An unmanned aerial vehicle-based networking radar distance gate joint decoy jamming method

Abstract

The application discloses a networked radar distance gate joint dragging jamming method based on a unmanned aerial vehicle, is applied to the field of electronic countermeasure technology, and aims at the problems that the existing technology is difficult to meet the optimal false track of cooperative constraint and the corresponding ECAVs control strategy, and guarantees the RGPO jamming effect; the application takes the RGPO false track as an optimization variable, takes the false track implementation integrity as a constraint, establishes a constraint optimization model with the jamming performance as an optimization target, and solves the model based on a particle swarm algorithm; aiming at the difficulty that the constraint is nonlinear and difficult to be explicitly expressed, the false track is evaluated by using a Deb criterion; in terms of constraint violation degree, a single-player Monte Carlo tree search algorithm and a divide-and-conquer idea are used for calculation; in terms of the RGPO jamming effect, independent repeated sampling of a scene is used for calculation, and a distance gate dragging jamming strategy planning for a networked radar is realized.

Description

Technical Field

[0001] This invention belongs to the field of electronic countermeasures technology, and specifically relates to a range gate dragging jamming technology for networked radar. Background Technology

[0002] When using Electronic Combat Air Vehicles (ECAVs, also known as unmanned jamming aircraft swarms) to perform track deception jamming on networked radars, how to fully utilize the capabilities of ECAVs and improve the jamming effect is a key research focus. In the problem of track deception jamming of networked radars, false tracks and ECAVs are two key entities: false tracks are the visual manifestation of deception jamming, and their form is a decisive factor in the effectiveness of the jamming; ECAVs are the specific controlled objects, and their control strategies affect the completeness of false track implementation and the flight distance of ECAVs. Furthermore, since the implementation of false tracks relies on the coordinated control of ECAVs, the initial state and maneuverability of ECAVs will significantly influence the selection of false tracks.

[0003] When the initial state and maneuverability of ECAVs are determined, the constraints introduced by the pseudo-tracks and ECAVs need to be considered, and the control strategies for pseudo-tracks and ECAVs need to be optimized collaboratively. Due to the complexity of the constraints, current research on collaborative planning methods for pseudo-tracks and ECAV control strategies either simplifies the scenario or model or breaks the problem down into sub-problems to be solved sequentially. The paper "Deception of radar systems using cooperatively controlled unmanned air vehicles" assumes that the pseudo-target moves at a constant speed, given the known necessary points of the pseudo-track, and establishes an optimization model by considering the flight conditions of each ECAV, solving for the pseudo-track between two adjacent necessary points and the flight trajectories of each ECAV. The paper "Radar deception through phantom track generation" addresses scenarios where the start and end positions of the pseudo-tracks are determined, considering the dynamic constraints of a single-frame UAV and the pseudo-track, as well as the relationship between them. It transforms the UAV constraints into constraints on the pseudo-target's point track, treating the pseudo-track planning problem under the dynamic and geometric constraints of multiple UAVs as a two-point boundary value problem, and proposes a single-step optimal pseudo-track and ECAV trajectory planning method. The paper "Optimal coherentphantom track design using virtual motion camouflage" considers the energy consumption problem of implementing dummy tracks and studies a method for planning the lowest energy-consuming track using specified coordinates. This method consists of two layers of search loops: the inner loop solves for the energy consumption of implementing the dummy track, and the outer loop adjusts the shape of the dummy track. This algorithm architecture reduces the difficulty of solving the problem. The paper "Networked Radar Deception and Jamming Strategy Based on Multi-Aircraft Coordination" considers the threat area avoidance problem. First, it plans a dummy track that can avoid threat areas based on stability, and then plans the trajectory of ECAVs based on stability. However, both methods give little consideration to the mutual constraints between ECAVs and dummy tracks, making it difficult to guarantee the feasibility of the planned dummy tracks.

[0004] Based on the above information, it can be seen that some studies take a global approach, simultaneously optimizing both the false tracks and ECAV trajectories, but this leads to high optimization model complexity and difficulty in solving the problem. Other studies solve the problem step-by-step, but the constraints between the false tracks and ECAVs are not comprehensively considered during the solution process, potentially resulting in violations of motion constraints and the inability to form the required false tracks. Furthermore, since RGPO (Range Gate Pull Off) interference requires multi-frame joint optimization of false tracks and has precise timing requirements for their implementation, the solution difficulty is further increased. Therefore, further research is needed on collaborative planning methods for RGPO false tracks and ECAV control strategies in networked radar systems. Summary of the Invention

[0005] To address the aforementioned technical issues, this invention proposes a network radar range gate joint dragging interference method based on unmanned aerial vehicles (UAVs). Considering the cooperative constraints between RGPO false tracks and ECAVs, it can solve for the optimal false track that satisfies the cooperative constraints and the corresponding ECAV control strategy, thus ensuring the effectiveness of RGPO interference.

[0006] The technical solution adopted in this invention is: a network radar range gate joint dragging jamming method based on UAVs, comprising the following steps:

[0007] S1. Construct a range-gate dragging jamming implementation scenario for networked radars; consider a two-dimensional scenario, assuming a total of N R There are [number] radar stations, and the location of each radar is [location]. There exists N F One false target and one real target; for each radar station, at each moment, each ECAV is on the line of sight connecting the radar and the false target;

[0008] S2. Analyze the collaborative constraints between RGPO dummy tracks and ECAVs control strategies, and establish their optimization model; the completeness of the implementation of each dummy track is constrained by the initial state of the ECAVs. and motion constraints The optimized model expression is:

[0009]

[0010]

[0011] Where θ(·) is the ECAVs control strategy solver, Φ represents the empty set; θ(Ψ,S init C ECAV )≠Φ indicates that in the initial state S init and motion constraints C ECAV Under these conditions, ECAVs possess a control strategy that can fully implement Ψ;

[0012] S3. By discretizing time and space, the ECAVs control strategy solver in step S2 is modeled as a tree-based optimal path search problem; the expression for the tree-based optimal path search problem is:

[0013]

[0014]

[0015] Where p is the number of nodes from the root node S root To leaf node The path, i.e., an ECAVs control strategy; S k,i Let V(k) represent the i-th vertex in the k-th layer of tree T, i.e., a state of ECAVs; M is the number of vertices in the path excluding the root node, M≤K, and the track consists of K frames; V(k) represents the set of vertices in tree T at the k-th layer; E(S) represents the set of vertices in tree T at the k-th layer. k,i ) represents node S k,i The edge set starting from S; e(S) k,i →S k+1,j ) represents node S k,i Starting from node S k+1,j The edge is the endpoint; C(·) is the objective function for path evaluation, i.e., the evaluation index of ECAVs control strategy;

[0016] S4. Solve for the optimal interference strategy using the particle swarm optimization algorithm, and randomly initialize N. P The position ψ of each particle i and its velocity v i Each particle represents a false trajectory;

[0017] In each iteration of the particle swarm optimization algorithm, for each particle, the optimal path search problem of the tree in step S3 is searched based on the SP-MCTS algorithm. False paths are classified according to the search process. Specifically: if any strategy can be fully implemented during the search process, the false path corresponding to that strategy is put into the set of particles that can be fully implemented; the remaining false paths are put into the set of particles that cannot be fully implemented.

[0018] The classified false tracks are evaluated and compared based on the Deb criterion. After iteration, the optimal distance-to-tow false track is obtained. The tree built by the false track is then searched again based on the SP-MCTS algorithm to finally obtain the optimal control strategy for ECAVs.

[0019] The beneficial effects of this invention are as follows: First, this invention constructs a scenario for ECAVs deception jamming in networked radar systems. Then, it analyzes the cooperative constraints between RGPO false tracks and ECAVs control strategies, establishes an optimization model, and considers the Deb criterion to evaluate the false tracks to address the cooperative constraint problem. For the constraint violation degree in the Deb criterion, a single-player Monte Carlo tree search algorithm and a divide-and-conquer approach are introduced for calculation. Finally, the search direction is guided based on the evaluation results of the Deb criterion, forming the PSO-Deb-OCBA algorithm to complete the cooperative planning of RGPO false tracks and ECAVs control strategies. This invention considers the cooperative constraints between RGPO false tracks and ECAVs, enabling it to solve for the optimal false tracks that satisfy the cooperative constraints and the corresponding ECAVs control strategies, ensuring the effectiveness of RGPO jamming. Attached Figure Description

[0020] Figure 1 This is a schematic diagram illustrating a scenario for ECAVs deception and jamming against networked radars.

