Track Backtracking and Alarm Event Tracing Method Based on Interactive Model

Abstract

A method for trajectory backtracking and alarm event traceability based on an interactive model, which relates to the field of trajectory backtracking. The present invention is to solve the problem that the existing trajectory backtracking methods cannot obtain the launch point, shutdown point and landing point of the missile at the same time, and at the same time, the selected motion model in the existing technology has a large difference from the motion of the real target, resulting in the inability to accurately obtain the complete ballistic trajectory. The present invention includes: obtaining the number of ballistic trajectories at each moment of the ballistic trajectory to be backtracked. If the number of ballistic trajectories at each moment is the same, it means that the ballistic trajectory is not interrupted, and directly obtain the shutdown point, landing point and launch point information of the missile trajectory. If there is a ballistic trajectory number that is inconsistent with other moments, the ballistic trajectory is interrupted at this moment, and the ballistic trajectory is associated and complemented, and then obtain the shutdown point, launch point and landing point information of the complemented ballistic trajectory; finally, trace the alarm event according to the obtained information. The present invention is used for ballistic trajectory backtracking and alarm event traceability.

Description

Technical Field

[0001] The present invention relates to the field of track backtracking, and particularly to a track backtracking and alarm event traceability method based on an interactive model. Background Art

[0002] A ballistic missile is a special missile that generally flies according to a predetermined program under the thrust of a rocket engine and flies along a free-falling body trajectory after the rocket engine is actively shut down or the fuel is exhausted. The flight process of a ballistic missile is generally divided into an active section and a passive section. The active section is the flight path of the missile from the launch point to the shutdown of the rocket engine under the action of the rocket engine thrust and the guidance system. The passive section includes a free flight section and a reentry section, which is the path of the missile flying inertially according to the given speed and ballistic angle obtained at the end of the active section until the final warhead lands and detonates. In the entire ballistic missile target track, the launch point, the shutdown point, and the landing point are crucial. However, in the actual combat environment, we cannot obtain the complete track of the target. Therefore, how to estimate the parameters of the launch point, the shutdown point, and the landing point of the ballistic missile through the existing partial track backtracking is of great significance.

[0003] Currently, it is only limited to using the motion model of a single stage alone to solve the launch point, the shutdown point, or the landing point, and it is impossible to obtain the launch point, the shutdown point, and the landing point of the missile at the same time. At the same time, the motion model selected by the existing technology for obtaining the launch point, the shutdown point, or the landing point has a large difference from the motion of the real target, resulting in the inability to accurately obtain the complete ballistic trajectory. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem that the existing track backtracking method cannot obtain the three points of the launch point, the shutdown point, and the landing point of the missile at the same time, and the motion model selected by the existing technology for obtaining the launch point, the shutdown point, or the landing point has a large difference from the motion of the real target, resulting in the inability to accurately obtain the complete ballistic trajectory. Therefore, a track backtracking and alarm event traceability method based on an interactive model is proposed.

[0005] The specific process of the track backtracking and alarm event traceability method based on an interactive model is as follows:

[0006] Step 1: Obtain the number of ballistic trajectories at each moment of the ballistic trajectory to be backtracked. If the number of ballistic trajectories at each moment is the same, it means that the ballistic trajectory is not interrupted, and then step 4 is executed. If there is a number of ballistic trajectories that is inconsistent with other moments, it means that the ballistic trajectory is interrupted at this moment, and then step 2 is executed;

[0007] Step 2: Correlate the interrupted ballistic trajectories to obtain a trajectory completion allocation method:

[0008] Step 2-1: Coarsely correlate the interrupted ballistic trajectories to obtain an effective correlation combination;

[0009] Step 2: Obtain the trajectory completion allocation method through fine association based on the valid association combination;

[0010] Step 3: Complete the interrupted ballistic trajectory according to the trajectory completion allocation method obtained in Step 2 to obtain the completed ballistic trajectory B, and then execute Step 4;

[0011] Step 4: Estimate the shutdown point, launch point, and landing point of the missile based on the uninterrupted ballistic trajectory A to be traced back obtained in Step 1 or the completed ballistic trajectory B obtained in Step 3, and obtain the information of the estimated launch point, shutdown point, and landing point of the missile;

[0012] Step 5: Obtain the information of the launch point, shutdown point, and landing point of the missile in the warning event, respectively obtain the similarity between the estimated missile launch point and the missile launch point in the warning event, the similarity between the estimated missile shutdown point and the missile shutdown point in the warning event, and the similarity between the estimated missile landing point and the missile landing point in the warning event, and determine the true warning information according to the similarity.

[0013] The beneficial effects of the present invention are as follows:

[0014] The present invention first considers the relationship between the trajectory characteristics of the target group and its internal structure, quantity and quality, initial state, and force situation. According to the characteristic that the target body's movement process is phased, the target track is modeled in stages according to the movement characteristics of the target group in different stages, and a movement model with a small difference from the real target movement is obtained. At the same time, considering that the track data obtained in the real environment may be interrupted, the present invention proposes an algorithm for interrupted track association and completion to complete the interrupted ballistic trajectory to obtain a complete ballistic trajectory, so that the launch point, shutdown point, and landing point of the missile can be obtained simultaneously. When several warning events are known, the present invention obtains the group track number corresponding to the warning event through the two-dimensional allocation method, thereby locking the group where the target is located, and thus obtaining an accurate warning event, improving the recognition accuracy of the warning event. Description of the Drawings

[0015] Figure 1 Schematic diagram of the single-track backtracking result;

[0016] Figure 2 Structural diagram of the active section tracking method for ballistic missiles;

[0017] Figure 3 Schematic diagram of extrapolation backtracking;

[0018] Figure 4 Schematic diagram of the simulated ballistic track;

[0019] Figure 5 Schematic diagram of the track after interrupted association and completion;

[0020] Figure 6 are the original individual target track charts;

[0021] Figure 7 are the individual target aircraft charts after interruption correlation completion;

