Unmanned cluster formation configuration design method for target tracking

Abstract

The invention discloses a target tracking-oriented unmanned cluster formation configuration design method, which comprises the following steps of: constructing a target motion model and an observation model of an unmanned cluster to a target; constructing a detection performance evaluation index of the unmanned cluster and a target tracking performance evaluation index of the unmanned cluster; establishing an unmanned cluster initial formation configuration optimization model for target tracking; establishing an unmanned cluster formation track optimization model for target tracking; and respectively solving the unmanned cluster initial formation configuration optimization model facing the target tracking and the unmanned cluster formation track optimization model facing the target tracking in combination with an interior point method. According to the method, the detection performance and the target tracking precision of the unmanned cluster can be maximized, the requirements of unmanned cluster spacing and maneuvering limitation can be met, the optimal formation initial configuration and the optimal formation route planning scheme at the subsequent moment can be obtained, and the detection tracking performance of the unmanned cluster is effectively improved.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to an unmanned cluster formation configuration design method for target tracking. Background Art

[0002] With the continuous expansion of the application field of unmanned platforms, the difficulty of a single unmanned platform to perform tasks has gradually increased, so the coordinated combat of multiple unmanned platforms has become particularly important. Unmanned swarm coordinated combat means that when multiple unmanned platforms perform combat tasks, they reasonably coordinate the combat behaviors between the combat platforms, so that the cluster resources can be reasonably used and higher combat effectiveness can be achieved.

[0003] Faced with the high dynamics and deep uncertainty of the modern battlefield environment, relying on multiple unmanned platforms to perform positioning and tracking tasks can obtain a wider observation range, higher positioning accuracy and robustness, thereby greatly improving the battlefield situation awareness capabilities. The unmanned cluster is equipped with multiple detection radars, using the interactive network to share detection signals in real time, and implement multi-directional and multi-dimensional detection of enemy targets by combining "side view", "overhead view" and "group view". Different from traditional positioning methods, the detection and tracking performance of the cluster on the target is not only affected by the detection system and detection algorithm, but also greatly affected by the cluster size and formation configuration.

[0004] At present, the research on the configuration design of unmanned swarm formations equipped with detection radars is still incomplete, especially the research on the configuration design of swarm formations and trajectory optimization under detection and tracking tasks is still relatively weak. Most studies focus on the target detection performance and area coverage when the swarm performs search tasks, and lack consideration of continuous tracking of targets. In summary, there is no unmanned swarm formation configuration design method for target tracking in the existing technology. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a target tracking-oriented unmanned cluster formation configuration design method that can improve the detection and tracking performance of unmanned clusters.

[0006] Technical solution: The unmanned cluster formation configuration design method for target tracking of the present invention comprises the following steps:

[0007] Construct the target motion model and the observation model of the unmanned swarm to the target;

[0008] Construct detection performance evaluation indicators for unmanned swarms and target tracking performance evaluation indicators for unmanned swarms;

[0009] Taking maximizing the coverage area of ​​the cluster detection area and minimizing the target tracking error as the optimization goals, a weighted function of the two is constructed. Under the constraints of cluster spacing and deployment area, the initial position of the unmanned cluster is optimized, and an initial formation configuration optimization model of the unmanned cluster for target tracking is established.

[0010] After obtaining the optimal initial formation configuration of the unmanned swarm, the target tracking error is minimized as the optimization goal. Considering the constraints of cluster spacing and maneuverability restrictions, the motion trajectory of the unmanned swarm when tracking the target at subsequent moments is optimized, and an unmanned swarm formation trajectory optimization model for target tracking is established.

[0011] Combined with the interior point method, the unmanned swarm initial formation configuration optimization model for target tracking and the unmanned swarm formation trajectory optimization model for target tracking are solved respectively.

[0012] Furthermore, the target motion model constructed is:

[0013]

[0014] in, represents the motion state vector of target q in the kth frame; F represents the state transfer matrix of target q; W q represents zero-mean Gaussian white noise.

[0015] Furthermore, the observation model of the unmanned cluster to the target is:

[0016]

[0017] in, represents the measurement vector of the unmanned platform i on the target q in the kth frame; A nonlinear transfer function representing the angle information and the distance information of the target; Indicates the unmanned platform-target pairing indicator. when When , it means that the unmanned platform i tracks the target q in the kth frame. When , it means that the unmanned platform i does not track the target q in the kth frame; represents the white Gaussian measurement noise with zero mean, and represents the measurement error of the distance and azimuth between the unmanned platform i and the target q in the kth frame, which can be written as in, is the distance measurement error, is the azimuth measurement error, noise The covariance of Independent of each other in range and azimuth.

