Game power allocation method for distributed radar alliance based on multi-target tracking

Abstract

The present invention discloses a distributed radar alliance game power allocation method based on multi-target tracking, including: constructing a target motion model; constructing a radar measurement model for a target; constructing a radio frequency stealth performance measurement index and a target tracking accuracy measurement index with multi-target tracking performance, alliance structure and total radiation power of a networked radar system as variables; taking a given multi-target tracking performance and radio frequency resource limitation as constraints, taking maximizing the radio frequency stealth performance measurement index of a networked radar as an optimization target, establishing a distributed radar alliance game power allocation optimization model based on multi-target tracking; solving the optimization model in combination with an SQP algorithm. The present invention can not only meet the target tracking accuracy requirements predefined by the networked radar system, but also obtain the best alliance structure and the best radiation power allocation scheme in real time, effectively improving the radio frequency stealth performance of the networked radar system.

Description

Technical Field

[0001] The present invention relates to radar signal processing technology, and in particular to a distributed radar alliance game power allocation method based on multi-target tracking. Background Art

[0002] Networked radar refers to the dispersed deployment of multiple single radars of different systems, frequencies and models, real-time control and point-trace fusion processing, integrating multiple radars in a designated area in a networking mode to form an organic whole with high precision and high anti-interference performance. Due to its advantages in signal and spatial diversity, the networked radar system is widely used in target detection, target positioning, target tracking, waveform design, parameter estimation, sensor selection and information extraction. At present, it is in the transition stage from theory to practice.

[0003] With the rapid development of passive detection systems, RF stealth technology is a fundamental issue that needs to be considered when designing radar systems. In order to achieve better RF stealth performance, it is necessary to strictly control the radiated power of the radar system. Game theory can provide a framework for coordination and confrontation between rational but selfish participants, so it can be an effective tool to solve the problem of distributed resource optimization.

[0004] At present, the research on game theory and its application in networked radar systems is still very incomplete, especially the research on the application of game theory in the control of RF radiation energy of networked radar systems is still very weak. Most studies apply game theory to the anti-interference and target detection problems of radars, and lack consideration of radar RF stealth performance. In summary, there is no distributed radar alliance game power allocation method based on multi-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 distributed radar alliance game power allocation method based on multi-target tracking, which can reduce the total radiation power of the networked radar system while meeting the predetermined target tracking performance, so as to maximize the benefit of the networked radar system.

[0006] Technical solution: The distributed radar alliance game power allocation method based on multi-target tracking of the present invention comprises the following steps:

[0007] S1, build target motion model;

[0008] S2, build a radar measurement model of the target;

[0009] S3. Construct a RF stealth performance measurement index with multi-target tracking performance, alliance structure, and total radiated power of the networked radar system as variables, as well as a target tracking accuracy measurement index;

[0010] S4. Taking the given multi-target tracking performance and RF resource limitation as constraints, and maximizing the networked radar RF stealth performance measurement index as the optimization goal, a distributed radar alliance game power allocation optimization model based on multi-target tracking is established;

[0011] S5. Solve the distributed radar alliance game power allocation optimization model based on multi-target tracking established in step S4 in combination with the SQP algorithm; including: initializing the target motion state; using the EKF algorithm to predict the target state; initializing the radiation power of each radar to be the same, and solving the optimization model in combination with the SQP algorithm, with the goal of maximizing the RF stealth performance measurement index, to obtain the optimal alliance structure at the current moment; under the obtained optimal alliance structure, also with the goal of maximizing the RF stealth performance measurement index, solving the optimization model in combination with the SQP algorithm, to obtain the optimal power allocation plan at the current moment, and obtain the target measurement information; using the EKF algorithm to update the target state; until the results at each moment are obtained.

[0012] Furthermore, the target motion model constructed in step S1 is:

[0013] x q,k =Fx q,k-1 +W q

[0014] Among them, x q,k represents the motion state vector of target q at time k; x q,k-1 represents the motion state vector of target q at time k-1; F represents the state transfer matrix of target q; W q represents zero-mean Gaussian white noise.

[0015] Furthermore, the radar measurement model for the target constructed in step S2 is:

[0016]

[0017] Where zm,q,k represents the measurement vector of radar m to target q at time k; h m (x q,k ) represents a nonlinear transfer function including the target's angle information and the target's distance information; v m,q,k represents the measurement error of the distance and azimuth between radar m and target q at time k; ρ m,q,k represents the radar-target selection situation, ρ m,q,k ∈{0,1}, when ρ m,q,k =1, it means that radar m selects to track target q at time k and joins it. m,q,k =0, it means that radar m does not choose to join the alliance tracking target q at time k.