[0022] Figure 8 is the partial track of a single target for simulation;

[0023] Figure 9 are the schematic diagrams of the target track for simulation;

[0024] Figure 10 is the schematic diagram of the group track for simulation. Specific implementation mode

[0025] Specific implementation mode one: The specific process of the track backtracking and warning event traceability method based on the interactive model in this implementation mode is as follows:

[0026] Step 1, obtain the number of estimated ballistic trajectories at each moment of the ballistic trajectory to be backtracked. If the number of ballistic trajectories at each moment is the same, it means that the ballistic trajectory is not interrupted, and step 4 is executed. If there is a number of ballistic trajectories that is inconsistent with other moments, the ballistic trajectory at that moment is interrupted, and step 2 is executed;

[0027] Step 2, perform correlation on the interrupted ballistic trajectory to obtain a completion allocation method;

[0028] Step 3, complete the interrupted ballistic trajectory according to the completion allocation method obtained in step 2 to obtain the completed ballistic trajectory B, and execute step 4;

[0029] Step 4, estimate the shutdown point, launch point, and landing point of the missile according to the uninterrupted ballistic trajectory A to be backtracked obtained in step 1 or the completed ballistic trajectory B obtained in step 3, and obtain the information of the estimated launch point, shutdown point, and landing point of the missile;

[0030] Step 5, obtain the information of the launch point, shutdown point, and landing point of the missile in the warning event, and respectively obtain the similarity between the estimated missile launch point and the missile launch point in the warning event, the similarity between the estimated missile shutdown point and the missile shutdown point in the warning event, and the similarity between the estimated missile landing point and the missile landing point in the warning event, and determine the true warning information according to the similarity.

[0031] Specific implementation mode two: The step of performing correlation on the interrupted ballistic trajectory to obtain a completion allocation method in step 2 includes the following steps:

[0032] Step 2-1, perform rough correlation on the interrupted ballistic trajectory to obtain an effective correlation combination:

[0033] Step 2-1: Obtain the segment trajectory before the interruption of the ballistic trajectory and record it as the old track:

[0034]

[0035] Among them, represents the set of old tracks at time k, represents the n'-th old track, and N is the total number of old tracks;

[0036] The "old track" is a track that has been determined to end because there are no measurement points associated with it, that is, the segment of the ballistic trajectory before the interruption;

[0037] Step 2-2: Obtain the segment trajectory after the interruption of the ballistic trajectory and record it as the new track:

[0038]

[0039] Among them, represents the set of new tracks at time k, represents the m'-th new track, and M is the number of new tracks;

[0040] Step 2-3: Use the old track obtained in Step 2-1 and the new track obtained in Step 2-2 to obtain all associated track combinations of the old track and the new track at time k:

[0041]

[0042]

[0043]

[0044] Among them, Φ T is all the associated combinations of old and new tracks, is the n'-th old track segment, is the m'-th new track segment, represents the starting time of the n'-th old track in the old track set, represents the ending time of the n'-th old track in the old track set, represents the starting time of the m'-th new track in the new track set, represents the ending time of the m'-th new track in the new track set, old track and new track are the two track segments before and after the interruption on the same track of the same target; is the vector of the track points on the n'-th old track, is the vector of the track points on the m'-th new track.

[0045] Step 214. Use all the associated track combinations obtained in Step 213 to perform speed matching on the two track segments before and after the interruption on the same track of the same target to obtain valid association combinations:

[0046] Old track and new track are the two track segments before and after the interruption on the same track of the same target, then and satisfy the matching relationship in terms of speed, that is, the ratio of the interruption distance to the interruption time is less than the maximum movement speed of the target. Perform speed matching detection on the last state update point after filtering each old track and the last state update point after performing reverse filtering on each new track. Those that satisfy the speed matching are valid association combinations Φ e :

[0047]

[0048] Among them, is the backward recursion position component of the old track, is the forward recursion position component of the new track, and are the termination time of any old track and the start time of the new track respectively, v max is the prior maximum speed of the target, C1 is a constant. Using speed information to achieve rough association of track segments greatly reduces the candidate combinations for fine association and reduces the computational complexity;

[0049] Step 22. Perform fine association according to the valid association combinations to obtain the track completion allocation method:

[0050] Step 221. Set the comparison time:

[0051]

[0052]

[0053]

[0054] Among them, represents the start time of the n'-th old track, represents the start time of the m'-th new track, represents the termination time of the n'-th old track, represents the termination time of the m'-th new track, s' is the termination time of each old track, and e' is the start time of each new track;

[0055] Step Two Two Two: Extrapolate the termination time of the old track to the comparison time, trace back the start time of the new track to the comparison time, obtain the state prediction values of the extrapolated old track and the traced-back new track, and obtain the state prediction value difference, as Figure 3 shown below:

[0056] First, considering that the state values at the missing intermediate times can be obtained through the missile free-flight motion model, the fourth-order Runge-Kutta method is selected to extrapolate to the start time of the new track in the possible associated track pair. After S o = t c - s' steps of extrapolation, the state prediction value of the corresponding end state of the old track extrapolated to the corresponding comparison time t c can be obtained

[0057] Then, after S y = e' - t c steps of tracing back, the state prediction value of the corresponding start time state of the new track traced back to the corresponding comparison time t c can be obtained

[0058] Finally, obtain the state prediction difference:

[0059]

[0060] Step Two Two Three: Use the state prediction difference obtained in Step Two Two Two and the effective association combination obtained in Step Two One to construct a two-dimensional global optimal assignment problem:

[0061]

[0062] C(n', m') = -log(exp(-0.5 * |Δ n'm' |)) (12)

[0063]

[0064] where C() is the cost function matrix and a(n', m') is the binary association variable;

[0065] where if the effective association combination formula holds, it proves that the old track and the new track may be associated, then a(n', m') = 1; if the effective association combination formula does not hold, it proves that the old track and the new track cannot be associated, then a(n', m') = 0;

[0066] Step Two Two Four: Use the auction algorithm to solve the two-dimensional global optimal assignment problem constructed in Step Two Two Three to obtain the track completion assignment method.