[0021] Figure 2 Schematic diagram of drag distance index

[0022] Figure 3 This is a schematic diagram illustrating the spatial impact of ECAVs on the solution of spurious tracks.

[0023] Figure 4 This is a schematic diagram illustrating the spatial impact of false tracks on the ECAVs control strategy.

[0024] Figure 5 This is a schematic diagram illustrating the interactions between ECAVs.

[0025] Figure 6 This is a schematic diagram of a single hypothetical target path planning scenario.

[0026] Figure 7 A schematic diagram of a tree structure for path planning in a single hypothetical target scenario.

[0027] Figure 8 A schematic diagram of a path planning scenario with multiple hypothetical targets;

[0028] (a) represents maintaining the matching relationship; (b) represents changing the matching relationship.

[0029] Figure 9 A schematic diagram of a tree structure for path planning in a scenario with multiple false targets.

[0030] Figure 10 A schematic diagram illustrating the characteristics of the degree of violation.

[0031] Figure 11 The convergence curves of the algorithm are shown for different initial states of ECAVs.

[0032] Figure 12 The convergence curves of the algorithm under different ECAVs motion constraints are shown.

[0033] Figure 13 Comparison of motion control parameters for ECAVs;

[0034] Among them, (a) is ECAV1-acceleration control; (b) is ECAV2-acceleration control; (c) is ECAV1-turn control; and (d) is ECAV2-turn control. Detailed Implementation

[0035] This invention is primarily verified using numerical simulation experiments. All steps and conclusions have been verified correctly using Matlab R2022a. The following is a summary of the appendix. Figure 1-12 The present invention will be further described below.

[0036] The purpose of this invention is to study and design a collaborative planning method for RGPO false tracks and ECAVs control strategies based on PSO-Deb-OCBA when performing range-gate dragging jamming on networked radars in a penetration attack scenario. Considering that this scenario consists of K frames, there exist N... R There are N radar stations. F Each RGPO false track is represented as a point sequence. The j-th RGPO false track is defined as a point sequence. The set of all false tracks is defined as For one of the decoy target locations, RGPO requires that the deceived radar station, ECAV, and the decoy target location be on the same straight line. Therefore, for each radar station, to achieve N... F A false RGPO track requires at least N F One ECAV. This invention assumes that each radar site uses N F An ECAV is used to interfere with the system. A constrained optimization model is established with the RGPO false track as the optimization variable, the integrity of the false track implementation as the constraint, and the interference performance as the optimization objective. The study investigates how to solve for the optimal false track that satisfies the cooperative constraints, as well as the corresponding ECAV control strategy, to maximize the RGPO interference effect.

[0037] Step 1: Constructing ECAVs deception and jamming implementation scenarios for networked radars

[0038] consider Figure 1 In the penetration and attack scenario shown, our side, as the attacker and jammer, uses attack units to carry out combat missions within the enemy's network radar monitoring area. At the same time, we use ECAVs to generate multiple false tracks to carry out RGPO jamming on the enemy, so as to affect the tracking of the network radar and make the tracking track deviate from the real target, thereby achieving the purpose of covering our attack units.

[0039] In RGPO jamming, the shape of the false track is a key factor affecting the jamming effect; different false tracks have different jamming effects. For ECAVs, each ECAV must be on the line of sight (LOS) connecting the radar and the false track at every moment for the ECAVs to transmit time-delayed echoes to the radar, enabling the radar to detect the false track. The problem this invention addresses is how to obtain the optimal false track and the corresponding ECAV control strategy under the ECAV motion constraints to maximize the RGPO jamming effect.

[0040] This invention considers a two-dimensional scenario, assuming that N exist in total. R There are [number] radar stations, and the location of each radar is [location]. There exists N F There is one false target and one real attacking unit, which is also a real target in the scenario, i.e., the target being covered.

[0041] First, the real target is modeled, mainly including its motion model and measurement model.

[0042] The motion model of the real target is described using the state variable method. To describe the iterative relationship of the target motion, time is uniformly divided into frames with a granularity of ΔT, and a total of K frames are considered. It is assumed that the motion state vector of the real target at the initial time t0 is X(0), and the motion model of the real target is defined as follows:

[0043] X(k+1)=f(k,X(k))+ψ(k,X(k),ε(k)) (1)

[0044] In this embodiment, ΔT is set to 1s, X(k) is the state vector of the k-th frame, ε(k) is the process noise vector of the k-th frame, f(·) describes the state transition relationship between two adjacent frames, and ψ(·) describes the transformation relationship between the process noise vector space and the state vector space.

[0045] When the real target moves, all radars search and detect the scene in each frame, and record measurements based on the echo signals. The measurement model of the i-th radar is defined as follows:

[0046] Z i (k)=h i (k,X(k))+ω i (k,X(k),υ i (k)) (2)

[0047] Where i = 1, 2, ..., N R Z i (k) represents the measurement of the target by the i-th radar in the k-th frame, υ i(k) is the measurement noise vector, h i (·) represents the transformation relationship between the state vector space and the measurement vector space, ω i (·) represents the transformation relationship between the measurement noise vector space and the measurement vector space.

[0048] Equations (1) and (2) uniformly describe the system model of the real target, and the specific definition changes according to the different motion characteristics.

[0049] The motion model and measurement model for false targets are explained below.

[0050] The motion model of the false target is also described using the state variable method, and the state vector of each false target is defined as follows: Where j = 0, 1, ..., N F ,and As an initial state, the motion model of the dummy target is defined as follows:

[0051]

[0052] in, For the input control vector, This indicates the state transition relationship between two adjacent frames.

[0053] Similarly, in each frame, all radar stations measure each false target separately, defining the measurement model of the i-th radar for the j-th false target as follows:

[0054]

[0055] in, Let i be the measurement of the i-th radar on the false target j in the k-th frame. This is the noise vector from this measurement. Describe the transformation relationship between the dummy target's state vector space and the measurement vector space. Describe the transformation relationship between the measurement noise vector space and the measurement vector space.

[0056] After modeling the motion and measurement models of the real and false targets, N at each time step can be obtained. R One radar for real targets and N F Let the set of all radar measurements for a dummy target be defined as follows:

[0057]

[0058] in, Let be the set of measurement results of radar j in the k-th frame, which is defined as follows:

[0059]

[0060] The meas() function describes the radar measurement process. Let be the number of measurements recorded by radar j in the k-th frame. Due to the existence of radar resolution cells, two targets within the same resolution cell will only have one measurement. The measurement results also match the actual target measurement Z in the above model. j (k) and pseudo-target measurement There are some differences.

[0061] In a centralized network radar system, the data center is responsible for centrally processing the measurement data from each radar site and performing fusion, tracking, and other processing.

[0062] Subsequently, the data center performs source detection, correlation, and fusion on all measurement data to obtain network radar measurement data. This processing can be represented as follows:

[0063]

[0064] Where fu(·) represents the data processing flow, and the number of measurements obtained after processing is N. fu (k).

[0065] After acquiring the measurement data, the data center uses it as a basis to track the target in the current frame. This invention considers a multi-target tracking model, assuming that the number of tracked trajectories in the k-th frame is... The state of each track is estimated as follows: State covariance estimation is in Define the set of states and state covariances of all tracks in the k-th frame as follows:

[0066]

[0067] Trackers are a feature of data centers.

[0068] The tracker's processing flow for each track includes stages such as state prediction, data association, and filtering. The entire process can be represented as follows:

[0069]

[0070] Here, tr(·) represents the tracking algorithm. Since multi-target tracking needs to consider factors such as track start and track end, the number of tracked tracks will change over time. and They may be different.