[0018] Furthermore, the measurement error v of the distance and azimuth between radar m and target q at time k is m,q,k The mean of G is zero and its covariance is G m,q,k It is expressed as:

[0019]

[0020] in, and Respectively represent R m,q,k and θ m,q,k The lower bound of the estimated mean square error; R m,q,k represents the distance between radar m and target q at time k; θ m,q,k represents the azimuth between radar m and target q at time k; and The signal-to-noise ratio (SNR) of the echo between radar m and target q at time k is m,q,k The relationship between them is expressed as:

[0021]

[0022] Among them, β m,q,k represents the bandwidth of the signal transmitted by radar m to target q at time k; θ W Indicates the width of the 3dB receiving beam; SNR m,q,k The expression is:

[0023]

[0024] Where, T represents the radar dwell time; T r represents the radar pulse repetition period; p m,q,k G represents the radiation power of radar m to target q at time k; t and G r Respectively represent the radar's transmitting antenna gain and receiving antenna gain; σ m,q,k represents the radar cross section (RCS) of radar m to target q at time k; λ is the wavelength of radar transmission signal; G RP represents the processing gain of the radar receiver; k B is the Boltzmann constant; T o is the noise temperature of the radar receiver; B r Indicates the bandwidth of the radar receiver matched filter; F r Represents the noise factor of the radar receiver; R m,q,k represents the distance between radar m and target q at time k.

[0025] Furthermore, the RF stealth performance measurement index constructed in step S3 is expressed as:

[0026]

[0027] Among them, u k (p m,q,k ) represents the RF stealth performance indicator of the networked radar system at time k; pm,q,k represents the radiation power of radar m to target q at time k; Q represents the total number of targets that the networked radar system needs to track; represents the target tracking accuracy threshold preset for target q, η q,k represents the target tracking accuracy for target q at time k; D represents the pricing variable related to target tracking performance, and D>0; δ represents the pricing variable related to radar radiation power; M represents the number of radars that make up the networked radar system; ρ m,q,k represents the selection of target q by radar m at time k; p max is the maximum radiated power of the radar in the networked radar system;

[0028] Target tracking accuracy η q,k It is expressed as:

[0029]

[0030] Among them, B q,k (1,1) and B q,k (3,3) represent the matrix B q,k The element corresponding to the target distance estimation accuracy; B q,k Represents the predicted Bayesian Cramér-Rao Lower Bound (BCRLB) matrix for the target q at time k.

[0031] Furthermore, the distributed radar alliance game power allocation optimization model based on multi-target tracking constructed in step S4 is:

[0032] max u k (p m,q,k )

[0033]

[0034] Among them, η q,k represents the target tracking accuracy for target q at time k; represents the target tracking accuracy threshold preset for target q; p min represents the minimum value of single radar radiation power; p max Represents the maximum radiated power of the radar in the networked radar system; ρ m,q,k represents the selection of target q by radar m at time k; M qIt indicates the number of radars that track a single target; M indicates the number of radars that make up the networked radar system; Q indicates the total number of targets that the networked radar system needs to track.

[0035] Furthermore, the specific steps of solving the optimization model in step S5 in combination with the SQP algorithm are:

[0036] (1) Let k = 1 and initialize the estimated motion state vector of each target at time k-1 and the target motion state estimation error covariance matrix P q,k-1|k-1 ;

[0037] (2) The EKF algorithm is used to predict the state of the target q at time k, and the result is:

[0038]

[0039] P q,k|k-1 =FP q,k-1|k-1 F T +U q

[0040] in, represents the state prediction value of target q at time k; F represents the state transfer matrix of target q; P q,k|k-1 represents the predicted value of the motion state estimation error covariance matrix of the target q at time k; U q represents the Gaussian white noise W in the target q motion model q The covariance matrix of T represents the transposed matrix of F.

[0041] (3) Initialize the radiation power of each radar to be the same, and use the SQP algorithm to solve the optimization model, with the goal of maximizing the RF stealth performance measurement index at time k, to obtain the optimal alliance structure at the current moment:

[0042] i) Initialization: The optimization starting point is set to A0 = ρ m,k,q , the Lagrange multiplier is initialized and the iteration factor is set to The termination index of the Lagrangian algorithm is set to ε>0;

[0043] ii) Construct and solve the quadratic model: perform Taylor series expansion on the optimization objective function and constraints; at the current optimization iteration point Nearby, A represents the optimization variable to be solved, and a quadratic model about the variable γ is constructed to approximate the original problem: Where E represents the matrix composed of the first-order partial derivatives of the objective function, E T represents the transposed matrix of E, Represents the matrix composed of the second-order partial derivatives of the objective function, γ Trepresents the transposed matrix of γ;

[0044] iii) Update the optimization iteration point: The result of solving the quadratic subproblem γ * As the next search direction Update to get the optimized iteration point

[0045] iv) Check the termination condition: check whether the objective function converges or the gradient is less than the algorithm termination indicator ε; if the condition is met, the algorithm terminates; otherwise, continue to the next iteration; update the Lagrange multiplier, iteration factor And return to step ii);

[0046] v) Output: Radar's selection of target ρ m,q,k ;

[0047] (4) Under the alliance structure obtained in step (3), the goal is to maximize the RF stealth performance indicator at time k, and the SQP algorithm is combined to solve the optimization model to obtain the optimal power allocation solution at the current time, and obtain the measurement information z of the target q m,q,k ;

[0048] (5) Using the EKF algorithm to update the state of the target q at time k, we get:

[0049]

[0050] Among them, S q,k represents the innovation covariance matrix; K q,k represents the Kalman gain matrix; H q,k express The Jacobian matrix of q,k|k-1 Indicates h m (x q,k ) in the predicted state The first derivative at P q,k|k-1 represents the predicted value of the motion state estimation error covariance matrix of the target q at time k; G q,k The measurement error v in the radar measurement model of target q is m,q,k The covariance matrix of Represents the state update value of the target q at time k; represents the state prediction value of the target q at time k; z q,k represents the measured value of the target q at time k; Indicates h m (x q,k )exist The value at P q,k|k Represents the updated value of the motion state estimation error covariance matrix of the target q at time k.

