Joint optimization method of detection threshold and radio frequency resources for networked radar under multi-target tracking

Abstract

The present invention discloses a joint optimization method for networked radar detection threshold and radio frequency resources under multi-target tracking, including: constructing a target motion model; constructing a target detection performance measurement index with radar radiation power, signal bandwidth and detection threshold as optimization variables; constructing a multi-target tracking performance measurement index with radar beam selection results, detection threshold, radiation power and signal bandwidth as optimization variables; establishing a joint optimization model for networked radar detection threshold and radio frequency resources under multi-target tracking; combining the SDP algorithm and the SQP algorithm to solve the joint optimization model for networked radar detection threshold and radio frequency resources under multi-target tracking. The present invention realizes the optimal networked radar beam allocation, detection threshold, radiation power and signal bandwidth optimization allocation, and effectively improves the radio frequency stealth performance of the networked radar.

Description

Technical Field

[0001] The present invention relates to radar signal processing technology, and in particular to a method for jointly optimizing a networked radar detection threshold and radio frequency resources under multi-target tracking. Background Art

[0002] In a complex battlefield environment, single-base radars have a small detection range and are difficult to achieve flexible radiation resource management, so the role they can play and the functions they can achieve are very limited. Compared with traditional single-base radars, networked radars can extract target feature information from different perspectives and dimensions, and have a wider detection area, which can fully obtain the battlefield environment situation. Through the allocation of radiation resources and the fusion processing of measurement data from multiple radars, it can efficiently perform multiple tasks, suppress interference, and effectively combat dense clutter environments and fluctuations in target radar scattering cross sections, etc., and has significant advantages in applications such as target search, detection, identification, and tracking.

[0003] In practical applications, the higher the radar radiation energy, the better the target detection and tracking performance. However, the radar's RF resources are limited. If it continues to radiate into space at maximum energy, it will not only lead to a large amount of resource consumption, but also greatly increase the probability of being discovered by the enemy's passive detection system, reducing the RF stealth performance of its own equipment. Therefore, the balance between radar RF radiation resource consumption and detection and tracking performance optimization is crucial.

[0004] At present, networked radar resource allocation under multi-target tracking has become a research hotspot, and many scholars at home and abroad have achieved remarkable results in this regard. However, most of the existing studies aim to optimize tracking performance, but fail to consider the joint optimization of RF stealth performance and other radar radiation parameters. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a method for jointly optimizing the detection threshold and radio frequency resources of a networked radar under multi-target tracking, so as to achieve the purpose of improving the radio frequency stealth performance of the networked radar.

[0006] Technical solution: The method for jointly optimizing the detection threshold and radio frequency resources of networked radar under multi-target tracking of the present invention comprises the following steps:

[0007] S1, build target motion model;

[0008] S2, constructing a target detection performance measurement index with radar radiation power, signal bandwidth and detection threshold as optimization variables;

[0009] S3, construct a multi-target tracking performance measurement index with radar beam selection results, detection threshold, radiation power and signal bandwidth as optimization variables;

[0010] S4. Taking the given target detection probability, multi-target tracking accuracy and RF resource limitation as constraints, and minimizing the total radiated power resource consumption of the networked radar as the optimization goal, a joint optimization model of networked radar detection threshold and RF resources under multi-target tracking is established;

[0011] S5. Combining the semi-definite programming (SDP) algorithm and the sequential quadratic programming (SQP) algorithm, the joint optimization model of the networked radar detection threshold and the radio frequency resource under the multi-target tracking established in step S4 is solved; including: firstly, the optimization model is decomposed into the optimization model of the networked radar beam selection result under the multi-target tracking and the joint optimization model of the networked radar detection threshold and the power bandwidth under the multi-target tracking; combining the SDP algorithm to solve the optimization model of the networked radar beam selection result under the multi-target tracking; combining the SQP algorithm to solve the joint optimization model of the networked radar detection threshold and the power bandwidth under the multi-target tracking; finally, the optimization result is output.

[0012] Furthermore, the target detection performance measurement index constructed in step S2 with radar radiation power, signal bandwidth and detection threshold as optimization variables is:

[0013]

[0014] in, V is the performance indicator of radar i for target n at time k, i,n,k represents the gate area, η i,n,k Represents the radar detection threshold, P i,n,k represents the radiation power of radar i to target n at time k, B i,n,k represents the bandwidth of the signal transmitted by radar i to target n at time k, represents the state measurement value of radar i to target n at time k, represents the detection probability within the resolution unit l, Represents the probability density function of the target state measurement value prediction, SNR i,n,k represents the signal-to-noise ratio of the radar i to the target n echo at time k, ξ i,n,k =(1+SNR i,n,k ) / SNR i,n,k , ν represents the spatial dimension, E i,n,k|k-1 Represents the target state measurement prediction value and state measurements The covariance between .

[0015] Furthermore, the target echo signal-to-noise ratio SNR i,n,k It is expressed as:

[0016]

[0017] Where T0 is the dwell time, T1 is the pulse repetition period, G t and G r They represent the transmit antenna and receive antenna gains respectively, λ represents the radar signal wavelength, G rp represents the receiver processing gain, s i,n,k represents the radar cross section (RCS) of radar i to target n at time k, k B represents the Boltzmann constant, T e represents the thermodynamic temperature, F r Represents the noise figure of the receiver, R i,n,k represents the distance between radar i and target n at time k.

