Method for integrated management and control of transceiving beams and radio frequency resources of aircraft cluster radar

Abstract

The application discloses a kind of aircraft cluster radar transmitting and receiving beam and radio frequency resource integration control method, comprising: constructing target motion model and radar measurement model;Improved probability data interconnection algorithm based on detection and tracking integrated closed-loop processing framework is constructed;Derivation aircraft cluster radar under different detection threshold target detection probability and tracking error BCRLB closed analytical expression;With minimization aircraft cluster radio frequency resource consumption as optimization goal, with given multi-target detection performance, multi-target tracking accuracy and aircraft cluster radar radio frequency resource limit as constraint condition, the mathematical optimization model of aircraft cluster radar transmitting and receiving beam and radio frequency resource integration control is constructed;Mathematical optimization model is solved step by step using SDP algorithm, greedy algorithm, tabu search method and SQP algorithm.The application reduces the total radio frequency resource consumption of aircraft cluster radar, realizes the improvement of aircraft cluster radar radio frequency stealth capability.

Description

Technical Field

[0001] This invention belongs to the technical field of radar signal processing, specifically relating to an integrated management and control method for the transceiver beams and radio frequency resources of aircraft cluster radar. Background Technology

[0002] In recent years, swarm radar technology for aircraft has gradually attracted the attention of many scholars and research institutions. To address the high-intensity challenges of complexity, unpredictability, and information-based warfare on the future battlefield, traditional single-platform radars, due to their simple architecture, limited performance, and poor anti-jamming capabilities, are no longer sufficient to meet operational requirements. With the development of signal processing technology, swarm radar technology for aircraft has emerged. Through multi-node collaboration and information fusion, and distributed deployment, it effectively expands the detection range, improves tracking accuracy, and enhances system survivability. Therefore, how to enhance the radio frequency stealth capability of swarm radar while ensuring detection effectiveness has become a key research focus for swarm radar technology.

[0003] Currently, domestic and international scholars have achieved a series of significant results in the research on the collaborative management and control of aircraft swarm radar resources. However, existing methods have several shortcomings and deficiencies: Firstly, current research mainly focuses on improving the accuracy of target detection and tracking, failing to fully utilize the radio frequency stealth capabilities of aircraft swarm radars. Secondly, current research mostly treats target detection as an independent process, failing to feed back the tracker's output information to the detection center, and lacking a joint detection and tracking processing framework. Furthermore, current research is mostly concentrated on two-dimensional target tracking scenarios, failing to consider the impact of integrated management and control of transmit and receive beams and radio frequency resources on the radio frequency stealth performance of aircraft swarm radars in three-dimensional multi-target tracking scenarios.

[0004] In summary, there is currently no integrated management and control method for the radar transmit and receive beams and radio frequency resources of aircraft clusters. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide an integrated management and control method for the transceiver beams and radio frequency resources of aircraft swarm radar, so as to reduce the total radio frequency resource consumption of aircraft swarm radar and improve the radio frequency stealth capability of aircraft swarm radar.

[0006] Technical solution: The integrated management and control method for the transceiver beams and radio frequency resources of aircraft cluster radar according to the present invention includes the following steps:

[0007] Construct a target motion model and a radar measurement model;

[0008] An improved PDA algorithm based on an integrated detection and tracking closed-loop processing framework is constructed: Before using the traditional PDA algorithm to calculate the tracking parameters, the integrated detection and tracking closed-loop processing framework dynamically adjusts the detection threshold according to the error between the predicted measurement and the actual measurement in each resolution unit, which is used to distinguish clutter from the real measurement, forming a collaborative enhancement closed loop from detection to tracking and then from tracking feedback to detection.

[0009] The closed-form analytical expressions of target detection probability and tracking error of aircraft swarm radar under different detection thresholds are derived, and they are used as the characterization indicators of target detection performance and tracking accuracy, respectively.

[0010] With the goal of minimizing the radio frequency resource consumption of the aircraft cluster, and with given multi-target detection performance, multi-target tracking accuracy, and limitations of the aircraft cluster radar radio frequency resources as constraints, a mathematical optimization model for the integrated management and control of the aircraft cluster radar transceiver beams and radio frequency resources is constructed.

[0011] The mathematical optimization model is solved step by step using the SDP algorithm, greedy algorithm, tabu search method and SQP algorithm. The results are obtained by minimizing the radio frequency resource consumption of each radar transmit beam node selection parameter, receive beam node selection parameter, pre-detection threshold, transmit power, signal bandwidth, pitch angle and heading angle under the constraints of pre-set multi-target detection performance, multi-target tracking accuracy and radio frequency resource limit of aircraft swarm radar.

[0012] Furthermore, the target motion model is represented as:

[0013] ;

[0014] in, express Momentary Goal The motion state vector, express Momentary Goal The three-dimensional coordinates express Momentary Goal Three-dimensional velocity, Represents the matrix transpose operation;

[0015] Define goals The equation of motion is:

[0016] ;

[0017] in, express Momentary Goal The motion state vector, Indicate target The state transition matrix, express Momentary Goal The motion state vector, This represents Gaussian white noise.

[0018] Furthermore, a radar measurement model is constructed, including:

[0019] Airborne radar For the target The matrix representation of candidate measurements within different gates is as follows:

[0020] ;

[0021] in, Indicates in Airborne radar For the target Matrix of candidate measurements within different gates Indicates airborne radar exist Time and Goal The number of relevant candidate measurements Indicates the first Each state measurement value ; Represented as:

[0022] ;

[0023] in, Indicates airborne radar exist Always on the target False alarms during measurement. This represents the Gaussian white noise during measurement, with a mean of zero and a covariance of... , This represents the mean square error of the distance estimation. This represents the mean square error of the azimuth estimation. Indicates airborne radar For the target motion state vector The nonlinear measurement function value.

[0024] Further, improved PDA algorithms include:

[0025] (1) Calculation of innovation and covariance: based on the measurement value at the current time. and in two hypotheses and Predicted probability density and Then, the innovation vector of this measurement is calculated. and its corresponding covariance matrix :

[0026] (2) Adaptive detection threshold setting: Based on the constructed integrated detection and tracking closed-loop framework, an echo detection threshold that is dynamically adjusted with the resolution unit is set for the airborne radar detector. This is to distinguish clutter from actual measurements;

[0027] Based on the existence of the target The target does not exist Based on the assumptions, the integrated detection and tracking closed-loop framework is constructed as follows:

[0028] ;

[0029] in, This indicates the detection threshold for each resolution unit of the radar echo signal. express Airborne radar For the target The amplitude of the echo signal obtained after detection and This indicates whether the target exists or not. Indicates the target echo signal-to-noise ratio. express Airborne radar For the target The pre-detection threshold, Indicates the predicted target state measurement value at the th State measurement values The probability at a given location follows a mean of . Covariance is The joint Gaussian distribution;

[0030] (3) Nearest neighbor measurement screening: The nearest neighbor algorithm is used, with Mahalanobis distance as the discrimination criterion, to screen the measurements of each resolution unit:

[0031] ;

[0032] in, This indicates the inverse operation. If the above inequality holds and the amplitude of the measured signal exceeds the threshold set in step (2), then it is included in the candidate set of measurements; otherwise, it is considered noise and is eliminated.

[0033] (4) Target state update and fusion: Based on the traditional PDA algorithm for tracking parameter calculation, the local estimates from multiple radar nodes are fused to update the target state and its covariance.