[0071] Depending on the strategic intent, there are different evaluation indicators to choose from for RGPO jamming against networked radars. The following will introduce the towing distance, towing success rate, and the hybrid indicators of towing success rate and towing distance.

[0072] In the following description, the real target tracking track refers to the track established for the real target before the implementation of RGPO jamming. Since this invention considers a multi-target tracking model, if the real target successfully escapes the range tracking gate as RGPO jamming is implemented, the multi-target tracking algorithm will restart the track for the real target. Since the new track is short and the tracking stability is not strong, it is difficult to pose a threat to the real target within K frames. Therefore, when evaluating the jamming effect, only the track established before the jamming is implemented is considered.

[0073] (1) Drag distance

[0074] The drag distance refers to the distance between the center of the tracking track gate and the actual target position after the RGPO interference ends, i.e., in the Kth frame. Its definition is as follows: Figure 2 As shown, in a two-dimensional scene, it is represented as

[0075]

[0076] Where x(·) and y(·) represent the actual positions of the real target. This represents the tracking system's estimate of the target's position. This index reflects the deviation of the tracking gate caused by RGPO interference. The larger the drag distance d, the farther the tracking gate deviates, the lower the tracking accuracy, and the better the interference effect.

[0077] (2) Success rate of dragging

[0078] The drag success rate refers to whether the real target is within the tracking gate after the RGPO interference ends. If the real target is not within the tracking gate in the Kth frame, the drag is successful; if the real target is still within the tracking gate in the Kth frame, the drag has failed. A variable μ is defined to represent whether the drag is successful.

[0079]

[0080] The expected value E[μ] represents the success rate of dragging RGPO interference.

[0081] This invention employs an elliptical gate, and determines whether the real target is within the tracking gate using the following formula.

[0082] d k =v T (K)S -1 (K)v(K)≤γ k (12)

[0083] Where S(K) is the innovation covariance of the Kth frame, γ k The threshold value is 16 when the gate probability is 99.97%. v(K) is the difference between the true target position and the gate center, defined as follows:

[0084]

[0085] Where, x p (K), y p (K) indicates the center position of the gate.

[0086] This indicator reflects the interruption of radar tracking of the real target. Due to the characteristics of RGPO jamming, a well-executed decoy track can interrupt radar tracking of the real target, thus protecting the real target. A higher towing success rate indicates a higher probability of radar tracking of the real target being interrupted, and a better jamming effect.

[0087] (3) Drag success rate - distance hybrid indicator

[0088] The two indicators mentioned above evaluate the jamming effect from different perspectives. The tow distance reflects the impact of RGPO jamming on radar tracking accuracy, while the tow success rate reflects the impact of RGPO jamming on the probability distribution of the radar tracker. However, the two indicators do not provide a comprehensive evaluation of the jamming effect. False tracks with larger tow distances may have lower tow success rates, and similarly, false tracks with higher tow success rates may have smaller tow distances. In order to comprehensively consider these two indicators, the following hybrid tow success rate-distance indicator is defined.

[0089]

[0090] μ and d have been defined above; d max This represents the maximum drag distance. If the drag distance reaches or exceeds d... max , indicating that the distance between the tracking gate and the real target is far enough that the tracking algorithm will have difficulty re-establishing the connection between the track and the real target after the RGPO is interrupted; α is the mixing coefficient, which ranges from [0,1]. The larger the value, the more emphasis is placed on the towing success rate index, and the smaller the value, the more emphasis is placed on the towing distance index.

[0091] Step 2: Analyze the cooperative constraints between RGPO false tracks and ECAVs control strategies, and establish an optimization model.

[0092] 2.1 Analysis of the Cooperative Constraints between RGPO False Tracks and ECAVs Control Strategies

[0093] First, let's explain the motion constraints of the ECAV: Assume the current position of the ECAV is (x... e ,y e The position of the fake target to be dragged in the next frame is (x). t ,y t Due to the range gate deception jamming principle, in the next frame, the ECAV needs to be on the line connecting the radar and the target, and its position (x,y) needs to satisfy the following relationship:

[0094]

[0095] Assuming the time difference between two frames is ΔT, the longest acceleration time t of ECAV during this period is... acc for

[0096]

[0097] Maximum travel distance d e,max for

[0098]

[0099] Longest deceleration time t dec for

[0100]

[0101] Minimum distance d that can be traveled e,min for

[0102]

[0103] Therefore, after the time interval ΔT, the distance that the ECAV can travel is between d. e,min and d e,max Between these conditions, the possible locations of the next ECAV frame must satisfy the following conditions.

[0104]

[0105] Then, considering the hypothetical trajectory and ECAVs together, it can be found that the initial state and maneuverability of ECAVs affect the hypothetical trajectory planning process, and the motion of the hypothetical target also affects the ECAV control strategy planning process. The two have the following four types of influence on each other:

[0106] (1) The influence of ECAVs motion constraints on the dummy target's selectable space

[0107] like Figure 3 As shown, assuming there is only one ECAV, in the first frame, according to the ECAV motion constraints, the set of possible ECAV positions can be determined to be E1. However, due to the characteristics of drag jamming, the false target needs to be on the line connecting the radar and the ECAV, so the false target must be on the ray LOS. 1,1 and LOS 1,2 The resulting sector-shaped space is denoted as <LOS 1,1 LOS 1,2 > Take the intersection of set S1 and the sector space to obtain the set S′1 of the false targets' positions in the first frame, that is

[0108] S′1=S1∩ <LOS 1,1 LOS1,2 > (21)

[0109] That is Figure 3 The non-shaded area within ellipse S1 is where the false target can be realized. Therefore, in Figure 3 In the context of the current frame, after constraints, position p... 1,3 No longer optional.

[0110] The impact on the second frame is similar. Assuming ECAV selects position e1 in the first frame, based on motion constraints, the set of possible positions for ECAV in the second frame can be determined to be E2. Therefore, the false target in the second frame must be within the range of ray LOS. 2,1 and LOS 2,2 The resulting sector-shaped space is denoted as <LOS 2,1 LOS 2,2 Assume the position of the false target in the first frame is p. 1,i This allows us to determine the set of possible locations S for the false target in the second frame. 2,i Take set S 2，i The intersection with this sector space yields the set of positions S′ of the false targets in the second frame. 2，i ,Right now

[0111] S′ 2,i =S 2,i ∩ <LOS 2,1 LOS 2,2 > (22)

[0112] Decoy targets can be deployed within this area.

[0113] (2) The impact of spurious target motion constraints on the driving path of ECAVs

[0114] like Figure 4 As shown, assuming there is only one ECAV, in the first frame, according to the initial position p init With the constraints of the decoy's motion, the possible positions of the decoy can be calculated as S1. Due to the principle of drag interference, the ECAV must be located on the line connecting the radar and the decoy. Therefore, the ECAV must be located on the ray LOS. 1,1 and LOS 1,2 The resulting fan-shaped region is denoted as <LOS 1,1 LOS 1,2 > Take the intersection of set E1 and the sector region. The set of ECAV positions in the first frame is denoted as E′1, i.e.

[0115] E′1=E1∩ <LOS 1,1 LOS 1,2 > (23)

[0116] That is Figure 4Within the non-shaded area of ​​the ellipse E1, the first frame of ECAV must be within this area to satisfy the constraint. Figure 4 In the middle, after the sham target constraint, the position e 1,2 No longer legal.

[0117] Assume the position of the false target in the first frame is p. 1,4 Based on motion constraints, the possible location set S of the false target in the second frame can be determined. 2,4 Assume the first frame ECAV selects position e. 1,1 Based on motion constraints, the possible position set E2 of ECAV in the second frame is determined. Similarly, ECAV must be located at ray LOS. 2,1 and LOS 2,2 The resulting fan-shaped region is denoted as <LOS 2,1 LOS 2,2 >, take the intersection of set E2 and the sector region to obtain the ECAV position set E′2 in the second frame, that is

[0118] E′2=E2∩ <LOS 2,1 LOS 2,2 > (24)

[0119] The second frame of ECAV must be within this region to satisfy the constraint.