[0051] (6) Let k=k+1 and jump to step (2).

[0052] The distributed radar alliance game power allocation system based on multi-target tracking of the present invention includes:

[0053] A target motion model building unit, used for building a target motion model;

[0054] A measurement model building unit, used to build a radar measurement model of a target;

[0055] An indicator construction unit, used to construct a measurement index of radio frequency stealth performance and a measurement index of target tracking accuracy with multi-target tracking performance, alliance structure and total radiated power of networked radar system as variables;

[0056] The optimization model building unit is used to establish a distributed radar alliance game power allocation optimization model based on multi-target tracking, taking the given multi-target tracking performance and radio frequency resource limitation as constraints and maximizing the networked radar radio frequency stealth performance measurement index as the optimization goal;

[0057] The optimization model solving unit is used to solve the distributed radar alliance game power allocation optimization model based on multi-target tracking established in step S4 in combination with the SQP algorithm; including: initializing the target motion state; using the EKF algorithm to predict the state of the target; initializing the radiation power of each radar to be the same, combining the SQP algorithm to solve the optimization model, with the goal of maximizing the radio frequency stealth performance measurement index, and obtaining the optimal alliance structure at the current moment; under the obtained optimal alliance structure, also with the goal of maximizing the radio frequency stealth performance measurement index, combining the SQP algorithm to solve the optimization model, obtain the optimal power allocation plan at the current moment, and obtain the measurement information of the target; using the EKF algorithm to update the state of the target; until the results at each moment are obtained.

[0058] An electronic device of the present invention comprises:

[0059] A memory storing executable program code;

[0060] a processor coupled to the memory;

[0061] The processor calls the executable program code stored in the memory to execute the steps of the above-mentioned distributed radar alliance game power allocation method based on multi-target tracking.

[0062] A computer-readable storage medium of the present invention stores computer instructions, and when the computer instructions are called, they are used to execute the steps of the distributed radar alliance game power allocation method based on multi-target tracking as described above.

[0063] Beneficial effects: Compared with the prior art, the advantages of the present invention are:

[0064] (1) The present invention reduces the total radiated power of the networked radar system by jointly optimizing the networked radar alliance structure and power allocation, while satisfying the given multi-target tracking performance and RF resource restrictions and other constraints, thereby maximizing the benefits of the networked radar system. The reason for this advantage is that a distributed radar alliance game power allocation method based on multi-target tracking is adopted. The method is guided by RF stealth performance, constructs a RF stealth performance measurement index that comprehensively considers multi-target tracking performance, alliance structure and total radiated power of the networked radar system, and defines a measurement index for target tracking accuracy; on this basis, with the given multi-target tracking performance and RF resource restrictions as constraints, and with maximizing the RF stealth performance measurement index of the networked radar as the optimization goal, a distributed radar alliance game power allocation optimization model based on multi-target tracking is established, and the networked radar alliance structure formation and power allocation are adaptively performed to achieve the purpose of improving the RF stealth performance of the networked radar system.

[0065] (2) The distributed radar alliance game power allocation method based on multi-target tracking proposed in the present invention can reduce the total radiation power of the networked radar system and obtain the maximum system benefit. It can not only meet the predefined target tracking accuracy requirements of the networked radar system, but also obtain the best alliance structure and the optimal radiation power allocation scheme in real time, effectively improving the RF stealth performance of the networked radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a flow chart of the power allocation method of distributed radar alliance game based on multi-target tracking;

[0067] Figure 2 To provide a map of network radar distribution and target movement trajectory;

[0068] Figure 3 This is the tracking error diagram of the networked radar system for target 1;

[0069] Figure 4 This is the tracking error diagram of the networked radar system for target 2;

[0070] Figure 5 This is a graph showing the alliance formation and power allocation results of the networked radar system when tracking target 1;

[0071] Figure 6 This is a graph showing the alliance formation and power allocation results of the networked radar system when tracking target 2;

[0072] Figure 7 This is a comparison chart of the total radiated power of the networked radar system under different methods. DETAILED DESCRIPTION

[0073] The structure and working process of the present invention will be further described below in conjunction with the accompanying drawings.

[0074] Starting from the actual combat scenario, the present invention proposes a distributed radar alliance game power allocation method based on multi-target tracking. Under the given multi-target tracking performance and RF resource limitation constraints, the networked radar RF stealth performance measurement index is maximized as the optimization goal, and the networked radar alliance structure and power allocation are adaptively optimized to achieve the purpose of improving the RF stealth performance of the networked radar system. The present invention assumes that there are several targets in space, and considers a networked radar system composed of multiple single radars to track multiple targets. For this scenario of networked radar tracking multiple targets, firstly, guided by the RF stealth performance, a RF stealth performance measurement index that comprehensively considers the multi-target tracking performance, alliance structure and total radiated power of the networked radar system is designed, and the measurement index of the target tracking accuracy is defined. Then, with the given multi-target tracking performance and RF resource limitation as constraints, and with the maximization of the networked radar RF stealth performance measurement index as the optimization goal, a distributed radar alliance game power allocation optimization model based on multi-target tracking is established. On this basis, the Sequential Quadratic Programming (SQP) algorithm is combined to solve the above optimization model, and the networked radar alliance structure and power allocation results are obtained under the given multi-target tracking performance and RF resource constraints, which makes the networked radar RF stealth performance the best and the system benefit the largest. That is, the joint optimization of the networked radar alliance structure and power allocation is achieved, the maximum system benefit is obtained, and then the RF stealth performance of the networked radar system is improved.

