Joint Optimization Method for Airborne Networked Radar Resource Allocation and Path Planning under Spectrum Coexistence

Abstract

This invention discloses a joint optimization method for airborne networked radar resource allocation and path planning under spectrum coexistence, comprising: S1, establishing the state equation of the moving target, the aircraft motion model, the radar observation model, and the interference model based on the multi-target tracking scenario of airborne networked radar; S2, deriving the predictive Bayesian Cramé-Robber lower bound expression as a performance metric for multi-target tracking; S3, establishing a joint optimization model for airborne networked radar resource allocation and path planning under spectrum coexistence; and S4, solving the joint optimization model for airborne networked radar resource allocation and path planning under spectrum coexistence using a semidefinite programming algorithm, a particle swarm optimization algorithm, and a cyclic minimization algorithm. This invention improves the multi-target tracking performance of airborne networked radar while meeting the tolerable interference energy threshold of the communication system by optimizing radar node selection, radiation resource allocation, and path planning.

Description

Technical Field

[0001] This invention relates to radar resource allocation and path planning technology, specifically to a joint optimization method for airborne network radar resource allocation and path planning under spectrum coexistence. Background Technology

[0002] Modern air warfare exhibits a trend towards system-wide strategic confrontation. With the rapid development of military equipment technology, the time-varying, complex, and unpredictable nature of the electromagnetic spectrum environment poses severe challenges to radar systems. How to establish effective management schemes to reduce mutual interference between radar and communication systems when they share overlapping frequency bands has become a hot topic.

[0003] Airborne networked radar systems feature a technical system that tightly integrates the collaborative use of multiple radar detection resources with information fusion, offering significant advantages in various scenarios such as target detection, tracking, and identification. For multi-target tracking tasks, the accuracy of multi-target tracking can be effectively improved by rationally allocating limited radio frequency resources. The multi-target tracking performance of an airborne networked radar system is also related to the spatial location of each airborne radar. During multi-target tracking missions, reasonable path planning for each aircraft can effectively enhance the multi-target tracking performance of the airborne networked radar.

[0004] There is currently no joint optimization method for airborne networked radar resource allocation and path planning that simultaneously considers the coexistence of radar and communication system spectrum and is geared towards multi-target tracking, which has certain limitations. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a joint optimization method for airborne network radar resource allocation and path planning under spectrum coexistence. By adaptively and dynamically optimizing radar node selection, radiation resource allocation, and aircraft path planning during multi-target tracking of airborne network radar, the method aims to improve the multi-target tracking performance of network radar while meeting the maximum tolerable radar interference energy threshold in the communication area and the total radiation resources of airborne network radar.

[0006] Technical solution: The joint optimization method for airborne network radar resource allocation and path planning under spectrum coexistence of the present invention includes the following steps:

[0007] S1. Based on the multi-target tracking scenario of airborne network radar, establish the state equation of the moving target, the motion model of the carrier aircraft, the radar observation model, and the interference model;

[0008] S2. Derive the expression for the predictive Bayesian Cramé-Robber lower bound BCRLB matrix as a performance metric for multi-target tracking.

[0009] S3. Taking the maximum tolerable radar interference energy in the communication area and the total amount of airborne network radar radiation resources as constraints, and minimizing multi-target tracking BCRLB as the optimization objective, a joint optimization model for airborne network radar resource allocation and path planning under spectrum coexistence is established.

[0010] S4. Adaptive joint dynamic optimization is performed on radar node selection, radiation resource allocation, and aircraft path planning for multi-target tracking of airborne networked radar. The joint optimization model of airborne networked radar resource allocation and path planning under spectrum coexistence is solved by using semidefinite programming algorithm, particle swarm algorithm, and cyclic minimization algorithm.

[0011] Furthermore, the state equation of the moving target established in step S1 is as follows:

[0012]

[0013] in, This represents the state vector of the q-th moving target at time k; Let F represent the state vector of the q-th moving target at time k-1; let F represent the state transition matrix of the q-th target, which can be expressed as: △T0 represents the sampling interval; I represents the Kronecker product; I2 is the second-order identity matrix; W represents Gaussian white noise with zero mean; q represents the q-th moving target; and Q represents the number of moving targets.

[0014] Furthermore, the aircraft motion model established in step S1 is as follows:

[0015]

[0016] Among them, [x n,k ,y n,k [x] represents the position coordinates of aircraft n at time k; n,k-1 ,y n,k-1 ] represents the position coordinates of aircraft n at time k-1; v n,k v represents the flight speed of aircraft n at time k; n,k-1 θ represents the flight speed of aircraft n at time k-1; n,k θ represents the orientation angle of aircraft n at time k; n,k-1 ΔT0 represents the orientation angle of aircraft n at time k-1; ΔT0 represents the sampling interval.