[0067] In this embodiment, for a specific association combination method, the termination time of each old track is different, and the start time of each new track is also different. Therefore, it is necessary to determine the common start time and termination time to solve a general two-dimensional matching problem. There is a serious problem of track interruption in the passive section data of ballistic missiles. The track interruption causes the batch numbers before and after the interrupted track of the same target to be inconsistent, which will cause serious interference to information fusion. We adopt an algorithm for associating interrupted tracks (Track Segment Association, TSA) based on two-dimensional assignment. It uses speed information to achieve rough association of track segments, greatly reducing the candidate combinations for fine association and improving the real-time performance of association. In fine association, a multi-dimensional global optimal track segment combination is searched with the logarithmic likelihood ratio function as the cost to achieve a high association accuracy rate.

[0068] Specific Embodiment 3: Completing the interrupted ballistic trajectory according to the trajectory completion assignment method obtained in Step 2 in Step 3 to obtain a completed ballistic trajectory B, including the following steps:

[0069] Considering that the missile motion curve is similar to the shape of a parabola and presents a turning motion form in the interrupted missing state, a three-segment model is used for approximation, namely the two end uniform linear models on both sides and the uniform turning model in the middle. There are three unknown parameters involved, namely the start time i of the uniform turning model, the termination time j of the uniform turning model, and the angular velocity w of the uniform turning model. The joint estimation and identification of the system state, turning model, and maneuvering moment are realized through Step 32 and Step 33. Step 33 estimates the state and solves the parameters to be identified, such as Figure 2 shown.

[0070] Step 31: Initialize the parameters to be identified w', i', j' as w0', i0', j0';

[0071] where w0' is the angular velocity w' of the initialized uniform turning model, i0' is the start time i' of the initialized uniform turning model, and j0' is the termination time j' of the initialized uniform turning model;

[0072] Step 32: Obtain the objective function for the parameters to be identified w', i', j':

[0073]

[0074] where e' is the termination time of the old track, s' is the start time of the new track, is the missing state sequence between the new track and the old track, is the state value at the start time s' of the new track;

[0075] In this step, the process of track completion is as follows: Starting from the state at the end time e' of the old track, extrapolation is performed according to the initial w', i', and j'. First, extrapolate to the starting time i' of uniform turning according to the uniform linear model, then extrapolate to the ending time j' of uniform turning through the uniform turning model, and finally extrapolate to the starting time s' of the new track according to the uniform linear model to obtain the final track extrapolation value;

[0076] Step 33: Iteratively calculate the objective function obtained in Step 32 until the objective function is less than the preset threshold, and obtain the unknown parameter values w', i', and j':

[0077] Step 331: Fix i' and j', and use the genetic algorithm to calculate w' (in actual use, due to the long missile interruption time, if the genetic algorithm is used, extrapolating the unknown parameters for dozens of time instants will cause problems such as insufficient memory capacity and slow operation speed. Here, in the actual algorithm, a search method within a predetermined range is used to calculate w');

[0078] Step 332: Fix w' as the calculated value in Step 331, and re-update i' and j';

[0079] Step 34: After calculating w', i', and j', the missing state values during the interruption can be filled in according to these three parameters, and then a completed ballistic trajectory can be obtained.

[0080] Specific Embodiment 4: Estimate the shutdown point, launch point, and landing point of the missile based on the non-interrupted ballistic trajectory A to be traced back obtained in Step 1 or the completed ballistic trajectory B obtained in Step 3, and obtain the information of the estimated launch point, shutdown point, and landing point of the missile, including the following steps:

[0081] Step 41: Obtain the position of the missile shutdown point:

[0082] Step 411: Use trajectory A or B as measurement data to initialize the probabilities of the free-flight segment model and the active-flight segment model;

[0083] The active-flight segment motion model is:

[0084]

[0085]

[0086]

[0087]

[0088] where a(t) is the acceleration of the missile, t is the motion time of the missile, a thrust (t) is the acceleration generated by the rocket thrust on the missile, adrag (t) is the acceleration generated by atmospheric drag on the missile, F axial is the axial force acting on the missile, m(t) is the mass of the missile, is the first derivative of a(t), is the relative mass loss rate of the missile, is the mass of fuel consumed per unit time, const is a constant, is the Euclidean distance from the center of mass of the missile to the center of the Earth, (x, y, x) are the coordinates of the missile in space, intermediate variables J2 is the second zonal harmonic coefficient of the Earth, with a value of 1.08263×10 -3 , a e is the semi-major axis of the Earth in the WGS-84 coordinate system, with a size of 6378.137 km, u is the gravitational constant of the Earth, with a value of 3.986005×1014 m 3 / s 2 , are the velocities of the missile in the x, y, and z directions respectively, are the accelerations of the missile in the x, y, and z directions respectively, is the first derivative of β(t);

[0089] The free-flight motion model is as follows:

[0090]

[0091] where the last two terms on the right side of the 4th and 5th equations are the Coriolis force and the centripetal force in the x and y directions respectively, ω is the angular velocity of the non-inertial coordinate, with a magnitude of 7.292115×10 -5 rad / s;

[0092] Step Four-One-Two: Use the UFK nonlinear filtering method to predict and update the initialized model;

[0093] Step Four-One-Three: Calculate the probability of each model at each moment, and the moment when a jump occurs is the moment of the shutdown point;

[0094] Step Four-One-Four: Substitute the state value at the starting point of A or B as the initial value into the active flight model, and use the fourth-order Runge-Kutta integration method to integrate the active flight model to the shutdown point moment obtained in Step Four-One-Three to obtain the state value at the shutdown point;

[0095] The state value includes: (x, y, z), (v x , v y , v z );

[0096] The specific integration of the active flight model using the fourth-order Runge-Kutta integration method is as follows:

[0097]

[0098] in

[0099]

[0100] Among them, t h is the integration step length, when t h When it is a positive value, it is integrated backwards; when it is a negative value, it is integrated forwards. 1i Yes h The initial slope, K 2i yes The slope of the point, using the slope K by Euler's method 1i To determine y ij At the point The value of K 3i Too The slope of the point, but using the slope K 2i Determine y ij Value, K 4i Yes h The slope of the end point, its y ij Value K 3i Decision, j represents the corresponding moment, j = 1, 2, ..., n, n is the total time of the target movement, S ij is the value of the ith variable at t j+1 =t j +t h The approximate value at the point, i = 1, 2, ..., m is the current variable index, m is the total number of target motion variables, F() represents the functional relationship, X = F(t, S1, S2, ..., S m ) represents the orbital motion equation, y ij is the value of the variable labeled i at time j, y ij+1 is the value of the variable labeled i at time j+1;

[0101] The variables i of the target movement include: x, y, z, v x ,v y ,v z ,

[0102] Step 42: Determine the location of the missile launch point using the location of the missile shutdown point obtained in step 41:

[0103] The estimated shutdown point is used as the initial value, the active segment model is selected as the model, and the integral step is selected as a negative value. The intersection of the trajectory curve and the earth surface can be obtained by forward integration recursion, which is considered to be the missile launch point.

[0104] Step 43: Get the location of the missile landing point:

[0105] Using the known radar detection data, select the position and velocity information of the last point of A or B as the initial state value. The moment corresponding to the position of the last point of A or B is the initial moment. The integration step size is selected as a positive value and integrated backward to obtain the state of each point in the reentry section. When the target position vector intersects the Earth's surface, the landing point position information and the landing time can be deduced.

[0106] The model of the reentry section is as follows:

[0107]

[0108] where ω is the magnitude of the angular velocity of the non-inertial coordinate, which is 7.292115×10 -5 rad / s. The last two terms on the right side of the 4th and 5th equations are the Coriolis force and the centripetal force in the x and y directions respectively. Different from the active section, in the passive section, the speed of the ballistic missile is very high and the time is relatively long, and these two forces cannot be ignored. ρ(h) is the air density, which is related to the local altitude h, and β0 is the ballistic coefficient of the target, which is approximately a constant.

[0109] In this embodiment, the accuracy of the estimation of the shutdown point depends on the accuracy of the active section tracking. Here, the parameter adaptive interactive multiple model algorithm is applied to the active section tracking of the ballistic missile. The use of a multiple model structure is more suitable for the active section tracking problem, especially for missiles with multiple-stage boosters. At the same time, the UKF nonlinear filtering method is combined to obtain better tracking accuracy. The state of the shutdown point is judged by the probabilities of each model. The probabilities of each model obtained in the interactive multiple model algorithm reflect the similarity between the model and the current motion state of the target. The higher the matching degree between the current motion state of the target and a certain model, the greater the model probability corresponding to this model. When the target reaches the shutdown point and enters the free section, the target will instantaneously lose the propulsion force from the fuel. At this time, the matching degree with the free section model is the highest, and the matching degree with each active section model will decrease. Therefore, by monitoring the model probabilities of each model at each moment, when the model probability corresponding to the free section model exceeds the model probabilities of each active section model, it can be considered that the target has reached the shutdown point, and thus the estimation of the shutdown point state is obtained.

[0110] Specific implementation method five: Obtain the launch point, shutdown point, and landing point information of the missile in the warning event in step five, and respectively obtain the similarity between the estimated missile launch point and the missile launch point in the warning event, the similarity between the estimated missile shutdown point and the missile shutdown point in the warning event, and the similarity between the estimated missile landing point and the missile landing point in the warning event, and determine the accuracy of the warning information according to the similarity, including the following steps:

[0111] Step 5.1: Obtain the shutdown point position and velocity, the landing time, and the launch point position of the missile in each trajectory of the alarm event;

[0112] Step 5.2: Respectively obtain the similarity between the estimated missile launch point and the missile launch point in the alarm event, the similarity between the estimated missile shutdown point and the missile shutdown point in the alarm event, and the similarity between the estimated missile landing point and the missile landing point in the alarm event;

[0113] The similarity S of the ath track and the bth alarm event in the cth parameter c is defined as (a', b')

[0114]

[0115] where σ c is the estimated standard deviation of the cth parameter, and Δx c is the estimated difference between the ath track and the bth alarm event for the cth parameter.

[0116] The total similarity between the ath track and the bth alarm event is:

[0117]

[0118] In the formula, C' is the total number of motion parameters;

[0119] The similarity between the estimated missile launch point and the missile launch point in the alarm event, the similarity between the estimated missile shutdown point and the missile shutdown point in the alarm event, and the similarity between the estimated missile landing point and the missile landing point in the alarm event are specifically:

[0120] Calculate the similarity for each track and each alarm event in turn to obtain the similarity matrix S. Then, transform the alarm event traceability into a two-dimensional assignment problem and use the auction algorithm to process the similarity matrix to obtain the final alarm event traceability result:

[0121] (1) Similarity of shutdown point position and velocity

[0122] Let the difference between the shutdown point state value of track a' and the shutdown point state value of alarm event b' be Δx1. The similarity between the ath track and the bth alarm event in the shutdown point position and velocity is defined as

[0123]

[0124] where P 1a' is the filtering covariance of the first parameter shutdown point. When the filtering covariance at the track shutdown point cannot be obtained, it can be calculated according to the prior-set variance σ1. At this time, the similarity is defined as

[0125]

[0126] (2) Similarity of the landing time

[0127] Let the difference between the landing time of track a' and the landing time of warning event b' be Δt. Since the covariance of the landing time cannot be obtained through tracking, the variance of the similarity calculation needs to be set a priori as σ2. At this time, the similarity between the a'-th track and the b'-th warning event at the landing time is defined as

[0128]

