A reentry glider trajectory prediction method

Abstract

The application discloses a reentry gliding vehicle trajectory prediction method and relates to the technical field of reentry gliding vehicle trajectory prediction. The application constructs a time-varying parameter model set, and updates the parameter model set in real time according to the historical motion law of a target and a lateral maneuvering direction, so that the target maneuvering mutation can be effectively coped with. The application constructs different-dimension intention cost functions, comprehensively considers the distance and angle relationship among an attack target, a no-fly zone and a vehicle, constructs a distance-dimension intention cost function based on an artificial potential field method and an angle-dimension intention cost function based on a pseudo-course angle, and provides a new solution for solving the intention cost quantization of the vehicle under the existence of the no-fly zone. The application innovatively proposes to construct a multi-dimension intention fusion model, fuses different-dimension intention costs in a Bayesian inference model, avoids the inference failure problem caused by unreasonable setting of a traditional cost coefficient, and improves the universality of the intention cost function.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of reentry glide vehicle trajectory prediction, in particular to a reentry glide vehicle trajectory prediction method. BACKGROUND

[0002] As a kind of global rapid strike weapon, reentry glide vehicle (RGV) has the characteristics of high speed, strong penetration ability and wide striking range in the long flight of near space, and is the focus of research of various military powers. 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 glide vehicle is of great significance.

[0003] Unlike ballistic targets, RGVs will perform large-scale high-speed maneuvers during reentry glide. 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 impact point, which puts high requirements on the trajectory prediction accuracy and prediction length of RGV.

[0004] From the prediction mechanism, the trajectory prediction technology for RGVs 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 vehicle trajectory, which has the characteristics of high short-term prediction accuracy and simple method implementation, but lacks deep model constraints and is difficult to meet the demand of high-precision and medium-long-term trajectory prediction. The second method is mainly divided into three types of parameter estimation, pattern recognition and intention inference from the prediction mechanism. Among them, parameter estimation regards RGV as a non-cooperative target, integrates unknown information such as vehicle mass, force area and aerodynamic coefficient into a parameter, and realizes iterative prediction of RGV by means of dynamic model. In the case of insufficient prior information, determining the appropriate and easy-to-predict parameter is the key to this method. The commonly used prediction parameters are lift-drag ratio, aerodynamic parameter and control variable, among which the lift-drag ratio has better prediction effect when it changes linearly, and the parameter has greater limitations. Aerodynamic parameters and control variables are widely used in RGV trajectory prediction because they are approximately linear with the attitude of the vehicle itself. However, when RGVs penetrate in a specific maneuvering mode or change the motion law in real time according to the predetermined attack intention during reentry, the parameter estimation method 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 glide vehicle.

[0005] In the aspect of target maneuver mode recognition, it has been proved to be a feasible direction to establish corresponding prediction model in advance according to different maneuver modes, and then to match the model through recognition technology. Hu et al. modeled the coupling relationship between the aerodynamic parameters of RGV based on vector autoregressive model, which provided a simple structure and unified form accurate description method for various maneuver modes. Cheng Yunpeng et al. generated a set of maneuver modes according to the definition of maneuver mode to train SVM, which realized the pattern recognition and prediction of target maneuver trajectory. Sun et al. composed the analytical expressions of altitude and velocity variables by linear decay term and amplitude decay sinusoidal term for the target longitudinal skip glide trajectory under simplified conditions, and realized the calculation of trajectory prediction pipeline by means of LSTM network. Since the guidance of reentry glide vehicle usually has purpose, the prediction results of maneuver mode recognition method can be further improved by introducing attack intent to correct the prediction results.

[0006] From the perspective of game theory, the guidance of RGV is always to achieve the maximum benefit with the minimum cost. By correlating the trajectory prediction of the aircraft with the game theory, the loss and benefit of RGV attacking different targets under different maneuver models are quantified, and the probability distribution of the targets and maneuver models in the reachable region of the aircraft is estimated, which provides data support for long-time and high-precision trajectory prediction. In the case of known aircraft attacking a target, limited by the guidance task and maneuver ability, and without considering the existence of the no-fly zone, the trajectory of the aircraft usually has the following characteristics: (1) the range between RGV and the target decreases with the increase of flight time; (2) the heading angle of RGV always points to the target or fluctuates within a certain range centered on the target. Based on this, Xu et al. established the relationship between the initial state of the aircraft, the control quantity and the flight region through deep neural network, and realized the rapid inference of the attack intention of the aircraft. However, RGV usually attacks high-value targets, and the detection radar and air defense weapons deployed near the target will form a no-fly zone with high risk for RGV. In order to reduce the flight risk and complete the attack task, RGV usually adopts C-type maneuver to avoid the no-fly zone, and the above-mentioned two flight characteristics do not hold. For the trajectory prediction of RGV under the existence of no-fly zone, scholars have made some explorations. Zhang Kai et al. assumed the attack intention, constructed the intention cost function based on the heading deviation angle, the remaining range, the target value and the dangerous zone radius, and derived the recursive formula of the maneuver mode and the motion state, realizing the trajectory prediction under the condition of target maneuver uncertainty. Hu et al. aimed at the problem of maneuver mode mutation, based on the literature [Zhang Kai, Xiong Jiajun, Li Fan, et al. Bayesian trajectory prediction of hypersonic gliding target based on intention inference [J]. Journal of Astronautics, 2018, 39(11): 1258-1265], transformed the trajectory prediction problem into solving the probability of the possible passing region of the target in the reachable region through the intention cost function and the Bayesian principle. The algorithm does not depend on the target dynamics, has high short-term prediction accuracy, but takes a long time, which is not conducive to online prediction; Li Jialai et al. improved the intention cost function based on the literature [Hu Y D, Gao C S, Li JL, et al. Novel trajectory prediction algorithms for hypersonic gliding vehicles based on maneuver mode on-line identification and intent inference [J]. Meas Sci Technol, 2021, 32(11): 115012], and constructed the time-varying prediction model set in the longitudinal and lateral directions respectively, realizing the multi-model and multi-intention fusion trajectory prediction of RGV, but the cost coefficients need to be given artificially, and the algorithm does not have universality.