[0018] Furthermore, noise The covariance of Described as:

[0019]

[0020] in, represents the distance between the unmanned platform i and the target q in the kth frame; represents the azimuth angle between the unmanned platform i and the target q in the kth frame; and Respectively and The measurement error variance is related to the target echo signal-to-noise ratio, which can be expressed as:

[0021]

[0022] Where c is the speed of light; β is the effective bandwidth of the radar transmission signal carried by the unmanned platform; represents the echo signal-to-noise ratio of the target q illuminated by the unmanned platform i in the kth frame; λ represents the signal wavelength; γ represents the antenna aperture; the target echo signal-to-noise ratio The expression is:

[0023]

[0024] Among them, T d represents the radar dwell time; T r Represents the repetition period of the radar pulse signal; P t Indicates radar transmission power; G t Represents the radar transmitting antenna gain; G r represents the radar receiving antenna gain; σ represents the radar cross-sectional area RCS of the target q observed by the unmanned platform; λ represents the wavelength of the radar transmitting signal; G RP represents the radar receiver processing gain; k B is the Boltzmann constant; T o Represents the noise temperature of the radar receiver; B r Indicates the bandwidth of the receiver matched filter; F r Represents the noise figure of the receiver; represents the distance between target q and unmanned platform i in the kth frame.

[0025] Furthermore, the detection performance evaluation indicators of unmanned clusters are constructed, including:

[0026] The detection coverage area of ​​the radar carried by the unmanned cluster at the kth frame is defined as the regional coverage performance evaluation index, which is expressed as:

[0027]

[0028] in, represents the total detection coverage area of ​​the radar carried by the unmanned cluster at the kth frame; N represents a total of N unmanned platforms; represents the overlapping area of ​​the unmanned cluster detection coverage area in the kth frame; S i It represents the maximum detectable area of ​​the radar carried by unmanned platform i, and its calculation formula is:

[0029]

[0030] in, Indicates the illumination angle range of the radar carried by unmanned platform i; Indicates the maximum detection distance of the radar carried by unmanned platform i.

[0031] Furthermore, the target tracking performance evaluation index of the unmanned cluster is constructed, including: the BCRLB matrix of the target state estimation error of the unmanned cluster is used to characterize the target tracking accuracy of the unmanned cluster, which is expressed as:

[0032]

[0033] in, and Respectively represent matrices The lower bound of the mean square error of the estimated target distance and speed; Represents the BCRLB matrix of the unmanned cluster for the target q at the kth frame.

[0034] Furthermore, the initial formation configuration optimization model of unmanned swarm for target tracking is constructed as follows:

[0035]

[0036] Among them, ω1 and ω2 are weighting factors; Represents the normalized value of the detection area coverage performance evaluation index; Represents the normalized value of the target tracking performance evaluation index; R ij represents the distance between unmanned platform i and unmanned platform j; R min Represents the minimum distance between any two unmanned platforms; R max represents the maximum distance between any two unmanned platforms; x i represents the horizontal coordinate of unmanned platform i; y i represents the ordinate of unmanned platform i; x min Indicates the minimum value of the horizontal coordinate of unmanned platform i; x max Indicates the maximum value of the horizontal coordinate of unmanned platform i; y min Indicates the minimum value of the vertical coordinate of the unmanned platform i; y max Indicates the maximum value of the vertical coordinate of unmanned platform i.

[0037] Furthermore, the unmanned swarm formation trajectory optimization model for target tracking is constructed as follows:

[0038]

[0039] Among them, x i,k represents the horizontal coordinate of the unmanned platform in the kth frame; y i,k represents the ordinate of the unmanned platform in the kth frame; Q represents the number of targets to be tracked; ψ i,k represents the heading angle of unmanned platform i at the kth frame; v i,k represents the velocity vector of unmanned platform i at the kth frame; ψ max Indicates the maximum offset of the unmanned platform heading angle in the next frame; V min Indicates the minimum speed of the unmanned platform; V max Indicates the maximum speed of the unmanned platform; R ij,k Represents the distance between unmanned platform i and unmanned platform j at the kth frame.

