S bS is the remaining range of the target to the center of the no-fly zone; remaining range S b is determined by the following formula:

[0021]

[0022] wherein: is the longitude and latitude of the center of the no-fly zone; ψ b The calculation formula of S is as follows:

[0023]

[0024] When the target instantaneous turning circle intersects with the no-fly zone, the following features exist:

[0025] S tb <R turn +R b (10)

[0026] wherein: R turn is the instantaneous turning radius, R b is the radius of the no-fly zone, S tb is the center distance of the instantaneous turning circle and the no-fly zone; wherein, the instantaneous turning radius R turn is determined by the following formula:

[0027]

[0028] The center distance of the instantaneous turning circle and the no-fly zone can be determined by the following formula:

[0029]

[0030] wherein: is the longitude and latitude of the center of the instantaneous turning circle of the aircraft, and the calculation formula is as follows:

[0031]

[0032] After judging the guidance task of the target according to formula (6), different prediction model sets are constructed according to the requirements of different guidance tasks.

[0033] Step 5: Constructing the parameter prediction model set Λ of the conventional guidance, and constructing the intention cost function I of the conventional guidance f , calculating the corresponding cost;

[0034] The parameter prediction model set of the conventional guidance includes:

[0035] 1) Longitudinal parameter prediction model set

[0036] When the reentry gliding target is longitudinally predicted, the least square method is used to perform function fitting on the filtering parameters of the tracking segment to obtain Further, the parameter prediction value at the future time is obtained For convenience of description, let M = [K D , σ, K L ], It is assumed that the parameter filtering value satisfies a Gaussian distribution with the true value as the mean value, and the parameter prediction value satisfies a Gaussian distribution with the prediction result as the mean value, and the parameter distribution is as follows:

[0037]

[0038] In the formula: is a possible value of the parameter prediction value at the future time, and are standard deviations of M e and M m respectively;

[0039] When it is judged by formula (6) that the target executes the guidance task T f , when the longitudinal parameter prediction model set is constructed, N parameters are extracted from each of the M m ~ N (M p , (σ p ) 2 ) distribution, to form N 3 model sets; in order to improve the trajectory prediction accuracy, the range of the model set should cover the true value as much as possible, and the number of the model set should be as small as possible to reduce the solving time of the algorithm; since the distribution of the predicted segment parameters is unknown, the value of σ p cannot be directly determined, therefore, σ e is obtained by scaling the standard deviation σ e of the parameter filtering value M p , that is

[0040] σ p = λσ e (15)

[0041] Since the true value M of the parameter is unknown during parameter tracking, it is assumed that the fitting result of the function is close to the true value, that is, the parameter filtering value also satisfies a Gaussian distribution with the fitting result as the mean value

[0042] M e ~ N (M f , (σ f ) 2 ) (16)

[0043]

[0044] In the formula: is the standard deviation of M e ;

[0045] Assume the parameter filtering value at different time The variance of the Gaussian distribution The same, by the definition of standard deviation:

[0046]

[0047] In the formula: n e The total step length of the tracking segment;

[0048] When the parameter sampling is performed by formula (14), the parameter M m Determined by the following formula:

[0049]

[0050] 2) Lateral parameter prediction model set

[0051] When the target is guided conventionally, the lateral parameter prediction model set is determined by using the track deviation angle corridor to determine the roll angle sign of the target at the current time. Unlike the traditional track deviation angle corridor, due to the possibility of the flight restricted area squeezing the corridor width, the sign of the roll angle may repeatedly deflect. In order to avoid this phenomenon, a certain compensation needs to be added when establishing the corridor. The schematic diagram of the track deviation angle corridor with compensation is shown in 3;

[0052] When the track deviation angle corridor is compensated, the upper and lower boundaries of the track deviation angle are determined according to the relative position relationship between the target and the flight restricted area; when ψ ≥ ψ bmax , it can be obtained that:

[0053]

[0054] When ψ ≤ ψ bmin , it can be obtained that:

[0055]

[0056] In the formula: Δψ fed represents the original track deviation angle corridor range of the target;

[0057] According to the compensated track deviation angle corridor, the roll angle sign of the target is determined:

[0058]

[0059] In the formula: ψ f represents the track angle of the target to the attack intention;

[0060] Combined with the target longitudinal parameter model set, the N 3 prediction model set is finally determined, that is, Λ = {M1, M2, … M N}, wherein

[0061] When the target task is T f , the intention cost function I f is constructed as follows:

[0062]

[0063] In the formula, max(|Δψ f |-Δψ fed ,0) is the angle cost, |Δψ f |=|ψ-ψ f | represents the absolute value of the difference between the track angle of the target and the track angle of the attack intention, when |Δψ f |≤Δψ fed , the angle cost is uniformly 0, when |Δψ f |>Δψ fed , the angle cost is |Δψ f |-Δψ fed , the intention cost function tends to select the parameter prediction model M that makes |Δψ f | decrease; |S ref -S f | is the energy cost, S ref represents the distance of the target under the current parameter prediction model when the speed decreases to the planning speed v ref , S f represents the remaining distance of the target to the attack intention, when S f =S ref , the energy cost is 0, when S f ≠S ref , the greater the difference between S f and S ref , the greater the energy cost, the intention cost function tends to select the parameter prediction model M that makes S f close to S ref .

[0064] The remaining distance S f is determined by the following formula:

[0065]

[0066] In the formula: is the longitude and latitude of the attack intention.