[0120] (3) Inverse effects between multiple frames

[0121] When considering multiple frames, the influence between false targets and ECAVs includes both positive and negative directions. If there are K frames in the scene, for the k-th frame, the positive influence means that the selectable range of false targets and ECAVs is affected by the selection in the previous k-1 frames. The negative influence means that the constraints between false targets and ECAVs in the subsequent k+1 to K frames will, in turn, affect the selectable space in the k-th frame. The positive influence is... Figure 3 , Figure 4 The principle behind the multi-frame accumulation of the two effects shown has been introduced above. The reverse effect will be explained below.

[0122] From a positive perspective, in Figure 3 In the first frame, the position p is determined after ECAV constraints. 1,1 The constraints are met, but conversely, in the second frame, the fake target needs to be within the fan-shaped region. <LOS 2,1 LOS 2,2 >Inside, and set S 2,1 If the position p is selected in the first frame and has no intersection with the sector, 1,1 If so, there is no valid position in the second frame; however, if position p is selected in the first frame... 1,4If so, interference can continue in the second frame. Simultaneously, due to the second effect mentioned above, the change in the selectable position of the false target in the first frame will further affect the selectable space of the ECAV. Therefore, the constraints introduced in the second frame, in turn, affect both the selectable space of the false target and the ECAV in the first frame, and so on, with the constraints introduced in frames k+1 to K having a reverse effect on frames 1 to k.

[0123] (4) Interactions among multiple ECAVs

[0124] When multiple ECAVs exist, the constraints of all ECAVs must be satisfied simultaneously. For example... Figure 5 As shown, assuming there are two ECAVs in the scene, in the first frame, the selectable range of the false target needs to be on both the line connecting radar 1 and ECAV1, and the line connecting radar 2 and ECAV2. Therefore, the selectable position area of ​​the false target in the first frame is...

[0125]

[0126] In other words, the selectable region is the intersection of S1 and the two sector regions. The determination of S1′, in turn, affects the selection of ECAVs' positions. Due to the constraint of ECAV2, the selectable position of ECAV1 in the first frame is...

[0127]

[0128] Similarly, in the first frame, the possible positions for ECAV2 are:

[0129]

[0130] Meanwhile, the constraints generated by multiple ECAVs simultaneously exacerbate inter-frame interference. For example... Figure 5 As shown, looking at it from a positive perspective, in the first frame, due to the motion constraints of multiple ECAVs, the false target position p 1,2 p 1,3 None of these are selectable, which in turn affects the selectable space in subsequent frames. Conversely, in the second frame, due to the constraints of ECAV1, region S... 2,1 Not selectable, due to the constraints of ECAV2, region S 2,4 Not selectable, indirectly causing the first frame position p 1,1 p 1,4 It's illegal. All things considered, in Figure 5 In the scenario shown, position p within the selectable range S1 of the first frame 1,1 p 1,2 p 1,3 p 1,4 None of them can be selected.

[0131] 2.2 Establishment of a Co-optimization Model for RGPO False Track and ECAVs Control Strategies. The mathematical essence of the RGPO false track planning problem is an optimization problem. When the influence of ECAVs on the RGPO false track is not considered, based on the false target motion model, the interference effect is maximized by optimizing the false target control vector. This optimization problem can be expressed as follows:

[0132]

[0133] Where Ψ is the false target control vector, and the false track can be calculated based on this control vector; Γ(·) is the interference effect evaluation equation, and the calculated value J reflects the interference effect of different false tracks. The larger the value, the better the interference effect; Σ is the feasible region of the independent variable.

[0134] In real-world interference scenarios, the initial state and maneuverability of ECAVs are often fixed when planning decoy tracks and cannot be arbitrarily adjusted. Therefore, the completeness of each decoy track implementation is constrained by the initial state of the ECAVs. and motion constraints Where, N F This represents the number of ECAVs. Initial conditions include initial position, initial velocity, and initial orientation. Motion constraints include velocity constraints, acceleration constraints, and angular velocity constraints. Considering a fully implementable RGPO dummy track, combined with S... init With C ECAV The optimization model of equation (28) needs to be modified to the following form:

[0135]

[0136] Where θ(·) is the ECAVs control strategy solver, Φ represents the empty set; θ(Ψ,S init C ECAV )≠Φ indicates that in the initial state S init and motion constraints C ECAV Under this constraint, ECAVs have a control strategy that can fully implement Ψ. This constraint needs to consider all radar sites and all ECAVs. Only when there is a feasible control strategy for all ECAVs at each radar site is the constraint satisfied.

[0137] The above model incorporates the initial state and maneuverability of ECAVs into the RGPO pseudo-track planning problem. By solving the above optimization model, a fully implementable pseudo-track Ψ with optimal interference effect can be obtained. * Once the false flight path is identified, the corresponding implementation strategy can be obtained through the ECAVs control strategy planning method described later.

[0138] Step 3: To address the cooperative constraint problem in Step 2, the Deb criterion is considered for evaluating false paths. A Single Player-Monte Carlo Tree Search (SP-MCTS) algorithm and a divide-and-conquer approach are introduced to calculate the constraint violation degree in the Deb criterion.

[0139] 3.1 A Deb Criterion-Based Method for Evaluating and Comparing Fake Tracks. When co-considering the planning of RGPO fake tracks and ECAV control strategies, complex constraints are introduced into the optimization problem. The complexity of these constraints lies in the mutual coupling between multiple ECAVs and multiple frames, and these constraints are difficult to express explicitly. Therefore, this invention introduces the Deb criterion to handle these constraints. This criterion guides the algorithm's search direction from two perspectives: constraint satisfaction and objective function calculation results, thus avoiding the explicit expression of complex constraints.

[0140] For a constrained optimization model that seeks to maximize a value, the Deb criterion consists of three main criteria: (1) when both individuals to be compared are feasible solutions, the individual with the larger objective function value wins; (2) when one of the individuals to be compared is a feasible solution and the other is an infeasible solution, the feasible solution wins; (3) when both individuals to be compared are infeasible solutions, the individual with the smaller constraint violation degree wins.

[0141] The Deb criterion considers both the constraint satisfaction of the alternative solutions and the calculation results of the objective function of the alternative solutions, and evaluates the quality of the alternative solutions by taking both factors into account. For nonlinear constrained programming problems, there are two key points that need to be clarified about this criterion:

[0142] (1) Determining constraint satisfaction

[0143] In the problem described in this invention, the constraint satisfaction of the alternative solution Ψ is defined as: under the current initial state and motion constraints, does there exist a feasible control strategy for ECAVs that can fully implement the pseudo-track represented by Ψ?

[0144] This problem can be solved using the ECAVs control strategy planning method described later: the initial state and motion constraints of the ECAVs serve as constraints for the control strategy planning algorithm, and the hypothetical trajectory represented by the candidate solution Ψ is used as the algorithm input. The algorithm is then used to solve the problem. During the solution process, it is not necessary to obtain the optimal solution; as long as any ECAVs control strategy that can fully implement the hypothetical trajectory is found, it indicates that the candidate solution Ψ satisfies the constraints.

[0145] It is important to note that the constraint satisfaction of dummy tracks needs to consider all ECAVs and all radar stations. If the number of radar stations is N, ... R Then there exists N REach ECAV group interferes with a different station, and the fake track is considered to meet the constraints only if each ECAV group has a feasible control strategy.

[0146] (2) Calculation of constraint violation degree

[0147] For the dummy trajectory represented by the alternative solution Ψ, if it cannot be fully implemented under the current initial state and maneuverability of the ECAVs, it is necessary to calculate its constraint violation degree. The reason for the inability to fully implement it is often that the acceleration or turning limits of the ECAVs cannot be met. If the range of acceleration and turning limits can be expanded, the feasible solution space of the ECAV control strategy will also expand accordingly, and the probability of the dummy trajectory being implemented will increase. Therefore, the constraint violation degree calculation method is defined as follows:

[0148]

[0149] Where, N F Let A be the number of ECAVs and the degree of constraint violation be A, representing the factor by which the range of motion constraints of the ECAVs is expanded. max Let A be the maximum possible value. This represents a control strategy solver that expands the motion constraint range of all ECAVs by a factor of A.