[0034] ;

[0035] ;

[0036] in, express Momentary Goal The fused state estimation vector express Airborne radar For the target The state estimation vector, express Momentary Goal The fused state estimation error covariance matrix, express Airborne radar For the target The state estimation error covariance matrix, This indicates the total number of aircraft.

[0037] Furthermore, the probability function for target detection by aircraft swarm radar is expressed as:

[0038] ;

[0039] in, This represents the average detection probability of targets within the associated gate. Represents the resolving unit Internal measurement The detection probability, This represents the probability density function for predicting the target's state measurement when the target exists. , Indicates the target echo signal-to-noise ratio. express Airborne radar For the target The pre-detection threshold, Indicates the predicted target state measurement value at the th State measurement values The probability at a given location follows a mean of . Covariance is The joint Gaussian distribution.

[0040] Furthermore, the target tracking accuracy function of the aircraft swarm radar is expressed as:

[0041] ;

[0042] in, This represents a function indicating the tracking accuracy of a cluster radar for multiple targets. and These represent the transmit beam node selection parameters and receive beam node selection parameters for the aircraft swarm radar, respectively. This indicates the pre-detection threshold value of the aircraft cluster radar. Indicates the target echo signal-to-noise ratio. and These represent the transmit power and signal bandwidth of the aircraft cluster radar, respectively. , and These represent the position, pitch angle, and heading angle of the aircraft cluster, respectively. express Target tracking accuracy at any given time.

[0043] Furthermore, the mathematical optimization model for the integrated management and control of radar transceiver beams and radio frequency resources of aircraft clusters is expressed as follows:

[0044] ;

[0045] in, This represents the total transmit power of the aircraft cluster radar. and These represent the total number of aircraft and the total number of targets, respectively. This represents the minimum average target detection probability threshold. This represents the average detection probability of targets within the associated gate. This indicates the target tracking accuracy at the next moment. This represents the minimum target tracking accuracy threshold. , , , , , and These represent the radar transmit beam node selection parameters, receive beam node selection parameters, pre-detection threshold, transmit power, signal bandwidth, pitch angle, and yaw angle of the aircraft cluster radar, respectively. This indicates the upper limit of the number of beams that a single target can be illuminated by the radar of an aircraft swarm. and These represent the maximum number of transmit beams and the maximum number of receive beams for a single airborne radar at each time point. and These represent the highest and lowest values ​​of the change in the radar pre-detection threshold of the aircraft swarm, respectively. and These represent the highest and lowest values ​​of the transmission power variation, respectively. and These represent the highest and lowest values ​​of the signal bandwidth variation, respectively. This indicates the upper limit of the total transmit power of a single aircraft cluster radar node. This represents the upper limit of the total signal bandwidth of a single aircraft cluster radar node. and These represent the minimum and maximum values ​​of the aircraft's heading angle change, respectively. and These represent the minimum and maximum values ​​of the aircraft's pitch angle change, respectively. and These represent the changes in the aircraft's heading angle and pitch angle, respectively.

[0046] Furthermore, the mathematical optimization model is solved step-by-step using the SDP algorithm, greedy algorithm, tabu search method, and SQP algorithm, including the following steps:

[0047] (1) The optimization problem is decomposed into a radar beam allocation model for aircraft clusters;

[0048] The position of the aircraft cluster is fixed as the starting coordinates. It is assumed that the receiving beam allocation is the same as the transmitting beam allocation, that is, all airborne radar nodes are in a self-transmitting and self-receiving state. The radio frequency resources of the aircraft cluster radar are fixed, that is, the pre-detection threshold, transmitting power and signal bandwidth are fixed, and the total power consumption is always kept consistent. Then, the target tracking error is reduced to improve the degree of freedom of subsequent optimization. At this time, the optimization model is transformed into the aircraft cluster radar transmitting beam allocation model.

[0049] (2) Solving the problem of selecting the radar transmit beam node for the aircraft cluster;

[0050] The model in step (1) is relaxed into a convex optimization problem using the SDP algorithm: based on Schur complement lemma, an auxiliary matrix is ​​constructed and a positive semidefinite constraint is established accordingly; the weight matrix for selecting radar transmit beam nodes of the aircraft cluster is obtained by solving the convex optimization problem using the interior point method. ;Will Each column The largest among the elements Set one element to 1 and the rest to 0 to generate the beam assignment matrix. ;Will All industries The largest element among the elements is set to . Set the remaining elements to Generate beam assignment matrix ;

[0051] matrix and A logical AND operation is performed on all row and column elements in the same position to obtain the final allocation result of the aircraft cluster nodes and targets;

[0052] (3) Decompose the optimization problem into a radar receiver beam allocation model for aircraft clusters and solve it;

[0053] Based on step (2), and considering the allocation results of the transmitted beams, each radar node can receive echoes generated by other nodes in the network to the target. The radio frequency resources and track positions of the aircraft cluster radar are fixed to obtain the aircraft cluster radar receiving beam allocation model. The model is solved by a greedy algorithm to obtain the final receiving beam node selection result.

[0054] (4) Decompose the optimization problem into a radar radio frequency resource management model for aircraft clusters and solve it;

[0055] Based on the obtained beam allocation of the aircraft cluster radar, a sub-model of the radio frequency resource optimization problem is constructed by adaptively managing the radio frequency resources of each node, that is, optimizing the pre-detection threshold, transmit power and signal bandwidth of the aircraft cluster radar. The model is then solved by the tabu search method to obtain the final radio frequency resource allocation result.

[0056] (5) Decompose the optimization problem into an aircraft swarm trajectory planning model and solve it;

[0057] Based on the results of transmit / receive beam allocation and radio frequency resource allocation, the heading angle of the aircraft cluster radar is optimized. and pitch angle To further improve multi-target tracking performance, an aircraft swarm trajectory planning model was constructed, and the SQP algorithm was used to solve the model to obtain the final trajectory planning result.

[0058] Furthermore, a greedy algorithm is used to solve the radar radio frequency resource management model for aircraft clusters, including:

[0059] (1) Based on the current solution Based on the preset neighborhood structure under small perturbations, a set of candidate solutions is generated. And iterate through the candidate set to eliminate all infeasible solutions that do not meet the model constraints;

[0060] (2) Among the remaining feasible candidate solutions In the middle, find the total transmission power of the aircraft cluster radar. Minimum solution ;

[0061] (3) If Not on the taboo list In the middle, or meeting the contempt principle:

[0062] ;

[0063] in, The total transmit power of the aircraft cluster radar is the minimum solution. This represents the current optimal total transmit power for aircraft cluster radars;

[0064] If it is accepted as the new solution, then it is accepted; otherwise, the next non-taboo optimal solution is searched in the candidate set. ;

[0065] (4) Add the variables that changed during this move and their directions to the taboo list. And remove the earliest added entry based on the taboo length;

[0066] (5) If the new non-taboo optimal solution satisfies the contempt criterion, then update , , To obtain the optimal solution, the unimproved counter is reset. Otherwise, update. ;

[0067] (6) Continue until the maximum number of iterations is reached. Or the counter exceeds the threshold without improvement Otherwise, proceed to the next iteration: update the iteration index. .