[0007] Therefore, a trajectory prediction method of reentry glider vehicle is proposed to solve the problems in the background.

[0008] The above information disclosed in this BACKGROUND section is only for increasing the understanding of the background of the application, therefore, can include matters known by those of ordinary skill in the art. SUMMARY

[0009] The object of the present application is to provide a trajectory prediction method of reentry glider vehicle to solve the problems in the background.

[0010] To achieve the above object, the present application provides the following technical scheme: a trajectory prediction method of reentry glider vehicle, comprising the following steps:

[0011] Step 1, initialization:

[0012] 1) initialize radar parameters, prediction parameters, no-fly zones and intended position information;

[0013] 2) initialize filter algorithm parameters and parameter model posterior probability;

[0014] Step 2, build parameter model set:

[0015] 1) track the vehicle according to the CS-UKF filtering algorithm to obtain the parameter model μ f ;

[0016] 2) use least squares method to fit the predicted μ p , build RGV parameter model set Λ;

[0017] Step 3, infer attack intent:

[0018] 1) calculate the reachable region of RGV to determine the attack base set Θ;

[0019] 2) calculate the distance dimension and angle dimension intent cost function I dis , I angle for each base in the reachable region;

[0020] 3) build a multi-dimensional intent fusion model to obtain the attack probability distribution of the vehicle, and determine the base η T with posterior probability not less than prior probability;

[0021] Step 4, infer parameter model:

[0022] 1) calculate the distance dimension and angle dimension intent cost function I dis , I angle for the RGV parameter model μ j in the prediction phase;

[0023] 2) According to the multi-dimensional intention fusion model, the maximum posterior probability parameter model μ is inferred;

[0024] Step 5, trajectory prediction:

[0025] 1) The predicted trajectory is obtained by combining the RGV dynamics equation set iterative integral, and the multi-intention predicted trajectory is fused;

[0026] 2) When the prediction time reaches the planning time, save the data and end the prediction, otherwise return to Step 4.

[0027] Preferably, in Step 2, the longitudinal parameter model estimated by the filtering algorithm is defined as The longitudinal parameter model obtained by least squares fitting is The longitudinal parameter model used for final prediction is Since errors will occur when estimating the aerodynamic parameter u, in order to improve the prediction accuracy, it is assumed that the predicted longitudinal parameter model satisfies the Gaussian distribution with the fitting result as the mean, that is

[0028]

[0029] In the formula: k is the time of prediction, and respectively represent the variance of the resistance parameter, the lift parameter and the amplitude of the roll angle;

[0030] According to the above formula, N longitudinal parameter models are randomly selected for each parameter, and the sign of the roll angle is combined to finally determine 2N 3 parameter models, and the model set is defined as Λ.

[0031] Preferably, in Step 3, the distance of the aircraft to the real intention position is usually gradually reduced, but when avoiding the no-fly zone, the closer the important point to the no-fly zone, the higher the risk and benefit of the aircraft; Therefore, it is very one-sided to infer the intention of the aircraft only by the distance. Referring to the concept of electromagnetic field in physics, an artificial virtual potential field is constructed in the transverse plane, the attack important point generates a gravitational field, and the no-fly zone generates a repulsive field. The aircraft is simultaneously subjected to the action of gravity and repulsion, and moves as much as possible in the direction of increasing the resultant force, and the distance dimension intention cost function is constructed, including:

[0032] 1) Repulsive field

[0033] The repulsive potential function of the no-fly zone is designed as

[0034]

[0035] In the formula: K b is the constant of the repulsive field, S bThe flight path of the aircraft to the center of the no-fly zone;

[0036] The repulsive force exerted on the aircraft by the no-fly zone is the negative gradient of the repulsive potential function.

[0037]

[0038] In the formula: i b c1 is the unit vector pointing from the center of the no-fly zone to the aircraft, and c1 is a positive constant to avoid singularities.