[0075] like Figure 1 As shown, the distributed radar alliance game power allocation method based on multi-target tracking of the present invention includes the following steps:

[0076] S1. Construct the motion model of target q at time k, which can be expressed as:

[0077] x q,k =Fx q,k-1 +W q (1)

[0078] Among them, x q,k represents the motion state vector of target q at time k; x q,k-1 represents the motion state vector of target q at time k-1; F represents the state transfer matrix of target q; W q represents zero-mean Gaussian white noise.

[0079] S2. Construct the measurement model of radar m to target q at time k, which can be expressed as:

[0080]

[0081] Among them, z m,q,k represents the measurement vector of radar m to target q at time k; h m (x q,k ) represents a nonlinear transfer function including the target's angle information and the target's distance information; v m,q,k represents the measurement error of the distance and azimuth between radar m and target q at time k; ρ m,q,k represents the radar-target selection situation, ρ m,q,k ∈{0,1}, when ρ m,q,k =1, it means that radar m selects to track target q at time k and joins it. m,q,k =0, it means that radar m does not choose to join the alliance tracking target q at time k.

[0082] In formula (2), v m,q,k Its mean is zero and its covariance G m,q,k It can be expressed as:

[0083]

[0084] Among them, R m,q,k represents the distance between radar m and target q at time k; θ m,q,k represents the azimuth between radar m and target q at time k; and Respectively represent R m,q,k and θ m,q,k The lower bound of the estimated mean square error of . and The signal-to-noise ratio (SNR) of the echo between radar m and target q at time k is m,q,k The relationship between them can be expressed as:

[0085]

[0086] Among them, β m,q,k represents the bandwidth of the signal transmitted by radar m to target q at time k; θ W Indicates the width of the 3dB receiving beam; SNR m,q,k The expression is:

[0087]

[0088] Where, T represents the radar dwell time; T r represents the radar pulse repetition period; p m,q,k G represents the radiation power of radar m to target q at time k; t and G rRespectively represent the radar's transmitting antenna gain and receiving antenna gain; σ m,q,k represents the radar cross section (RCS) of radar m to target q at time k; λ is the wavelength of radar transmission signal; G RP represents the processing gain of the radar receiver; k B is the Boltzmann constant; T o is the noise temperature of the radar receiver; B r Indicates the bandwidth of the radar receiver matched filter; F r Represents the noise factor of the radar receiver; R m,q,k represents the distance between radar m and target q at time k.

[0089] S3. Construct a RF stealth performance index and a target tracking accuracy index with multi-target tracking performance, alliance structure, and total radiated power of the networked radar system as variables. The RF stealth performance index can be expressed as:

[0090]

[0091] Among them, u k (p m,q,k ) represents the RF stealth performance indicator of the networked radar system at time k; p m,q,k represents the radiation power of radar m to target q at time k; Q represents the total number of targets that the networked radar system needs to track; represents the target tracking accuracy threshold preset for target q, η q,k represents the target tracking accuracy for target q at time k; D represents the pricing variable related to target tracking performance, and D>0; δ represents the pricing variable related to radar radiation power; M represents the number of radars that make up the networked radar system; ρ m,q,k represents the selection of target q by radar m at time k; p max It is the maximum radiated power of the radar in the networked radar system.

[0092] Target tracking accuracy η q,k The specific explanation is as follows, which can be expressed as:

[0093]

[0094] Among them, B q,k (1,1) and B q,k (3,3) represent the matrix B q,k The element corresponding to the target distance estimation accuracy; B q,k Represents the predicted Bayesian Cramér-Rao Lower Bound (BCRLB) matrix for the target q at time k.

[0095] S4. Construct a distributed radar alliance game power allocation optimization model based on multi-target tracking;

[0096] Taking the given multi-target tracking performance and RF resource limitation as constraints, and maximizing the networked radar RF stealth performance measurement index as the optimization goal, a distributed radar alliance game power allocation optimization model based on multi-target tracking is established, which is expressed as follows:

[0097] max u k (p m,q,k )

[0098]

[0099] Among them, η q,k represents the target tracking accuracy for target q at time k; represents the target tracking accuracy threshold preset for target q; p min represents the minimum value of single radar radiation power; p max Represents the maximum radiated power of the radar in the networked radar system; ρ m,q,k represents the selection of target q by radar m at time k; M q It indicates the number of radars that track a single target; M indicates the number of radars that make up the networked radar system; Q indicates the total number of targets that the networked radar system needs to track.

[0100] In formula (8), the first constraint condition represents the tracking accuracy η of the target q at time k: q,k Should be less than or equal to the target tracking accuracy threshold The second constraint states that the radiated power of each radar cannot exceed the peak power p max and not less than the minimum value p min ; The third constraint states that each radar can track at most one target at time k, and each target is q Department radar tracking.