[0040] Furthermore, the initial formation configuration optimization model of unmanned swarm for target tracking is solved by combining the interior point method, specifically:

[0041] Step 1: Let the number of iterations Take (x i ,y j ) (0) is the initial point when the number of iterations is 1, ε>0 is the algorithm termination indicator, and the penalty factor ξ (1) >0, penalty factor reduction coefficient c≥2;

[0042] Step 2: Solve the following subproblems for the initial point:

[0043]

[0044] st(x i ,y j )∈D1

[0045] Among them, Θ1 represents the optimization objective function in the unmanned swarm initial formation configuration optimization model, g a represents the constraints in the unmanned swarm initial formation configuration optimization model, g1=R min -R 12 , g2=R min -R 13 , g3=R min -R 23 ,…, where R 12 Represents the distance between unmanned platform 1 and unmanned platform 2, R 13 and R23 The meaning of is similar; (x i ,y j ) represents the plane coordinates of the unmanned platform i; D1 represents the feasible domain, D1={(x i ,y j )|g a (x i ,y j )≤0}, g a (x i ,y j ) = g a ; Let the minimum point of the above problem be

[0046] Step 3: Check the termination condition. If The algorithm terminates; otherwise, Skip to step 2.

[0047] Furthermore, the interior point method is combined to solve the trajectory optimization model of unmanned swarm formation for target tracking, specifically:

[0048] Step 1: Let the number of iterations Take (ψ i,k ,v i,k ) (0) is the initial point when the number of iterations is 1, ε>0 is the algorithm termination indicator, and the penalty factor ξ (1) >0, penalty factor reduction coefficient c≥2;

[0049] Step 2: Solve the following subproblems for the initial point:

[0050]

[0051] st(ψ i,k ,v i,k )∈D2

[0052] Among them, Θ2 represents the optimization objective function in the unmanned swarm formation trajectory optimization model, g b represents the constraint conditions in the unmanned swarm formation trajectory optimization model, g1=R min -R 12,k , g2=R min -R 13,k , g3=R min -R 23,k ,…, where R 12,k represents the distance between unmanned platform 1 and unmanned platform 2 in the kth frame, R 13,k and R 23,k The meaning of is similar; (ψ i,k,v i,k ) represents the optimization variable combination, ψ i,k represents the heading angle of unmanned platform i at the kth frame; v i,k represents the velocity vector of unmanned platform i at the kth frame; D2 represents the feasible domain, D2={(ψ i,k ,v i,k )|g b (ψ i,k ,v i,k )≤0}, g b (ψ i,k ,v i,k ) = g b ; Let the minimum point of the above problem be

[0053] Step 3: Check the termination condition. If The algorithm terminates; otherwise, Skip to step 2.

[0054] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are: by optimizing the initial configuration of the formation of the unmanned cluster, and then optimizing the trajectory of the formation at subsequent moments, the detection and tracking performance of the unmanned cluster is improved while meeting the constraints of cluster spacing and maneuverability restrictions; it can maximize the detection performance and target tracking accuracy of the unmanned cluster; it can not only meet the requirements of unmanned cluster spacing and maneuverability restrictions, but also obtain the optimal initial configuration of the formation and the optimal formation trajectory planning scheme at subsequent moments, effectively improving the detection and tracking performance of the unmanned cluster. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 A flow chart of the method for designing the configuration of unmanned swarm formation for target tracking;

[0056] Figure 2 It is the optimal initial formation configuration diagram of the unmanned swarm;

[0057] Figure 3 It is a schematic diagram of the initial configuration 1 of the conventional formation of the unmanned swarm;

[0058] Figure 4 It is a schematic diagram of the initial configuration 2 of the conventional formation of the unmanned swarm;

[0059] Figure 5 It is a schematic diagram of the initial configuration 3 of the conventional formation of the unmanned swarm;

[0060] Figure 6 It is a schematic diagram of the initial configuration 4 of the conventional formation of the unmanned swarm;

[0061] Figure 7 Performance comparison chart of unmanned swarms with different initial configurations;

[0062] Figure 8 Optimize the trajectory of the unmanned swarm at subsequent times;

[0063] Fig. 9 This is the tracking error diagram of the unmanned cluster for the target. DETAILED DESCRIPTION

[0064] The structure and working process of the present invention will be further described below in conjunction with the accompanying drawings.

[0065] Starting from the actual combat scenario, this paper proposes a method for designing the unmanned cluster formation configuration for target tracking. Under the constraints of the unmanned cluster spacing and maneuverability restrictions, the initial formation configuration of the unmanned cluster is firstly optimized to maximize the detection area coverage and target tracking accuracy of the unmanned cluster. Then, the heading angle and speed of the unmanned cluster are jointly optimized to maximize the target tracking accuracy, so as to achieve the purpose of improving the detection and tracking performance of the unmanned cluster.

[0066] like Figure 1 As shown, the unmanned cluster formation configuration design method for target tracking of the present invention comprises the following steps:

[0067] (1) Construct the motion model of target q in the kth frame, which can be expressed as:

[0068]

[0069] in, represents the motion state vector of target q in the kth frame; represents the motion state vector of target q in the k-1th frame; F represents the state transfer matrix of target q; W q represents zero-mean Gaussian white noise.