[0150] Equation (30) means that in order to fully implement the pseudo-track, the minimum expansion factor of the ECAVs motion constraint range is required. The greater the degree of constraint violation, the more difficult it is to implement the pseudo-track. When the degree of constraint violation is 1, it means that under the current initial state and maneuverability of the ECAVs, the pseudo-track Ψ can be fully implemented, that is, the cooperative constraint is satisfied.

[0151] After introducing the Deb criterion, the comparison between different pseudo-tracks no longer relies solely on the magnitude of the objective function calculation value. It is necessary to consider the feasibility of the pseudo-track, the interference effect, and the degree of constraint violation simultaneously. Assuming there are two pseudo-tracks ψ1 and ψ2, the process for determining their superiority is shown in Table 1. First, based on the initial state and maneuverability of ECAVs, it is determined whether the two pseudo-tracks can be fully implemented. If neither can be fully implemented, the degree of constraint violation is calculated separately, and the pseudo-track with a lower degree of constraint violation is better. If both can be fully implemented, the interference effect of the two pseudo-tracks is calculated separately, and the pseudo-track with a better interference effect is better. If only one pseudo-track can be fully implemented, the fully implementable pseudo-track is better.

[0152] Table 1. Fake track comparison process based on Deb criterion

[0153]

[0154] In the process shown in Table 1, for completeness, if both dummy tracks can be fully implemented and have the same interference effect, the ECAV control strategies implementing the dummy tracks are compared, and the dummy track with the shorter ECAV flight distance is superior. Since the interference effect of the dummy tracks is expressed as a decimal and has a certain degree of randomness, the probability of this situation occurring is very low. The determination of the completeness of dummy track implementation and the calculation of the ECAV flight distance can both be accomplished using the ECAV control strategy planning method introduced later.

[0155] 3.2 ECAVs Control Strategy Planning Algorithm Based on SP-MCTS

[0156] When planning ECAVs control strategies, to reduce the solution space, the scene can be discretized in both time and space dimensions. First, in the time dimension, time is divided into frames with an interval of ΔT, focusing on the positions of ECAVs at times ΔT, 2ΔT, 3ΔT, etc. Then, in the spatial dimension, at each time step, ECAVs need to be considered on the LOS (Location of Observation) between the radar and spurious points. To reduce the search difficulty, the LOS is discretized into a point sequence with an interval of ΔD, where ΔD is set to 2m in this embodiment. After discretization, the changes in the ECAVs' positions at different times lead to changes in their states.

[0157] When there is only one dummy target, an ECAV is needed to carry out the jamming. The ECAV state changes as follows: Figure 6 As shown. Assume the initial position of ECAV is P. init Based on its initial velocity, orientation, and motion constraints, the selectable range of ECAV positions in the first frame can be calculated. Assume there are two selectable positions, P... 11 and P 12 When moving from the initial position to different positions, the required acceleration, rotation angle, and other information vary, resulting in different states for ECAV in the first frame. When moving to P... 11 When determining the position, assume the possible position for the second frame is P. 21 P 22 P 23 When the movement reaches P 12 When determining the position, assume the possible position for the second frame is P. 23 P 24 P 25 Similarly, moving to different positions causes the ECAV to have different states. Based on the above state transition relationships, a system can be established as follows: Figure 7 The tree structure shown.

[0158] When multiple false targets exist, the state transition process also needs to consider the matching relationship between ECAVs and false tracks, such as... Figure 8As shown, when two ECAVs are used to implement two false tracks, assuming the initial positions of the two ECAVs are P and P respectively... 1,init and P 2,init In the initial state, ECAV1 matches false track 1, and ECAV2 matches false track 2. The state transition process to maintain the matching relationship is as follows: Figure 8 As shown in (a), the optional position of ECAV1 is P. 1,11 and P 1,12 The optional position for ECAV2 is P. 2,11 and P 2,12 The process of changing the state transition of the matching relationship is as follows: Figure 8 As shown in (b), the optional position of ECAV1 is P. 1,13 and P 1,14 The optional position for ECAV2 is P. 2,13 and P 2,14 After establishing the state transition relationship based on the optional positions for each case, we obtain Figure 9 The tree structure shown.

[0159] In summary, after discretizing the scene, a tree T{V,E} can be constructed with the initial states of the ECAVs as vertices, based on the state transition process of the ECAVs. Here, V is the set of vertices, where each vertex represents a state of the ECAV cluster, and E is the set of edges, where each edge represents a state transition process of the ECAV cluster. The size of tree T is related to the total number of fake track frames, the discretization granularity, and the number of ECAVs. The depth of the tree increases with the number of fake track frames, and the width of the tree increases with the finer level of discretization and the greater the number of ECAVs.

[0160] Once the tree structure is established, the ECAVs control strategy optimization problem can be transformed into an optimal path search problem in tree T, that is, searching for the shortest path from the root node to the leaf node in the tree. Assuming the pseudo-track consists of K frames, it can be transformed into the following problem:

[0161]

[0162] Where p is the number of nodes from the root node S root To leaf node S M,tM The path, which is a control strategy for ECAVs, S k,i Let V(k) represent the i-th vertex in the k-th layer of tree T, and also represent a state of ECAVs. M is the number of vertices in this path excluding the root node. Since ECAVs have motion constraints, all K frames of fake paths may not be fully implemented, so M≤K; V(k) represents the set of vertices in the k-th layer of tree T, and E(S) represents the set of vertices in the k-th layer of tree T. k,i ) represents node S k,i The edge set starting from point S, e(S) k,i →Sk+1,j ) represents node S k,i Starting from node S k+1,j The edge is the endpoint. C(·) is the objective function for path evaluation, which is also the evaluation index for ECAVs control strategy;

[0163] The evaluation index of ECAVs control strategy needs to consider two factors: the completion rate of fake track implementation and the ECAVs flight distance. When comparing different control strategies, the following needs to be met: (1) If the completion rate of fake track implementation of the two control strategies is different, the control strategy with higher completion rate is better; (2) If the completion rate of fake track implementation of the two control strategies is the same, the control strategy with shorter ECAVs flight distance is better. Considering both the completion rate of fake track implementation and the ECAVs cluster travel distance, the following objective function can be used for optimization:

[0164]

[0165] Where, N F v represents the number of spurious traces generated by ECAVs at a given moment. e,i,max This is the maximum speed of ECAV. Indicates from node Transition to node The objective function represents the total distance traveled by ECAVs. Other symbols have been defined above. The objective function contains two terms: the first is the longest distance traveled by all ECAVs in M ​​frames of flight, and the second is the average length of the actual flight path in each frame. This metric considers both the completion rate of the simulated flight path and the flight distance of the ECAVs. The higher the completion rate, the larger the calculated value. For the same completion rate, the shorter the actual travel distance, the larger the calculated value.

[0166] The ECAVs control strategy optimization model was established above, and the model was transformed into a tree-based optimal path search problem through discretization. Since any ECAVs state change adds nodes to the tree, the tree size is large and difficult to solve globally using traditional algorithms. Therefore, this invention introduces the SP-MCTS algorithm to find its numerical solution. The SP-MCTS algorithm is a heuristic tree search algorithm characterized by simultaneous path search and tree construction. It utilizes upper confidence bounds applied to trees (UCT) to heuristically guide the search direction, reducing the computational cost of path search and making it suitable for the problem described. The overall framework of the SP-MCTS-based ECAVs path collaborative planning algorithm is shown in Table 2.