[0018] Furthermore, the multi-target tracking performance measurement index constructed in step S3 with radar beam selection result, detection threshold, radiation power and signal bandwidth as optimization variables is:

[0019]

[0020] in, represents the radar target detection performance measurement index, represents the tracking accuracy of the radar to the target n, μ i,n,k represents the radar beam selection result, η i,n,k Represents the radar detection threshold, P i,n,k represents the radiation power of radar i to target n at time k, B i,n,k It represents the bandwidth of the signal transmitted by radar i to target n at time k, and N represents the total number of targets.

[0021] Furthermore, the radar's tracking accuracy for target n Specifically:

[0022] make To characterize the tracking accuracy of target n, where C n,k|k-1 represents the predicted Bayesian Cramer-Rao lower bound (BCRLB) matrix, C n,k|k-1 The diagonal elements C n,k|k-1 (1,1) and C n,k|k-1 (3,3) represents the lower bound of the mean square error of the predicted target position and velocity estimation, C n,k|k-1 The expression is:

[0023]

[0024] in,{·} -1 represents the inverse operation of the matrix, F represents the state transfer matrix of the target, and F T represents the transposed matrix of F, X n,k-1 represents the motion model of target n at time k-1, J(X n,k-1) represents the Bayesian information matrix, J -1 (X n,k-1 ) represents the inverse operation of the Bayesian information matrix, COV n represents the covariance of Gaussian noise, H i,n,k|k-1 represents the Jacobian matrix, Indicates H i,n,k|k-1 The transposed matrix, G i,n,k|k-1 represents the predicted value of the measurement noise covariance, Represents G i,n,k|k-1 is the inverse operation of , where I represents the total number of radars.

[0025] Furthermore, the joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking established in step S4 is:

[0026]

[0027]

[0028] Among them, W max Indicates the upper limit of the beam generated by a single radar, U max represents the upper limit of the number of times a single target is illuminated by the radar, η max and η min Respectively represent the upper and lower limits of the detection threshold; P max and P min Respectively represent the upper and lower limits of the radiation power of each radar to a single target, P total Indicates the upper limit of the total radiated power of a single radar; B max and B min They represent the upper and lower limits of the bandwidth of the signal transmitted by each radar to a single target, B total Represents the upper limit of the total signal bandwidth of a single radar, P D,min represents the minimum acceptable average target detection probability, represents the worst acceptable multi-target tracking accuracy, N represents the total number of targets, and I represents the total number of radars.

[0029] Furthermore, step S5 is specifically as follows:

[0030] (1) The joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking is decomposed into a networked radar beam selection result optimization model under multi-target tracking and a joint optimization model of networked radar detection threshold and power bandwidth under multi-target tracking;

[0031] The optimization model of networked radar beam selection results under multi-target tracking is expressed as:

[0032]

[0033]

[0034] The joint optimization model of networked radar detection threshold and power bandwidth under multi-target tracking is expressed as:

[0035]

[0036]

[0037] in, and represents the uniform distribution of radar detection threshold, radiation power and signal bandwidth, and They represent the mean values ​​of radar detection threshold, radiation power and signal bandwidth at time k respectively;

[0038] (2) The semi-definite programming (SDP) algorithm is used to solve the optimization model of networked radar beam selection results under multi-target tracking:

[0039] i) Combined with Schur's complement lemma, it can be transformed into an equivalent SDP problem:

[0040]

[0041]

[0042] in, trace(·) represents the matrix trace operation, I4 represents the 4×4 identity matrix, A n represents the auxiliary matrix of the alternative optimization objective function, N represents the total number of objectives,;

[0043] ii) Solve the optimization result of the weight coefficient representing the matching between the radar beam and the target

[0044]

[0045] in, for For the elements in, i=1,2,…,I, n=1,2,…,N;

[0046] iii) The largest first U of the I elements in each column max Set the elements to 1 and the rest to 0 to generate the beam allocation matrix

[0047] iv) The largest first W of the N elements in each row max Set the elements to 1 and the rest to 0 to generate the beam allocation matrix

[0048] v) The matrix and All the elements at the corresponding positions of and Perform logical AND operation to obtain the final radar beam selection result μ i,n,k ;

[0049] (3) Combined with the sequential quadratic programming (SQP) algorithm, the joint optimization model of networked radar detection threshold and power bandwidth under multi-target tracking is solved:

[0050] i) Initialization: Setting the optimization starting point and Respectively represent the initial radar detection threshold, radiation power and signal bandwidth, set the iteration factor Initialize the Lagrange multiplier and set the algorithm termination indicator ε>0;

[0051] ii) Construct and solve the quadratic model: perform Taylor series expansion on the objective function and constraints. Nearby, Construct a quadratic model about the variables S to approximate the original problem: in, and Respectively represent the radar detection threshold, radiation power and signal bandwidth of the current iteration point, X = [η i,n,k ,P i,n,k ,B i,n,k ], is the matrix composed of the second-order partial derivatives of the objective function, C is the matrix composed of the first-order partial derivatives, S T is the transposed matrix of S, C T is the transposed matrix of C;

[0052] iii) Update the iteration point: Update the result S of the solved quadratic subproblem * As the next search direction of the original problem Update iteration point

[0053] iv) Check the termination condition: check whether the objective function converges or the gradient is less than the algorithm termination indicator ε; if it is satisfied, the algorithm terminates; otherwise, execute the next iteration: update the Lagrange multiplier and increase the iteration factor Return to step ii);

[0054] v) Output: Detection threshold η i,n,k , radiated power P i,n,k and signal bandwidth B i,n,k .