[0070] (2) Construct the observation model of the unmanned platform i for the target q in the kth frame, which can be expressed as:

[0071]

[0072] in, represents the measurement vector of the unmanned platform i on the target q in the kth frame; A nonlinear transfer function representing the angle information and the distance information of the target; Indicates the unmanned platform-target pairing indicator. when When , it means that the unmanned platform i tracks the target q in the kth frame. , it means that the unmanned platform i does not track the target q in the kth frame. represents the white Gaussian measurement noise with zero mean, which represents the measurement error of the distance and azimuth between the unmanned platform i and the target q in the kth frame, and can be written as in, is the distance measurement error, is the azimuth measurement error, and T represents the transpose of the matrix. The covariance of are independent of each other in range and azimuth and can be described as:

[0073]

[0074] in, represents the distance between the unmanned platform i and the target q in the kth frame; represents the azimuth angle between the unmanned platform i and the target q in the kth frame; and Respectively and The measurement error variance is . They are all related to the target echo signal-to-noise ratio and can be expressed as:

[0075]

[0076] Where c = 3 × 10 8 m / s represents the speed of light; β is the effective bandwidth of the radar transmission signal carried by the unmanned platform; represents the echo signal-to-noise ratio of the target q illuminated by the unmanned platform i in the kth frame; λ represents the wavelength of the radar transmission signal; γ represents the antenna aperture; the target echo signal-to-noise ratio The expression is:

[0077]

[0078] Among them, T d represents the radar dwell time; T r Represents the repetition period of the radar pulse signal; P t Indicates radar transmission power; G t Represents the radar transmitting antenna gain; G r represents the radar receiving antenna gain; σ represents the radar cross section (RCS) of the target q observed by the unmanned platform; G RP represents the radar receiver processing gain; k B is the Boltzmann constant; T o Represents the noise temperature of the radar receiver; B r Indicates the bandwidth of the receiver matched filter; F r Represents the noise figure of the receiver; represents the distance between target q and unmanned platform i in the kth frame.

[0079] (3) Construct the detection performance evaluation index of the unmanned cluster. The sum of the detection coverage area of ​​the radar carried by the unmanned cluster at the kth frame is defined as the regional coverage performance evaluation index, which can be expressed as:

[0080]

[0081] in, represents the total detection coverage area of ​​the radar carried by the unmanned cluster at the kth frame; N represents a total of N unmanned platforms; S represents the overlapping area of ​​the unmanned cluster detection coverage area in the kth frame. i It represents the maximum detectable area of ​​the radar carried by unmanned platform i, and its calculation formula is:

[0082]

[0083] in, Indicates the illumination angle range of the radar carried by unmanned platform i; Indicates the maximum detection distance of the radar carried by unmanned platform i.

[0084] (4) Construct the target tracking performance evaluation index of the unmanned cluster to measure the target tracking accuracy. The Bayesian Cramer-Rao lower bound BCRLB matrix of the target state estimation error of the unmanned cluster is used to represent the target tracking accuracy of the unmanned cluster, which can be expressed as:

[0085]

[0086] in, represents the tracking accuracy of unmanned cluster targets, and Respectively represent matrices The lower bound of the mean square error of the estimated target distance and speed; Represents the BCRLB matrix of the unmanned cluster for the target q at the kth frame.

[0087] (5) Constructing an optimization model for the initial formation configuration of unmanned swarms for target tracking:

[0088] At the initial moment, the optimization objectives are to maximize the coverage of the cluster detection area and minimize the target tracking error. A weighted function of the two is constructed. Under the constraints of cluster spacing and deployment area, the initial position of the unmanned cluster is optimized, and an initial formation configuration optimization model of the unmanned cluster for target tracking is established, which is expressed as follows:

[0089]

[0090] Among them, ω1 and ω2 are weighting factors; Represents the normalized value of the detection area coverage performance evaluation index; Represents the normalized value of the target tracking performance evaluation index; R ij represents the distance between unmanned platform i and unmanned platform j; R min Represents the minimum distance between any two unmanned platforms; R max represents the maximum distance between any two unmanned platforms; x i represents the horizontal coordinate of unmanned platform i; y i represents the ordinate of unmanned platform i; x min Indicates the minimum value of the horizontal coordinate of unmanned platform i; x max Indicates the maximum value of the horizontal coordinate of unmanned platform i; y min Indicates the minimum value of the vertical coordinate of the unmanned platform i; y max Indicates the maximum value of the vertical coordinate of unmanned platform i.

[0091] In formula (9), the detection area coverage performance evaluation index is The normalization formula is as follows:

[0092]

[0093] Among them, S initial represents the total detection coverage area of ​​the unmanned cluster in the k = 1 frame, that is, S o Represents the normalization factor of the detection coverage area.