[0067] Since the target takes too much time to calculate S ref according to the parameter prediction model M by integration, it is not suitable for the defense party to quickly make mode inference; in order to improve the prediction speed and facilitate the measurement of the intention cost of different parameter prediction models, S r ′ ef under the target balanced gliding condition is used to replace the actual Sref The range deviation caused by the actual longitudinal movement of the target is ignored in the comparison; the range and the speed of the target under the balanced gliding condition are determined to determine S r ef The calculation formula is as follows:

[0068]

[0069] In the formula, v0 is the current speed of the target, represents the lift-drag ratio of the target.

[0070] Step 6: Construct a parameter prediction model set Λ for avoiding the forbidden flight area, and construct an intention cost function I for avoiding the forbidden flight area b , and calculate the corresponding cost;

[0071] The parameter prediction model set Λ for avoiding the forbidden flight area includes:

[0072] 1) The longitudinal prediction model set

[0073] When the target performs the guidance task of avoiding the forbidden flight area, there are two cases in which the current turning ability is insufficient to completely avoid the forbidden flight area; the first case is that ψ and ψ f are on the two sides of ψ b , the instantaneous turning circle of the target intersects the forbidden flight area, and the forbidden flight area needs to be bypassed to achieve avoidance; the second case is that ψ and ψ f are on one side of ψ b , and the instantaneous turning circle when sign(σ) = sign(ψ-ψ b ) intersects the forbidden flight area, and a small part of the forbidden flight area blocks the guidance trajectory of the target; the schematic diagrams of the two cases are shown in Figure 4 and Figure 5 ;

[0074] At this time, the amplitude of the bank angle needs to be appropriately increased to improve the turning ability; on the basis of the longitudinal parameter prediction model set of the conventional guidance parameter prediction model set, the value of the bank angle amplitude |σ p | covers the domain [0, π / 2] as much as possible, and the specific process is as follows:

[0075] In the range [0, π / 2], N equidistant points are sampled, and the weight of each sampling point can be obtained according to formula (14)

[0076]

[0077] The weights of the sampling points are normalized

[0078]

[0079] ​When actually sampling, a random number δ' is generated in [0, 1], and the weight of N points The new sampling point |σ is obtained by comparison and interpolation m |

[0080] 2) Lateral parameter prediction model set

[0081] In lateral prediction, there are multiple cases of relative position relationship of targets, no-fly zones and attack intentions. The target needs to consider the influence on the regular guidance task of reaching the attack intention while evading the no-fly zone, and the minimum cost lateral maneuver mode can be made by comprehensively considering the maneuvering ability, energy loss and task completion of itself; Therefore, the lateral parameter prediction model set considers two cases of the sign of the roll angle {1, -1}, and the final lateral maneuver mode is inferred by the intention cost function;

[0082] Combined with the target longitudinal parameter model set, the final 2N 3 prediction model set is determined, that is, Λ = {M 1, M 2, …M 2N}, wherein

[0083] When the target task is T b , since the primary task at this time is to evade the no-fly zone, but at the same time the influence on the final guidance task should be minimized, therefore, when constructing the intention cost function I b , the energy cost is not considered, and the evasion angle cost and guidance angle cost are mainly considered; The specific form is as follows:

[0084] I b = ε1Δψ b + ε2Δψ bf (28)

[0085] In the formula: ε1Δψ b is the evasion angle cost, and ε1 is the evasion cost coefficient; ε2Δψ bf is the guidance angle cost, and ε2 is the guidance cost coefficient;

[0086] 1) Evasion angle cost

[0087] In the evasion angle cost, the larger Δψ b , the larger the evasion angle cost; Since the turning ability of the target is limited, it is necessary to quantitatively describe the evasion of the target in the parameter prediction model M under the control of the roll angle, and select the parameter prediction model with the minimum evasion cost; Δψ b is determined by the following formula:

[0088]

[0089] When calculating the evasion cost coefficient, ψ, ψb and ψ f ; in the set of the target's bank angle amplitude, when the trajectory and the forbidden zone are tangent, the energy loss is the least; therefore, the evasion cost coefficient is defined as follows:

[0090]

[0091] wherein σ tan is the bank angle required when the target's instantaneous turning circle and the forbidden zone are tangent, σ' is the bank angle amplitude at the previous moment, when |σ| = σ tan , the evasion cost coefficient is 1, when |σ| ≠ σ tan , the greater the deviation between |σ| and σ tan , the greater the evasion cost coefficient, and the intent cost function tends to select |σ| when the target's instantaneous turning circle and the forbidden zone are tangent; σ tan The specific calculation process is as follows:

[0092] From the relationship between the target's instantaneous turning circle and the forbidden zone, we have

[0093] S tb = R turn + R b (31)

[0094] From equations (12) and (13), we have

[0095]

[0096] The above equation can be expanded to

[0097]

[0098] The expression of the instantaneous turning radius is obtained by rearranging

[0099]

[0100] By combining equations (11) and (34), we have

[0101]

[0102] 2) Guidance angle cost

[0103] In the guidance angle cost, Δψ bf is defined as follows:

[0104]

[0105] When ψ bmin ≤ ψ f ≤ ψ bmax , the attack intent is behind the forbidden zone relative to the target, and no matter which direction the target evades, sign(Δψbf ) are all 1, i.e. the target evades the no-fly zone while the guidance cost increases; when ψ f > ψ bmax or ψ f < ψ bmin , the attack intention is on the side of the no-fly zone relative to the target, and the target evades in the direction of the attack intention, which results in a smaller guidance cost, otherwise, a larger guidance cost will be generated;

[0106] The guidance cost coefficient ε2is defined as follows

[0107]

[0108] When S b < S f / 2, ε2< 0.5, which means that the target is far away from the attack site, and the influence of the guidance task on the evasion of the no-fly zone is small, so the guidance cost is small; when S b ≥ S f / 2, ε2≥ 0.5, which means that the target is close to the attack site, and the evasion of the no-fly zone will directly affect the completion of the final guidance task of the target, so the guidance cost is large;

[0109] When there are multiple no-fly zones affecting the target trajectory, the closest no-fly zone is selected as the main no-fly zone to represent the intention cost of comprehensive evasion of the no-fly zone, i.e.