[0068] Furthermore, the SQP algorithm is used to solve the aircraft swarm trajectory planning model, including:

[0069] (1) Construct a quadratic programming model and perform a Taylor series expansion of the objective function and constraints; at the current iteration point Nearby, , For heading angle and pitch angle The constructed two-dimensional vector, Indicates the heading angle to be optimized. and pitch angle The constructed two-dimensional vectors, constructing information about the variables Primitive approximation problem of quadratic model:

[0070] ;

[0071] in, for transpose; Indicates at point Lagrange function with respect to variable An approximation of the Hessian matrix, Let Lagrange multiplier vector be the current vector. Describe the objective function. Indicates the objective function in The gradient vector at that point, Indicates the first Inequality constraints express transpose, Represents the set of inequality constraint indexes;

[0072] (2) Solve the above subproblems using quadratic programming to obtain the optimal solution under the current quadratic model. That is, to obtain the optimal search direction. and the corresponding Lagrange multiplier estimates ;

[0073] (3) Along the search direction Perform a one-dimensional line search to determine the step size. To satisfy the descent condition of the augmented Lagrangian function; then update the iteration point:

[0074] ;

[0075] in, The solution after iterative update;

[0076] (4) Use the multiplier estimates obtained from solving the subproblems as the initial multipliers for the next iteration. The approximate Hessian matrix is ​​updated using a quasi-Newton method. This allows it to approximate the second derivative of the Lagrange function using the gradient information of the current iteration;

[0077] (5) Continue until the maximum number of iterations is reached. Or the gradient is less than the algorithm termination index Otherwise, proceed to the next iteration: update the iteration index. .

[0078] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are: (1) By jointly optimizing the parameters such as the transmit and receive beam allocation, detection threshold, radiated power, signal bandwidth and aircraft platform trajectory of each radar node in the aircraft cluster radar, the radio frequency resource consumption of the aircraft cluster radar is minimized to the maximum extent while meeting the constraints such as the pre-set target detection performance, target tracking accuracy and radio frequency resource limitations of the aircraft cluster radar; (2) It can minimize the radio frequency resource consumption of the aircraft cluster radar to the maximum extent while meeting the constraints such as the pre-set target detection performance, target tracking accuracy and radio frequency resource limitations of the aircraft cluster radar, thereby improving its radio frequency stealth capability. Attached Figure Description

[0079] Figure 1 This is a flowchart of the method of the present invention;

[0080] Figure 2 For aircraft cluster radar and multi-target motion trajectories;

[0081] Figure 3The results of radar beam selection and resource allocation for each target are shown below; (a) shows the radar beam selection and resource allocation results for target 1, (b) shows the radar beam selection and resource allocation results for target 2, (c) shows the radar beam selection and resource allocation results for target 3, and (d) shows the radar beam selection and resource allocation results for target 4.

[0082] Figure 4 Comparison of total transmit power of aircraft swarm radar under different methods;

[0083] Figure 5 The results show the comparison of the average root mean square error of radar tracking of aircraft clusters for each target under different methods. Detailed Implementation

[0084] The structure and working process of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0085] Based on actual combat scenarios, this invention considers the multi-target detection and tracking tasks performed by aircraft swarm radar in a three-dimensional scene. It proposes an integrated management and control method for the transceiver beams and radio frequency resources of aircraft swarm radar. Under the constraints of pre-set target detection performance, target tracking accuracy and radio frequency resource limitations of aircraft swarm radar, this method minimizes the consumption of radio frequency resources of aircraft swarm radar, thereby improving its radio frequency stealth capability. First, a closed-loop processing framework for integrated detection and tracking based on improved probabilistic data interconnection is established. Closed-form analytical expressions for the target detection probability and tracking error of the aircraft swarm radar under different detection thresholds are derived, and these expressions are used as characterization indicators for target detection performance and tracking accuracy, respectively. Based on this, with minimizing the radio frequency (RF) resource consumption of the aircraft swarm as the optimization objective, and given constraints such as multi-target detection performance, multi-target tracking accuracy, and RF resource limitations of the aircraft swarm radar, a mathematical optimization model for the integrated management and control of the aircraft swarm radar's transceiver beams and RF resources is constructed. Finally, a combination of semi-definite programming (SDP), greedy algorithms, tabu search, and sequential quadratic programming (SQPC) algorithms is employed. The SQP algorithm solves the above mathematical optimization model step by step, and jointly optimizes parameters such as transmit and receive beam allocation, detection threshold, radiated power, signal bandwidth and aircraft platform trajectory of each radar node in the aircraft swarm radar, so as to minimize the total radio frequency resource consumption of the aircraft swarm radar and improve the radio frequency stealth capability of the aircraft swarm radar.

[0086] like Figure 1 As shown, the method of the present invention includes the following steps:

[0087] S1, Construction Momentary Goal The motion model is shown in equation (1):

[0088] (1)

[0089] in, express Momentary Goal The motion state vector, express Momentary Goal The three-dimensional coordinates express Momentary Goal Three-dimensional velocity, This represents the matrix transpose operation.

[0090] Define goals The equation of motion is:

[0091] (2)

[0092] in, Indicate target The state transition matrix, express Momentary Goal The motion state vector, This represents Gaussian white noise with a mean of 0 and a covariance matrix of... The joint Gaussian distribution.

[0093] 2. Construct a radar measurement model;

[0094] Assuming that for the same target, each airborne radar can receive at most one measurement value within a single tracking frame, then Airborne radar For the target The matrix for candidate measurements within different gates is defined as follows:

[0095] (3)

[0096] in, Indicates in Airborne radar For the target Matrix of candidate measurements within different gates Indicates airborne radar exist Time and Goal The number of relevant candidate measurements, the first State measurement values It can be represented as:

[0097] (4)

[0098] in, Indicates the first Each state measurement value , Indicates airborne radar exist Always on the target False alarms during measurement. The Gaussian white noise used in the measurement process has a mean of zero and a covariance of . , This represents the mean square error of the distance estimation. This represents the mean square error of the azimuth estimation. Indicates airborne radar Target motion state vector The nonlinear measurement function value.

[0099] In equation (4), the false alarm under measurement Follows a uniform distribution:

[0100] (5)

[0101] (6)

[0102] in, The probability density function representing a false alarm. Indicates the relevant gate area. Indicates the new information covariance. This represents the operation of finding the determinant of a matrix. Represents the measurement dimension and threshold factor in the scene. Value by The distribution table is determined. Representation and Dimension The specific form of the relevant normalization coefficients is determined by the gate shape and probability confidence region used.

[0103] Mean square error of distance and azimuth estimation , Signal-to-noise ratio with target echo Size is inversely proportional:

[0104] (7)

[0105] (8)

[0106] in, and These represent the mean square errors of the distance and azimuth estimates, respectively. express Airborne radar For the target Bandwidth of the transmitted signal, This indicates the 3dB bandwidth of the beam. Indicates the target echo signal-to-noise ratio. Indicates the radar's dwell time. Indicates the pulse repetition period. express Time Radar Target drone Radiated power and These represent the transmit and receive antenna gains, respectively. Indicates the signal wavelength. Indicates the receiver processing gain. Indicate target RCS value, Represents Boltzmann's constant. Represents thermodynamic temperature. express Time Radar For the target Matched filter bandwidth, Indicates the receiver noise figure. express Constantly transmitting radar nodes With the goal The distance between, express Constantly receiving radar nodes With the goal The distance between,

[0107] 3. Construct an integrated closed-loop framework for detection and tracking.