[0094] In formula (9), the target tracking performance evaluation index is The normalization formula is as follows:

[0095]

[0096] in, represents the target tracking accuracy of target q in frame k = 1, that is, F o Represents the normalization factor of target tracking accuracy.

[0097] (6) Constructing an unmanned swarm formation trajectory optimization model for target tracking:

[0098] After obtaining the optimal initial formation configuration of the unmanned cluster, at the subsequent moment, based on the obtained optimal formation initial configuration, the target tracking error is minimized as the optimization goal, and the constraints of cluster spacing and maneuverability are considered. The motion track of the unmanned cluster when tracking the target at the subsequent moment is optimized, and the joint optimization of the heading angle and speed when the unmanned cluster tracks the target is achieved. The unmanned cluster formation track optimization model for target tracking is established, which is expressed as follows:

[0099]

[0100] Among them, x i,k represents the horizontal coordinate of the unmanned platform in the kth frame; y i,k represents the ordinate of the unmanned platform in the kth frame; Q represents the number of targets to be tracked; ψ i,k represents the heading angle of unmanned platform i at the kth frame; v i,k represents the velocity vector of unmanned platform i at the kth frame; ψ max Indicates the maximum offset of the unmanned platform heading angle in the next frame; V min Indicates the minimum speed of the unmanned platform; V max Indicates the maximum speed of the unmanned platform; R ij,k Represents the distance between unmanned platform i and unmanned platform j at the kth frame.

[0101] (7) Combined with the interior point method, the optimization model (9) is solved. The specific steps are as follows:

[0102] Step 1: Let the number of iterations Take (x i ,y j ) (0) is the initial point when the number of iterations is 1, ε>0 is the algorithm termination indicator, and the penalty factor ξ (1) >0, the penalty factor reduction coefficient c≥2.

[0103] Step 2: Solve the following subproblems for the initial point:

[0104]

[0105] Among them, Θ1 represents the optimization objective function in the optimization model (9), g a represents the constraints in the optimization model (9), g1 = R min -R 12 , g2=R min -R 13 , g3=R min -R 23 ,…, where R 12 Represents the distance between unmanned platform 1 and unmanned platform 2, R 13 and R 23 The meaning of is similar; (x i ,y j ) represents the plane coordinates of the unmanned platform i; D1 represents the feasible domain, D1={(x i ,y j )|g a (x i ,y j )≤0}, g a(x i ,y j ) = g a Let the minimum point of the above problem be

[0106] Step 3: Check the termination condition. If The algorithm terminates; otherwise, Skip to step 2.

[0107] (8) Combined with the interior point method, the optimization model (12) is solved. The specific steps are as follows:

[0108] Step 1: Let the number of iterations Take (ψ i,k ,v i,k ) (0) is the initial point when the number of iterations is 1, ε>0 is the algorithm termination indicator, and the penalty factor ξ (1) >0, the penalty factor reduction coefficient c≥2.

[0109] Step 2: Solve the following subproblems for the initial point:

[0110]

[0111] Where Θ2 represents the optimization objective function in the optimization model (12), g b represents the constraints in the optimization model (12), g1 = R min -R 12,k , g2=R min -R 13,k , g3=R min -R 23,k ,…, where R 12,k represents the distance between unmanned platform 1 and unmanned platform 2 in the kth frame, R 13,k and R 23,k The meaning of is similar; (ψ i,k ,v i,k ) represents the optimization variable combination, ψ i,k represents the heading angle of unmanned platform i at the kth frame; v i,k represents the velocity vector of unmanned platform i at the kth frame; D2 represents the feasible domain, D2={(ψ i,k ,v i,k )|g b (ψ i,k ,v i,k )≤0}, g b (ψ i,k ,v i,k ) = g bLet the minimum point of the above problem be

[0112] Step 3: Check the termination condition. If The algorithm terminates; otherwise, Skip to step 2.

[0113] Simulation results:

[0114] Consider that the unmanned cluster consists of N = 3 unmanned platforms, each of which is equipped with a detection radar, and assume that the unmanned cluster needs to track Q = 1 target. The system simulation parameters are set as follows: The radar pulse repetition period is T r =5×10 - 4 s; the radar's dwell time on the target is T d = 0.01s; the radar's transmitting antenna gain and receiving antenna gain are G t =G r =25dB; the wavelength of the radar transmission signal is λ = 0.03m; the processing gain of the radar receiver is G RP =12dB; Boltzmann constant is k B =1.38×10 -23 J / k; radar transmission signal effective bandwidth β = 1MHz; antenna aperture γ = 1m 2 ; The noise factor of the radar receiver is F r =1.5dB; Radar transmission power P t =1000W; the RCS of the target is σ=5000m 2 ; The sampling interval is T = 2s; ω1 = 0.4; ω2 = 0.6; S o =100; F o =50×10 6 ; The minimum distance between unmanned platforms is R min = 10km; the maximum distance between unmanned platforms is R max =30km; the maximum offset of the heading angle of the unmanned platform in the next frame is ψ max =20°; the minimum speed of the unmanned platform is V min =200m / s; the maximum speed of the unmanned platform is V max =400m / s; the simulation is 30 consecutive frames, and the sampling interval is T=2s.