[0055] The networked radar detection threshold and radio frequency resource joint optimization system under multi-target tracking of the present invention comprises:

[0056] A target motion model building unit, used for building a target motion model;

[0057] A target detection performance measurement index construction unit is used to construct a target detection performance measurement index with radar radiation power, signal bandwidth and detection threshold as optimization variables;

[0058] A multi-target tracking performance measurement index construction unit is used to construct a multi-target tracking performance measurement index with radar beam selection results, detection threshold, radiation power and signal bandwidth as optimization variables;

[0059] The optimization model building unit is used to establish a joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking, taking given target detection probability and multi-target tracking accuracy and radio frequency resource limitation as constraints, and minimizing the total radiated power resource consumption of the networked radar as the optimization goal;

[0060] The optimization model solving unit is used to solve the joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking established in the optimization model building unit by combining the semi-definite programming (SDP) algorithm and the sequential quadratic programming (SQP) algorithm; including: firstly decomposing the optimization model into an optimization model of networked radar beam selection results under multi-target tracking and an optimization model of networked radar detection threshold and power bandwidth joint optimization under multi-target tracking; combining the SDP algorithm to solve the optimization model of networked radar beam selection results under multi-target tracking; combining the SQP algorithm to solve the optimization model of networked radar detection threshold and power bandwidth joint optimization under multi-target tracking; and finally outputting the optimization result.

[0061] An electronic device of the present invention comprises:

[0062] A memory storing executable program code;

[0063] a processor coupled to the memory;

[0064] The processor calls the executable program code stored in the memory to execute the steps of the method for jointly optimizing the detection threshold and radio frequency resources of the networked radar under multi-target tracking as described above.

[0065] A computer-readable storage medium of the present invention stores computer instructions, which, when called, are used to execute the steps of the method for jointly optimizing the detection threshold and radio frequency resources of a networked radar under multi-target tracking as described above.

[0066] Beneficial effects: Compared with the prior art, the advantages of the present invention are:

[0067] (1) The present invention minimizes the total radiation power resource consumption of the networked radar by jointly optimizing the networked radar beam allocation, detection threshold, radiation power and signal bandwidth under the given constraints of target detection probability, multi-target tracking accuracy and radio frequency resource limitation. The reason for this advantage is that a joint optimization method of networked radar detection threshold and radio frequency resource under multi-target tracking is adopted. The method constructs an evaluation index characterizing target detection performance and an evaluation index characterizing multi-target tracking performance. At the same time, the networked radar beam allocation, detection threshold, radiation power and signal bandwidth will also affect the index. On this basis, with the given target detection probability and multi-target tracking accuracy and radio frequency resource limitation as the constraints, and minimizing the total radiation power resource consumption of the networked radar as the optimization goal, a joint optimization model of networked radar detection threshold and radio frequency resource under multi-target tracking is established, and the networked radar beam allocation, detection threshold, radiation power and signal bandwidth are adaptively optimized to achieve the purpose of improving the radio frequency stealth performance of the networked radar.

[0068] (2) The method for jointly optimizing the detection threshold and radio frequency resources of networked radar under multi-target tracking proposed in the present invention realizes the optimal allocation of networked radar beam, detection threshold, radiation power and signal bandwidth, and effectively improves the radio frequency stealth performance of networked radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is a flow chart of the joint optimization method of networked radar detection threshold and radio frequency resources under multi-target tracking;

[0070] Figure 2 It is the movement trajectory of multiple targets and the location distribution map of networked radar;

[0071] Figure 3 The network radar is used to optimize the detection threshold and radio frequency resources of target 1;

[0072] Figure 4 The network radar is used to optimize the detection threshold and radio frequency resources of target 2;

[0073] Figure 5 Optimize the detection threshold and radio frequency resources of target 3 for networked radar;

[0074] Figure 6 Optimize the detection threshold and radio frequency resources of target 4 for networked radar;

[0075] Figure 7 It is the target tracking error result of networked radar;

[0076] Figure 8 Comparison results of total radiated power consumption under different methods. DETAILED DESCRIPTION

[0077] The structure and working process of the present invention are further described below in conjunction with the accompanying drawings and specific embodiments.

[0078] There is no joint optimization method for the detection threshold and radio frequency resources of networked radar under multi-target tracking in the prior art, and from the perspective of improving the radio frequency stealth performance of networked radar, it is of great significance to carry out research on the detection threshold and radio frequency resource control method of networked radar under multi-target tracking. Starting from the actual combat scenario, the present invention proposes a joint optimization method for the detection threshold and radio frequency resources of networked radar under multi-target tracking. Under the constraints of given target detection probability, multi-target tracking accuracy and radio frequency resource limitation, the total radiation power resource consumption of the networked radar is minimized as the optimization goal, and the networked radar beam allocation, detection threshold, radiation power and signal bandwidth are adaptively optimized and designed, thereby improving the radio frequency stealth performance of the networked radar. The main task accomplished by this method is to consider a phased array networked radar with multi-beam transmission capability to track multiple moving targets dispersed in space. First, a phased array networked radar with multi-beam transmission capability is considered to track multiple moving targets dispersed in space. Then, under the condition of adopting the closed-loop architecture of integrated detection and tracking, the target detection probability is derived as the measurement index of target detection performance, and the BCRLB is derived as the measurement index of multi-target tracking performance. Finally, with the given target detection probability, multi-target tracking accuracy and RF resource limitation as constraints, and minimizing the total radiated power resource consumption of the networked radar as the optimization goal, a joint optimization model of networked radar detection threshold and RF resources under multi-target tracking is established, and the networked radar beam allocation, detection threshold, radiated power and signal bandwidth are jointly optimized to achieve the purpose of improving the RF stealth performance of the networked radar.