[0039] Considering the aircraft's maneuverability and the influence range of the no-fly zone, the repulsion formula is modified as follows:

[0040]

[0041] In the formula: η b η is the repulsive force adjustment factor. To ensure the continuity of the repulsive force, η is constructed based on the relationship between the instantaneous turning circle of the aircraft and the position of the no-fly zone. b

[0042]

[0043] When multiple no-fly zones affect the trajectory of an aircraft, the one with the greatest repulsive force is selected as the primary no-fly zone.

[0044] F rep,m =max(F rep,1 ,F rep,2 ,…,F rep,n (26)

[0045] In the formula: n is the number of no-fly zones that affect the trajectory of the aircraft;

[0046] 2) Gravitational field

[0047] The gravitational potential function for designing the attack target is as follows:

[0048]

[0049] In the formula: K g S is the gravitational field constant. bf For the flight distance from attack strongholds to the center of the main no-fly zone, S f The flight distance of the aircraft to the target location;

[0050] The corresponding gravitational force exerted on the target area by the aircraft is the negative gradient of the gravitational potential function.

[0051]

[0052] In the formula: i f c2 is the unit vector pointing the aircraft towards the target area, and c2 is a normal constant to avoid singularities.

[0053] Therefore, the net force acting on the aircraft is

[0054] F = F att +F rep,m (29)

[0055] Construct the intention cost function with distance dimension as follows

[0056] I dis =|F|cos <F,F att >=|F att +F rep,m |cos <F,F att >=F att +|F rep,m |cos <F att ,F rep,m >(30)

[0057] Define gravity F att and repulsive force F rep,m The angle between them is γ. A schematic diagram of the forces acting on RGV in an artificial potential field is shown below. Figure 1 As shown. The above equation shows that the resultant force F is influenced by the gravitational force F. att The larger the component on the surface, the greater the intention cost I. dis The larger.

[0058] Preferably, in Step 3, constructing the angular dimension intention cost function includes:

[0059] When an aircraft evades a no-fly zone to complete a guidance mission, the yaw angle of the velocity vector relative to the actual attack intent may be too large. Therefore, the concept of a pseudo-yaw angle is proposed.

[0060] Δψ=Δψ f -λΔψ b (31)

[0061] In the formula: Δψ f Δψ is the actual heading angle of the aircraft from the target area to the attack point. b Δψ represents the correction value under the influence of the no-fly zone, where λ is the correction coefficient; f The calculation formula is

[0062] Δψ f =ψ-ψ f (32)

[0063] In the formula: ψ is the heading angle of the aircraft, ψ f The heading angle of the aircraft as it points towards the target area;

[0064] Since, in the absence of a no-fly zone, the velocity vector of an aircraft is usually near the heading angle pointing to its true intention, the portion of the heading angle affected by the no-fly zone must be corrected to increase the angular cost of protecting key locations within the no-fly zone; Δψ b The calculation formula is

[0065]

[0066] In the formula: ψ ed The range of the heading deflection corridor;

[0067] The formula for calculating the correction factor is as follows:

[0068]

[0069] In the formula: c3 is a positive constant to prevent singularity of the correction coefficient. The intention cost function constructed in the angular dimension is:

[0070] I angle =e -Δψ (35)

[0071] As shown in the above formula, the closer the aircraft's heading angle and key location are to the boundary of the no-fly zone, the greater the heading angle correction value due to the influence of the no-fly zone, the smaller the pseudo-heading angle Δψ, and the lower the intention cost I. angle The larger, such as Figure 2 As shown.

[0072] Preferably, in Step 3, traditional methods directly construct a single function for cost functions of different dimensions through simple scaling. However, under different situations, the dimensions of distance and angle differ significantly, and an inappropriate scaling factor can lead to an overemphasis on factors affecting a particular dimension, thus obscuring the cost dimension that reflects the true attack intent. Therefore, a multi-dimensional intent fusion model is constructed to address this issue. Constructing the multi-dimensional intent fusion model includes:

[0073] The likelihood probability calculated based on the intent cost function of different dimensions is:

[0074]

[0075] In the formula: N′ represents the total number of intentions. Let be the likelihood probability in the intention-distance dimension. Let be the likelihood probability in the intention dimension; from the Bayesian inference model, the posterior probability of different intentions can be obtained as follows:

[0076]

[0077] In the formula: and P i,dis Let be the prior probability and posterior probability of the intention distance dimension, respectively. and Pi,angle These are the prior and posterior probabilities, respectively, for the intention dimension.

[0078] Weighted fusion of posterior probabilities from different dimensions

[0079] P i =λP i,dis +(1-λ)P i,angle (38)

[0080] In the formula: λ is the weighting coefficient of the distance dimension inference result, P i The posterior probability of the fused intent;

[0081] In summary, firstly, by calculating the posterior probabilities of different intentions in different dimensions, the problem of coefficient selection caused by different units of measurement is avoided; then, weighted fusion is performed on the posterior probabilities of different dimensions, transforming the problem of cost coefficient selection into the selection of cost weights.

[0082] Preferably, in Step 4, during the prediction stage, due to the lack of observational information, the accuracy and reliability of intention recognition based on predicted aerodynamic parameters are both low. Considering that the aircraft's intention does not change frequently during flight, the probability distribution of attack points is calculated by comprehensively analyzing the filtered values ​​of each state tracked in history. Based on the multi-dimensional intention fusion model, the posterior probability of attacking key points within the RGV reachable area at time k can be obtained.