[0108] To further improve multi-target detection performance and tracking capabilities, this invention introduces an integrated closed-loop framework for detection and tracking. This framework is based on the existence of the target. The target does not exist Based on the assumptions, the integrated detection and tracking closed-loop framework is constructed as follows:

[0109] (9)

[0110] in, This indicates the detection threshold for each resolution unit of the radar echo signal. express Airborne radar For the target The amplitude of the echo signal obtained after detection and This indicates whether the target exists or not. express Airborne radar For the target The pre-detection threshold, Indicates the predicted target state measurement value at the th State measurement values The probability at a given location follows a joint Gaussian distribution with a mean of 1 / 2. Covariance is .in, Represents Jacobian matrix operations. Indicates the target of motion Predictive covariance matrix of error under state feature estimation.

[0111] It can be seen that, within the integrated detection and tracking closed-loop framework, each resolution unit, based on its predicted measurement, operates within the same associated gate. With resolution unit Actual measurement inside Different detection thresholds are set for the measurement errors between the two measurements, and the detection threshold is inversely proportional to the measurement error. When predicting the measurement... With resolution unit Actual measurement inside When the error between them is small, The detection threshold is relatively high, at which point the aircraft swarm radar system lowers its detection threshold. This makes it easier for measurements that match the predicted state to pass detection; conversely, it increases the detection threshold. Echo data is removed. The predicted state corresponds to the predicted measurement. The predicted state is the predicted position of the target in the actual three-dimensional space, while the predicted measurement is the projection of the predicted state onto the radar observation space.

[0112] To achieve accurate target detection and tracking, before using the traditional PDA algorithm to calculate the tracking parameters, the detection and tracking integrated closed-loop framework constructed by equation (9) is introduced to set an adaptive detection threshold for the radar detector, so as to distinguish clutter from real measurements. Then, the real measurements are further filtered out through the nearest neighbor algorithm, thus achieving accurate target detection and tracking. The specific steps are as follows:

[0113] (1) Calculation of innovation and covariance: based on the measurement value at the current time. and in two hypotheses and Predicted probability density and Then, the innovation vector of this measurement is calculated. and its corresponding covariance matrix :

[0114] (10)

[0115] (11)

[0116] in, Indicates airborne radar based on Time measurement Momentary Goal The state prediction error covariance matrix, Indicates airborne radar For the target characteristic state vector The nonlinear measurement function value, Represents the target characteristic state vector Jacobian matrix, This indicates the transpose operation. This is the prediction covariance matrix of the measurement noise;

[0117] (2) Adaptive detection threshold setting: Based on the detection and tracking integrated closed-loop framework constructed according to equation (9), the echo detection threshold of the airborne radar detector is set to be dynamically adjusted with the resolution unit. This is to distinguish clutter from actual measurements;

[0118] (3) Nearest neighbor measurement screening: The nearest neighbor algorithm is used, with Mahalanobis distance as the discrimination criterion, to screen the measurements of each resolution unit:

[0119] (12)

[0120] in, This indicates the inverse operation. If the above inequality holds and the amplitude of the measured signal exceeds the threshold set in step (2), then it is included in the candidate set of measurements; otherwise, it is considered noise and is eliminated.

[0121] (4) Target state update and fusion: Based on the traditional probabilistic data interconnection algorithm for tracking parameter calculation, the local estimates from multiple radar nodes are fused to update the target state and its covariance.

[0122] (13)

[0123] (14)

[0124] in, express Momentary Goal The fused state estimation error covariance matrix, express Airborne radar For the target The state estimation error covariance matrix, express Momentary Goal The fused state estimation vector express Airborne radar For the target The state estimation vector.

[0125] 4. Derive the target detection probability function of the aircraft swarm radar:

[0126] (15)

[0127] in, This represents the average detection probability of targets within the associated gate. Represents the resolving unit Internal measurement The detection probability, This represents the probability density function for predicting the state measurement of the target when the target exists. .

[0128] It can be seen that, With signal-to-noise ratio As can be seen from equation (8), Also related to the pre-detection threshold Transmission power and signal bandwidth Phase coupling.

[0129] 5. Derive the target tracking accuracy function of the aircraft swarm radar:

[0130] Introducing information decay factor This characterizes the problem of decreased reliability of target tracking information due to uncertainty in the measurement source, among which The Bayesian information matrix expression for the predicted state is:

[0131] (16)

[0132] in, The Bayesian information matrix for predicting the state. It is the mathematical expectation operator. It is the prediction covariance matrix of measurement noise. This represents finding the inverse of a matrix.

[0133] (17)

[0134] in, This represents a function indicating the tracking accuracy of a cluster radar for multiple targets. and These represent the transmit beam node selection parameters and receive beam node selection parameters for the aircraft swarm radar, respectively. This indicates the pre-detection threshold value of the aircraft cluster radar. and These represent the transmit power and signal bandwidth of the aircraft cluster radar, respectively. , and These represent the position, pitch angle, and heading angle of the aircraft cluster, respectively. express Target tracking accuracy at any given time.

[0135] In equation (17), The corresponding predicted BCRLB matrix is ​​obtained from the measurement error of the corresponding three-dimensional position in the BCRLB matrix. The inverse of the Bayesian information matrix for predicting the state .

[0136] 6. Establish a mathematical optimization model for the integrated management and control of radar transceiver beams and radio frequency resources of aircraft clusters;

[0137] In three-dimensional multi-target detection and tracking scenarios, aircraft swarm radars equipped with multi-beam phased array radars can simultaneously perform detection and tracking tasks against multiple targets. By dynamically optimizing the transmit and receive beam allocation, detection threshold, transmit power, signal bandwidth, and aircraft platform trajectory of each radar node in the swarm radar, the optimization objective of minimizing the RF resource consumption of the aircraft swarm radar is achieved while meeting pre-set requirements for multi-target detection performance, multi-target tracking accuracy, and RF resource limitations of the aircraft swarm radar. Based on this, a mathematical optimization model for the integrated management and control of transmit and receive beams and RF resources of the aircraft swarm radar is constructed.

[0138] (18)

[0139] in, This represents the total transmit power of the aircraft cluster radar. and These represent the total number of aircraft and the total number of targets, respectively. and These represent the maximum number of transmit beams and the maximum number of receive beams for a single airborne radar at each time point. and These represent the minimum and maximum values ​​of the aircraft's heading angle change, respectively. and These represent the minimum and maximum values ​​of the aircraft's pitch angle change, respectively. and These represent the changes in the aircraft's heading angle and pitch angle, respectively. This represents the minimum average target detection probability threshold. This represents the minimum target tracking accuracy threshold. This indicates the upper limit of the number of beams that a single target can be illuminated by the radar of an aircraft swarm. and These represent the highest and lowest values ​​of the change in the radar pre-detection threshold of the aircraft swarm, respectively. and These represent the highest and lowest values ​​of the transmission power variation, respectively. and These represent the highest and lowest values ​​of the signal bandwidth variation, respectively. This indicates the upper limit of the total transmit power of a single aircraft cluster radar node. This indicates the upper limit of the total signal bandwidth of a single aircraft cluster radar node.

[0140] The first constraint in the optimization model (18) represents the minimum performance limit for the radar detection and tracking task of the aircraft swarm; the second constraint represents the maximum number of transmit beams of a single airborne radar at each time step. And the target is at most The third constraint indicates that the maximum number of transmit beams for a single airborne radar at any given time is [number of beams to be filled in]. The fourth constraint represents the limitation on the change of the pre-detection threshold of the aircraft cluster radar at each time step; the fifth constraint represents the limitation on the change of transmit power and signal bandwidth; the sixth constraint represents the limitation on the total transmit power and total signal bandwidth of a single node; the seventh constraint represents the limitation on the change of the heading angle and pitch angle of each aircraft; and the last constraint represents that the transmit beam node selection parameters and receive beam node selection parameters of the aircraft cluster radar are both binary variables.