[0110]

[0111] where n b is the number of no-fly zones affecting the target trajectory.

[0112] Step 7: infer the attack intention η T with the minimum cost

[0113] The posterior probability of the attack intention η T is derived;

[0114]

[0115] Similarly, the state quantity is divided into two parts, and the following can be obtained:

[0116]

[0117] where P(x k | x 1:k-1 , η T ) is the likelihood probability of the intention η T solved by equation (44) above, and P(η T | x 1:k-1 ) is the intention η Tthe posterior probability of the target's attack intention η k 1:k-1 is the conditional probability of one-step prediction of the target, and the calculation formula is as follows:

[0118]

[0119] According to the Bayes theorem, the posterior probability of the target's attack intention η is as follows:

[0120]

[0121] Therefore, the posterior probability of the attack intention η T is as follows:

[0122]

[0123] According to formula (52) and the minimum cost criterion, the most likely attack intention of the target is:

[0124]

[0125] Step 8: Inference of the parameter prediction model M n with the minimum cost, and iterative integration is performed according to the reconstructed target motion equation set to obtain the predicted target position.

[0126] When the attack intention of the target is η T , the likelihood probability of state transition under the parameter prediction model M n is determined according to the intention cost function,

[0127]

[0128] wherein,

[0129] According to the Bayes theorem, the posterior probability of the parameter model M n is as follows:

[0130]

[0131] When the fraction on the right side of the equation is processed, the state quantity is divided into two parts and expressed in the form of likelihood probability multiplied by prior probability:

[0132]

[0133] The two prior probabilities on the numerator and denominator combine to form the posterior probability of the parameter model M n at the previous time:

[0134]

[0135] ​Since the process of state transition has Markov property, the state transition under the parameter model M n is simplified, and the following equation is obtained:

[0136]

[0137] where P(x k |x k-1 ,M n ,η T ) is the likelihood probability of the parameter model M n , which has been determined by the intention cost function, P(M n |x 1:k-1 ,η T ) is the posterior probability of the parameter model M n at the last time, and P(x k |x 1:k-1 ,η T ) represents the likelihood probability of the intention η T , and the calculation formula is as follows:

[0138]

[0139] According to the Bayes theorem, the posterior probability of M n is:

[0140]

[0141] Therefore, the posterior probability of the parameter model M n is as follows:

[0142]

[0143] According to equation (46) and the minimum cost criterion, the parameter prediction model under the attack intention η T is most likely to be:

[0144]

[0145] Step 9: When the prediction time reaches the planning time, the prediction is ended, otherwise Steps 4-6 and 8 are executed in a loop.

[0146] Compared with the prior art, the beneficial effects of the present application are:

[0147] (1) The present application reduces the redundancy of the lateral parameter model by dividing the target guidance task and constructing a time-varying parameter prediction model set matched with the task, ensures the rapid implementation of the prediction algorithm, considers the target maneuvering ability, guidance intention and battlefield situation comprehensively, proposes an intention cost function with adaptive cost coefficient, and improves the accuracy of the guidance intention cost estimation; and infers the target attack intention and parameter model based on the Bayesian theory and minimum cost criterion, and reduces the error accumulation in the prediction process.

[0148] (2) The simulation experiment results of the present application show that the prediction method proposed in the present application can realize the accurate inference of the target attack intention and the accurate prediction of the position under various conditions, has the advantages of high prediction precision and short algorithm time compared with the existing method.

[0149] The above summary is merely intended to illustrate the present application and is not intended to limit in any way. In addition to the illustrative aspects, embodiments and features described above, further aspects, embodiments and features of the present application will be readily apparent to those skilled in the art by reference to the drawings and the following detailed description. BRIEF DESCRIPTION OF DRAWINGS

[0150] Figure 1 A prediction block diagram of the reentry gliding target trajectory prediction algorithm;

[0151] Figure 2 A target guidance task judgment logic diagram;

[0152] Figure 3 A schematic diagram of the track deviation angle corridor with compensation;

[0153] Figure 4 A schematic diagram of the first case of insufficient target turning ability;

[0154] Figure 5 A schematic diagram of the second case of insufficient target turning ability;

[0155] Figure 6 A schematic diagram of the guidance trajectory of the reentry gliding target of case 1;

[0156] Figure 7 A schematic diagram of the prediction result (t0=200s) of case 1;

[0157] Figure 8 A schematic diagram of the prediction result (t0=400s) of case 1;

[0158] Figure 9 A schematic diagram of the guidance trajectory of the reentry gliding target of case 2;

[0159] Figure 10 A schematic diagram of the prediction result (t0=300s) of case 2;

[0160] Figure 11 This is a schematic diagram of the prediction results for Case 2 (t0 = 500s). Detailed Implementation

[0161] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0162] Experimental simulation