[0101] S5. Solve the optimization model (8) by combining the SQP algorithm. The specific steps are as follows:

[0102] Step 1: Set k = 1 and initialize the estimated motion state vector of each target at time k-1 and the target motion state estimation error covariance matrix P q,k-1|k-1 ;

[0103] Step 2: Use the EKF algorithm to predict the state of the target q at time k and obtain:

[0104]

[0105] P q,k|k-1 =FP q,k-1|k-1 F T +U q (10)

[0106] in, represents the state prediction value of target q at time k; F represents the state transfer matrix of target q; P q,k|k-1 represents the predicted value of the motion state estimation error covariance matrix of the target q at time k; U q represents the Gaussian white noise W in the target q motion model q The covariance matrix of T represents the transposed matrix of F.

[0107] Step 3: Initialize the radiation power of each radar to be the same, and use the SQP algorithm to solve the optimization model (8), with the goal of maximizing the RF stealth performance measurement index at time k, to obtain the optimal alliance structure at the current moment:

[0108] i) Initialization: The optimization starting point is set to A0 = ρ m,k,q , the Lagrange multiplier is initialized and the iteration factor is set to The termination index of the Lagrangian algorithm is set to ε>0;

[0109] ii) Construct and solve the quadratic model: perform Taylor series expansion on the optimization objective function and constraints. Nearby, A represents the optimization variable to be solved, and a quadratic model about the variable γ is constructed to approximate the original problem: Where E represents the matrix composed of the first-order partial derivatives of the objective function, E T represents the transposed matrix of E, Represents the matrix composed of the second-order partial derivatives of the objective function, γ T represents the transposed matrix of γ;

[0110] iii) Update the optimization iteration point: The result of solving the quadratic subproblem γ * As the next search direction Update to get the optimized iteration point

[0111] iv) Check the termination condition: Check whether the objective function converges or the gradient is less than the algorithm termination indicator ε. If the condition is met, the algorithm terminates; otherwise, continue to the next iteration; update the Lagrange multiplier, iteration factor And return to step ii);

[0112] v) Output: Radar's selection of target ρ m,q,k .

[0113] Step 4: Under the alliance structure obtained in step 3, the goal is also to maximize the RF stealth performance indicator at time k. Similar to step 3, the SQP algorithm is combined to solve the optimization model (8) to obtain the optimal power allocation solution at the current moment and obtain the measurement information z of the target q. m,q,k ;

[0114] Step 5: Use the EKF algorithm to update the state of the target q at time k and obtain:

[0115]

[0116] Among them, S q,k represents the innovation covariance matrix; K q,k represents the Kalman gain matrix; H q,k express The Jacobian matrix of q,k|k-1 Indicates h m (x q,k ) in the predicted state The first derivative at P q,k|k-1 represents the predicted value of the motion state estimation error covariance matrix of the target q at time k; G q,k The measurement error v in the radar measurement model of target q is m,q,k The covariance matrix of Represents the state update value of the target q at time k; represents the state prediction value of the target q at time k; z q,k represents the measured value of the target q at time k; Indicates h m (x q,k )exist The value at P q,k|k Represents the updated value of the motion state estimation error covariance matrix of the target q at time k;

[0117] Step 6: Let k=k+1 and jump to step 2.

[0118] Simulation results:

[0119] Consider a networked radar system consisting of M = 8 radars, and assume that the networked radar system needs to track Q = 2 targets. The system parameters are set as follows: the radar's dwell time on the target is T = 100ms; the radar's transmitting antenna gain and receiving antenna gain are G t =G r =30dB; the wavelength of the radar transmission signal is λ = 0.03m; the processing gain of the radar receiver is G RP =10dB; Boltzmann constant is k=1.38×10 -23 ; The effective bandwidth of the radar transmission signal is β = 1MHz; The noise coefficient of the radar receiver is F r=1.5dB; radar pulse repetition period is T r =5×10 -4 s; the peak value of radar radiation power is p max =1000W, p min =0.05p max ; The sampling interval is △T = 3s; The number of radars tracking a target is M q =4; pricing variable D = 100, δ = 10 -6 The simulation is a continuous 50-frame process, and N MC = 100 Monte Carlo experiments.

[0120] The designed network radar distribution and target movement trajectory are as follows Figure 2 As shown, the initial position of target 1 is [25, 25] km, and the speed is [-350, -200] m / s; the initial position of target 2 is [-25, -25] km, and the speed is [350, 200] m / s. The target RCS value is set to σ = 1m 2 .

[0121] Figure 3 and Figure 4 The root mean square error (RMSE) and Bayesian Cramér-Rao lower bound (BCRLB) of the networked radar system for target 1 and target 2 are given respectively. It can be seen that the target tracking error is low and can converge quickly.