[0115] At the initial time k = 1 frame, the ship target is located at (40,80) km, its navigation speed is (0,-16) m / s, and the deployment area of ​​the unmanned cluster at the initial time is {(x i ,y i )|-20km≤x i≤20km,0≤y i ≤15km}.

[0116] Figure 2 The optimal formation configuration of the unmanned cluster at the initial moment is given, with the position of unmanned platform 1 at (-10,15) km, the position of unmanned platform 2 at (0,15) km, and the position of unmanned platform 3 at (20,15) km. It can be observed that within the set cluster initial deployment area, the optimized cluster is located at the boundary of the area close to the target to achieve better target state estimation accuracy; at the same time, in order to obtain a larger detection coverage area, the cluster is distributed at a certain distance in the horizontal direction to reduce the overlapping area of ​​the detection area.

[0117] In order to verify the superiority of the method proposed in the present invention, it was compared with four other conventional formation initial configurations. Figure 3 , Figure 4 , Figure 5 , Figure 6 They are conventional formation initial configuration 1, conventional formation initial configuration 2, conventional formation initial configuration 3, and conventional formation initial configuration 4. Figure 7 The corresponding Θ1 objective function values ​​of each formation's initial configuration are given. This function value is related to the detection and tracking performance of the target. The smaller the value, the better the detection and tracking performance. By comparing various configurations, the optimal initial configuration obtained by this method has the smallest Θ1 value, which can achieve both good tracking performance and a larger detection area, verifying the effectiveness and superiority of the proposed method.

[0118] by Figure 2 The optimal formation configuration given in is used as the formation configuration of the cluster's initial frame, and the cluster's trajectory is optimized in subsequent frames. Figure 8 The trajectory optimization diagram of the unmanned swarm in the subsequent frames is given. The unmanned swarm continues to track the target and moves towards the target, verifying the effectiveness of the proposed method. Among them, each platform moves in the general direction of the target. This is because the target tracking accuracy is proportional to the signal-to-noise ratio, and the signal-to-noise ratio is inversely proportional to the fourth power of the distance. In the initial frame, the cluster approaches the target from a long distance. The change in the distance to the target in a short period of time cannot significantly change the tracking accuracy of the target, so the formation configuration does not change significantly. After approaching the target to a certain distance, the formation configuration of the cluster will change significantly, that is, it will approach the target directly.

[0119] Fig. 9 The root mean square error (RMSE) and BCRLB result diagrams of the unmanned cluster tracking target are given. As the cluster gradually approaches the target, the estimation error of the target tracking accuracy gradually decreases, and the RMSE curve of the target tracking error is above its lower bound BCRLB curve, which verifies the effectiveness of the proposed method.

[0120] The working principle and working process of the invention are as follows:

[0121] The present invention aims at the scenario of unmanned cluster collaborative detection and tracking based on self-transmitting and self-receiving radars. It assumes that there is a single target in space and considers that a single target is detected and tracked by multiple unmanned platforms equipped with radars. Under the constraints of cluster spacing, maneuverability restrictions, etc., the formation configuration of the unmanned cluster in the collaborative detection process is optimized and designed, and an unmanned cluster formation configuration optimization model at different times is established, so that the unmanned cluster maintains good detection performance and tracking performance. Firstly, considering the detection range of a single self-transmitting and self-receiving radar, the detection area coverage performance evaluation index of the unmanned cluster is established based on this; then, the Bayesian Cramér-Rao Lower Bound (BCRLB) matrix of the target state estimation error of the unmanned cluster is derived, and the measurement index of the target tracking accuracy of the unmanned cluster is defined based on this; then, the initial formation configuration optimization model of the unmanned cluster and the trajectory optimization model of the formation at subsequent moments are established. Firstly, taking the maximization of the cluster detection area coverage performance and the target tracking accuracy as the optimization goal, a weighted function of the two is constructed, and the initial position of the unmanned cluster is optimized under the constraints of the cluster spacing and deployment area; on the basis of obtaining the optimal initial configuration, taking the maximization of the target tracking accuracy as the optimization goal, considering the constraints of the cluster spacing and maneuvering restrictions, the motion trajectory of the unmanned cluster when tracking the target is optimized. Finally, for the above optimization problem, the above optimization model is solved in combination with the interior point method to improve the detection and tracking performance of the unmanned cluster.