[0079] like Figure 1 As shown, the method for jointly optimizing the detection threshold and radio frequency resources of networked radar under multi-target tracking of the present invention comprises the following steps:

[0080] S1. Construct the motion model of target n at time k, as shown in formula (1):

[0081] X n,k =FX n,k-1 +N n (1)

[0082] Among them, X n,k represents the motion model of target n at time k, F represents the state transfer matrix of the target, X n,k-1 represents the motion model of target n at time k-1, Nn represents Gaussian process white noise.

[0083] S2. Construct a target detection performance measurement index with radar radiation power, signal bandwidth and detection threshold as optimization variables, as shown in formula (2):

[0084]

[0085] in, V is the performance indicator of radar i for target n at time k, i,n,k represents the gate area, η i,n,k Represents the radar detection threshold, P i,n,k represents the radiation power of radar i to target n at time k, B i,n,k represents the bandwidth of the signal transmitted by radar i to target n at time k, represents the state measurement value of radar i to target n at time k, represents the detection probability within the resolution unit l, Represents the probability density function of the target state measurement value prediction, SNR i,n,k represents the signal-to-noise ratio of the radar i to the target n echo at time k, ξ i,n,k =(1+SNR i,n,k ) / SNR i,n,k , ν represents the spatial dimension, E i,n,k|k-1 Represents the target state measurement prediction value and state measurements The covariance between .

[0086] In formula (2), the target echo signal-to-noise ratio SNR i,n,k It is expressed as:

[0087]

[0088] Where T0 is the dwell time, T1 is the pulse repetition period, G t and G r They represent the transmit antenna and receive antenna gains respectively, λ represents the radar signal wavelength, G rp represents the receiver processing gain, s i,n,k represents the radar cross section (RCS) of radar i to target n at time k, k B represents the Boltzmann constant, T e represents the thermodynamic temperature, F r Represents the noise figure of the receiver, R i,n,k represents the distance between radar i and target n at time k.

[0089] S3. Construct a multi-target tracking performance measurement index with radar beam selection results, detection threshold, radiation power and signal bandwidth as optimization variables, as shown in formula (4):

[0090]

[0091] in, represents the radar target detection performance measurement index, represents the tracking accuracy of the radar to the target n, μ i,n,k represents the radar beam selection result, η i,n,k Represents the radar detection threshold, P i,n,k represents the radiation power of radar i to target n at time k, B i,n,k It represents the bandwidth of the signal transmitted by radar i to target n at time k, and N represents the total number of targets.

[0092] The specific explanations of the parameters in the multi-target tracking performance measurement indicators are as follows:

[0093] make To characterize the tracking accuracy of target n. n,k|k-1 represents the predicted Bayesian Cramér-Rao Lower Bound (BCRLB) matrix, C n,k|k-1 The diagonal elements C n,k|k-1 (1,1) and C n,k|k-1 (3,3) represents the lower bound of the mean square error of the predicted target position and velocity estimation, C n,k|k-1 The expression of is shown in formula (5):

[0094]

[0095] in,{·} -1 represents the inverse operation of the matrix, F represents the state transfer matrix of the target, FT represents the transposed matrix of F, Xn,k-1 represents the motion model of target n at time k-1, J(X n,k-1 ) represents the Bayesian information matrix, J -1 (X n,k-1 ) represents the inverse operation of the Bayesian information matrix, COV n represents the covariance of Gaussian noise, H i,n,k|k-1 represents the Jacobian matrix, Indicates H i,n,k|k-1 The transposed matrix, G i,n,k|k-1 represents the predicted value of the measurement noise covariance, Represents G i,n,k|k-1 is the inverse operation of , where I represents the total number of radars.

[0096] S4. Establish a joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking:

[0097] Taking the given target detection probability, multi-target tracking accuracy and RF resource limitation as constraints, and minimizing the total radiated power resource consumption of the networked radar as the optimization goal, a joint optimization model of networked radar detection threshold and RF resources under multi-target tracking is established, as shown in formula (6):

[0098]

[0099] Among them, W max Indicates the upper limit of the beam generated by a single radar, U max represents the upper limit of the number of times a single target is illuminated by the radar, η max and η min Respectively represent the upper and lower limits of the detection threshold; P max and P min Respectively represent the upper and lower limits of the radiation power of each radar to a single target, P total Indicates the upper limit of the total radiated power of a single radar; B max and B min They represent the upper and lower limits of the bandwidth of the signal transmitted by each radar to a single target, B total Represents the upper limit of the total signal bandwidth of a single radar, P D,min represents the minimum acceptable average target detection probability, represents the worst acceptable multi-target tracking accuracy, N represents the total number of targets, and I represents the total number of radars.

[0100] The first constraint in the optimization model (6) states that each radar can generate at most W max beams, each used to illuminate a different target, and each target needs to be illuminated by U at most max The second constraint condition represents the radar beam selection result μ i,n,k is a binary variable; the third constraint represents the value range of each radar detection threshold; the fourth constraint represents the value range of each radar radiation power and the upper limit of the total power allocated to the illuminated target; the fifth constraint represents the value range of each radar transmission signal bandwidth and the upper limit of the total bandwidth allocated to the illuminated target; the sixth constraint represents the target detection probability and the threshold requirement of multi-target tracking accuracy.