[0129] (3) Similarity of the landing position

[0130] Let the estimated covariance of the landing point of track a' be P 3a' , and the error between the landing point state value of track a' and the landing point given by warning event b' be Δx3. At this time, the similarity is defined as

[0131]

[0132] Similarly, if the estimated covariance of the landing position cannot be obtained, the variance of the similarity calculation needs to be set a priori as σ3. At this time, the similarity is defined as

[0133]

[0134] (4) Similarity of the launch point position

[0135] Let the estimated covariance of the launch point of track a' be P 4a' , and the difference between the launch point state value of track a' and the launch point position of warning event b' be Δx4. The similarity between the a'-th track and the b'-th warning event at the launch point position is defined as

[0136]

[0137] When the filtering covariance at the shutdown point of the track cannot be obtained, it can be calculated according to the variance σ4 set a priori. At this time, the similarity is defined as

[0138]

[0139] The comprehensive similarity is defined as

[0140]

[0141] Step Five Three. The warning event with the largest similarity value of the launch point, shutdown point, and shutdown point obtained in Step Five Two is the true warning information.

[0142] Example: To verify the feasibility of the present invention, a simulation experiment is carried out according to the method described in the specific implementation manner:

[0143] Step 1. Model different stages of the ballistic motion to obtain the motion models for different stages of the ballistic trajectory:

[0144] Step 1-1. Model the powered phase of the ballistic trajectory to obtain the motion model for the powered phase of the ballistic trajectory:

[0145] Currently, there are usually three types of powered-phase models for ballistic trajectories: the constant acceleration model, also known as the CA model (Constant Acceleration CA), the gravity turn model (Gravity Turn, GT), and the improved gravity turn model. The CA model uses a third-order linear polynomial to fit and approximate the motion model of the powered phase. It is simple and easy to implement, but it does not consider the motion characteristics of ballistic missiles. Using a linear method to fit a non-linear equation has certain limitations. The GT model believes that the thrust and atmospheric drag in the powered phase play a major role, and the lateral force and lift of the atmosphere are relatively small and can be ignored. At the same time, since the thrust and atmospheric drag are almost in a straight line with the missile velocity, all external forces except gravity can be combined into an axial force, and the bending of the ballistic trajectory is completely caused by gravity, which describes the motion characteristics of the powered phase to a certain extent. However, its description of the acceleration change is not sufficient, and the GT model needs to be further improved and perfected. The improved gravity turn (Modified Gravity Turn, MGT) model fully considers the mass change caused by fuel consumption on the basis of GT, and is closer to the real powered-phase model. The model is as follows:

[0146]

[0147]

[0148]

[0149]

[0150] where a(t) is the acceleration of the missile, t is the motion time of the missile, a thrust (t) is the acceleration generated by the rocket thrust on the missile, a drag (t) is the acceleration generated by the atmospheric drag on the missile, F axial is the axial force received by the missile, m(t) is the mass of the missile, is the first derivative of a(t), is the relative mass loss rate of the missile, is the mass of fuel consumed per unit time, const is a constant, is the Euclidean distance from the center of mass of the missile to the center of the earth, (x, y, x) are the coordinates of the missile in space, and the intermediate variable J2 is the second zonal harmonic coefficient of the Earth, with a value of 1.08263×10 -3 , a e is the semi-major axis of the Earth in the WGS-84 coordinate system, with a size of 6378.137 km. u is the gravitational constant of the Earth, with a value of 3.986005×10^14 m 3 / s 2 , are the velocities of the missile in the x, y, and z directions respectively, are the accelerations of the missile in the x, y, and z directions respectively, is the first derivative of β(t).

[0151] Steps 1 and 2: Model the free-flight segment of the trajectory to obtain the motion model of the free-flight segment of the trajectory:

[0152] When the missile target is in the free-flight segment, the engine thrust acceleration is 0, and the atmospheric drag acceleration is 0. Only considering the centripetal force and Coriolis force caused by the Earth's gravity and the Earth's rotation, its kinematic equations are as follows:

[0153]

[0154] where the last two terms on the right side of the 4th and 5th equations are the Coriolis force and centripetal force in the x and y directions respectively. ω is the angular velocity of the non-inertial coordinate, with a magnitude of 7.292115×10 -5 rad / s;

[0155] Steps 1 and 3: Model the reentry segment of the trajectory to obtain the motion model of the reentry segment of the trajectory:

[0156] During the free-flight segment, the ballistic target is mainly affected by the inertial forces (including the Coriolis force and centripetal force) caused by the Earth's gravity and the Earth's rotation. Since the air in outer space is thin and the atmospheric density is almost zero, the aerodynamic force can be ignored. At this time, it is feasible to use the two-body motion to describe the motion state of the ballistic target. However, the velocity of the ballistic target during the reentry segment is very fast, and as the altitude decreases, the atmospheric density gradually increases, and the atmospheric drag will gradually replace the Earth's gravity as the main force acting on the ballistic target during the reentry segment. Therefore, the effect of the atmospheric drag must be considered. By adding the influence of the atmospheric drag to the two-body motion model, the differential equations of motion of the ballistic target during the reentry segment can be obtained:

[0157]

[0158] where ω is the angular velocity of the non-inertial coordinate, with a magnitude of 7.292115×10 -5rad / s. The last two terms on the right side of the fourth and fifth equations are the Coriolis force and the centripetal force in the x and y directions respectively. Different from the active section, in the passive section, the speed of the ballistic missile is very high and the time is relatively long, so these two forces cannot be ignored. ρ(h) is the air density, which is related to the local altitude h, and β0 is the ballistic coefficient of the target, which is approximately a constant.