[0083]

[0084] Based on the posterior probability of historical moments, the probability of a key location being attacked can be obtained.

[0085]

[0086] In the formula: ω i The weights are the posterior probabilities of historical moments; weight ω i The exponential decay method is used to determine this, and the calculation formula is as follows:

[0087] ω′ i =e -λ(n-i+1) (41)

[0088]

[0089] In the formula: λ is the attenuation coefficient.

[0090] Based on equation (39), it can be deduced that the most likely target location is...

[0091]

[0092] With attack intent η TAt that time, the posterior probability of the parametric model of RGV at time k can be obtained according to the multidimensional intent fusion model.

[0093] P(μ j |x 1:k ,η T )=ε1P dis (μ j |x 1:k ,η T )+(1-ε1)P angle (μ j |x 1:k ,η T (44)

[0094] Finally, the parametric model for the maximum a posteriori probability is determined as follows:

[0095]

[0096] Compared with the prior art, the beneficial effects of the present invention are:

[0097] (1) The present invention constructs a time-varying parameter model set and updates the parameter model set in real time according to the target's historical motion law and lateral maneuver direction, effectively responding to sudden changes in target maneuver.

[0098] (2) This invention constructs intention cost functions of different dimensions, comprehensively considers the distance and angle relationship between the attack site, the no-fly zone and the aircraft, and constructs a distance-dimensional intention cost function based on the artificial potential field method and an intention cost function based on pseudo heading angle and angle dimension, providing a new solution for quantifying the intention cost of aircraft in the presence of a no-fly zone.

[0099] (3) This invention innovatively proposes to construct a multi-dimensional intent fusion model. By fusing different dimensions of intent costs in the Bayesian inference model, it avoids the inference failure problem caused by unreasonable setting of traditional cost coefficients and improves the universality of the intent cost function.

[0100] The above overview is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features of the invention will become readily apparent from the accompanying drawings and the following detailed description. Attached Figure Description

[0101] Figure 1 This is a schematic diagram of the forces acting on an RGV in an artificial potential field.

[0102] Figure 2 A schematic diagram of the relevant variables that make up the pseudo-heading angle;

[0103] Figure 3 A schematic diagram of the guidance trajectory of the RGV;

[0104] Figure 4 This is a schematic diagram of the prediction results for Case 1 (t0 = 500s);

[0105] Figure 5 A diagram illustrating the inference of attack intent for Case 1;

[0106] Figure 6 This is a schematic diagram of the trajectory prediction error in Case 1;

[0107] Figure 7 This is a schematic diagram of the prediction results for Case 2 (t0 = 700s).

[0108] Figure 8 This is a schematic diagram of the trajectory prediction error in Case 2. Detailed Implementation

[0109] 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.

[0110] Numerical simulation

[0111] To verify the effectiveness of the algorithm proposed in this invention, CAV-H was tested.

[35] A simulation experiment was conducted on the reentry glide phase. The aircraft has a mass of 907 kg and an area of ​​0.4839 m². The initial state of reentry glide... The values ​​are (0°, 0°, 70km, 6000m / s, -0.1°, 65°). Three no-fly zones and twelve attack intentions are set up in the simulation, with corresponding parameters shown in Table 1. The key location value and prior probability are the same for each attack intention. Figure 8 For the attack target, a predictive correction method is used for guidance, with a guidance period of 1 second. The deployment location of the early warning radar is set at [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 period and guidance period are the same. The basic parameters involved in the algorithm are: number of parameter model sets N = 5, normal numbers c1 = c2 = c3 = 0.01, attenuation coefficient λ = 0.0069, weighting coefficient λ = 0.5 for the posterior probability of the intention in the range dimension, and track deviation angle corridor Δψ. fed =5°, artificial potential constant K b =K g =1.

[0112] Table 1. Attack Intent and Parameters for No-Fly Zones

[0113] Attribute Longitude / (°) Latitude / (°) Radius / (°) Attribute Longitude / (°) Latitude / (°) No-fly zone 1 15 11 2 It is Figure 6 24 24 No-fly zone 2 24 17 2 It is Figure 7 27 22 No-fly zone 3 32 14 2 It is Figure 8 30 25 It is Figure 1 12 14 - Intention 9 31 18 It is Figure 2 15 18 - Intention 10 34 20 It is Figure 3 17 14 - Intention 11 35 16 It is Figure 4 22 21 - Intention 12 37 22 It is Figure 5 24 20 -

[0114] The guidance trajectory of the RGV is as follows Figure 3 As shown. From Figure 3 (a) It can be seen that during the reentry glide, the aircraft traversed between no-fly zones and reached its destination. Figure 8 ;from Figure 3 (b) It can be seen that the longitudinal altitude of the aircraft is relatively smooth overall, without any significant jumps. The entire gliding phase lasts approximately 1200 seconds, with a range of approximately 4300 km. When predicting this trajectory, the reachable area of ​​the re-entry gliding target is calculated using the constant tilt angle method.