[0163] To verify the effectiveness of the prediction method of this invention, a simulation experiment was conducted on the reentry glide phase of the US CAV-H. The typical target had a mass of 907 kg and an area of ​​0.4839 m². 2 Re-entering the initial gliding state The target area is (0°, 0°, 70km, 6000m / s, -0.1°, 65°). Guidance is achieved using a predictive correction method with a guidance period of 1 second. The deployment location of the early warning radar is set to [23°πR]. e / 180°m, 3.6°πR e / 180°m, 100m] T The detection error is [30m, 0.05°, 0.05°]. T The detection and guidance cycles are the same. Since the location of different no-fly zones can cause significant differences in the target's guidance trajectory, to fully verify the effectiveness of the algorithm, two no-fly zone cases were set in the simulation, and three additional attack intentions were also set, as shown in Table 1. The basic parameters involved in the algorithm are: longitudinal parameter model set size N = 5, scaling factor λ = 0.5, and track deviation angle corridor Δψ. fed =5°, planned speed v ref =1500m / s.

[0164] Table 1. Intent and No-Fly Zone Parameters for Different Cases

[0165]

[0166]

[0167] Calculating the reachable area of ​​a reentry gliding target using the constant tilt angle method

[33] where the value range of the roll angle is [-70°, 70°]. To verify the superiority of the prediction method of the application, the prediction algorithms in documents [1], [2] and [3] are used for simulation comparison. For convenience of expression, the above three algorithms are denoted as method 1, method 2 and method 3, and the prediction method of the application is denoted as method 4. The cost coefficients in method 2 and method 3 are set the same as in document [3].

[0168] Document [1] Li Shijie, Lei Humin, Zhou Chijun, et al. Trajectory prediction algorithm for hypersonic reentry gliding target based on control variable estimation[J]. System Engineering and Electronics Technology, 2020, 42(10): 2320-2327.

[0169] Document [2] HU Y, GAO C, LI J, et al. Novel trajectory prediction algorithms for hypersonic gliding vehicles based on maneuver mode on-line identification and intent inference[J]. Measurement Science and Technology, 2021, 32(11): 115012.

[0170] Document [3] Li Jialai, Guo Jie, Tang Shengjing. Multi-model multi-intent fusion trajectory prediction for hypersonic gliding target[J]. Journal of Spacecraft Technology, 2024, 45(2): 167-180.

[0171] Case 1

[0172] The guidance trajectory of the reentry gliding target in case 1 is shown in Figure 6 From Figure 6 (a), it can be seen that the target passes through the middle of the two no-fly zones during reentry gliding, and reaches the second attack intent; from Figure 6 (b), it can be seen that the target's longitudinal height changes smoothly in the early stage, and jumps in the later stage due to the imbalance of longitudinal force. The flight time of the entire gliding stage is about 1200s, and the range is about 4300km. When the trajectory of case 1 is predicted, the target position 150s after the start point is tracked for 200s and 400s respectively. The target attack intent inference probability in the reachable area is shown in Table 2, and the prediction algorithm simulation results are shown in Figure 6 (a) and Figure 6 (b), and the prediction effect is shown in Table 3.

[0173] Table 2: Intent posterior probability of case 1

[0174]

[0175] From Figure 7 (a) can be seen, at t0=200s, the attack intent and maneuverability of the target, the intent Figure 2 and intent Figure 3 In the reachable region, the intent Figure 1 not in the reachable region. From Table 2 can be seen, the three kinds of algorithm with intent inference to the intent target in the reachable region gives different posterior probability. Since the intent cost coefficient of method 2 and method 3 is given, in the case of case 1, method 2 judges the true attack intent, and method 3 judges the intent Figure 3 The posterior probability of attack intent is as high as 93.15%, and the intent cost function proposed in the application better integrates the purpose of avoiding the no-fly zone and achieving the guidance task, plus the adaptive cost coefficient, which greatly improves the correctness of the target attack intent inference.

[0176] From Figure 7 (b) can be seen, the prediction error of method 1 and method 4 is generally lower than the other two prediction methods, method 2 is to convert the prediction of target control parameters into the position prediction in one-step reachable region, so the prediction error is high in short term, but as the prediction time increases, the error gradually increases, and method 3 leads to continuous increase of prediction error due to the error of target attack intent inference. Combined with Table 3, from Figure 7 (c) and Figure 7 (d) can be seen, the prediction error of method 2 and method 3 in the meridian and latitude is the main reason for the final overall prediction error, because the position inference algorithm in method 2 cannot accurately infer the trajectory inclination, the prediction error of the zenith is also the largest among the four prediction methods, and method 1 causes large meridional error due to error accumulation caused by least square fitting, and method 4 reduces the prediction error accumulation by selecting the parameter model that makes the intent cost as small as possible on the basis of accurately judging the target task as avoiding the no-fly zone and heading to the Figure 2 guidance, finally reduces the prediction error of method 4 to less than half of that of method 1.