[0159] Step 2: Use the numerical integration method based on the Runge-Kutta method to estimate the target ballistic trajectory by using the motion models of different stages of the ballistic established in Step 1, and obtain the estimated ballistic trajectory as follows:

[0160]

[0161] where

[0162]

[0163] where t h is the integration step size. When t h is positive, integrate backward; when it is negative, integrate forward. K 1i is the slope at the start of t h . K 2i is the slope at the point. Determine the value of y 1i at the point ij by using the slope K ; K 3i is also the slope at the point, but determine the value of y 2i by using the slope K ij . K 4i is the slope at the end of t h , and its value of y ij is determined by K 3i . t j represents the corresponding moment, j = 1, 2,..., n, where n is the total time of the target movement. S ij is the approximate value of the i-th variable at t j+1 = t j + t h . i = 1, 2,..., m is the current variable label, and m is the total number of target movement variables. F() represents the functional relationship. X = F(t, S1, S2,..., S m ) is the orbital motion equation. y ij is the value of the variable with label i at time j, and y ij+1 is the value of the variable with label i at time j + 1;

[0164] The variables i of the target movement include: x, y, z, v x , v y , v z ,

[0165] As Figure 1 shown, by selecting the measured data of a certain target in the measured data and integrating it on the motion models at different stages through the Runge - Kutta method, the complete ballistic trajectory information can be obtained. The dark - gray part is the active section, the light - gray part is the free section, and the black part is the re - entry section.

[0166] During the simulation process, according to the motion models of the active section, free section, and re - entry section of the ballistic missile, the positions of the ballistic missile at each moment are generated through the fourth - order Runge - Kutta method. The motion parameters of the ballistic missile are set as follows

[0167] Table 4 - 1 Parameter Settings

[0168]

[0169] Step 3: Correlate and complete the track:

[0170] The extrapolation step size of the Runge - Kutta method is 0.5 s. The probability of interruption at each moment is set to 0.01, and each interruption lasts for 20 moments. Then, a new track starts again. The measurement error is 20 m in all three xyz directions, and the intercepted track position is a partial track between 100 s and 700 s. As Figure 4 shown, after unscented Kalman filtering, the schematic diagram of the track after adding interruptions input into the system is obtained. After the track interruption correlation algorithm and the track interruption completion based on the interruption correlation result, the track after interruption correlation completion is obtained, as Figure 5 shown.

[0171] After the track interruption correlation and completion, the interrupted tracks are correlated, and the measurements missing due to interruptions are also completed by the completion algorithm. Finally, the completed track is obtained.

[0172] Results of measured data interruption correlation and completion:

[0173] The original tracks of each target are as Figure 6 shown. After the interruption correlation and completion of each track, the tracks obtained are as Figure 7 shown. After statistics, the number of interrupted positions of successfully connected and completed single targets is 208. It can also be seen from the obtained track diagram that some measurements missing in the original data due to interruptions are supplemented by the interruption correlation completion algorithm, improving the continuity of a single track.

[0174] Step 4: Estimation results of the simulation shutdown point, launch point, and landing point parameters:

[0175] During the simulation process, according to the motion models of the active section, free section, and re - entry section of the ballistic missile, the positions of the ballistic missile at each moment are generated through the fourth - order Runge - Kutta method.

[0176] The extrapolation step size of the Runge-Kutta method is 0.5 s. The probability of interruption at each moment is set to 0.01, and each interruption lasts for 20 moments. After that, a new track is started again. The measurement error is 20 m in all three directions of x, y, and z. The intercepted track position is a partial track between 100 s and 700 s. After unscented Kalman filtering, the track after adding interruptions is finally input into the system. After the interruption completion by the method in Section 2, the partial track of a single target in the simulation is obtained as Figure 8 shown;

[0177] Calculate the backtracking results of each parameter and compare them with the true values. The records are as follows:

[0178] Table 4-2 Launch point parameters

[0179]

[0180] Table 4-3 Shutdown point parameters

[0181]

[0182]

[0183] Table 4-4 Landing point parameters

[0184]

[0185] From the above results, it can be seen that both the launch point position and the landing point position can be estimated relatively accurately. Compared with the estimation accuracy of about 10 km obtained in existing literature, the parameter estimation accuracy obtained by the phased model adopted in this paper is higher.

[0186] Step 5. Simulation alarm event traceability results

[0187] During the simulation process, 4 launch points are set, and 10 targets are launched from each launch point, for a total of 40 targets. According to the motion models of the active section, free section, and reentry section of the ballistic missile, the positions of the ballistic missile at each moment are generated by the fourth-order Runge-Kutta method. The motion parameters of the ballistic missile are set as follows:

[0188] Table 4-5 Parameter settings

[0189]

[0190]

[0191] The extrapolation step size of the Runge-Kutta method is 0.5 s. Set the probability of interruption at each moment to 0.01, and each interruption lasts for 20 moments. After that, a new track is restarted. The measurement error is 20 m in all three directions of x, y, and z. The intercepted track positions are the tracks between 100 s and 700 s as Figure 9 shown. After unscented Kalman filtering, group tracking based on the evolutionary network model, and group track interruption correlation completion, the schematic diagram of the simulated group track is as Figure 10 shown

[0192] Set 3 warning events, and the corresponding single target numbers are 1, 11, and 25 respectively. (Launch point 1 corresponds to targets 1 - 10, launch point 2 corresponds to targets 11 - 20, launch point 3 corresponds to targets 21 - 30, launch point 4 corresponds to targets 31 - 40), and obtain their respective warning event parameters.

[0193] By estimating the ballistic parameters and calculating the comprehensive similarity with the warning events, the comprehensive similarity cost matrix between the group track and the single target warning events is obtained. Among them, each column corresponds to the warning event of a single target, and each row corresponds to each group generated by tracking. According to the number of targets in the group (here each group contains 10 targets), each group occupies 10 rows of the matrix. In this way, when the warning event contains multiple targets in the same group during two-dimensional allocation, it can also be correctly allocated one-to-many.

[0194] The results after allocating and restoring the original track numbers of the warning events are shown in the following table:

[0195] Table 4 - 6 Tracing Results

[0196]

[0197] From the above results, it can be seen that in the case of known warning events, by solving the allocation results of the warning events and the tracing results of the obtained group tracks, the group track where the warning event is located can be accurately known, thus locking the target.