[37] The tilt angle ranges from -70° to 70°.

[0115] To verify the superiority of the proposed algorithm, simulations were performed using the prediction algorithms in references

[15] ,

[27] , and

[28] . For ease of description, the three algorithms mentioned above are referred to as Method 1, Method 2, and Method 3, and the algorithm proposed in this invention is referred to as Method 4. The cost coefficient settings in Method 2 and Method 3 are the same as those in reference

[28] . To verify the effectiveness of Method 4, the causes of prediction errors were analyzed and compared, and simulations were performed using the 500s mark near the no-fly zone and the 700s mark near the guidance position as the tracking starting points.

[0116] Literature

[15] HU YD, GAO CS, LI JL, et al. Maneuver mode analysis and parametric modeling for hypersonic glide vehicles [J]. Aerosp Sci Technol, 2021, 119.

[0117] Literature

[27] HU YD, GAO CS, LI JL, et al. Novel trajectory prediction algorithms for hypersonic gliding vehicles based on maneuver mode on-lineidentification and intent inference[J]. Meas Sci Technol, 2021, 32(11):115012.

[0118] Reference

[28] Li Jiali, Guo Jie, Tang Shengjing. Multi-model multi-intent fusion trajectory prediction for hypersonic gliding targets [J]. Journal of Astronautics, 2024, 45(2):167-180.

[0119] Case 1

[0120] Using the 500s mark as the tracking start point, tracking for 200s, predicting the RGV trajectory position 150s later, the prediction result is as follows. Figure 4 As shown in Table 2, the attack probability distribution is shown in Table 3, and the terminal prediction error is shown in Table 4.

[0121] from Figure 4 (a) It can be seen that the key locations within the reachable area of ​​the aircraft include... Figure 7 , 8 9, 10. As can be seen from Table 2, Method 2, by better considering the relationship between range and angle, results in a relatively consistent attack probability distribution for key locations within the reachable area. Method 3 tends to select key locations with shorter ranges when inferring attack intentions, and its constructed cost function uses fixed coefficients, leading to the failure of the inference method under the simulation conditions of this invention, and the calculated attack probability distribution differs significantly from the actual situation. Method 4 comprehensively considers the relationship between the no-fly zone, key locations, and aircraft based on the artificial potential field method in the distance dimension, corrects the heading angle affected by the no-fly zone in the angle dimension, and uses a multi-dimensional intent fusion model to improve the attack probability of key locations under uncertain conditions. The resulting probability distribution has high reference value and facilitates the defender's inference of the aircraft's true attack intentions.

[0122] Table 2 Attack Probability Distribution of Case 1

[0123]

[0124] In method 4, meaning Figure 7 Harmony Figure 8 The posterior probabilities are all higher than the prior probabilities. After multi-intent trajectory fusion, from... Figure 4 (b) It can be seen that the prediction error is generally lower than the other three prediction methods, significantly improving the accuracy of long-term trajectory prediction. Method 1, due to its use of a vector autoregression model to model the aerodynamic parameters of the tracking segment, cannot adapt to changes in the maneuver model of the prediction segment, leading to a gradual divergence in prediction error. Method 2, due to incorrect inference of attack intent, causes a rapid divergence in prediction error; however, since this method essentially converts the prediction of aircraft aerodynamic parameters into position prediction within a one-step reachable zone, it has the characteristic of high prediction accuracy in the short term. Although Method 3 also incorrectly inferred the aircraft's attack intent, it adopted a multi-model, multi-intent fusion prediction strategy, resulting in a significantly smaller prediction error than Method 2. Combined with Table 3, from... Figure 4As can be seen from (c) and (d), the meridional and latitudinal prediction errors of methods 1, 2, and 3 are the main reasons for the large overall prediction error. Method 1, due to the lack of intent information to correct aerodynamic parameters, shows significant deviations from the actual trajectory in both the lateral and longitudinal directions. Methods 2 and 3 suffer from significant deviations in the lateral predicted trajectory due to errors in intent recognition. Furthermore, Method 2's celestial prediction error is the largest among the four methods because its position inference algorithm cannot accurately infer the ballistic inclination angle. Method 4, drawing on the idea of ​​artificial potential fields, improves trajectory prediction accuracy by selecting a parameter model with a larger resultant force in the gravitational direction from the model set.

[0125] Regarding prediction time, Table 3 shows that Method 1 has the shortest prediction time, followed by Method 4, and Method 2 has the longest. Method 1, because it directly models the aerodynamic parameters of the tracking segment without involving parameter processing in the prediction segment, has the shortest prediction time. Method 2, however, uses the Monte Carlo algorithm to solve for the posterior probability of the discrete region after discretizing the reachable area of ​​the aircraft, resulting in a longer algorithm time. Method 3's prediction time is increased due to redundancy in the lateral maneuver model set. The proposed method 4, by constructing a simplified parameter model set and completing the aircraft's intent recognition during the tracking phase, significantly reduces the algorithm's prediction time. Therefore, the proposed method, while greatly improving prediction accuracy, has a shorter algorithm time, meeting the defense side's need for rapid prediction.