[0167] Table 2 ECAVs Control Strategy Planning Algorithm Based on SP-MCTS

[0168]

[0169]

[0170] In Table 1, t max In the simulation of this embodiment, the value is taken as 100000, Eval(S) leaf ) represents the strategy evaluation function, which evaluates the control strategy using the above equation (32), S leaf A leaf node represents a node that uniquely determines the control strategy within the tree, and r represents the control strategy determined by Eval(S). leaf The calculated strategy evaluation result, i.e., the reward value, S cur This represents the node selected in the current iteration. The algorithm mainly consists of four stages: Selection, Expand, Simulation, and Backpropagation. Each stage corresponds to a key processing function, which will be described in detail in subsequent steps.

[0171] (1) The SP-MCTS selection stage processing function Selection() has the following flowchart as shown in Table 3.

[0172] Table 3 SP-MCTS Selection Phase Processing Flow

[0173]

[0174] In this process, calculating the confidence upper limit UCT requires recording the total number of visits N to tree T. total and each node S i Number of visits N(S) i ) and cumulative reward value Q(S) i ), N(S i ) and Q(S i The initial value is 0, and the specific iteration method is given by the subsequent backpropagation function Backpropagation(). Using this data, the UCT can be calculated, and its formula is:

[0175]

[0176] Where c is the control coefficient.

[0177] The selection phase processing function Selection() aims to select a leaf node S within tree T, guided by UCT. leaf This function starts from the root node S. rootThe process begins by progressively selecting leaf nodes. For non-leaf nodes, if all their child nodes have been visited, the node with the largest UCT value among their child nodes is selected for the next iteration. If any child node has not been visited, an unvisited child node is randomly selected. Guided by UCT, this selection process is biased towards the optimal path, avoiding a global search of tree T.

[0178] (2) The SP-MCTS expansion stage processing function Expand() has the following flow as shown in Table 4.

[0179] Table 4 SP-MCTS Extension Stage Processing Flow

[0180]

[0181] The Expand() function in the expansion phase aims to calculate the leaf node S based on the motion constraints of ECAVs. leaf The set V contains all subsequent nodes. This function needs to handle the matching relationships between ECAVs and fake tracks. Here, a matching vector m represents the matching relationship between ECAVs and fake tracks. For an ECAV with number i, the number of the fake track it matches is denoted as m(i). During Expand() processing, the set V is first initialized to an empty set; if S... leaf If it corresponds to the last frame, there are no subsequent nodes, and the result of Expand() is an empty set; if it is not the last frame, then it is necessary to traverse each matching relationship m between ECAVs and pseudo tracks, and calculate the set of possible coordinates PS for the next frame of all ECAVs under each matching relationship. i For ECAV numbered i, according to the RGPO false track... With the matching vector m, we can obtain the false dots (x) that need to be formed in the next frame. t ,y t Then, with ΔD as the interval, the radar -(x) t ,y t Discretize the connecting line segments to obtain a set of candidate coordinates. Then, filter the candidate coordinates using the motion constraints described in step 2.1 derived in step 2.2 to obtain the feasible set PS. i After obtaining the selectable coordinates of ECAVs, if the current frame is for N... F A feasible set of spurious dots If none of them are empty, then from these N F In each set, select a coordinate as the next frame position for the corresponding ECAV. The Comb() function in Table 3 selects a coordinate from the feasible set. Choose one coordinate from each of the options, and iterate through all feasible choices. Each choice corresponds to S. leaf A subsequent child node; using Comb() to continuously expand set V, eventually obtaining S.leaf The set of subsequent nodes.

[0182] (3) The Simulation() function of SP-MCTS simulation stage is shown in Table 5.

[0183] Table 5. Processing Flow for SP-MCTS Simulation Phase

[0184]

[0185] The simulation phase processing function `Simulation()` aims to evaluate the input using the Monte Carlo method and obtain its reward value `r`. This function takes a leaf node as input, randomly selects its subsequent nodes, generates a random policy, and calculates the reward value `r` for that random policy. Although this process uses `Expand()` to calculate the optional child nodes of a node, it does not update the tree `T`, thus preventing the tree `T` from expanding in size.

[0186] (4) The process flow of the SP-MCTS backpropagation phase processing function Backpropagation() is shown in Table 6.

[0187] Table 6 SP-MCTS Backtracking Phase Processing Flow

[0188]

[0189] The backpropagation() function in the backpropagation phase updates the tree T with the policy reward value r. Starting from the leaf nodes, this function updates the number of visits N, the cumulative reward Q, and the confidence cap UCT for each node, progressing upwards to the root node.

[0190] Using the above algorithm, tree construction and optimal policy search are performed simultaneously. For a single false track scenario, after t... max After one iteration, executing Selection() will yield the optimal control strategy for ECAVs; for scenarios involving multiple false tracks and track switching, the optimal control strategy can be obtained after t iterations. max After iteration, the correspondence between ECAVs and false tracks is determined, and the sequence of false target points corresponding to all K frames of the j-th ECAV is denoted as... The set of point sequences corresponding to all ECVAs is defined as follows: After that, with replace At this point, the scenario with multiple fake flight paths can be considered as N. F By iterating and optimizing a single dummy trajectory scenario that does not require trajectory switching, the optimal control strategy for ECAVs can be obtained.

[0191] The calculation of ECAVs flight distance requires the use of this algorithm to obtain the optimal result, while the determination of the completeness of the fake track does not require the use of this algorithm to obtain the optimal result. As long as any strategy that can completely implement the fake track is found during the solution process, it means that the fake track can be completely implemented.

[0192] 3.3. A method for calculating the degree of violation of pseudo-track constraints based on divide and conquer.

[0193] The process shown in Table 1 requires calculating the degree of violation of the false track constraints, which can be obtained by solving equation (30); Figure 10 As shown, the optimization independent variable dimension of the problem represented by Equation (30) is 1, and for each value of the independent variable A, there is only a feasible and an infeasible judgment. The goal of solving the problem is to find the boundary value A between the feasible and infeasible variables. * .

[0194] This invention uses the divide-and-conquer approach to solve for the degree of constraint violation. The algorithm flow is shown in Table 7.

[0195] Table 7. Calculation Method for Fake Track Constraint Violation Based on Divide and Conquer

[0196]

[0197] In Table 7, δ A This indicates the precision of the solution; the smaller the value, the higher the precision of the calculation result. This algorithm uses A... left A right Record the current search interval and initialize the interval to [1, A]. max As the algorithm iterates, the interval gradually decreases, eventually converging to A. * nearby.

[0198] Step 4: Based on the evaluation results of the Deb criterion, guide the search direction, propose the PSO-Deb-OCBA algorithm, and complete the collaborative planning of RGPO false track and ECAVs control strategy.

[0199] 4.1. Co-planning Algorithm for RGPO Fake Tracks and ECAVs Control Strategies Based on PSO-Deb-OCBA. Combining the fake track comparison method and constraint violation degree calculation method described in step 3, the co-planning algorithm for RGPO fake tracks and ECAVs control strategies based on PSO-Deb-OCBA is obtained. The algorithm flow is shown in Table 8.

[0200] Table 8. Co-planning Algorithm for RGPO False Tracks and ECAVs Control Strategies Based on PSO-Deb-OCBA

[0201]

[0202]

[0203] The algorithm first solves for the optimal RGPO dummy track that can be fully implemented, and then plans the ECAVs control strategy using the algorithm described in step 3.2. When solving for the RGPO dummy track, for each iteration, it first uses the method described in step 3.2 to determine whether the dummy track can be fully implemented, then only calculates the interference effect of the dummy track that can be fully implemented, and finally compares the merits of the particles according to the process described in Table 1.

[0204] Table 8 covers the PSO particle update method, OCBA sampling number allocation criteria, and RGPO spurious track interference effect evaluation method, which will be introduced in turn below.

[0205] 4.2 PSO (Particle Swarm Optimization) Particle Update Method. During the PSO algorithm iteration process, the position ψ of each particle needs to be recorded and updated. i With velocity v i Particle position ψ i This represents the feasible solution of the optimization model, i.e., the alternative paths of the RGPO pseudo-track, where each particle ψ i Includes N F Distance control quantity for all K frames of a fake flight path With azimuth control It contains a total of 2KN F Each component.