Claims

1. The unmanned swarm formation configuration design method for target tracking is characterized by: The following steps are involved: Construct the target motion model and the observation model of the unmanned swarm to the target; Construct detection performance evaluation indicators for unmanned swarms and target tracking performance evaluation indicators for unmanned swarms; Taking maximizing the coverage area of ​​the cluster detection area and minimizing the target tracking error as the optimization goals, a weighted function of the two is constructed. Under the constraints of cluster spacing and deployment area, the initial position of the unmanned cluster is optimized, and an optimization model of the initial formation configuration of the unmanned cluster for target tracking is established. After obtaining the optimal initial formation configuration of the unmanned swarm, the target tracking error is minimized as the optimization goal. Considering the constraints of cluster spacing and maneuverability restrictions, the motion trajectory of the unmanned swarm when tracking the target at subsequent moments is optimized, and an unmanned swarm formation trajectory optimization model for target tracking is established. Combined with the interior point method, the unmanned swarm initial formation configuration optimization model for target tracking and the unmanned swarm formation trajectory optimization model for target tracking are solved respectively.

2. The unmanned swarm formation configuration design method for target tracking according to claim 1 is characterized in that: The target motion model constructed is: in, represents the motion state vector of target q in the kth frame; F represents the state transfer matrix of target q; W q represents zero-mean Gaussian white noise.

3. The unmanned swarm formation configuration design method for target tracking according to claim 1 is characterized in that: The observation model of the unmanned swarm to the target is: in, represents the measurement vector of the unmanned platform i on the target q in the kth frame; A nonlinear transfer function representing the angle information and the distance information of the target; Indicates the unmanned platform-target pairing indicator. when When , it means that the unmanned platform i tracks the target q in the kth frame. When , it means that the unmanned platform i does not track the target q in the kth frame; represents the white Gaussian measurement noise with zero mean, and represents the measurement error of the distance and azimuth between the unmanned platform i and the target q in the kth frame, which can be written as in, is the distance measurement error, is the azimuth measurement error, noise The covariance of Independent of each other in range and azimuth.

4. The unmanned swarm formation configuration design method for target tracking according to claim 3 is characterized in that: noise The covariance of Described as: in, represents the distance between the unmanned platform i and the target q in the kth frame; represents the azimuth angle between the unmanned platform i and the target q in the kth frame; and Respectively and The measurement error variance is related to the target echo signal-to-noise ratio, which can be expressed as: Where c is the speed of light; β is the effective bandwidth of the radar transmission signal carried by the unmanned platform; represents the echo signal-to-noise ratio of the target q illuminated by the unmanned platform i in the kth frame; λ represents the signal wavelength; γ represents the antenna aperture; the target echo signal-to-noise ratio The expression is: Among them, T d represents the radar dwell time; T r Represents the repetition period of the radar pulse signal; P t Indicates radar transmission power; G t Represents the radar transmitting antenna gain; G r represents the radar receiving antenna gain; σ represents the radar cross-sectional area RCS of the target q observed by the unmanned platform; λ represents the wavelength of the radar transmitting signal; G RP represents the radar receiver processing gain; k B is the Boltzmann constant; T o Represents the noise temperature of the radar receiver; B r Indicates the bandwidth of the receiver matched filter; F r Represents the noise figure of the receiver; represents the distance between target q and unmanned platform i in the kth frame.

5. The method for designing a target tracking-oriented unmanned swarm formation configuration according to claim 1, characterized in that: Construct detection performance evaluation indicators for unmanned clusters, including: The detection coverage area of ​​the radar carried by the unmanned cluster at the kth frame is defined as the regional coverage performance evaluation index, which is expressed as: in, represents the total detection coverage area of ​​the radar carried by the unmanned cluster at the kth frame; N represents a total of N unmanned platforms; represents the overlapping area of ​​the unmanned cluster detection coverage area in the kth frame; S i It represents the maximum detectable area of ​​the radar carried by unmanned platform i, and its calculation formula is: in, Indicates the illumination angle range of the radar carried by unmanned platform i; Indicates the maximum detection distance of the radar carried by unmanned platform i.