[0177] Table 3 prediction effect of case 1

[0178]

[0179] From Figure 8 (a) can be seen, at t0=400s, only the intent Figure 2 in the target reachable region, so the difference of prediction error caused by different prediction methods is irrelevant to the attack intent inference. From Figure 8(b) It can be seen that the prediction errors of methods 1, 3, and 4 all fluctuate, with method 4 having the smallest final prediction error of only 6.9792 km, while the prediction error of method 2 continuously increases, eventually reaching as high as 33.8378 km at 150 s. Referring to Table 3, from... Figure 8 (c) It can be seen that the predicted trajectories of the four prediction methods are all around the actual trajectory on the horizontal plane without significant deviation. Method 2, however, does not consider changes in the target control quantity when predicting the trajectory, resulting in a large meridional prediction error. Method 1 struggles to fit the roll angle reversal pattern during least-squares fitting, also leading to a large error. Method 3 is an improvement over Methods 1 and 2. Based on the fitting of control parameters, it combines the intention cost function to estimate multiple lateral maneuvering modes and fuses the trajectories of multiple models. Compared to Methods 1 and 2, the prediction effect is improved; however, the fusion of trajectories from incorrect lateral maneuvering modes reduces the final prediction accuracy. This invention, based on the judgment that the target is conventionally guided, constructs a set of parameter prediction models matching the mission, reducing the number of lateral parameter models. It selects the parameter model with the lowest cost through the intention cost function and the minimum cost criterion, eliminating the influence of incorrect models on the prediction error, ultimately improving the prediction accuracy of Method 3 by approximately two times. Figure 8 (d) It can be seen that the longitudinal trajectory of the target jumps significantly in the predicted segment. The predicted trajectories of methods 1, 3 and 4 are relatively smooth. Therefore, the prediction error is large in the segment where the target height decreases, but the overall error remains at a low level.

[0180] Regarding prediction time, as shown in Table 3, Method 2 takes the longest. This is because Method 2 uses the Monte Carlo algorithm to solve for the posterior probability of the discrete region after discretizing the target reachable area, resulting in a longer algorithm time. Method 3 has redundancy in its lateral parameter prediction model set, which increases the prediction time. Although the prediction method 4 of this invention also constructs a parameter prediction model set, it reduces the lateral parameter prediction model to 1 / 4 to 1 / 2 of the original by dividing the target guidance task and analyzing the target motion characteristics. The algorithm prediction time is significantly reduced to less than 0.5 seconds, comparable to the simplest Method 1. Therefore, the method proposed in this invention significantly improves prediction accuracy while having a shorter algorithm time, meeting the needs of the defender for rapid prediction.

[0181] Case 2

[0182] The guidance trajectory of the reentry gliding target in Case 2 is as follows: Figure 9 As shown. From Figure 9 (a) It can be seen that during its reentry and gliding, the target evaded one side of the two no-fly zones, thus achieving its second attack objective; from Figure 9(b) It can be seen that the target's longitudinal altitude change is relatively smooth, and the flight time and range of the entire gliding segment are comparable to those in Case 1. When predicting the trajectory of Case 2, the target was tracked for 200 seconds starting from the starting point at 300s and 500s respectively, and the target position was predicted 150s later. The probability of inferring the attack intent of targets within the reachable area is shown in Table 4, and the simulation results of the prediction algorithm are as follows: Figure 10 and Figure 11 As shown in Table 5, the prediction results are as follows.

[0183] Table 4. Posterior probability of intent in Case 2

[0184]

[0185] from Figure 10 (a) It can be seen that, similar to Case 1, at t0 = 300s, the meaning Figure 2 Harmony Figure 3 Within the reachable zone, Italy Figure 1 It is not within the reachable zone. As can be seen from Table 4, Method 4 accurately inferred the target's true attack intention, Method 2 still only barely made a correct judgment, while the probability of error in the intent judgment of Method 3 rose to 99.99%.

[0186] from Figure 10 (b) It can be seen that Method 4 has the lowest prediction error, Methods 1 and 3 are comparable, and Method 2's prediction error remains highly accurate in the short term but diverges rapidly in the long term. Referring to Table 5, from... Figure 10 (c) It can be seen that although Method 2 correctly judged the target's attack intent, its intent cost function, under the effect of a fixed cost coefficient, did not achieve the purpose of avoiding the no-fly zone when predicting the trajectory, but instead went straight towards the intent. Figure 2 Method 1, while incorrectly inferring the attack intent due to the intention cost function, is more accurate in its parameter model inference and makes reasonable selection of parameters for avoiding the no-fly zone. Compared with Method 2, its prediction accuracy is significantly improved. Since the target in the prediction segment mainly performs C-shaped maneuvers to avoid the no-fly zone, Method 1 achieves high prediction accuracy through least-squares fitting of the control parameters. Method 4 still has the lowest prediction error, but its meridional error is relatively large. The reason for this is that the target in the prediction segment adopts a mixed approach of C-shaped and S-shaped maneuvers. The S-shaped maneuver causes the target's trajectory deflection to be closer to the intended trajectory. Figure 2 The C-shaped maneuver caused the target's trajectory to deflect away from the no-fly zone and also away from the intended target. Figure 2, the target's guidance task will be repeatedly judged as regular guidance or evasion of the forbidden flight zone guidance under the influence of tracking error and prediction error, resulting in the accumulation of meridian error. In the prediction method proposed in the present application, the judgment of the guidance task is the key. If the track angle space of the judgment of the guidance task as evasion of the forbidden flight zone is increased, the prediction target will be in C-type maneuver for a long time, and the influence of S-type maneuver on the target trajectory will be ignored, and vice versa. Therefore, in this special case of case 2, the large accumulation of meridian prediction error is inevitable, but the final prediction error is 14.0876km, which still has high prediction accuracy. From Figure 10 (d) It can be seen that method 1 accurately predicts the target height change, and the remaining methods have a large error in predicting the height, but the maximum error is within 2km, indicating that in the case of relatively smooth target longitudinal height change, the prediction accuracy is generally high.