[0141] 7. Solve the optimization model;

[0142] The optimization model (18) contains seven optimization variables, namely the radar transmit beam node selection parameters of the aircraft cluster. Receive beam node selection parameters Pre-detection threshold Transmission power Signal bandwidth Pitch angle and heading angle It includes both binary and continuous variables. As can be seen from equation (17), these seven variables influence each other and are coupled in the multi-target tracking accuracy constraint. Therefore, this model is a non-convex, nonlinear mixed integer programming problem with multiple performance constraints. As a large-scale multidimensional optimization problem, it is difficult to solve by traditional methods. This invention introduces a hierarchical solution strategy, decomposes it into four sub-problems and solves them step by step using the SQP algorithm, greedy algorithm, tabu search method and SDP algorithm respectively. The specific steps are as follows:

[0143] Step 1: Decompose the optimization problem into an aircraft cluster radar transmit beam allocation model.

[0144] Location of the aircraft cluster Fixed as starting coordinates Assuming the receive beam allocation is the same as the transmit beam allocation This means that all airborne radar nodes are in a self-transmitting and self-receiving state. The radio frequency resources of the fixed aircraft cluster radar, i.e., the pre-detection threshold... Transmission power Signal bandwidth , , and The pre-detection threshold, transmit power, and signal bandwidth are to be fixed, respectively, while the total power consumption remains constant. Therefore, the target tracking error should be minimized to increase the degrees of freedom in subsequent optimization. The optimization model can then be transformed into an aircraft swarm radar transmit beam allocation model:

[0145] (19)

[0146] in, The variable represents the transmit beam assignment. The tracking accuracy of aircraft swarm radar for multiple targets;

[0147] Step 2: Solving the problem of selecting radar transmission beam nodes for aircraft clusters.

[0148] Based on step 1, equation (19) is solved. Based on the Schul complement lemma, slack variables are introduced into equation (19) to construct an auxiliary matrix. And based on this, the transformed positive semidefinite constraints are established:

[0149] (20)

[0150] in, express A matrix of all 1s This represents a matrix consisting entirely of zeros. The objective function then transforms into... ,in The trace operation of a matrix is ​​represented as follows:

[0151] (twenty one)

[0152] in, for The tracking accuracy of aircraft swarm radar for multiple targets is improved by relaxing the SDP algorithm;

[0153] Based on this, a weighting coefficient is introduced. To solve the transmit beam node selection problem, the interior-point method can be used to obtain the set of weights for selecting mission nodes in an aircraft swarm. :

[0154] (twenty two)

[0155] Indicates aircraft For the target The weighting coefficient of the transmitted beam will Each column The largest among the elements Set one element to 1 and the rest to 0 to generate the beam assignment matrix. ;Will All industries The largest element among the elements is set to . Set the remaining elements to Generate beam assignment matrix .

[0156] matrix and Perform a logical AND operation on all row and column elements in the same position to obtain the final task area allocation result for the spacecraft cluster nodes:

[0157] (twenty three)

[0158] In the formula, This represents the Hadamard product operation of matrices. This indicates the final transmit beam node selection and allocation result.

[0159] Step 3: Decompose the optimization problem into an aircraft cluster radar receiving beam allocation model and solve it.

[0160] Based on step 2, and considering the allocation results of the transmitted beams, and taking into account that each radar node can receive echoes generated by other nodes in the network towards the target, while keeping the radio frequency resources and track positions of the aircraft cluster radar fixed, a sub-model can be obtained:

[0161] (twenty four)

[0162] in, The variable represents the receive beam assignment. The tracking accuracy of aircraft swarm radar for multiple targets;

[0163] Considering that the actual receiving beam node selection matrix and the transmitting beam node selection matrix are related, i.e., the airborne radar node needs to allocate a transmitting beam to illuminate the target in order to generate a corresponding echo signal for reception. Therefore, the number of receiving beams needs to be determined by the constraints in equation (19). and It can be seen that the maximum number of radars generated by the aircraft cluster at any given time is [number missing]. One transmission beam, however, all targets in the airspace can be at most [number] beams. Each emitted beam illuminates the system. Therefore, the system generates a total of [number] beams. Each beam is considered in turn for the selection of receiving nodes.

[0164] Based on this, the number of beams generated by the system The beam node selection and allocation results obtained in step 2 can be used to determine the beams that illuminate each target in sequence. The beams that illuminate each target are numbered sequentially. The independent variables in the subproblem are... It can be regarded as Each beam for The issue of assigning individual airborne radar nodes The optimization problem can then be transformed into:

[0165] (25)

[0166] in, express Airborne radar Select to receive the first One beam, This means that a beam has one and only one radar node receiving it. Indicates the variable is The tracking accuracy of the aircraft cluster radar for multiple targets is improved; the above problem is solved by a greedy algorithm to obtain the final receiving beam node selection result.

[0167] Step 4: Decompose the optimization problem into an aircraft cluster radar radio frequency resource management model and solve it.

[0168] The beam allocation of the aircraft swarm radar obtained from the above steps maximizes the multi-target tracking accuracy. Based on this, further optimization of the radio frequency stealth performance of the aircraft swarm radar is considered. By adaptively managing the radio frequency resources of each node, an optimization problem sub-model is constructed:

[0169] (26)

[0170] in, This represents the total transmit power of the aircraft cluster radar. These are the optimization variables that need to be solved;

[0171] The greedy algorithm is used to solve the problem, and the specific steps are as follows:

[0172] (1) Based on the current solution Based on the preset neighborhood structure under small perturbations, a set of candidate solutions is generated. And iterate through the candidate set to eliminate all infeasible solutions that do not satisfy the constraints of model (26);

[0173] (2) Among the remaining feasible candidate solutions In the middle, find the total transmission power of the aircraft cluster radar. Minimum solution ;

[0174] (3) If Not on the taboo list In the middle, or meeting the contempt principle:

[0175] (27)

[0176] in, The total transmit power of the aircraft cluster radar is the minimum solution. This represents the current optimal total transmit power for aircraft cluster radars;

[0177] If it is accepted as the new solution, then it is accepted; otherwise, the next non-taboo optimal solution is searched in the candidate set. ;

[0178] (4) Add the variables that changed during this move and their directions to the taboo list. And remove the earliest added entry based on the taboo length;

[0179] (5) If the new non-taboo optimal solution satisfies the contempt criterion, then update , , To obtain the optimal solution, the unimproved counter is reset. Otherwise, update. ;

[0180] (6) Continue until the maximum number of iterations is reached. Or no improved counter exceeds threshold Otherwise, proceed to the next iteration: update the iteration index. .

[0181] Step 5: Decompose the optimization problem into an aircraft swarm trajectory planning model and solve it.