[0126] Table 3 Predictive Results of Case 1

[0127] Method Meridional error (km) Latitudinal error (km) Celestial error (km) Overall error (km) Prediction time (s) 1 35.287 -23.028 3.457 42.278 0.005 2 126.632 -125.199 5.293 178.153 11.482 3 73.496 -54.567 0.399 91.539 2.002 4 28.147 -3.202 0.700 28.338 0.623

[0128] To verify the stability of the algorithm, continuous predictions were made for 100 seconds with a prediction interval of 2 seconds based on the simulation conditions of this invention. The simulation results are as follows: Figure 5 and Figure 6 As shown.

[0129] from Figure 5 (d) It can be seen that among the three algorithms capable of intent inference, method 4 infers the true intent throughout the entire process, method 2 infers the true intent of the aircraft relatively early, and method 3 infers the aircraft's intent over a larger range. From Figure 5 (a) It can be seen that the difference in the attack probability distribution of the intent within the reachable area of ​​Method 2 is too small, almost the same as the prior probability. This small difference is insufficient to provide strong inference evidence for the decision-maker. From Figure 5 (b) It can be seen that for a long period of time, Method 3 estimated a very high probability of attack for Intent 9, while incorrectly estimating the true probability. Figure 8 The estimated probability of an attack is extremely low. This probability distribution of attack intent could lead decision-makers to make significant strategic misjudgments, directly resulting in interception failure. From Figure 5(c) It can be seen that before 704s, Italy Figure 8 The estimated probability is as high as nearly 40%, but... Figure 7 The posterior probability is higher than the prior probability. Therefore, when predicting the trajectory of an aircraft, the decision-maker should consider both attack intent trajectories simultaneously to reduce the risk of misjudgment. After 704 seconds, the posterior probability is higher than the prior probability. Figure 7 The attack probability drops to 0 because the intended location is not within the reachable zone. At this point, the intended location can be seen... Figure 8 The probability of attacks has increased significantly, providing strong inference evidence for decision-makers.

[0130] from Figure 6 It can be seen that Method 1 uses autoregressive modeling of the entire aerodynamic parameter vector. Although it lacks aircraft intent information, the trajectory prediction results are generally stable, with errors generally within 50km. Method 2's error increases continuously in the early stages of prediction due to incorrect intent recognition. After 722s, it identifies the aircraft's true attack intent, and the prediction error gradually decreases, but it is still higher than the prediction results of Method 1 and Method 4. Method 3, due to its multi-model, multi-intent fusion approach, has a relatively stable overall error in the early stages of prediction. After 774s, the error decreases rapidly as the algorithm identifies the true attack intent, and its prediction accuracy is slightly higher than Method 2. Method 4's prediction error remains at a low level overall. In the early stages of prediction, due to the lack of intent recognition, the error increases. Figure 7 Harmony Figure 8 All of them possess a high probability of attack, and in the case of multi-intent trajectory fusion, the trajectory prediction error remains within a small range. In the later stages of prediction, since the parametric model inference cannot always be accurate, the prediction error fluctuates, with a maximum variation not exceeding 25km.

[0131] In summary, inferring the true attack intent and predicting long-term trajectories during aircraft evading no-fly zones present significant challenges. The method proposed in this invention can infer a more reasonable attack intent and significantly reduce trajectory prediction errors, demonstrating superior overall prediction performance compared to other methods.

[0132] Case 2

[0133] Using the 700s mark as the tracking start point, tracking for 200s, predicting the RGV trajectory position 150s later, the prediction result is as follows. Figure 7 As shown in Table 4, the prediction error of the final point is as follows.

[0134] from Figure 7 (a) It can be seen that only intention Figure 8 Within the reachable region of RGV, the differences in prediction errors caused by different prediction methods are irrelevant to the inference of attack intent. Figure 7(b) It can be seen that the prediction error of Method 4 is still generally lower than that of the other three methods, and the prediction error is less than 10 km; the prediction error of Method 1 is slightly larger than that of Method 4, but significantly smaller than that of Methods 2 and 3, indicating that the changes in aerodynamic parameters are less affected by the intended information; the prediction error of Method 2 shows a change of first increasing and then decreasing with the increase of prediction time, and the overall error remains within 25 km; the prediction error of Method 3 gradually diverges, but the error after 150 s is still within 35 km. Combined with Table 4, from... Figure 7 (c) It can be seen that the lateral predicted trajectories of all four methods are close to the actual trajectories, with the prediction errors of methods 2 and 3 being several times greater than those of methods 1 and 4. The reason for this is that method 2 did not consider the dynamic constraints of the aircraft when making discrete predictions in the reachable region, resulting in the predicted trajectory pointing directly towards the intended path. Figure 8 The actual trajectory deviates significantly from the true trajectory. While Method 3 estimates the posterior probability of different maneuver models using the intention cost function based on aerodynamic parameter fitting, it fuses multiple model trajectories during prediction. This results in the trajectory under the incorrect lateral maneuver model reducing the final prediction accuracy. Method 4, however, uses the maximum a posteriori estimation parameter model during prediction, avoiding this effect. Figure 7 (d) It can be seen that the longitudinal predicted trajectories of methods 3 and 4 are closely related to the actual trajectories. The predicted height of method 1 has increased slightly, while the predicted height of method 2 deviates from the actual value by a large margin. The reasons for this are the same as in case 1, and will not be repeated here.