[0122] Figure 5 The alliance formation and power allocation results of the networked radar system when tracking target 1 are given, that is, alliance 1 performs the task of tracking target 1. Figure 5 If the radar corresponds to the black part, it means that the radar does not belong to Alliance 1, that is, it does not participate in the task of tracking target 1 at the corresponding time. On the contrary, it means that the radar belongs to Alliance 1 and performs the task of tracking target 1 at the corresponding time. Figure 5 It can be seen that in the first 35 frames of the simulation, radar 5, radar 6, radar 7 and radar 8 form alliance 1 to track target 1. Figure 2 By analyzing the changes in the power allocation of each radar, it can be found that the networked radar system will choose radars with closer positions and better observation positions in the alliance to allocate more power. After 15 frames, the alliance structure gradually changes to radar 1, radar 2, radar 3 and radar 5. The change in the alliance structure also shows that for target 1, the networked radar system will give priority to radars that are closer to the target and have better observation positions to join alliance 1. In addition, it can be found that the networked radar system will still choose radars that are closer to the target and have better observation positions in the alliance to allocate more power to ensure the overall benefits of the alliance and the total benefits of the networked radar system. Figure 6 The coalition formation and power allocation results of the networked radar system when tracking target 2 are given. For target 2, the same conclusion as that for target 1 can be obtained.

[0123] In order to verify the superiority of the method proposed in the present invention, it is compared with three other methods, namely:

[0124] Method 1: This method considers that the networked radar system optimizes the configuration of radar nodes and then adopts the principle of average distribution for the power allocation of each radar.

[0125] Method 2: This method considers that at each tracking moment, the networked radar system adopts a random radar node selection scheme to track the target and optimizes the configuration of the radar radiation power parameters.

[0126] Method 3: This method considers that at each tracking moment, the networked radar system uses the default radar node selection scheme to track the target and optimizes the configuration of the radar radiation power parameters.

[0127] The results of comparison of different methods are as follows Figure 7 As shown, it can be seen that the method proposed in the present invention can obtain the minimum total radiation power of the networked radar system while meeting the predefined target tracking accuracy requirements compared with other methods, that is, the radar's RF stealth performance is optimal, which proves the superiority of the proposed method.

[0128] The working principle and working process of the invention are as follows:

[0129] The present invention considers reducing the total radiated power of the networked radar system while meeting the predetermined target tracking performance, so as to maximize the benefits of the networked radar system. First, guided by the RF stealth performance, a RF stealth performance measurement index that comprehensively considers the multi-target tracking performance, the alliance structure and the total radiated power of the networked radar system is designed, and the measurement index of the target tracking accuracy is defined. Then, with the given multi-target tracking performance and RF resource restrictions as constraints, and with maximizing the RF stealth performance measurement index of the networked radar as the optimization goal, a distributed radar alliance game power allocation optimization model based on multi-target tracking is established. On this basis, the above optimization model is solved in combination with the SQP algorithm, and the networked radar alliance structure and power allocation are jointly optimized to obtain the optimal networked radar alliance structure and power allocation, so as to maximize the system benefits and thus improve the RF stealth performance of the networked radar system.

[0130] The invention of the present invention:

[0131] The present invention assumes that there are several targets in space and considers a networked radar system consisting of multiple single radars to track multiple targets. Aiming at the scenario of this networked radar tracking multiple targets, a RF stealth performance measurement index is designed that comprehensively considers the multi-target tracking performance, alliance structure and total radiated power of the networked radar system, and defines a measurement index for target tracking accuracy.

[0132] At the same time, the present invention takes the given multi-target tracking performance and radio frequency resource limitation as the constraint conditions, takes the maximization of the radio frequency stealth performance measurement index of the networked radar system as the optimization goal, and establishes a distributed radar alliance game power allocation optimization model based on multi-target tracking. On this basis, the above optimization model is solved in combination with the SQP algorithm. By solving the optimization model, the networked radar alliance structure and power allocation results that make the networked radar radio frequency stealth performance optimal and the system benefit maximum under the given multi-target tracking performance and radio frequency resource limitation constraints are obtained.

[0133] The distributed radar alliance game power allocation system based on multi-target tracking of the present invention includes:

[0134] A target motion model building unit, used for building a target motion model;

[0135] A measurement model building unit, used to build a radar measurement model of a target;

[0136] An indicator construction unit, used to construct a measurement index of radio frequency stealth performance and a measurement index of target tracking accuracy with multi-target tracking performance, alliance structure and total radiated power of networked radar system as variables;

[0137] The optimization model building unit is used to establish a distributed radar alliance game power allocation optimization model based on multi-target tracking, taking the given multi-target tracking performance and radio frequency resource limitation as constraints and maximizing the networked radar radio frequency stealth performance measurement index as the optimization goal;

[0138] The optimization model solving unit is used to solve the distributed radar alliance game power allocation optimization model based on multi-target tracking established in step S4 in combination with the SQP algorithm; including: initializing the target motion state; using the EKF algorithm to predict the state of the target; initializing the radiation power of each radar to be the same, combining the SQP algorithm to solve the optimization model, with the goal of maximizing the radio frequency stealth performance measurement index, and obtaining the optimal alliance structure at the current moment; under the obtained optimal alliance structure, also with the goal of maximizing the radio frequency stealth performance measurement index, combining the SQP algorithm to solve the optimization model, obtain the optimal power allocation plan at the current moment, and obtain the measurement information of the target; using the EKF algorithm to update the state of the target; until the results at each moment are obtained.

[0139] An electronic device of the present invention comprises:

[0140] A memory storing executable program code;

[0141] a processor coupled to the memory;

[0142] The processor calls the executable program code stored in the memory to execute the steps of the above-mentioned distributed radar alliance game power allocation method based on multi-target tracking.

[0143] A computer-readable storage medium of the present invention stores computer instructions, and when the computer instructions are called, they are used to execute the steps of the distributed radar alliance game power allocation method based on multi-target tracking as described above.