[0182] Assuming the aircraft's speed remains constant, optimization of its pitch angle is the only way to achieve this. With heading angle By adjusting the flight path, the following aircraft swarm trajectory planning model can be obtained:

[0183] (28)

[0184] in, For aircraft cluster radar at heading angle and pitch angle Tracking accuracy for multiple targets under constraints;

[0185] The SQP algorithm is used to solve this problem, and the specific steps are as follows:

[0186] (1) Construct a quadratic programming model and perform a Taylor series expansion of the objective function and constraints; at the current iteration point Nearby, , For heading angle and pitch angle The constructed two-dimensional vector, Indicates the heading angle to be optimized. and pitch angle The constructed two-dimensional vectors, constructing information about the variables Primitive approximation problem of quadratic model:

[0187] (29)

[0188] in, for Transpose of; Indicates at point Lagrange function with respect to variable An approximation of the Hessian matrix, Let Lagrange multiplier vector be the current vector. Describe the objective function. Indicates the objective function in The gradient vector at that point, Indicates the first Inequality constraints express transpose, Represents the set of inequality constraint indexes;

[0189] (2) Solve the above subproblems using quadratic programming to obtain the optimal solution under the current quadratic model. That is, to obtain the optimal search direction. and the corresponding Lagrange multiplier estimates ;

[0190] (3) Along the search direction Perform a one-dimensional line search to determine the step size. This satisfies the descent condition of the augmented Lagrange function. The iteration point is then updated:

[0191] (30)

[0192] in, The solution is the one that has been iteratively updated.

[0193] (4) Use the multiplier estimates obtained from solving the subproblems as the initial multipliers for the next iteration. The approximate Hessian matrix is ​​updated using a quasi-Newton method. This allows it to approximate the second derivative of the Lagrange function using the gradient information of the current iteration;

[0194] (5) Continue until the maximum number of iterations is reached. Or the gradient is less than the algorithm termination index Otherwise, proceed to the next iteration: update the iteration index. .

[0195] 8. Simulation results and analysis;

[0196] To demonstrate the feasibility and superiority of the proposed method, this invention designs the following simulation scenario for aircraft swarms simultaneously performing multi-target detection and tracking tasks: considering the presence of... A cluster of aircraft, each equipped with a phased array airborne radar capable of simultaneously transmitting and receiving multiple beams, with each radar node configured to generate a maximum of [number missing] beams simultaneously. One transmit beam, with a maximum simultaneous reception of [number] beams. One beam. Sampling interval All aircraft have the same dynamic performance, and the initial coordinates are set as shown in Table 1. The flight speed at each node is constant. Minimum pitch angle change of flight path and maximum pitch angle change Minimum heading angle change and maximum heading angle change The scene contains Each target needs to be detected and tracked, and all targets are in uniform linear motion. The corresponding initial coordinates and flight speeds are shown in Table 2. A single target can be detected at most once. One beam of illumination.

[0197] Table 1. Starting coordinate settings for each aircraft

[0198]

[0199] Table 2. Initial coordinates and flight speed settings for each target

[0200]

[0201] Furthermore, considering that the radio frequency characteristics of each airborne radar node are the same, the maximum value of the radar pre-detection threshold of the aircraft cluster is... and minimum value Maximum transmit power and minimum value Maximum signal bandwidth and minimum value On the other hand, the upper limit of the power of all transmitted beams of a single aircraft cluster radar node. The upper limit of total signal bandwidth The tracking accuracy threshold for all targets is set to... The target average detection probability threshold is set to .

[0202] Assuming that the aircraft swarm radar system maintains constant illumination of each target at different times... At this time, the radar data of the aircraft cluster and the movement of the target are obtained, such as... Figure 2 As shown, the corresponding transmit beam node selection and resource allocation results are as follows: Figure 3 As shown in (a) to (d), the aircraft swarm radar tends to select targets that are closer to it for beam illumination and tracking. To further improve tracking accuracy, the aircraft also tends to fly towards the assigned target direction over time. This is mainly due to the influence of the distance between the airborne radar and the target. By minimizing the distance, the signal-to-noise ratio of the echo is improved, which ultimately indirectly ensures the detection and tracking performance of the aircraft swarm radar.

[0203] Specifically, target 1 is primarily illuminated by radars 1 and 2 because its trajectory remains to the left of the aircraft swarm radar system, thus these two closer radars are chosen for tracking. Similarly, target 3 is relatively close to radars 1 and 3 in the aircraft swarm radar system, and is therefore primarily tracked by them. On the other hand, target 2 is primarily illuminated by radars 2 and 3, and target 4 is primarily illuminated by radars 1 and 2. This is because these two targets are relatively close to the entire swarm and are located at the front center of the swarm, so the performance of each airborne radar node after illuminating them is relatively similar. The system prioritizes illuminating the more distant targets 1 and 3 with the closer radar nodes to ensure optimal detection and tracking performance. Furthermore, the aircraft swarm radar system tends to allocate more resources to targets that are farther away. As target 1 moves closer to the aircraft swarm radar system, its resource allocation decreases in the latter half of the process. However, because target 3 remains relatively far away, the swarm system tends to allocate more radio frequency resources to it throughout the entire process to maintain good detection and tracking performance.

[0204] To further highlight the reliability of the proposed method in terms of optimization effect, this invention, while keeping other parameters unchanged, demonstrates its superiority by comparing its optimization performance with existing methods. The comparison method is described in detail below:

[0205] (1) Method 1: While keeping other parameters the same, the SQP algorithm and the greedy algorithm are still used to solve the transmit and receive beam node selection parameters of the aircraft cluster radar. Based on this, the pre-detection threshold values ​​for each airborne radar node are fixed. The tabu search method is used to determine the transmission power. and signal bandwidth The optimized allocation of the aircraft's trajectory is achieved by using the SDP algorithm, and its detection and stealth performance is evaluated by the target tracking accuracy function of the aircraft swarm and the total radiated power.

[0206] (2) Method 2: While keeping other parameters the same, the SQP algorithm and the greedy algorithm are still used to solve the transmit and receive beam node selection parameters of the aircraft cluster radar. Based on this, the SDP algorithm is used to sequentially set the pre-detection threshold for each airborne radar node. Transmission power Signal bandwidth The optimization of the aircraft's flight path and the assessment of its detection and stealth performance through the target tracking accuracy function of the aircraft swarm and the total radiated power.

[0207] (3) Method 3: While keeping other parameters the same, the SQP algorithm and the greedy algorithm are still used to solve the transmit and receive beam node selection parameters of the aircraft cluster radar. And the pre-detection threshold of airborne radar nodes is solved using the tabu search method. Transmission power and signal bandwidth The optimal allocation was then implemented. Based on this, the flight path positions of the downloaders at each time point were fixed, and their detection and stealth performance was evaluated using the target tracking accuracy function of the aircraft swarm and the total radiated power.

[0208] Figure 4 and Figure 5 The paper presents a comparison of the total radiated power of aircraft swarm radar for each target using different methods, as well as a comparison of the average root mean square error (ARMSE) during tracking. As shown in the figure, the method proposed in this invention achieves the lowest total radiated power and the best overall tracking accuracy.

[0209] The working principle and process of this invention:

[0210] This invention considers multi-target detection and tracking tasks performed by aircraft swarm radar in a three-dimensional scene. First, an integrated closed-loop processing framework for detection and tracking based on improved probabilistic data interconnection is established. Closed-form analytical expressions for target detection probability and tracking error (BCRLB) of the aircraft swarm radar under different detection thresholds are derived, and these are used as characterization indicators of target detection performance and tracking accuracy, respectively. Based on this, with minimizing the radio frequency (RF) resource consumption of the aircraft swarm as the optimization objective, and given constraints such as multi-target detection performance, multi-target tracking accuracy, and RF resource limitations of the aircraft swarm radar, a mathematical optimization model for the integrated management and control of the aircraft swarm radar's transmit and receive beams and RF resources is constructed. Finally, the SDP algorithm, greedy algorithm, tabu search, and SQP algorithm are used to solve the above mathematical optimization model step by step, obtaining the selection parameters for each radar transmit beam node that minimize the RF resource consumption of the aircraft swarm radar under the pre-set constraints of multi-target detection performance, multi-target tracking accuracy, and RF resource limitations of the aircraft swarm radar. Receive beam node selection parameters Pre-detection threshold Transmission power Signal bandwidth Pitch angle and heading angle .