[0101] S5. Combining the Semi-definite Programming (SDP) algorithm and the Sequential Quadratic Programming (SQP) algorithm, the optimization model (6) is solved in three steps:

[0102] Step 1: Decompose the optimization model (6) into the optimization model of the networked radar beam selection result under multi-target tracking and the joint optimization model of the networked radar detection threshold and power bandwidth under multi-target tracking:

[0103]

[0104]

[0105] in, and represents the uniform distribution of radar detection threshold, radiation power and signal bandwidth, and They represent the mean values ​​of radar detection threshold, radiation power and signal bandwidth at time k respectively.

[0106] Step 2: Solve the optimization model (7) by combining the semi-definite programming (SDP) algorithm:

[0107] i) Combined with Schur's complement lemma, it can be transformed into an equivalent SDP problem:

[0108]

[0109] in, trace(·) represents the matrix trace operation, I4 represents the 4×4 identity matrix, A n The auxiliary matrix representing the alternative optimization objective function;

[0110] ii) Use the CVX toolbox to solve the optimization results of the weight coefficients that represent the matching between the radar beam and the target

[0111]

[0112] in, for In the element, i=1,2,…,I, n=1,2,…,N.

[0113] iii) The largest first U of the I elements in each column max Set the elements to 1 and the rest to 0 to generate the beam allocation matrix

[0114] iv) The largest first W of the N elements in each row max Set the elements to 1 and the rest to 0 to generate the beam allocation matrix

[0115] v) The matrix and All the elements at the corresponding positions of and Perform logical AND operation to obtain the final radar beam selection result μ i,n,k .

[0116] Step 3: Solve the optimization model (8) using the Sequential Quadratic Programming (SQP) algorithm:

[0117] i) Initialization: Setting the optimization starting point and Respectively represent the initial radar detection threshold, radiation power and signal bandwidth, set the iteration factor Initialize the Lagrange multiplier and set the algorithm termination indicator ε>0;

[0118] ii) Construct and solve the quadratic model: perform Taylor series expansion on the objective function and constraints. Nearby, Construct a quadratic model about the variables S to approximate the original problem: in, and Respectively represent the radar detection threshold, radiation power and signal bandwidth of the current iteration point, X = [η i,n,k ,P i,n,k ,B i,n,k ], is the matrix composed of the second-order partial derivatives of the objective function, C is the matrix composed of the first-order partial derivatives, S T is the transposed matrix of S, C T is the transposed matrix of C;

[0119] iii) Update the iteration point: Update the result S of the solved quadratic subproblem * As the next search direction of the original problem Update iteration point

[0120] iv) Check the termination condition: Check whether the objective function converges or the gradient is less than the algorithm termination indicator ε. If it is satisfied, the algorithm terminates; otherwise, execute the next iteration: update the Lagrange multiplier and increase the iteration factor Return to step ii);

[0121] v) Output: Detection threshold η i,n,k , radiated power P i,n,k and signal bandwidth B i,n,k .

[0122] Simulation results:

[0123] In order to verify the feasibility and superiority of the method proposed in the present invention, the following simulation scenario is designed: Consider a networked radar consisting of I = 3 phased array radars, each of which can generate at most W max = 3 beams. There are N = 4 moving targets in the space that need to be tracked, and each target needs to be tracked by U at most max = 2 radars tracking. The RCS of each target relative to each radar is 1m at all times 2 The wavelength of the signal transmitted by each radar is λ = 0.02m, and the detection threshold value range is η min = 0.03 to η max =6; the upper and lower limits of the power radiated by irradiating a single target are P max =8kW and P min =0.8kW, the total radiation power consumed by irradiating each target does not exceed P total =10kW; the upper and lower limits of the bandwidth of the signal transmitted to a single target are B max =8MHz and B min =0.8MHz, the total bandwidth required to illuminate each target does not exceed B total =10MHz. The lower limit of the average detection probability for each target is P Dmin = 0.92, the upper limit of the sum of all target tracking errors 20 consecutive frames of simulation data are used, the sampling interval is T0 = 3s, and M = 100 Monte Carlo experiments are performed.

[0124] The distribution of networked radars and target movement trajectories are as follows: Figure 2 As shown, the initial target motion state parameters are shown in Table 1:

[0125] Table 1 Initial target motion state parameters

[0126]

[0127] Figures 3 to 6 The beam allocation, detection threshold and power bandwidth optimization results of the networked radar for four targets are given respectively, and it can be seen that the beam allocation results in this scenario are relatively stable. Figure 2 Analysis shows that at the beginning of the simulation, target 4 is located at the most remote position. Considering the constraints of the overall multi-target tracking accuracy requirements, in order to make the tracking error converge as quickly as possible, the networked radar chooses to observe target 4 by radar 2 and radar 3, which are closest to target 4. During the simulation, target 1 and target 2 are mainly observed by radar 1 and radar 2, which are closer; similarly, target 3 is mainly observed by radar 1 and radar 3, which are closer. Figure 7The tracking errors of each target are given, and it can be seen that the proposed methods have achieved high tracking accuracy.

[0128] After comparative analysis, it can be seen that in this scenario, the distance between the radar and the target is the main factor affecting the beam allocation result. Most radars tend to select closer targets for detection and tracking. Among the radars illuminating the same target, when the tracking accuracy meets the requirements, in order to reduce false alarms, the radars at a longer distance have higher detection thresholds. In addition, the change in the bandwidth of the transmitted signal is far less obvious than the detection threshold and the radiation power. Radar 2 and Radar 3 allocate roughly equal power bandwidth resources to the distant target 4; while Radar 1 and Radar 2 allocate more power and bandwidth resources to target 1 and target 2 respectively than Radar 3. In this way, the spatial position advantages of Radar 1 and Radar 2 can be fully utilized to minimize the tracking error of closer targets.