[0187] Table 5 Prediction effect of case 2

[0188]

[0189] From Figure 11 (a) It can be seen that at t0=500s, only the intended Figure 2 in the target reachable area. Combined with Table 5, from Figure 11 (b) and Figure 11 (c) It can be seen that method 1 has a large prediction error due to the lack of prediction ability of the lateral control variable change rule, and method 2 has a large prediction error because the dynamics constraint of the target is not considered when predicting the reachable area. The predicted trajectory is directly towards the intended Figure 2 , which is quite different from the real trajectory. Method 3 also has a large prediction error because of the redundancy of the lateral parameter model, but compared with methods 1 and 2, the prediction accuracy has been greatly improved. Method 4 reduces the prediction error to 8.1388km under the constraint of the track deviation angle corridor with compensation after judging the target task as regular guidance. From Figure 11 (d) It can be seen that the longitudinal height predicted by methods 1, 2 and 3 jumps, resulting in a large error, among which the skyward prediction error of method 2 reaches 4.5507km, and the longitudinal height change predicted by method 4 is relatively smooth, and the accuracy is also the highest. In terms of prediction time, the same conclusion as that of case 1 is obtained.

[0190] In summary, the application comprehensively considers the task attribute and loss and benefit of the target, and proposes a trajectory prediction algorithm for reentry gliding targets based on the minimum cost criterion. By dividing the target guidance task, a set of time-varying parameter prediction models matched with the task is constructed, which reduces the redundancy of the lateral parameter model and ensures the rapid implementation of the prediction algorithm; considering the target's maneuvering ability, guidance intention and battlefield situation, an intention cost function with adaptive cost coefficient is proposed, which improves the accuracy of the guidance intention cost estimation; based on the Bayesian theory and the minimum cost criterion, the target's attack intention and parameter model are inferred, which reduces the error accumulation in the prediction process. The simulation results show that the prediction method proposed in the application can accurately infer the target's attack intention and accurately predict the target's position under various conditions, and compared with the existing methods, the prediction method has the advantages of high prediction accuracy and short algorithm time.

[0191] Although the embodiments of the application have been shown and described above, it should be understood by those skilled in the art that the above embodiments are exemplary and cannot be construed as limiting the application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments within the scope of the application.

Claims

1. A method for predicting the trajectory of a reentry glider based on the minimum cost criterion, characterized in that, Includes the following steps: Step 1: Initialize radar parameters, prediction parameters, no-fly zone and intended location information; Step 2: Track the target using the CS-UKF filtering algorithm to obtain control parameters. The prediction was obtained by fitting using the least squares method. Step 3: Calculate the reachable area of ​​the target, determine the set of attack intentions Θ, and execute Step 4 to Step 6 for each possible attack intention; Step 4: Determine the target guidance mission. When the target mission is T... f When the target task is T, proceed to Step 5; b Proceed to Step 6; Step 5: Construct the parameter prediction model set Λ for conventional guidance and construct the intention cost function I for conventional guidance. f Calculate the corresponding cost; Step 6: Construct the parameter prediction model set Λ for avoiding no-fly zones, and construct the intention cost function I for avoiding no-fly zones. b Calculate the corresponding cost; Step 7: Determine the attack intent η that minimizes the cost. T ; Step 8: Infer the parameter prediction model M with the lowest cost n The predicted target position is obtained by iterative integration based on the reconstructed target motion equations. Step 9: When the predicted time reaches the planned time, end the prediction; otherwise, repeat Steps 4 to 6 and Step 8.

2. The method for predicting the trajectory of a reentry glider based on the minimum cost criterion according to claim 1, characterized in that: In Step 4, the determination of the target guidance task includes: Based on whether the no-fly zone affects the target trajectory, guidance missions are divided into no-fly zone avoidance and conventional guidance, denoted as T, respectively. b and T f The judgment logic consists of angle conditions and distance conditions, and its specific form is as follows: In the formula: ψ∈(ψ bmin ,ψ bmax ) is an angular condition, indicating that the target's velocity is pointing towards the no-fly zone at this moment, ψ bmin ψ represents the minimum track deflection angle from the target to the boundary of the no-fly zone. bmax This indicates the maximum track deflection angle of the target from the boundary of the no-fly zone; The distance condition indicates that if the target continues to fly at the current or changed bank angle, it will intersect the no-fly zone. In other words, the no-fly zone affects the target's normal trajectory. σ ,Γ -σ Γ represents the sides of the instantaneous turning circle with positive and negative signs, respectively. b Indicates the edge of the no-fly zone; Where, ψ bmin and ψ bmax The expression is as follows: In the formula: ψ b It is the track deflection angle from the target to the center of the no-fly zone, R b It is the radius of the no-fly zone, S b The remaining distance from the target to the center of the no-fly zone; remaining distance S b Determined by the following formula: In the formula: The latitude and longitude of the center of the no-fly zone; ψ b The calculation formula is as follows: When the target's instantaneous turning circle intersects with the no-fly zone, the following characteristics exist: S tb <R turn +R b (10) In the formula: R turn R is the instantaneous turning radius. b S is the radius of the no-fly zone. tb The distance between the centers of the instantaneous turning circle and the no-fly zone is given by R; where the instantaneous turning radius is R. turn Determined by the following formula: The distance between the center of the instantaneous turning circle and the center of the no-fly zone can be determined by the following formula: In the formula: The latitude and longitude of the center of the instantaneous turning circle of the aircraft are calculated using the following formula: After determining the target's guidance task based on equation (6), different prediction model sets are constructed to meet the requirements of different guidance tasks.