Claims

1. A method for track backtracking and warning event traceability based on an interactive model, characterized in that The specific process of the method is as follows: Step 1: Obtain the number of ballistic trajectories at each moment of the ballistic trajectory to be traced back. If the number of ballistic trajectories at each moment is the same, it means that the ballistic trajectory is not interrupted, and then execute Step 4. If there is a number of ballistic trajectories that is inconsistent with other moments, the ballistic trajectory at that moment is interrupted, and then execute Step 2. Step 2: Correlate the interrupted ballistic trajectories to obtain a trajectory completion allocation method. Step 2-1: Coarsely correlate the interrupted ballistic trajectories to obtain effective correlation combinations. Step 2-2: Perform fine correlation based on the effective correlation combinations to obtain a trajectory completion allocation method, including the following steps: Step 2-2-1: Set a comparison moment. Among them, represents the start time of the n'-th old track, represents the start time of the m'-th new track, represents the end time of the n'-th old track, represents the end time of the m'-th old track, s is the end moment of each old track, e' is the start moment of each new track, M is the number of new tracks, and N is the total number of old tracks; Step 2-2-2: Extrapolate the termination moment of the old track to the comparison moment, trace back the start moment of the new track to the comparison moment, obtain the state prediction value of the old track after extrapolation and the state prediction value of the new track after tracing back, and obtain the state prediction value difference. First, using the four - order Runge - Kutta method through the missile free - flight motion model, extrapolate the termination time of the old track by S o = t c - s' steps to obtain the extrapolated state of the end of the old track at the comparison time t c The state prediction value Then, using the fourth-order Runge-Kutta method through the missile free-flight motion model, the starting moment of the new track is traced back by S y = e'-t c steps to obtain the state prediction value of the state at the starting moment of the new track traced back to the comparison moment t c ​ Finally, obtain the state prediction difference. Step 2-2-3: Use the state prediction difference obtained in Step 2-2-2 and the effective correlation combination obtained in Step 2-1 to construct a two-dimensional global optimal allocation problem: where C() is a cost function matrix, and a(n', m') is a binary correlation variable; The assignment method of a(n', m') is as follows: Substitute n' and m' into the effective correlation combination formula obtained in Step 2-1. If the effective correlation combination formula holds, then a(n', m') = 1; if the effective correlation combination formula does not hold, then a(n', m') = 0. Step 2-2-4: Use the auction algorithm to solve the two-dimensional global optimal allocation problem constructed in Step 2-2-3 to obtain a trajectory completion allocation method. Step 3: Complete the interrupted ballistic trajectories according to the trajectory completion allocation method obtained in Step 2 to obtain the completed ballistic trajectory B, and then execute Step 4. Step 4: Estimate the shutdown point, launch point, and landing point of the missile according to the uninterrupted ballistic trajectory A to be traced back obtained in Step 1 or the completed ballistic trajectory B obtained in Step 3, and obtain the information of the estimated launch point, shutdown point, and landing point of the missile. Step 5: Obtain the information of the launch point, shutdown point, and landing point of the missile in the warning event, and respectively obtain the similarity between the estimated missile launch point and the missile launch point in the warning event, the similarity between the estimated missile shutdown point and the missile shutdown point in the warning event, and the similarity between the estimated missile landing point and the missile landing point in the warning event, and determine the true warning information according to the similarity.

2. The method for track backtracking and alarm event traceability based on an interactive model according to claim 1, wherein: The coarse correlation of the interrupted ballistic trajectories in Step 2-1 to obtain effective correlation combinations includes the following steps: Step 2-1-1: Obtain the segment trajectory before the interruption of the ballistic trajectory and record it as the old track. Among them, represents the set of old tracks at time k, represents the n'-th old track, and N is the total number of old tracks; Step 2-1-2: Obtain the segment trajectory after the interruption of the ballistic trajectory and record it as the new track. Among them, represents the set of new tracks at time k, represents the m'-th new track, and M is the number of new tracks; Step 2-1-3: Use the old track obtained in Step 2-1-1 and the new track obtained in Step 2-1-2 to obtain all associated track combinations of the old track and the new track at time k. Among them, Φ T is the association combination of all old and new track segments, is the n'-th old track segment, is the m'-th new track segment, is the starting time of the n'-th old track in the old track set, represents the ending time of the n'-th old track in the old track set, represents the starting time of the m'-th new track in the new track set, represents the ending time of the m'-th new track in the new track set, is the vector of the track point on the n'-th old track, is the vector of the track point on the m'-th new track; Old track and new track are the two successive track segments on the same track of the same target with an interruption in between; Step 2-1-4: Use all the associated track combinations obtained in Step 2-1-3 to perform speed matching on the two track segments before and after the interruption on the same target track to obtain effective correlation combinations. Among them, is the backward recursion position component of the old track, is the forward recursion position component of the new track, and are respectively the termination time of the old track interrupted on a track of the same target and the start time of the new track. v max is the prior maximum speed of the target, and C1 is a constant.

3. The method for track backtracking and warning event traceability based on an interactive model according to claim 2, wherein: In step 3, according to the trajectory completion and allocation method obtained in step 2, the interrupted ballistic trajectory is completed to obtain a completed ballistic trajectory B, including the following steps: Step 3-1: Initialize the parameters to be recognized w', i', j' as w0', i0', j0'; where w0' is the angular velocity w' of the uniformly turning model after initialization, i0' is the starting time i' of the uniformly turning model after initialization, and j0' is the ending time j' of the uniformly turning model after initialization; Step 3-2: Obtain the objective function for the parameters to be recognized w', i', j'; Among them, e' is the termination time of the old track, and s' is the starting time of the new track. is the missing state sequence between the new track and the old track. is the state value at the starting time s' of the new track. Step 3-3: Iteratively calculate the objective function obtained in step 3-2 until the objective function is less than a preset threshold to obtain the parameters to be recognized w', i', j'. The iterative calculation method is as follows: Step 3-3-1: Fix i' and j', and use the genetic algorithm to calculate w'; Step 3-3-2: Fix w' as the calculated value in step 3-3-1, and re-update i' and j'; Step 3-4: Use the obtained w', i', and j' to complete the missing state values, and then obtain a completed ballistic trajectory.