6. The unmanned swarm formation configuration design method for target tracking according to claim 1 is characterized in that: Construct the target tracking performance evaluation index of the unmanned cluster, including: using the BCRLB matrix of the target state estimation error of the unmanned cluster to represent the target tracking accuracy of the unmanned cluster, expressed as: in, and Respectively represent matrices The lower bound of the mean square error of the estimated target distance and speed; Represents the BCRLB matrix of the unmanned cluster for the target q at the kth frame.

7. The method for designing a target tracking-oriented unmanned swarm formation configuration according to claim 1, characterized in that: The constructed unmanned swarm initial formation configuration optimization model for target tracking is: Among them, ω1 and ω2 are weighting factors; Represents the normalized value of the detection area coverage performance evaluation index; Represents the normalized value of the target tracking performance evaluation index; R ij represents the distance between unmanned platform i and unmanned platform j; R min Represents the minimum distance between any two unmanned platforms; R max represents the maximum distance between any two unmanned platforms; x i represents the horizontal coordinate of unmanned platform i; y i represents the ordinate of unmanned platform i; x min Indicates the minimum value of the horizontal coordinate of unmanned platform i; x max Indicates the maximum value of the horizontal coordinate of unmanned platform i; y min Indicates the minimum value of the vertical coordinate of the unmanned platform i; y max Indicates the maximum value of the vertical coordinate of unmanned platform i.

8. The method for designing a target tracking-oriented unmanned swarm formation configuration according to claim 1, characterized in that: The unmanned swarm formation trajectory optimization model for target tracking is constructed as follows: Among them, x i,k represents the horizontal coordinate of the unmanned platform in the kth frame; y i,k represents the ordinate of the unmanned platform in the kth frame; Q represents the number of targets to be tracked; ψ i,k represents the heading angle of unmanned platform i at the kth frame; v i,k represents the velocity vector of unmanned platform i at the kth frame; ψ max Indicates the maximum offset of the unmanned platform heading angle in the next frame; V min Indicates the minimum speed of the unmanned platform; V max Indicates the maximum speed of the unmanned platform; R ij,k Represents the distance between unmanned platform i and unmanned platform j at the kth frame.

9. The method for designing a target tracking-oriented unmanned swarm formation configuration according to claim 1, characterized in that: The initial formation configuration optimization model of unmanned swarm for target tracking is solved by combining the interior point method, specifically: Step 1: Let the number of iterations Take (x i ,y j ) (0) is the initial point when the number of iterations is 1, ε>0 is the algorithm termination indicator, and the penalty factor ξ (1) >0, penalty factor reduction coefficient c≥2; Step 2: Solve the following subproblems for the initial point: s.t . (x i ,y j )∈D1 Among them, Θ1 represents the optimization objective function in the unmanned swarm initial formation configuration optimization model, g a represents the constraints in the unmanned swarm initial formation configuration optimization model, g1=R min -R 12 , g2=R min -R 13 , g3=R min -R 23 ,…, where R 12 Represents the distance between unmanned platform 1 and unmanned platform 2, R 13 and R 23 The meaning of is similar; (x i ,y j ) represents the plane coordinates of the unmanned platform i; D1 represents the feasible domain, D1={(x i ,y j )|g a (x i ,y j )≤0}, g a (x i ,y j ) = g a ; Let the minimum point of the above problem be Step 3: Check the termination condition. If The algorithm terminates; otherwise, Skip to step 2.

10. The unmanned swarm formation configuration design method for target tracking according to claim 1, characterized in that: The trajectory optimization model of unmanned swarm formation for target tracking is solved by combining the interior point method, specifically: Step 1: Let the number of iterations Take (ψ i,k ,v i,k ) (0) is the initial point when the number of iterations is 1, ε>0 is the algorithm termination indicator, and the penalty factor ξ (1) >0, penalty factor reduction coefficient c≥2; Step 2: Solve the following subproblems for the initial point: s.t.(ψ i,k ,v i,k )∈D2 Among them, Θ2 represents the optimization objective function in the unmanned swarm formation trajectory optimization model, g b represents the constraint conditions in the unmanned swarm formation trajectory optimization model, g1=R min -R 12,k , g2=R min -R 13,k , g3=R min -R 23,k ,…, where R 12,k represents the distance between unmanned platform 1 and unmanned platform 2 in the kth frame, R 13,k and R 23,k The meaning of is similar; (ψ i,k ,v i,k ) represents the optimization variable combination, ψ i,k represents the heading angle of unmanned platform i at the kth frame; v i,k represents the velocity vector of unmanned platform i at the kth frame; D2 represents the feasible domain, D2={(ψ i,k ,v i,k )|g b (ψ i,k ,v i,k )≤0}, g b (ψ i,k ,v i,k ) = g b ; Let the minimum point of the above problem be Step 3: Check the termination condition. If The algorithm terminates; otherwise, Skip to step 2.

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