3. The method for predicting the trajectory of a reentry glider based on the minimum cost criterion according to claim 2, characterized in that: In Step 5, constructing the parameter prediction model set for conventional guidance includes: 1) Longitudinal parameter prediction model set When predicting the longitudinal trajectory of a reentry gliding target, the least squares method is used to filter the parameters during the tracking segment. By performing function fitting, we can obtain This allows us to obtain the predicted parameter values ​​for future times. For ease of description, let M = [K D ,σ,K L ], Assume the filtered parameter values ​​follow a Gaussian distribution with the mean of the true values, and the predicted parameter values ​​follow a Gaussian distribution with the mean of the predicted values. The parameter distributions are shown below: In the formula: For the possible values ​​of the parameter at future time points, and M respectively e and M m Standard deviation; When it is determined by equation (6) that the target is to perform a guidance task T f When constructing the longitudinal parameter prediction model set, from M m ~N(M) p ,(σ p ) 2 N parameters are drawn from each of the distributions to form N 3 A model set is needed; to improve trajectory prediction accuracy, the range of the model set should cover the true values ​​as much as possible, while the number of models should be kept as small as possible to reduce the algorithm's solution time; since the distribution of the parameters in the prediction segment is unknown, σ cannot be directly determined. p The value of M is determined by filtering the parameter value. e Standard deviation σ e Scaling yields σ p ,Right now s p =lọ e (15) Since the true value of the parameter M is unknown during parameter tracking, it is assumed that the result of the function fitting is close to the true value, meaning that the filtered parameter values ​​also satisfy a Gaussian distribution with the fitting result as the mean. M e ~N(M f ,(s f ) 2 ) (16) In the formula: For M e Standard deviation; Assuming the parameter filtering values ​​at different times The variance of the Gaussian distribution The same applies, as can be seen from the definition of standard deviation: Where: n e This is the total step length of the tracking segment; When sampling parameters using equation (14), parameter M m Determined by the following formula: 2) Lateral parameter prediction model set When the target is under conventional guidance, the trajectory deviation angle corridor is used to determine the sign of the target's current tilt angle, thereby forming a set of lateral parameter prediction models; When compensating for track deviation angles in a corridor, the upper and lower bounds of the track deviation angle are determined based on the relative position of the target and the no-fly zone; when ψ≥ψ bmax At that time, we can obtain: When ψ≤ψ bmin At that time, we can obtain: In the formula: Δψ fed This indicates the original trajectory deviation angle corridor range of the target; The sign of the target's roll angle is determined based on the compensated track deviation angle corridor: In the formula: ψ f Indicates the deflection angle of the target from the intended attack point; By combining the target longitudinal parameter model set, N is finally determined. 3 A set of prediction models, namely Λ = {M1, M2, ... M N },in 4. The method for predicting the trajectory of a reentry glider based on the minimum cost criterion according to claim 3, characterized in that: In Step 5, when the target task is T f At that time, construct the intention cost function I. f The main considerations are angular cost and energy cost, specifically as follows: In the formula: max(|Δψ) f |-Δψ fed ,0) represents the angle cost, |Δψ f |=|ψ-ψ f | represents the absolute value of the difference between the target's trajectory deflection and the trajectory deflection to the attack intent, when |Δψ f |≤Δψ fed When the angle cost is uniformly 0, when |Δψ f |>Δψ fed At that time, the angle cost is |Δψ f |-Δψ fed The intentional cost function tends to choose one that makes |Δψ f |Reduced parameter prediction model M;|S ref -S f |For the cost of energy, S ref This indicates that the target's velocity, under the current parameter prediction model, decreases to the planned velocity v. ref The flight distance at that time, S f This represents the remaining distance from the target to the intended attack point, when S f =S ref When the energy cost is 0, when S f ≠S ref At that time, S f and S ref The greater the difference, the greater the energy cost, and the intentional cost function tends to choose the option that makes S... f Approaching S ref The parameter prediction model M; Remaining range S f Determined by the following formula: In the formula: The latitude and longitude of the intended attack. S′ under equilibrium gliding conditions for the target ref To replace the actual S ref A comparison is made, ignoring the range deviation caused by the actual longitudinal motion of the target; based on the relationship between range and speed under the target's equilibrium gliding conditions, S′ is determined. ref The calculation formula is: In the formula: v0 is the target's current velocity. This indicates the lift-to-drag ratio of the target.