Claims

1. A distributed radar alliance game power allocation method based on multi-target tracking, characterized in that: The following steps are involved: S1, build target motion model; S2, build a radar measurement model of the target; S3. Construct a RF stealth performance measurement index with multi-target tracking performance, alliance structure, and total radiated power of the networked radar system as variables, as well as a target tracking accuracy measurement index; S4. Taking the given multi-target tracking performance and RF resource limitation as constraints, and maximizing the networked radar RF stealth performance measurement index as the optimization goal, a distributed radar alliance game power allocation optimization model based on multi-target tracking is established; the model expression is: max u k (p m,q,k ) Among them, η q,k represents the target tracking accuracy for target q at time k; represents the target tracking accuracy threshold preset for target q; p min represents the minimum value of single radar radiation power; p max Represents the maximum radiated power of the radar in the networked radar system; ρ m,q,k represents the selection of target q by radar m at time k; M q Indicates the number of radars that track a single target; M indicates the number of radars that make up the networked radar system; Q indicates the total number of targets that the networked radar system needs to track; S5. Solve the distributed radar alliance game power allocation optimization model based on multi-target tracking established in step S4 in combination with the SQP algorithm; including: initializing the target motion state; using the EKF algorithm to predict the target state; initializing the radiation power of each radar to be the same, and solving the optimization model in combination with the SQP algorithm, with the goal of maximizing the RF stealth performance measurement index, to obtain the optimal alliance structure at the current moment; under the obtained optimal alliance structure, also with the goal of maximizing the RF stealth performance measurement index, solving the optimization model in combination with the SQP algorithm, to obtain the optimal power allocation plan at the current moment, and obtain the target measurement information; using the EKF algorithm to update the target state; until the results at each moment are obtained.

2. The distributed radar alliance game power allocation method based on multi-target tracking according to claim 1 is characterized in that: The target motion model constructed in step S1 is: x q,k =Fx q,k-1 +W q Among them, x q,k represents the motion state vector of target q at time k; x q,k-1 represents the motion state vector of target q at time k-1; F represents the state transfer matrix of target q; W q represents zero-mean Gaussian white noise.

3. The distributed radar alliance game power allocation method based on multi-target tracking according to claim 1 is characterized in that: The radar measurement model for the target constructed in step S2 is: Among them, z m,q,k represents the measurement vector of radar m to target q at time k; h m (x q,k ) represents a nonlinear transfer function including the target's angle information and the target's distance information; v m,q,k represents the measurement error of the distance and azimuth between radar m and target q at time k; ρ m,q,k represents the radar-target selection situation, ρ m,q,k ∈{0,1}, when ρ m,q,k =1, it means that radar m selects to track target q at time k and joins it. m,q,k =0, it means that radar m does not choose to join the alliance tracking target q at time k.

4. The distributed radar alliance game power allocation method based on multi-target tracking according to claim 3 is characterized in that: The measurement error v of the distance and azimuth between radar m and target q at time k is m,q,k The mean of G is zero and its covariance is G m,q,k It is expressed as: in, and Respectively represent R m,q,k and θ m,q,k The lower bound of the estimated mean square error; R m,q,k represents the distance between radar m and target q at time k; θ m,q,k represents the azimuth between radar m and target q at time k; and The signal-to-noise ratio (SNR) of the echo between radar m and target q at time k is m,q,k The relationship between them is expressed as: Among them, β m,q,k represents the bandwidth of the signal transmitted by radar m to target q at time k; θ W Indicates the width of the 3dB receiving beam; SNR m,q,k The expression is: Where, T represents the radar dwell time; T r represents the radar pulse repetition period; p m,q,k G represents the radiation power of radar m to target q at time k; t and G r Respectively represent the radar's transmitting antenna gain and receiving antenna gain; σ m,q,k represents the radar cross section (RCS) of radar m to target q at time k; λ is the wavelength of the radar transmission signal; G RP represents the processing gain of the radar receiver; k B is the Boltzmann constant; T o is the noise temperature of the radar receiver; B r Indicates the bandwidth of the radar receiver matched filter; F r Represents the noise factor of the radar receiver; R m,q,k represents the distance between radar m and target q at time k.

5. The distributed radar alliance game power allocation method based on multi-target tracking according to claim 1 is characterized in that: The RF stealth performance measurement index constructed in step S3 is expressed as: Among them, u k (p m,q,k ) represents the RF stealth performance indicator of the networked radar system at time k; p m,q,k represents the radiation power of radar m to target q at time k; Q represents the total number of targets that the networked radar system needs to track; represents the target tracking accuracy threshold preset for target q, η q,k represents the target tracking accuracy for target q at time k; D represents the pricing variable related to target tracking performance, and D>0; δ represents the pricing variable related to radar radiation power; M represents the number of radars that make up the networked radar system; ρ m,q,k represents the selection of target q by radar m at time k; p max is the maximum radiated power of the radar in the networked radar system; Target tracking accuracy η q,k It is expressed as: Among them, B q,k (1,1) and B q,k (3,3) represent the matrix B q,k The element corresponding to the target distance estimation accuracy; B q,k represents the predicted Bayesian Cramer-Rao lower bound (BCRLB) matrix for the target q at time k.