[0129] In order to verify the superiority of the method proposed in this paper, it is compared with three other methods, namely:

[0130] Method 1: Adopting an integrated closed-loop architecture of detection and tracking, keeping the detection threshold constant, and jointly optimizing the beam allocation mode, radiation power, and signal bandwidth allocation of the networked radar;

[0131] Method 2: Adopting an integrated closed-loop architecture of detection and tracking, keeping the radar transmission signal bandwidth constant, and jointly optimizing the networked radar beam allocation method, detection threshold, and radiation power;

[0132] Method 3: Using the traditional probabilistic data association (PDA) method under the open-loop tracking structure, the detection threshold is kept constant and the beam allocation method, radiation power and signal bandwidth of the networked radar are jointly optimized.

[0133] The comparison results are as follows Figure 8 As shown in the figure, it can be seen that under the condition of ensuring a certain target detection probability and multi-target tracking accuracy, the proposed method can minimize the radiation power resources consumed by the networked radar, that is, the radar's RF stealth performance is optimal.

[0134] The working principle and working process of the invention are as follows:

[0135] The present invention considers a phased array networked radar with multi-beam transmission capability to track multiple moving targets dispersed in space. First, under the condition of adopting an integrated closed-loop architecture of detection and tracking, the target detection probability is derived as a measure of target detection performance, and BCRLB is derived as a measure of multi-target tracking performance. Then, with the given target detection probability, multi-target tracking accuracy and radio frequency resource restrictions as constraints, and minimizing the total radiated power resource consumption of the networked radar as the optimization goal, a joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking is established. Finally, the SDP algorithm and the SQP algorithm are used to solve the optimization model. By solving the optimization model, the radar beam selection result μ that maximizes the radio frequency stealth performance of the networked radar under the given target detection probability, multi-target tracking accuracy and radio frequency resource restrictions as constraints is obtained. i,n,k , detection threshold η i,n,k , radiated power P i,n,k And the transmission signal bandwidth B i,n,k is the optimal solution of the model.

[0136] The invention of the present invention:

[0137] The present invention assumes that several targets are dispersed in space, and considers a networked radar system composed of multiple phased array radars with multi-beam transmission capability to track the targets. For the scenario of networked radar tracking multiple targets, under the condition of adopting the detection and tracking integrated closed-loop architecture, the radar transmission signal bandwidth and radiation power are used as optimization variables to construct the target detection probability as the target detection performance measurement index, and the radar beam selection result, detection threshold, radiation power and transmission signal bandwidth are used as optimization variables to construct BCRLB as the multi-target tracking performance measurement index.

[0138] At the same time, the present invention takes the given target detection probability and multi-target tracking accuracy and radio frequency resource limitation as the constraint conditions, takes minimizing the total radiation power resource consumption of the networked radar as the optimization goal, and establishes a joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking. Finally, the SDP algorithm and SQP algorithm are used to solve the optimization model. By solving the optimization model, the radar beam selection result μ that maximizes the radio frequency stealth performance of the networked radar under the given target detection probability and multi-target tracking accuracy and radio frequency resource limitation as the constraint conditions is obtained. i,n,k , detection threshold η i,n,k , radiated power P i,n,k And the transmission signal bandwidth B i,n,k is the optimal solution of the model.

[0139] The networked radar detection threshold and radio frequency resource joint optimization system under multi-target tracking of the present invention comprises:

[0140] A target motion model building unit, used for building a target motion model;

[0141] A target detection performance measurement index construction unit is used to construct a target detection performance measurement index with radar radiation power, signal bandwidth and detection threshold as optimization variables;

[0142] A multi-target tracking performance measurement index construction unit is used to construct a multi-target tracking performance measurement index with radar beam selection results, detection threshold, radiation power and signal bandwidth as optimization variables;

[0143] The optimization model building unit is used to establish a joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking, taking given target detection probability and multi-target tracking accuracy and radio frequency resource limitation as constraints, and minimizing the total radiated power resource consumption of the networked radar as the optimization goal;

[0144] The optimization model solving unit is used to solve the joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking established in the optimization model building unit by combining the semi-definite programming (SDP) algorithm and the sequential quadratic programming (SQP) algorithm; including: firstly decomposing the optimization model into an optimization model of networked radar beam selection results under multi-target tracking and an optimization model of networked radar detection threshold and power bandwidth joint optimization under multi-target tracking; combining the SDP algorithm to solve the optimization model of networked radar beam selection results under multi-target tracking; combining the SQP algorithm to solve the optimization model of networked radar detection threshold and power bandwidth joint optimization under multi-target tracking; and finally outputting the optimization result.

[0145] An electronic device of the present invention comprises:

[0146] A memory storing executable program code;

[0147] a processor coupled to the memory;

[0148] The processor calls the executable program code stored in the memory to execute the steps of the method for jointly optimizing the detection threshold and radio frequency resources of the networked radar under multi-target tracking as described above.

[0149] A computer-readable storage medium of the present invention stores computer instructions, which, when called, are used to execute the steps of the method for jointly optimizing the detection threshold and radio frequency resources of a networked radar under multi-target tracking as described above.