[0206] To update the PSO algorithm, it is also necessary to record the individual optimal and global optimal states; the individual particle optimal fitness r i,pbest This refers to the maximum fitness of the particle from the start of the algorithm to the present, corresponding to the individual's optimal position ψ. i,pbest Global optimal fitness r gbest This refers to the maximum fitness value of all particles from the start of the algorithm to the present, and its corresponding position is the global optimal position ψ. gbest Those skilled in the art will know that the optimal state includes optimal fitness and optimal position.

[0207] During algorithm initialization, within the bounding interval [ψ] min ,ψ max ]、[v min ,v max Within [the area], the position ψ of each particle is randomly set. i With velocity v i During algorithm execution, for each iteration, it is necessary to determine the global optimal position ψ. gbest Individual optimal position ψ i,pbest and the particle's current state update speed v i The calculation method is as follows

[0208] v i =wv i +c1rand()(ψ i,pbest -ψ i )+c2rand()(ψ gbest -ψ i (34)

[0209] Where w is the inertia weight, c1 and c2 are learning factors, and rand() represents taking a random number in the range [0,1]. If the speed exceeds the limit interval [v... min ,v max If the value is greater than v, then the corresponding component is set as the boundary value, i.e., greater than v. max The component is set to v max less than v min The component is set to v min In this embodiment, [ψ] min ,ψ max The value of [v] is [-50m, 50m]. min ,v max The value is [-5°, 5°], w is 0.8, c1 is 0.5, and c2 is 0.5.

[0210] After the velocity is updated, the particle position ψ is updated using equation (28). i

[0211] ψ i =ψ i +v i (35)

[0212] Similarly, if the update result exceeds the position boundary interval [ψ] min ,ψ max If ], then the corresponding component will be set as the boundary value.

[0213] As the algorithm iterates, each particle gradually moves towards the globally optimal direction; the globally optimal position ψ at the end of the algorithm's execution. gbest This is the result of RGPO pseudo-track planning.

[0214] 4.3 OCBA Sampling Count Allocation Algorithm. In the algorithm flow shown in Table 9, the calculation of the fake track interference effect requires extensive scene sampling. In each iteration of the algorithm, the OCBA algorithm is used to allocate the sampling count for each particle. The OCBA algorithm aims to maximize the probability of successfully selecting the optimal particle, allocating the total sampling count N... S Assigned to N P The algorithm flowchart is shown in Table 9.

[0215] Table 9 OCBA Sampling Count Allocation Algorithm

[0216]

[0217] The OCBA algorithm first assigns a small number of sampling attempts n0 to each particle, and then uses the results of these n0 sampling attempts as the basis for allocating subsequent sampling attempts. Let particle ψ i The number of samplings is N S,i ψ particles i The evaluation result of the j-th sampling is The sampling increment is Δ, for particle ψ i Perform N S,i After the sampling, the mean value of the interference effect can be calculated based on the sampling results.

[0218]

[0219]

[0220] Wherein, mean r i Also for particle ψ i Evaluation of interference effect.

[0221] Then, extract the index of the current optimal particle as...

[0222]

[0223] Finally, based on the mean and variance of each particle, the sampling increment Δ is allocated to N. P For each particle, the next step involves an increment of n sampling times. S,i The following three conditions must be met.

[0224]

[0225]

[0226]

[0227] The OCBA algorithm can be used in N P The optimal particle is selected from among the N particles to meet the requirements of the particle swarm optimization (PSO) algorithm. For the PSO algorithm, a key step is to find the best particle in each iteration and use its position as a reference to optimize the other N particles. P -1 particles are adjusted. Combining the PSO algorithm with the OCBA algorithm can effectively allocate the number of samplings and improve the algorithm's solution performance.

[0228] 4.4 Evaluation Method for RGPO False Track Interference Effect Based on Single Sampling

[0229] In the RGPO pseudo-track planning algorithm based on PSO-Deb-OCBA, a local simulation system is needed to evaluate the interference effect of the pseudo-track. In the PSO algorithm, for each particle ψ i The digital simulation system needs to simulate the K-frame interference process. Before the simulation, a tracking track needs to be established based on the historical motion data of the real target. Then, the following process is executed for each subsequent frame:

[0230] (1) Calculate the measurement data of each radar station in the subsequent k-th frame. First, predict the target position in the subsequent K frames based on the real target motion model, and then calculate ψ. i Converted to a false track, it also contains K frames, with the number of false points in each frame equal to the number of false targets N. F Then, the measurement process of each radar station is simulated according to equation (6) to obtain the measurement results of each radar station. In the above process, it is necessary to use computers to generate pseudo-random numbers to simulate the noise of the real target process and the radar measurement noise.

[0231] (2) Utilizing measurement results Based on equation (7), the process of correlation and measurement fusion of source points in the simulated network radar data center is used to obtain the fused measurement data.

[0232] (3) Simulate the multi-target tracking algorithm according to equation (9) and use the tracking results of the previous frame. as well as Track the current frame and obtain the tracking result. Simultaneously, track initiation is performed for unrelated measurements, and tracking tracks with long-term unrelated measurements are terminated.

[0233] After executing the above process for K frames, all K-frame tracking results are obtained. For the actual target tracking trajectory established before the interference was implemented, the subsequent K-frame tracking results are... The state estimate for the Kth frame is: The interference effect can then be evaluated using the evaluation function described in step 1.

[0234] The effects of this invention are further illustrated by the following simulation experiments:

[0235] Assume there are two radar stations in the scenario, located at (0,0) and (50km,0) respectively. The measurement noise follows a zero-mean Gaussian distribution, the standard deviation of the range vector measurement noise is 10m, the standard deviation of the azimuth vector measurement noise is 0.5°, the radar scan cycle is 1s, and the target detection probability is 99%.

[0236] Assume there is a real target in the scene, with a starting position of (15km, 50km). The real target moves at a constant speed, with speeds of 100m / s and -400m / s in the x and y directions, respectively. The noise during the motion process follows a zero-mean Gaussian distribution, and the standard deviation of the process noise in the x and y directions is 5m.

[0237] This simulation assumes that the digital simulation system uses the same tracking algorithm as the radar data center. The tracking model uses uniform Kalman filtering, the data association algorithm uses JPDA, and the tracking gate uses an elliptical gate with a gate probability of 99.97% and a gate threshold of 16.0. In the tracking model, the process noise in the x and y directions is set to have a zero-mean Gaussian distribution with a standard deviation of 10m.

[0238] This simulation utilizes a single CI fake track to perform RGPO jamming on a networked radar, executing for a total of 15 frames. When planning the RGPO fake track and ECAVs control strategy using the algorithm described in this invention, the range control value for each frame of the fake track is set to [-50m, 50m], and the azimuth control value is set to [-5°, 5°]. The total number of algorithm iterations t is set. max 50, PSO particle number N P 50, the total number of samples N in a single iteration of the OCBA algorithm S 10 5 .

[0239] In the above scenario, ECAVs were set with different initial states and motion constraints, and simulation comparison experiments were conducted. Since the solution results of the PSO algorithm have a certain degree of randomness, in order to reduce the influence of randomness, 20 Monte Carlo experiments were conducted under each set of simulation parameters, and the algorithm was evaluated using the average of the simulation results.

[0240] First, we verify the impact of the initial state of ECAVs on the planning results. Since there are two radar stations and a false track in the scene, we need to use two ECAVs to carry out interference. We use ECAV1 to interfere with the radar station located at (0,0) and use ECAV2 to interfere with the radar station located at (50km,0). The motion constraints of ECAVs are set as shown in Table 10.

[0241] Table 10 Motion constraint parameters for ECAVs

[0242]

[0243] Considering that ECAVs have different initial states, including the initial position, initial velocity, and initial angle of each ECAV, five cases are set as shown in Table 11, and simulation experiments are carried out in sequence.