[0211] In summary, this invention constructs an integrated closed-loop processing framework for aircraft swarm radar detection and tracking, and introduces an improved probabilistic data interconnection algorithm within this framework. This enables the aircraft swarm radar to adaptively adjust the detection threshold of each resolution unit within the associated gate based on the predicted target measurement distribution, thereby increasing the degree of freedom in radio frequency (RF) resource management. This invention derives the Bayesian Cramer-Rao lower bound closed-form analytical expressions for target detection probability and tracking error of the aircraft swarm radar under different detection thresholds, and uses these expressions as characterization indicators for target detection performance and tracking accuracy, respectively. This invention aims to minimize the RF resource consumption of the aircraft swarm, and uses pre-set constraints such as multi-target detection performance, multi-target tracking accuracy, and RF resource limitations of the aircraft swarm radar as constraints to construct a mathematical optimization model for the integrated management of the aircraft swarm radar's transceiver beams and RF resources. This invention introduces a hierarchical solution strategy to solve the radar transmit and receive beam and radio frequency resource management model of an integrated detection and tracking aircraft swarm radar. It decomposes the model into four sub-problems and solves them step by step using the SQP algorithm, greedy algorithm, tabu search method, and SDP algorithm, respectively. Under pre-set constraints such as target detection performance, target tracking accuracy, and radio frequency resource limitations of the aircraft swarm radar, the invention obtains the radar transmit beam node selection parameters, receive beam node selection parameters, pre-detection threshold, transmit power, signal bandwidth, pitch angle, and heading angle of the aircraft swarm radar that minimize the radio frequency resource consumption of the aircraft swarm radar.

Claims

1. A method for integrated management and control of radar transceiver beams and radio frequency resources of aircraft clusters, characterized in that, Includes the following steps: Construct a target motion model and a radar measurement model; An improved PDA algorithm based on an integrated detection and tracking closed-loop processing framework is constructed: Before using the traditional PDA algorithm to calculate the tracking parameters, the integrated detection and tracking closed-loop processing framework dynamically adjusts the detection threshold according to the error between the predicted measurement and the actual measurement in each resolution unit, which is used to distinguish clutter from the real measurement, forming a collaborative enhancement closed loop from detection to tracking and then from tracking feedback to detection. The closed-form analytical expressions of target detection probability and tracking error of aircraft swarm radar under different detection thresholds are derived, and they are used as the characterization indicators of target detection performance and tracking accuracy, respectively. With the goal of minimizing the radio frequency resource consumption of the aircraft cluster, and with given multi-target detection performance, multi-target tracking accuracy, and limitations of the aircraft cluster radar radio frequency resources as constraints, a mathematical optimization model for the integrated management and control of the aircraft cluster radar transceiver beams and radio frequency resources is constructed. The mathematical optimization model is solved step by step using the SDP algorithm, greedy algorithm, tabu search method and SQP algorithm. The results are obtained by minimizing the radio frequency resource consumption of each radar transmit beam node selection parameter, receive beam node selection parameter, pre-detection threshold, transmit power, signal bandwidth, pitch angle and heading angle under the constraints of pre-set multi-target detection performance, multi-target tracking accuracy and radio frequency resource limit of aircraft swarm radar.

2. The method according to claim 1, characterized in that, The target motion model is represented as: ； in, express Momentary Goal The motion state vector, express Momentary Goal The three-dimensional coordinates express Momentary Goal Three-dimensional velocity, Represents the matrix transpose operation; Define goals The equation of motion is: ； in, express Momentary Goal The motion state vector, Indicate target The state transition matrix, express Momentary Goal The motion state vector, This represents white noise in a Gaussian process.

3. The method according to claim 1, characterized in that, Constructing a radar measurement model includes: Airborne radar For the target The matrix representation of candidate measurements within different gates is as follows: ； in, Indicates in Airborne radar For the target Matrix of candidate measurements within different gates Indicates airborne radar exist Time and Goal The number of relevant candidate measurements Indicates the first Each state measurement value ; Represented as: ； in, Indicates airborne radar exist Always on the target False alarms during measurement. This represents the Gaussian white noise during measurement, with a mean of zero and a covariance of... , This represents the mean square error of the distance estimation. This represents the mean square error of the azimuth estimation. Indicates airborne radar For the target motion state vector The nonlinear measurement function value.

4. The method according to claim 1, characterized in that, Improved PDA algorithms include: (1) Calculation of innovation and covariance: based on the measurement value at the current time. and in two hypotheses and Predicted probability density and Then, the innovation vector of this measurement is calculated. and its corresponding covariance matrix : (2) Adaptive detection threshold setting: Based on the constructed integrated detection and tracking closed-loop framework, an echo detection threshold that is dynamically adjusted with the resolution unit is set for the airborne radar detector. This is to distinguish clutter from actual measurements; Based on the existence of the target The target does not exist Based on the assumptions, the integrated detection and tracking closed-loop framework is constructed as follows: ； in, This indicates the detection threshold for each resolution unit of the radar echo signal. express Airborne radar For the target The amplitude of the echo signal obtained after detection and This indicates whether the target exists or not. Indicates the target echo signal-to-noise ratio. express Airborne radar For the target The pre-detection threshold, Indicates the predicted target state measurement value at the th State measurement values The probability at a given location follows a mean of . Covariance is The joint Gaussian distribution; (3) Nearest neighbor measurement screening: The nearest neighbor algorithm is used, with Mahalanobis distance as the discrimination criterion, to screen the measurements of each resolution unit: ； in, This indicates the inverse operation. If the above inequality holds and the amplitude of the measured signal exceeds the threshold set in step (2), then it is included in the candidate set of measurements; otherwise, it is considered noise and is eliminated. (4) Target state update and fusion: Based on the traditional PDA algorithm for tracking parameter calculation, the local estimates from multiple radar nodes are fused to update the target state and its covariance. ； ； in, express Momentary Goal The fused state estimation vector express Airborne radar For the target The state estimation vector, express Momentary Goal The fused state estimation error covariance matrix, express Airborne radar For the target The state estimation error covariance matrix, This indicates the total number of aircraft.

5. The method according to claim 1, characterized in that, The probability function for target detection by aircraft swarm radar is expressed as: ； in, This represents the average detection probability of targets within the associated gate. Represents the resolving unit Internal measurement The detection probability, This represents the probability density function for predicting the target's state measurement when the target exists. , Indicates the target echo signal-to-noise ratio. express Airborne radar For the target The pre-detection threshold, Indicates the predicted target state measurement value at the th State measurement values The probability at a given location follows a mean of . Covariance is The joint Gaussian distribution.