Claims

1. A joint optimization method of networked radar detection threshold and radio frequency resources under multi-target tracking, characterized in that: The following steps are involved: S1, build target motion model; S2, constructing a target detection performance measurement index with radar radiation power, signal bandwidth and detection threshold as optimization variables; S3, construct a multi-target tracking performance measurement index with radar beam selection results, detection threshold, radiation power and signal bandwidth as optimization variables; S4. Taking the given target detection probability, multi-target tracking accuracy and RF resource limitation as constraints, and minimizing the total radiated power resource consumption of the networked radar as the optimization goal, a joint optimization model of networked radar detection threshold and RF resources under multi-target tracking is established; S5. Combining the semi-positive definite programming SDP algorithm and the sequential quadratic programming SQP algorithm, solving the joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking established in step S4; including: firstly decomposing the optimization model into a networked radar beam selection result optimization model under multi-target tracking and a networked radar detection threshold and power bandwidth joint optimization model under multi-target tracking; Combined with the SDP algorithm, the optimization model of the networked radar beam selection results under multi-target tracking is solved; combined with the SQP algorithm, the joint optimization model of the networked radar detection threshold and power bandwidth under multi-target tracking is solved; and finally the optimization results are output.

2. The method for joint optimization of networked radar detection threshold and radio frequency resources under multi-target tracking according to claim 1 is characterized in that: The target detection performance measurement index constructed in step S2 with radar radiation power, signal bandwidth and detection threshold as optimization variables is: in, V is the performance indicator of radar i for target n at time k, i,n,k represents the gate area, η i,n,k represents the radar detection threshold, P i,n,k represents the radiation power of radar i to target n at time k, B i,n,k represents the bandwidth of the signal transmitted by radar i to target n at time k, represents the state measurement value of radar i to target n at time k, represents the detection probability within the resolution unit l, Represents the probability density function of the target state measurement value prediction, SNR i,n,k represents the signal-to-noise ratio of the radar i to the target n echo at time k, ξ i,n,k =(1+SNR i,n,k ) / SNR i,n,k , ν represents the spatial dimension, E i,n,kk-1 Represents the target state measurement prediction value and state measurements The covariance between .

3. The method for joint optimization of networked radar detection threshold and radio frequency resources under multi-target tracking according to claim 2 is characterized in that: Target echo signal-to-noise ratio SNR i,n,k It is expressed as: Where T0 is the dwell time, T1 is the pulse repetition period, G t and G r They represent the transmit antenna and receive antenna gains respectively, λ represents the radar signal wavelength, G rp represents the receiver processing gain, s i,n,k represents the radar cross section RCS of radar i to target n at time k, k B represents the Boltzmann constant, T e represents the thermodynamic temperature, F r Represents the noise figure of the receiver, R i,n,k represents the distance between radar i and target n at time k.

4. The method for joint optimization of networked radar detection threshold and radio frequency resources under multi-target tracking according to claim 1 is characterized in that: The multi-target tracking performance measurement index constructed in step S3 with radar beam selection result, detection threshold, radiation power and signal bandwidth as optimization variables is: in, represents the radar target detection performance measurement index, represents the tracking accuracy of the radar to the target n, μ i,n,k represents the radar beam selection result, η i,n,k represents the radar detection threshold, P i,n,k represents the radiation power of radar i to target n at time k, B i,n,k It represents the bandwidth of the signal transmitted by radar i to target n at time k, and N represents the total number of targets.

5. The method for joint optimization of networked radar detection threshold and radio frequency resources under multi-target tracking according to claim 4 is characterized in that: The radar's tracking accuracy for target n Specifically: make To characterize the tracking accuracy of target n, where C n,k|k-1 represents the predicted Bayesian Cramer-Rao lower bound BCRLB matrix, C n,k|k-1 The diagonal elements C n,k|k-1 (1,1) and C n,k|k-1 (3,3) represents the lower bound of the mean square error of the predicted target position and velocity estimation, C n,k|k-1 The expression is: in,{·} -1 represents the inverse operation of the matrix, F represents the state transfer matrix of the target, and F T represents the transposed matrix of F, X n,k-1 represents the motion model of target n at time k-1, J(X n,k-1 ) represents the Bayesian information matrix, J -1 (X n,k-1 ) represents the inverse operation of the Bayesian information matrix, COV n represents the covariance of Gaussian noise, H represents the detection performance index of radar i to target n at time k, i,n,k|k-1 represents the Jacobian matrix, Indicates H i,n,k|k-1 The transposed matrix, G i,n,k|k-1 represents the predicted value of the measurement noise covariance, Represents G i,n,k|k-1 is the inverse operation of , where I represents the total number of radars.

6. The method for joint optimization of networked radar detection threshold and radio frequency resources under multi-target tracking according to claim 1 is characterized in that: The joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking established in step S4 is: Among them, μ i,n,k represents the radar beam selection result, η i,n,k represents the radar detection threshold, P i,n,k represents the radiation power of radar i to target n at time k, B i,n,k represents the bandwidth of the signal transmitted by radar i to target n at time k, represents the detection performance indicator of radar i to target n at time k, represents the radar target detection performance measurement index, W max Indicates the upper limit of the beam generated by a single radar, U max represents the upper limit of the number of times a single target is illuminated by the radar, η max and η min Respectively represent the upper and lower limits of the detection threshold; P max and P min Respectively represent the upper and lower limits of the radiation power of each radar to a single target, P total Indicates the upper limit of the total radiated power of a single radar; B max and B min They represent the upper and lower limits of the bandwidth of the signal transmitted by each radar to a single target, B total Represents the upper limit of the total signal bandwidth of a single radar, P D,min represents the minimum acceptable average target detection probability, represents the worst acceptable multi-target tracking accuracy, N represents the total number of targets, and I represents the total number of radars.