5. The method for predicting the trajectory of a reentry glider based on the minimum cost criterion according to claim 4, characterized in that: In Step 6, constructing the parameter prediction model set for avoiding no-fly zones includes: 1) Longitudinal prediction model set When a target performs a guidance mission to avoid a no-fly zone, there are two situations where the current turning capability is insufficient to completely avoid the no-fly zone; the first is when ψ and ψ f In ψ b When ψ and ψ are on either side, there is a momentary turning circle of the target intersecting with the no-fly zone, requiring detouring around the no-fly zone to avoid it; the second scenario is when ψ and ψ f In ψ b On one side, simultaneously at sign(σ)=sign(ψ-ψ) b The instantaneous turning circle intersects with the no-fly zone, and a small part of the no-fly zone obstructs the target's guidance trajectory; Based on the longitudinal parameter prediction model set of the conventional guidance parameter prediction model set, the tilt angle amplitude |σ p The value of | should cover its domain [0, π / 2] as much as possible. The specific process is as follows: Within the range [0, π / 2], N points are sampled at equal intervals, and the weight of each sampling point can be obtained according to equation (14). Normalize the weights of the sampling points During actual sampling, a random number δ′ is generated within [0,1], along with the weights of N points. By comparison, interpolation yields a new sampling point |σ m |; 2) Lateral parameter prediction model set The lateral parameter prediction model set considers two cases of the side angle sign {1,-1}, and the final lateral maneuver pattern is inferred with the aid of the intention cost function; By combining the target longitudinal parameter model set, 2N was finally determined. 3 A set of prediction models, namely Λ={M1,M2,…M 2N },in 6. The method for predicting the trajectory of a reentry glider based on the minimum cost criterion according to claim 5, characterized in that: In Step 6, when the target task is T b At that time, construct the intention cost function I. b At this stage, energy costs are not considered; the main considerations are avoidance angle costs and guidance angle costs. The specific forms are as follows: I b =ε1Δψ b +ε2Δψ bf (28) In the formula: ε1Δψ b It is the cost of avoiding angles, where ε1 is the avoidance cost coefficient; ε2Δψ bf ε2 is the guidance angle cost, and ε2 is the guidance cost coefficient. 1) Avoiding the cost of angle In the cost of avoiding angles, Δψ b The larger the angle, the greater the cost of avoiding it; A quantitative description of target avoidance of no-fly zones under the control of the roll angle in the parametric prediction model M is presented, and the parametric prediction model with the lowest avoidance cost is selected; Δψ b Determined by the following formula: When calculating the avoidance cost coefficient, ψ and ψ' need to be considered. b and ψ f The relationship is as follows: Within the set of tilt angle amplitudes for targets that can evade no-fly zones, the energy loss is minimized when the trajectory is tangent to the no-fly zone; therefore, the evasion cost coefficient is defined as follows: In the formula: σ tan Let σ' be the roll angle required for the target's instantaneous turning circle and the outer tangent of the no-fly zone, and σ' be the roll angle amplitude at the previous moment. When |σ|=σ tan When |σ|≠σ, the avoidance cost coefficient is 1. tan , |σ| and σ tan The greater the deviation, the greater the avoidance cost coefficient. The intention cost function tends to select |σ| when the target's instantaneous turning circle and the outer tangent of the no-fly zone are chosen. tan The specific calculation process is as follows: From the instantaneous turning circle of the target and the external tangent of the no-fly zone, we can obtain S tb =R turn +R b (31) From equations (12) and (13), we can obtain Expanding the above equation, we get Rearranged into an expression for the instantaneous turning radius By combining equations (11) and (34), we can obtain 2) Guidance angle cost In the guidance angle cost, Δψ bf The definition is as follows: When ψ bmin ≤ψ f ≤ψ bmax At that time, relative to the target, the attack intent is behind the no-fly zone. Regardless of which direction the target evades, sign(Δψ) bf When both ψ and ψ are 1, it means that while the target avoids the no-fly zone, the guidance cost will increase; when ψ f >ψ bmax or ψ f <ψ bmin At that time, if the attack intent is on the side of the no-fly zone relative to the target, the target will evade in the direction of the attack intent, resulting in a smaller guidance cost; otherwise, it will result in a larger guidance cost. The guidance cost coefficient ε2 is defined as follows: When S b <S f When ε = 2, ε2 < 0.5, indicating that the target is far from the attack point, and the impact of the guidance mission on avoiding the no-fly zone is relatively small, so the guidance cost is low; when S b ≥S f When ε = 2, ε2 ≥ 0.5, indicating that the target is close to the attack point. Avoiding the no-fly zone will directly affect the completion of the target's final guidance mission, so the guidance cost is relatively high. When multiple no-fly zones affect a target's trajectory, the nearest no-fly zone is selected as the primary no-fly zone to represent the overall cost of avoiding no-fly zones. Where: n b The number of no-fly zones that affect the target's trajectory.

7. The method for predicting the trajectory of a reentry glider based on the minimum cost criterion according to claim 6, characterized in that: Step 7 specifically refers to: attack intent η T The posterior probability is derived accordingly; Similarly, by splitting the state variable into two parts, we can obtain: In the formula, P(x k |x 1:k-1 ,η T ) represents the intention η sought by equation (44) above. T The likelihood probability, P(η) T |x 1:k-1 η represents the intention of the previous moment. T The posterior probability, P(x) k |x 1:k-1 The conditional probability of the target prediction in one step is calculated using the following formula: By Bayes' theorem, we can obtain The posterior probability is: Therefore, intention η T The posterior probability is: According to equation (52) and the minimum cost criterion, the most likely attack intent of the target is:

8. The method for predicting the trajectory of a reentry glider based on the minimum cost criterion according to claim 7, characterized in that: In Step 8, when the target's attack intent is ηT, the parameter prediction model M is determined based on the intent cost function. n The likelihood probability of the next state transition. in, According to Bayes' theorem, the parametric model M n The posterior probability is: When processing the fraction on the right side of the equals sign, the state variable is split into two parts and expressed as the likelihood probability multiplied by the prior probability: The two prior probabilities in the numerator and denominator are combined to form the parametric model M of the previous time step. n Posterior probability: Because the state transition process exhibits Markov property, for the parametric model M... n Simplifying the state transitions below, we get: In the formula: P(x k |x k-1 M n ,η T ) is the parametric model M n The likelihood probability has been determined by the intention cost function, P(M n |x 1:k-1 ,η T ) represents the parameter model M from the previous time step. n The posterior probability, P(x) k |x 1:k-1 ,η T ) indicates intention η T The likelihood probability is calculated using the following formula: By Bayes' theorem, we can obtain The posterior probability is: Therefore, the parametric model M n The posterior probabilities are as follows: According to equation (46) and the minimum cost criterion, the target is in attack intent η T The most likely parameter prediction model is:

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