[0135] Table 4 Predictive Results of Case 2

[0136] Method Meridional error (km) Latitudinal error (km) Celestial error (km) Overall error (km) Prediction time (s) 1 0.427 -10.524 2.550 10.837 0.005 2 -17.712 6.152 11.427 21.958 10.304 3 23.279 -20.891 0.362 31.280 0.517 4 -5.477 -6.467 1.287 8.571 0.189

[0137] Based on the simulation conditions of this invention, continuous predictions were made for 100 seconds with a prediction interval of 2 seconds. The simulation results are as follows: Figure 8 As shown.

[0138] from Figure 8 It can be seen that Method 1, due to the lack of aircraft intent information, has a large fluctuation in trajectory prediction results; Method 2, when identifying the aircraft's true attack intent, gradually reduces the prediction error, and its prediction accuracy is higher than that of Method 3, while its algorithm stability is higher than that of Method 1; Method 3, due to the use of multi-model fusion, has a large prediction error in the early stage, which gradually decreases in the later stage; Method 4 maintains a low overall prediction error, and its prediction accuracy and algorithm stability are better than other methods.

[0139] In summary, when the aircraft is close to the actual attack intent, the prediction accuracy of all four methods remains at a high level, but the method proposed in this invention is superior to the traditional methods overall.

[0140] in conclusion

[0141] This invention comprehensively considers the distance and angular relationships between no-fly zones, key locations, and aircraft, and proposes a trajectory prediction algorithm for reentry gliders based on the concept of multi-dimensional intent fusion. First, based on the estimation and prediction of target aerodynamic parameters, a set of time-varying target maneuvering models is constructed. By covering lateral maneuvering modes, the adaptability of the prediction method is improved. Then, distance and angular dimension intent cost functions are constructed separately, and a multi-dimensional intent fusion model based on a normalization method is proposed. Compared with traditional cost functions, this inference model does not require manual determination of cost coefficients and has higher universality. Finally, based on the Bayesian inference model and the multi-dimensional intent fusion model, the aircraft's attack intent and parameter model are inferred, achieving long-term prediction of the aircraft's trajectory. Simulation results show that the prediction method proposed in this invention outperforms existing methods in terms of intent recognition accuracy, prediction error, and method execution time.

[0142] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for predicting the trajectory of a reentry glider, characterized in that, Includes the following steps: Step 1, Initialization: 1) Initialize radar parameters, prediction parameters, no-fly zone, and intended location information; 2) Initialize the filtering algorithm parameters and the posterior probability of the parameter model; Step 2: Construct the parameter model set: 1) Track the aircraft using the CS-UKF filtering algorithm to obtain the parameter model μ. f ; 2) The predicted μ is obtained by fitting using the least squares method. p Construct the RGV parameter model set Λ; Step 3: Determine the attack intent: 1) Calculate the reachable zone of RGV and determine the set of attack targets Θ; 2) Calculate the distance and angle dimensions of the intention cost function I for each key location within the reachable area during the tracking phase. dis I angle ; 3) Construct a multi-dimensional intent fusion model to obtain the attack probability distribution of the aircraft and determine the key locations η whose posterior probability is not lower than their prior probability. T ; The construction of the distance dimension intent cost function includes: Repulsive field: The repulsive potential function for the no-fly zone is designed as follows: In the formula: K b S is the repulsive field constant. b The flight path of the aircraft to the center of the no-fly zone; The repulsive force exerted on the aircraft by the no-fly zone is the negative gradient of the repulsive potential function. In the formula: i b c1 is the unit vector pointing from the center of the no-fly zone to the aircraft, and c1 is a positive constant to avoid singularities. Considering the aircraft's maneuverability and the influence range of the no-fly zone, the repulsion formula is modified as follows: In the formula: η b The repulsive force adjustment factor is used; to ensure the continuity of the repulsive force, η is constructed based on the relationship between the instantaneous turning circle of the aircraft and the position of the no-fly zone. b When multiple no-fly zones affect the trajectory of an aircraft, the one with the greatest repulsive force is selected as the primary no-fly zone. F rep,m =max(F rep,1 ,F rep,2 ,…,F rep,n ) (26) In the formula: n The number of no-fly zones that affect the trajectory of aircraft; gravitational field: The gravitational potential function for designing the attack target is as follows: In the formula: K g S is the gravitational field constant. bf For the flight distance from attack strongholds to the center of the main no-fly zone, S f The flight distance of the aircraft to the target location; The corresponding gravitational force exerted on the target area by the aircraft is the negative gradient of the gravitational potential function. In the formula: i f c2 is the unit vector pointing the aircraft towards the target area, and c2 is a normal constant to avoid singularities. Therefore, the net force acting on the aircraft is F=F att +F rep,m (29) Construct the intention cost function with distance dimension as follows I dis =|F|cos<F,F att >=|F att +F rep,m |cos<F,F att >=F att +|F rep,m |cos<F att ,F rep,m > (30) Define gravity F att and repulsive force F rep,m The angle between them is γ. The above equation shows that the resultant force F is under the influence of the gravitational force F. att The larger the component on the surface, the greater the intention cost I. dis The larger; The construction of the angular dimension intent cost function includes: When an aircraft evades a no-fly zone to complete a guidance mission, the yaw angle of the velocity vector relative to the actual attack intent may be too large. Therefore, the concept of a pseudo-yaw angle is proposed. Δψ=Δψ f -λΔψ b (31) In the formula: Δψ f Δψ is the actual heading angle of the aircraft from the target area to the attack point. b Δψ represents the correction value under the influence of the no-fly zone, where λ is the correction coefficient; f The calculation formula is Dp f =ψ-ψ f (32) In the formula: ψ is the heading angle of the aircraft, ψ f The heading angle of the aircraft as it points towards the target area; Since, in the absence of a no-fly zone, the velocity vector of an aircraft is usually near the heading angle pointing to its true intention, the portion of the heading angle affected by the no-fly zone must be corrected to increase the angular cost of protecting key locations within the no-fly zone; Δψ b The calculation formula is In the formula: ψ ed The range of the heading deflection corridor; The formula for calculating the correction factor is as follows: In the formula: c3 is a positive constant to prevent singularity of the correction coefficient; the intention cost function constructed in the angular dimension is: I angle =e -Δψ (35) As shown in the above formula, the closer the aircraft's heading angle and key location are to the boundary of the no-fly zone, the greater the heading angle correction value due to the influence of the no-fly zone, the smaller the pseudo-heading angle Δψ, and the lower the intention cost I. angle The larger; Step 4: Inferring the parameter model: 1) For the RGV parameter model μ in the prediction stage j Calculate the intention cost function I in the distance and angle dimensions. dis I angle ; 2) Based on the multidimensional intent fusion model, infer the parameter model μ of the maximum a posteriori probability; Step 5, Trajectory Prediction: 1) Combine the iterative integration of the RGV dynamic equations to obtain the predicted trajectory, and then fuse the predicted trajectories from multiple intentions; 2) Once the predicted time reaches the planned time, save the data and end the prediction; otherwise, return to Step 4.