7. The method for joint optimization of networked radar detection threshold and radio frequency resources under multi-target tracking according to claim 1 is characterized in that: Step S5 is specifically as follows: (1) The joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking is decomposed into a networked radar beam selection result optimization model under multi-target tracking and a joint optimization model of networked radar detection threshold and power bandwidth under multi-target tracking; The optimization model of networked radar beam selection results under multi-target tracking is expressed as: Among them, P i,n,k represents the radiation power of radar i to target n at time k, I represents the total number of radars, N represents the total number of targets, μ i,n,k represents the radar beam selection result, η i,n,k represents the radar detection threshold, B i,n,k represents the bandwidth of the signal transmitted by radar i to target n at time k, represents the radar target detection performance measurement index, W max Indicates the upper limit of the beam generated by a single radar, U max Indicates the upper limit of the number of times a single target is illuminated by the radar; The joint optimization model of networked radar detection threshold and power bandwidth under multi-target tracking is expressed as: in, and represents the uniform distribution of radar detection threshold, radiation power and signal bandwidth, and They represent the mean values ​​of radar detection threshold, radiation power and signal bandwidth at time k respectively, represents the detection performance indicator of radar i for target n at time k, η max and η min Respectively represent the upper and lower limits of the detection threshold, P max and P min Respectively represent the upper and lower limits of the radiation power of each radar to a single target, P total Indicates the upper limit of the total radiated power of a single radar, B max and B min They represent the upper and lower limits of the bandwidth of the signal transmitted by each radar to a single target, B total Represents the upper limit of the total signal bandwidth of a single radar, P D,min represents the minimum acceptable average target detection probability, Indicates the worst acceptable multi-target tracking accuracy; (2) Combined with the semi-positive programming SDP algorithm, the optimization model of networked radar beam selection results under multi-target tracking is solved: i) Combined with Schur's complement lemma, it can be transformed into an equivalent SDP problem: in, trace(·) represents the matrix trace operation, I4 represents the 4×4 identity matrix, A n represents the auxiliary matrix of the alternative optimization objective function, W max Indicates the upper limit of the beam generated by a single radar, U max Indicates the upper limit of the number of times a single target is illuminated by the radar; ii) Solve the optimization result of the weight coefficient representing the matching between the radar beam and the target in, for For the elements in, i=1,2,…,I, n=1,2,…,N; iii) The largest first U of the I elements in each column max Set the elements to 1 and the rest to 0 to generate the beam allocation matrix iv) The largest first W of the N elements in each row max Set the elements to 1 and the rest to 0 to generate the beam allocation matrix v) The matrix and All the elements at the corresponding positions of and Perform logical AND operation to obtain the final radar beam selection result μ i,n,k ; (3) Combined with the sequential quadratic programming (SQP) algorithm, the joint optimization model of networked radar detection threshold and power bandwidth under multi-target tracking is solved: i) Initialization: Setting the optimization starting point and Respectively represent the initial radar detection threshold, radiation power and signal bandwidth, set the iteration factor Initialize the Lagrange multiplier and set the algorithm termination indicator ε>0; ii) Construct and solve the quadratic model: perform Taylor series expansion on the objective function and constraints; at the current iteration point Nearby, Construct a quadratic model about the variables S to approximate the original problem: in, and Respectively represent the radar detection threshold, radiation power and signal bandwidth of the current iteration point, X = [η i,n,k ,P i,n,k ,B i,n,k ], is the matrix composed of the second-order partial derivatives of the objective function, C is the matrix composed of the first-order partial derivatives, S T is the transposed matrix of S, C T is the transposed matrix of C; iii) Update the iteration point: Update the result S of the solved quadratic subproblem * As the next search direction of the original problem Update 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 it is satisfied, the algorithm terminates; otherwise, execute the next iteration: update the Lagrange multiplier and increase the iteration factor Return to step ii); v) Output: Detection threshold η i,n,k , radiated power P i,n,k and signal bandwidth B i,n,k .

8. A networked radar detection threshold and radio frequency resource joint optimization system under multi-target tracking, characterized in that: include: A target motion model building unit, used for building a target motion model; A target detection performance measurement index construction unit is used to construct a target detection performance measurement index with radar radiation power, signal bandwidth and detection threshold as optimization variables; A multi-target tracking performance measurement index construction unit is used to construct a multi-target tracking performance measurement index with radar beam selection results, detection threshold, radiation power and signal bandwidth as optimization variables; The optimization model building unit is used to establish a joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking, taking given target detection probability and multi-target tracking accuracy and radio frequency resource limitation as constraints, and minimizing the total radiated power resource consumption of the networked radar as the optimization goal; The optimization model solving unit is used to solve the joint optimization model of networked radar detection threshold and radio frequency resources under multi-target tracking established in the optimization model building unit by combining the semi-positive programming SDP algorithm and the sequential quadratic programming SQP algorithm; the optimization model is first decomposed into a networked radar beam selection result optimization model under multi-target tracking and a networked radar detection threshold and power bandwidth joint optimization model under multi-target tracking; Combined with the SDP algorithm, the optimization model of the networked radar beam selection results under multi-target tracking is solved; combined with the SQP algorithm, the joint optimization model of the networked radar detection threshold and power bandwidth under multi-target tracking is solved; and finally the optimization results are output.

9. 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 method for jointly optimizing the detection threshold and radio frequency resources of a networked radar under multi-target tracking as described in any one of claims 1-7.

10. 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 method for jointly optimizing the detection threshold and radio frequency resources of a networked radar under multi-target tracking as described in any one of claims 1-7.

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