6. The distributed radar alliance game power allocation method based on multi-target tracking according to claim 1 is characterized in that: The specific steps of solving the optimization model in step S5 in combination with the SQP algorithm are: (1) Let k = 1 and initialize the estimated motion state vector of each target at time k-1 and the target motion state estimation error covariance matrix P q,k-1|k-1 ; (2) The EKF algorithm is used to predict the state of the target q at time k, and the result is: P q,k|k-1 =FP q,k-1|k-1 F T +U q in, represents the state prediction value of target q at time k; F represents the state transfer matrix of target q; P q,k|k-1 represents the predicted value of the motion state estimation error covariance matrix of the target q at time k; U q represents the Gaussian white noise W in the target q motion model q The covariance matrix of T represents the transposed matrix of F; (3) Initialize the radiation power of each radar to be the same, and use the SQP algorithm to solve the optimization model, with the goal of maximizing the RF stealth performance measurement index at time k, to obtain the optimal alliance structure at the current moment: i) Initialization: The optimization starting point is set to A0 = ρ m,k,q , the Lagrange multiplier is initialized and the iteration factor is set to The termination index of the Lagrangian algorithm is set to ε>0; ii) Construct and solve the quadratic model: perform Taylor series expansion on the optimization objective function and constraints; at the current optimization iteration point Nearby, A represents the optimization variable to be solved, and a quadratic model about the variable Υ is constructed to approximate the original problem: Where E represents the matrix composed of the first-order partial derivatives of the objective function, E T represents the transposed matrix of E, Represents the matrix composed of the second-order partial derivatives of the objective function, Υ T represents the transposed matrix of Y; iii) Update the optimization iteration point: The result of solving the quadratic subproblem Υ * As the next search direction Update to get the optimized iteration point iv) Check the termination condition: check whether the objective function converges or the gradient is less than the algorithm termination indicator ε; if the condition is met, the algorithm terminates; otherwise, continue to the next iteration; update the Lagrange multiplier, iteration factor And return to step ii); v) Output: Radar's selection of target ρ m,q,k ; (4) Under the alliance structure obtained in step (3), the goal is to maximize the RF stealth performance indicator at time k, and the SQP algorithm is combined to solve the optimization model to obtain the optimal power allocation solution at the current time, and obtain the measurement information z of the target q m,q,k ; (5) Using the EKF algorithm to update the state of the target q at time k, we get: Among them, S q,k represents the innovation covariance matrix; K q,k represents the Kalman gain matrix; H q,k express The Jacobian matrix of q,k|k-1 Indicates h m (x q,k ) in the predicted state The first derivative at P q,k|k-1 represents the predicted value of the motion state estimation error covariance matrix of the target q at time k; G q,k The measurement error v in the radar measurement model of target q is m,q,k The covariance matrix of Represents the state update value of the target q at time k; represents the state prediction value of the target q at time k; z q,k represents the measured value of the target q at time k; Indicates h m (x q,k )exist The value at P q,k|k Represents the updated value of the motion state estimation error covariance matrix of the target q at time k; (6) Let k=k+1 and jump to step (2).

7. A distributed radar alliance game power allocation system based on multi-target tracking, characterized in that: include: A target motion model building unit, used for building a target motion model; A measurement model building unit, used to build a radar measurement model of a target; An indicator construction unit, used to construct a measurement index of radio frequency stealth performance and a measurement index of target tracking accuracy with multi-target tracking performance, alliance structure and total radiated power of networked radar system as variables; The optimization model building unit is used to establish a distributed radar alliance game power allocation optimization model based on multi-target tracking, taking the given multi-target tracking performance and RF resource restrictions as constraints and maximizing the networked radar RF stealth performance measurement index as the optimization goal; the model expression is: max u k (p m,q,k ) Among them, η q,k represents the target tracking accuracy for target q at time k; represents the target tracking accuracy threshold preset for target q; p min represents the minimum value of single radar radiation power; p max Represents the maximum radiated power of the radar in the networked radar system; ρ m,q,k represents the selection of target q by radar m at time k; M q Indicates the number of radars that track a single target; M indicates the number of radars that make up the networked radar system; Q indicates the total number of targets that the networked radar system needs to track; The optimization model solving unit is used to solve the distributed radar alliance game power allocation optimization model based on multi-target tracking established in step S4 in combination with the SQP algorithm; including: initializing the target motion state; using the EKF algorithm to predict the state of the target; initializing the radiation power of each radar to be the same, combining the SQP algorithm to solve the optimization model, with the goal of maximizing the radio frequency stealth performance measurement index, and obtaining the optimal alliance structure at the current moment; under the obtained optimal alliance structure, also with the goal of maximizing the radio frequency stealth performance measurement index, combining the SQP algorithm to solve the optimization model, obtain the optimal power allocation plan at the current moment, and obtain the measurement information of the target; using the EKF algorithm to update the state of the target; until the results at each moment are obtained.

8. An electronic device, characterized in that: The device comprises: A memory storing executable program code; a processor coupled to the memory; The processor calls the executable program code stored in the memory to execute the steps of the distributed radar alliance game power allocation method based on multi-target tracking as described in any one of claims 1-6.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, which, when called, are used to execute the steps of the distributed radar alliance game power allocation method based on multi-target tracking as described in any one of claims 1 to 6.

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