2. The method for predicting the trajectory of a reentry glider according to claim 1, characterized in that: In Step 2, the longitudinal parameter model estimated by the filtering algorithm is defined as follows: The longitudinal parameter model obtained by least squares fitting is The longitudinal parameter model used for the final prediction is Since estimation of aerodynamic parameter u introduces errors, to improve prediction accuracy, it is assumed that the predicted longitudinal parameter models all follow a Gaussian distribution with the fitted results as the mean. In the formula: k For the predicted time, and These represent the variances of the drag parameter, lift parameter, and roll angle amplitude, respectively. In summary, based on the above formula, N parameters are randomly selected to form the longitudinal parameter model. Combined with the sign of the tilt angle, the final value of 2N is determined. 3 A parameterized model is defined as the model set Λ.

3. The method for predicting the trajectory of a reentry glider according to claim 1, characterized in that: In Step 3, constructing the multi-dimensional intent fusion model includes: The likelihood probability calculated based on the intent cost function of different dimensions is: In the formula: N ′ represents the total number of intentions. Let be the likelihood probability in the intention-distance dimension. Let be the likelihood probability in the intention dimension; from the Bayesian inference model, the posterior probability of different intentions can be obtained as follows: In the formula: and P i,dis Let be the prior probability and posterior probability of the intention distance dimension, respectively. and P i,angle These are the prior and posterior probabilities, respectively, for the intention dimension. Weighted fusion of posterior probabilities from different dimensions P i =λP i,dis +(1-λ)P i,angle (38) In the formula: λ is the weighting coefficient of the distance dimension inference result, P i The posterior probability of the fused intent; In summary, firstly, by calculating the posterior probabilities of different intentions in different dimensions, the problem of coefficient selection caused by different units of measurement is avoided; then, weighted fusion is performed on the posterior probabilities of different dimensions, transforming the problem of cost coefficient selection into the selection of cost weights.

4. The method for predicting the trajectory of a reentry glider according to claim 3, characterized in that: In Step 4, the posterior probability of the attack target within the RGV reachable area at time k can be obtained based on the multidimensional intent fusion model. Based on the posterior probability of historical moments, the probability of a key location being attacked can be obtained. In the formula: ω i The weights are the posterior probabilities of historical moments; weight ω i The exponential decay method is used to determine this, and the calculation formula is as follows: oh' i =e -λ(n-i+1) (41) In the formula: λ is the attenuation coefficient; Based on equation (39), it can be deduced that the most likely target location is... With attack intent η T At that time, the posterior probability of the parametric model of RGV at time k can be obtained according to the multidimensional intent fusion model. P(μ j |x 1:k ,or T )=ε1P dis (m j |x 1:k ,or T )+(1-ε1)P angle (m j |x 1:k ,or T ) (44) Finally, the parametric model for the maximum a posteriori probability is determined as follows:

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