6. The method according to claim 1, characterized in that, The target tracking accuracy function of a cluster radar is expressed as: ； in, This represents a function indicating the tracking accuracy of a cluster radar for multiple targets. and These represent the transmit beam node selection parameters and receive beam node selection parameters for the aircraft cluster radar, respectively. This indicates the pre-detection threshold value of the aircraft cluster radar. Indicates the target echo signal-to-noise ratio. and These represent the transmit power and signal bandwidth of the aircraft cluster radar, respectively. , and These represent the position, pitch angle, and heading angle of the aircraft cluster, respectively. express Target tracking accuracy at any given time.

7. The method according to claim 1, characterized in that, The mathematical optimization model for integrated management and control of radar transceiver beams and radio frequency resources of aircraft clusters is expressed as follows: ； in, This represents the total transmit power of the aircraft cluster radar. and These represent the total number of aircraft and the total number of targets, respectively. This represents the minimum average target detection probability threshold. This represents the average detection probability of targets within the associated gate. This indicates the target tracking accuracy at the next moment. This represents the minimum target tracking accuracy threshold. , , , , , and These represent the radar transmit beam node selection parameters, receive beam node selection parameters, pre-detection threshold, transmit power, signal bandwidth, pitch angle, and yaw angle of the aircraft cluster radar, respectively. This indicates the upper limit of the number of beams that a single target can be illuminated by the radar of an aircraft swarm. and These represent the maximum number of transmit beams and the maximum number of receive beams for a single airborne radar at each time point. and These represent the highest and lowest values ​​of the change in the radar pre-detection threshold of the aircraft swarm, respectively. and These represent the highest and lowest values ​​of the transmission power variation, respectively. and These represent the highest and lowest values ​​of the signal bandwidth variation, respectively. This indicates the upper limit of the total transmit power of a single aircraft cluster radar node. This represents the upper limit of the total signal bandwidth of a single aircraft cluster radar node. and These represent the minimum and maximum values ​​of the aircraft's heading angle change, respectively. and These represent the minimum and maximum values ​​of the aircraft's pitch angle change, respectively. and These represent the changes in the aircraft's heading angle and pitch angle, respectively.

8. The method according to claim 1, characterized in that, The mathematical optimization model is solved step-by-step using the SDP algorithm, greedy algorithm, tabu search algorithm, and SQP algorithm, including the following steps: (1) The optimization problem is decomposed into a radar beam allocation model for aircraft clusters; The position of the aircraft cluster is fixed as the starting coordinates. It is assumed that the receiving beam allocation is the same as the transmitting beam allocation, that is, all airborne radar nodes are in a self-transmitting and self-receiving state. The radio frequency resources of the aircraft cluster radar are fixed, that is, the pre-detection threshold, transmitting power and signal bandwidth are fixed, and the total power consumption is always kept consistent. Then, the target tracking error is reduced to improve the degree of freedom of subsequent optimization. At this time, the optimization model is transformed into the aircraft cluster radar transmitting beam allocation model. (2) Solving the problem of selecting the radar transmit beam node for the aircraft cluster; The model in step (1) is relaxed into a convex optimization problem using the SDP algorithm: based on Schur complement lemma, an auxiliary matrix is ​​constructed and a positive semidefinite constraint is established accordingly; the weight matrix for selecting radar transmit beam nodes of the aircraft cluster is obtained by solving the convex optimization problem using the interior point method. ;Will Each column The largest among the elements Set one element to 1 and the rest to 0 to generate the beam assignment matrix. ;Will All industries The largest element among the elements is set to . Set the remaining elements to Generate beam assignment matrix ; matrix and A logical AND operation is performed on all row and column elements in the same position to obtain the final allocation result of aircraft cluster nodes and targets; (3) Decompose the optimization problem into a radar receiver beam allocation model for aircraft clusters and solve it; Based on step (2), and considering the allocation results of the transmitted beams, each radar node can receive echoes generated by other nodes in the network to the target. The radio frequency resources and track positions of the aircraft cluster radar are fixed to obtain the aircraft cluster radar receiving beam allocation model. The model is solved by a greedy algorithm to obtain the final receiving beam node selection result. (4) Decompose the optimization problem into a radar radio frequency resource management model for aircraft clusters and solve it; Based on the obtained beam allocation of the aircraft cluster radar, a sub-model of the radio frequency resource optimization problem is constructed by adaptively managing the radio frequency resources of each node, that is, optimizing the pre-detection threshold, transmit power and signal bandwidth of the aircraft cluster radar. The model is then solved by the tabu search method to obtain the final radio frequency resource allocation result. (5) Decompose the optimization problem into an aircraft swarm trajectory planning model and solve it; Based on the results of transmit / receive beam allocation and radio frequency resource allocation, the heading angle of the aircraft cluster radar is optimized. and pitch angle To further improve multi-target tracking performance, an aircraft cluster trajectory planning model was constructed, and the SQP algorithm was used to solve the model to obtain the final trajectory planning result.

9. The method according to claim 8, characterized in that, A greedy algorithm is used to solve the radar radio frequency resource management model for aircraft clusters, including: (1) Based on the current solution Based on the preset neighborhood structure under small perturbations, a set of candidate solutions is generated. And iterate through the candidate set to eliminate all infeasible solutions that do not meet the model constraints; (2) Among the remaining feasible candidate solutions In the middle, find the total transmission power of the aircraft cluster radar. Minimum solution ; (3) If Not on the taboo list In the middle, or meeting the contempt principle: ； in, The total transmit power of the aircraft cluster radar is the minimum solution. This represents the current optimal total transmit power for aircraft cluster radars; If it is accepted as the new solution, then it is accepted; otherwise, the next non-taboo optimal solution is searched in the candidate set. ; (4) Add the variables that changed during this move and their directions to the taboo list. And remove the earliest added entry based on the taboo length; (5) If the new non-taboo optimal solution satisfies the contempt criterion, then update , , To obtain the optimal solution, the unimproved counter is reset. Otherwise, update. ; (6) Continue until the maximum number of iterations is reached. Or the counter exceeds the threshold without improvement Otherwise, proceed to the next iteration: update the iteration index. .

10. The method according to claim 8, characterized in that, The SQP algorithm is used to solve the aircraft swarm trajectory planning model, including: (1) Construct a quadratic programming model and perform a Taylor series expansion of the objective function and constraints; at the current iteration point Nearby, , For heading angle and pitch angle The constructed two-dimensional vector, Indicates the heading angle to be optimized. and pitch angle The constructed two-dimensional vectors, constructing information about the variables Primitive approximation problem of quadratic model: ； in, for transpose; Indicates at point Lagrange function with respect to variable An approximation of the Hessian matrix. Let Lagrange multiplier vector be the current vector. Describe the objective function. Indicates the objective function in The gradient vector at that point, Indicates the first Inequality constraints express transpose, Represents the set of inequality constraint indexes; (2) Solve the above subproblems using quadratic programming to obtain the optimal solution under the current quadratic model. That is, to obtain the optimal search direction. and the corresponding Lagrange multiplier estimates ; (3) Along the search direction Perform a one-dimensional line search to determine the step size. To satisfy the descent condition of the augmented Lagrangian function; then update the iteration point: ； in, The solution is the one that has been iteratively updated. (4) Use the multiplier estimates obtained from solving the subproblems as the initial multipliers for the next iteration. The approximate Hessian matrix is ​​updated using a quasi-Newton method. This allows it to approximate the second derivative of the Lagrange function using the gradient information of the current iteration; (5) Continue until the maximum number of iterations is reached. Or the gradient is less than the algorithm termination index Otherwise, proceed to the next iteration: update the iteration index. .

Images