4. The method for track backtracking and warning event traceability based on an interactive model according to claim 3, wherein: In step 4, based on the uninterrupted ballistic trajectory A to be traced back obtained in step 1 or the completed ballistic trajectory B obtained in step 3, estimate the shutdown point, launch point, and landing point of the missile to obtain the information of the estimated launch point, shutdown point, and landing point of the missile, including the following steps: Step 4-1: Obtain the position of the missile shutdown point: Step 4-1-1: Use A or B as measurement data to initialize the probabilities of the free-flight segment model and the active-flight segment model; Step 4-1-2: Use the UFK nonlinear filtering method to predict and update the initialized model; Step 4-1-3: Calculate the probability of each model at each moment, and obtain the moment of jump as the moment of the shutdown point; Step 4-1-4: Substitute the state value of the starting point of A or B into the active-flight segment model as the initial value, and use the fourth-order Runge-Kutta integration method to integrate the active-flight segment model to the shutdown point moment obtained in step 4-1-3 to obtain the position of the missile shutdown point; Step 4-2: Use the position of the missile shutdown point obtained in step 4-1 to determine the position of the missile launch point: Use the state value of the shutdown point as the initial value, and perform forward integration recursion with a negative integration step for the active-flight segment model to obtain the intersection point of the ballistic curve and the earth's surface, which is the position of the missile launch point; Step 4-3: Obtain the position of the missile landing point according to A or B: Use the position and velocity information of the last point of A or B as the state initial value, and the moment corresponding to the position of the last point of A or B as the initial moment. Perform backward integration with a positive integration step for the re-entry segment model to obtain the states of each point in the re-entry segment, and obtain the intersection point of the target position vector and the earth's surface, which is the landing point position information. The moment corresponding to the landing point position information is the landing moment.

5. The method for track backtracking and warning event traceability based on an interactive model according to claim 4, wherein: In step 4-1-4, using the fourth-order Runge-Kutta integration method to integrate the active-flight segment model specifically means: where where t h is the integration step. When t h is positive, integration is performed backward; when it is negative, integration is performed forward. K 1i is the slope at the start of t h . K 2i is the slope at the point. By using the Euler method with the slope K 1i , the value of y ij at the point is determined; K 3i is also the slope at the point, but the slope K 2i is used to determine the value of y ij . K 4i is the slope at the end of t h . Its value of y ij is determined by K 3i . t j represents the corresponding moment. j = 1, 2, …, n, where n is the total time of the target motion. S ij is the approximation of the i-th variable at t j+1 = t j + t h . i = 1, 2, …, m is the current variable label, and m is the total number of target motion variables. F() represents the functional relationship. y ij is the value of the variable with label i at time j, and y ij+1 is the value of the variable with label i at time j + 1.

6. The method for track backtracking and alarm event traceability based on an interactive model according to claim 5, wherein: The active-flight segment motion model is: where a(t) is the acceleration of the missile, t is the movement time of the missile, a thrust (t) is the acceleration generated by the rocket thrust on the missile, a drag (t) is the acceleration generated by the atmospheric drag on the missile, F axial is the axial force received by the missile, m(t) is the mass of the missile, is the first derivative of a(t), is the relative mass loss rate of the missile, is the mass of fuel consumed per unit time, const is a constant, is the Euclidean distance from the center of mass of the missile to the center of the earth, (x, y, x) are the coordinates of the missile in space, intermediate variable J2 is the second zonal harmonic coefficient of the earth, with a value of 1.08263×10 -3 ,a e is the semi-major axis of the earth in the WGS-84 coordinate system, with a size of 6378.137 km, u is the gravitational constant of the earth, with a value of 3.986005×1014 m 3 / s 2 , are the velocities of the missile in the x, y, and z directions respectively, are the accelerations of the missile in the x, y, and z directions respectively, is the first derivative of β(t).

7. The method for track backtracking and warning event traceability based on an interactive model according to claim 6, characterized in that: The free-flight segment motion model is as follows: where ω is the angular velocity of the self-rotation of the non-inertial coordinate.

8. The method for track backtracking and warning event traceability based on an interactive model according to claim 7, wherein: The ballistic re-entry segment motion model is as follows: where ρ(h) is the air density and β0 is the ballistic coefficient of the target.

9. The method for track backtracking and warning event traceability based on an interactive model according to claim 8, wherein: In step five, obtain the launch point, shutdown point, and landing point information of the missile in the warning event, and respectively obtain the similarity between the estimated missile launch point and the missile launch point in the warning event, the similarity between the estimated missile shutdown point and the missile shutdown point in the warning event, and the similarity between the estimated missile landing point and the missile landing point in the warning event, and determine the true warning information according to the similarity, including the following steps: Step 5-1: Obtain the shutdown point position and speed, landing time, and launch point position of the missile in each ballistic trajectory of the warning event; Step 5-2: Respectively obtain the similarity between the estimated missile launch point and the missile launch point in the warning event, the similarity between the estimated missile shutdown point and the missile shutdown point in the warning event, and the similarity between the estimated missile landing point and the missile shutdown point in the warning event; Among them, S c (a', b') is the similarity between the a'-th track and the b'-th warning event on the c-th parameter, and σ c is the estimated standard deviation of the c-th parameter, and Δx c is the estimated difference between the a'-th track and the b'-th warning event for the c-th parameter. S(a', b') is the total similarity between the a'-th track and the b'-th warning event, and C' is the total number of motion parameters; Step 5-3: The warning event with the largest similarity values of the launch point, shutdown point, and shutdown point obtained in step 5-2 is the true warning information.

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