[0244] Table 11 Initial State Parameters of ECVAs under Different Conditions

[0245]

[0246]

[0247] Table 12 Degrees of constraint violation in RGPO dummy tracks without cooperative constraints under different conditions

[0248]

[0249] In the above five cases, if the constraints introduced by the initial state and maneuverability of ECAVs are not considered, the planned RGPO pseudo-track cannot be fully implemented. The degree of constraint violation for each case is calculated sequentially using the algorithm shown in Table 7, and the calculation results are shown in Table 12.

[0250] Figure 11 The convergence curves of the algorithm under these five conditions are presented. The interference performance is evaluated using a hybrid index of towing success rate and distance, with the hybrid coefficient α = 0.5. The results show that, compared to the optimal RGPO false track without considering cooperative constraints, the initial state and maneuverability of ECAVs influence the selection of the RGPO false track. Referring to Table 11, from condition 1 to condition 5, the initial state of ECAVs gradually deviates, the degree of constraint violation of the RGPO false track without cooperative constraints gradually increases, the restrictions imposed by ECAVs on the RGPO false track gradually increase, and the final achievable interference performance gradually decreases.

[0251] exist Figure 11 In cases 1-4, feasible false tracks were found in the first step, while in case 5, a track was only found in the 18th step. The false tracks from the first 17 steps could not be fully implemented. Guided by the Deb criterion, the algorithm gradually moves towards the feasible region. Case 1 showed the greatest convergence. From case 2 to case 5, the initial state of ECAVs gradually deviated from case 1, and the final interference performance became increasingly lower.

[0252] Similarly, for the scenario described above, in order to verify the impact of ECAVs motion constraints on RGPO interference, simulation experiments were conducted under different motion constraint conditions with parameters such as the initial state of ECAVs, minimum drag distance, and minimum safe distance between radar and ECAVs fixed. The fixed values ​​of the initial state of ECAVs are shown in Table 13.

[0253] Table 13 Initial State Parameters of ECAVs

[0254]

[0255] Under the parameters in Table 13, ECAVs are set with different motion constraints, mainly including acceleration constraints and rotation constraints. The specific settings are shown in Table 14.

[0256] Table 14 Motion constraint parameters of ECVAs under different conditions

[0257]

[0258] Table 15 Degrees of constraint violation in RGPO dummy tracks without cooperative constraints under different conditions

[0259]

[0260] In the three cases shown in Table 14, the RGPO dummy tracks without considering cooperative constraints have different degrees of constraint violation. The calculation results are shown in Table 15. In Case 1, the degree of constraint violation is 1, which means that in this scenario, the RGPO dummy track without cooperative constraints can be fully implemented.

[0261] Figure 12 The convergence curves of the algorithm in these three cases are given, and the interference performance is calculated in the same way as above. Since case 1 satisfies the cooperative constraints, the algorithm solution is basically consistent with the interference performance of the RGPO pseudo-track under the five cooperative constraints (the slight difference comes from the randomness of the algorithm itself); the interference performance in cases 2 and 3 is lower than that in case 1. Combining Tables 14 and 15, as the deviation of ECAVs from the motion constraints increases, the degree of constraint violation gradually increases, and the interference effect gradually decreases.

[0262] exist Figure 12 In cases 2 and 3, both cases found fully implementable false tracks starting from the second iteration, demonstrating the guiding role of the Deb criterion in the algorithm.

[0263] To visually demonstrate the impact of ECAVs' initial state and maneuverability on RGPO interference, scenario 3 in Table 14 is used. Figure 13 The control strategies for ECAVs considering and without cooperative constraints were compared. (See Table 15 for details.) Figure 13 For RGPO false tracks without cooperative constraints, the cornering constraints of ECAV1 cannot meet the requirements, and its constraint range needs to be expanded by at least 1.237 times to be fully implemented. However, the method described in this invention can meet the motion constraints of ECAVs.

[0264] In summary, from the perspective of RGPO pseudo-tracks alone, without considering cooperative constraints, the RGPO pseudo-track planning algorithm can perform a global solution, resulting in better interference. However, given a fixed initial state and maneuverability of ECAVs, the optimal RGPO pseudo-track cannot be fully implemented, and the interference effect is difficult to achieve. The algorithm described in this invention considers the cooperative constraints between ECAVs and RGPO pseudo-tracks, enabling it to solve for the optimal pseudo-track that satisfies the cooperative constraints, as well as the corresponding ECAV control strategy, thus ensuring the effectiveness of RGPO interference.

[0265] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A method for drone-based networked radar range gate joint towed jamming, characterized in that, The method comprises the following steps: S1, constructing a distance gate decoy implementation scene for a networking radar; Consider a two-dimensional scenario, assume that there are radar sites, each radar is located at , represents the radar, , is the total number of radar sites, there are false targets, and one real target; At each radar site, at each time, each ECAV is on the radar and the false point connection line of sight; S2, analyze the cooperative constraints between the distance gate towed false track and the ECAVs control strategy, and establish its optimization model; the implementation integrity of each false track is subject to the initial state of the ECAVs and motion constraints ; the optimization model expression is: ； wherein, is the false target control vector, according to which the false track can be calculated; is the interference effect evaluation equation, the numerical value reflects the interference effect of different false tracks, and the larger the numerical value is, the better the interference effect is; is the feasible region of the independent variable; is the ECAVs control strategy solver, represents an empty set; represents that, under the initial state and the motion constraint , the ECAVs have a control strategy that can be completely implemented . S3, modeling the ECAV control strategy solver in step S2 into a tree optimal path search problem through discretization of time and space; the tree optimal path search problem expression is: ； in, From the root node To leaf node The path, i.e., an ECAVs control strategy; The objective function for path evaluation is the evaluation index for ECAV control strategies. Tree No. The first in the layer A vertex, that is, a state of ECAVs; This represents the number of vertices in the path excluding the root node. The flight path is frame; Tree In the The set of vertices of the layer; Represented by node The edge set starting from the edge set; Represented by node Starting from nodes The edge that terminates at the endpoint; S4. Solve for the optimal interference strategy using the particle swarm optimization algorithm, with random initialization. The position of each particle and its speed Each particle represents a false trajectory; In each iteration of the particle swarm algorithm, for each particle, search the tree optimal path search problem in step S3 based on the SP-MCTS algorithm, and classify the false tracks according to the search process. Specifically, if there is any strategy that can completely implement the false track in the search process, the false track corresponding to the strategy is put into the complete implementation particle set; the remaining false tracks are put into the non-complete implementation particle set; Based on the Deb criterion, the classified false tracks are evaluated and compared, and the best distance decoy false track is obtained after iteration. The tree established based on the SP-MCTS algorithm is searched again, and the optimal control strategy of the ECAVs is finally obtained.

2. The method of claim 1, wherein the method further comprises: The classified false tracks are evaluated based on the Deb criterion, and the specific steps are as follows: The interference effect of each false track in the complete implementation particle set is calculated; the constraint violation degree of each false track in the non-complete implementation particle set is calculated; By comparing all false tracks in pairs, the best distance decoy false track is finally obtained. The comparison process is as follows: if both cannot be completely implemented, the false track with a lower constraint violation degree is better; if both can be completely implemented, the false track with a better interference effect is better; if only one false track can be completely implemented, the completely implemented false track is better.

3. The method of claim 2, wherein the method further comprises: The constraint violation degree calculation method is defined as: ； wherein, is a constraint violation degree, representing a multiple of expansion of the motion constraint range of ECAVs, is the maximum possible value of represents a control strategy solver that expands all motion constraint ranges of ECAVs by a multiple of 4. The method of claim 3, wherein the method further comprises: In the process of calculating the interference effect of the false track, the OCBA algorithm is used to allocate the sampling number of each particle.

5. The method of claim 4, wherein the method further comprises: The interference effect is evaluated according to the following formula: ； wherein, represents that the real target is in the gate, represents that the real target is not in the gate, represents the distance between the tracking gate center and the real target position; represents the maximum value of the trailing distance, is a mixing coefficient.

6. The method of claim 5, wherein the method further comprises: The expression is: ； wherein, denotes the number of false targets, is the maximum speed of the ECAVs, denotes the transition from a node to a node the total distance traveled by the ECAVs, denotes the interval time of adjacent frames.

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