[0017] Furthermore, the radar observation model established in step S1 is as follows:

[0018]

[0019] in, This represents the measurement vector corresponding to the airborne radar n tracking the moving target q at time k; Represents a nonlinear observation function; This represents a measurement noise vector that follows a zero-mean Gaussian distribution. This indicates that at time k, the airborne radar n tracks the moving target q; This indicates that at time k, the airborne radar n did not track the moving target q.

[0020] Furthermore, the interference model established in step S1 includes a radar interference model to a communication base station and a communication base station interference model to a radar.

[0021] The radar interference model for communication base stations is as follows:

[0022]

[0023] in, Represents a binary variable; x represents the transmit power of airborne radar n tracking target q at time k; C,m The coordinates of communication base station m represent the location of the target; Q represents the number of moving targets. Indicates the spatial distribution of radar transmitted signal energy; s n =[s n (1),…,s n (L)] T Represents a waveform sequence with finite intervals; Φ m,n Represented as:

[0024]

[0025] Among them, f U,m,n and f L,m,n T represents the upper and lower bounds of the frequency band jointly covered by the communication area m and the airborne radar n, respectively. s Indicates the signal sampling period;

[0026] The interference model of a communication base station to radar is as follows:

[0027]

[0028] in, χ represents the interference covariance matrix received by airborne radar n from communication base stations; M represents the number of communication base stations; m,n T represents the strength coefficient of the transmission channel; m,n Let m be the time-domain covariance matrix of the interference signal generated by communication base station m on radar n; x represents the half-wavelength steering vector of airborne radar n; R,n This represents the position coordinates of radar n.

[0029] Furthermore, the expression for the BCRLB matrix of target q at time k in step S2 is:

[0030]

[0031] in, The Bayesian information matrix represents the target q state at time k-1; U represents the inverse of the Bayesian information matrix of the target q state at time k-1; q Let F be the Gaussian white noise matrix; F represents the state transition matrix of the q-th target. T This represents the transpose of the state transition matrix of the q-th objective; Represents a binary variable; Represents the nonlinear observation function The Jacobian matrix; This represents the observation error covariance matrix at time k;

[0032] The trace of the predicted BCRLB matrix is ​​used as a metric to characterize the performance of multi-target tracking.

[0033]

[0034] Where trace(·) represents the trace operation of a matrix; This represents the set of radar node selection parameters; and These represent the sets of radar transmit power and dwell time, respectively; v k and θ k Let K represent the set of flight speeds and heading angles of each aircraft at time k.

[0035] Furthermore, the joint optimization model for airborne network radar resource allocation and path planning under spectrum coexistence established in step S3 is as follows:

[0036]

[0037]

[0038] in, Let n represent the transmit power of airborne radar n tracking target q at time k; V represents the signal bandwidth of radar n tracking target q at time k; n,k θ represents the flight speed of aircraft n at time k; n,k θ represents the orientation angle of aircraft n at time k; n,k-1 This represents the orientation angle of aircraft n at time k-1; This represents the set of radar node selection parameters; and These represent the sets of radar transmit power and dwell time, respectively; v k and θ kLet x represent the set of flight velocities and heading angles of each aircraft at time k; C,m The coordinates of the communication base station m are represented by Q; the number of moving targets is represented by ν. min and ν max θ represents the minimum and maximum flight speed of the aircraft, respectively; max Indicates the maximum turning angle of the aircraft; T min and T max These represent the lower and upper bounds of the radar dwell time, respectively; P min and P max These represent the lower and upper bounds of the radar transmit power, respectively; β min and β max These represent the lower and upper bounds of the radar signal bandwidth, respectively. E represents the number of radar nodes allocated to the networked radar system at each moment when tracking each moving target; max This indicates the maximum radar interference energy that a communication base station can tolerate. This indicates that at time k, each airborne radar tracks at most one moving target; T total P represents the sum of the dwell times of all radars illuminating a single moving target; total β represents the sum of the transmitted power of all radars illuminating a single moving target. total It represents the sum of the bandwidths of all radar signals illuminating a single moving target.

[0039] Furthermore, the model solution steps in step S4 are as follows:

[0040] S41. Determine the moving target to be tracked, set the initial values ​​of the transmit power, dwell time, and signal bandwidth of each radar node at time k, and fix the speed and heading angle parameters of the carrier aircraft. (This involves a binary variable...) relaxation The SDP algorithm is used to calculate the weight coefficient of each radar node, and the node with the largest weight coefficient is selected. Each radar node performs target tracking and sets its weighting coefficient. The remaining radar node weighting coefficients

[0041] S42. Based on the radar node selection scheme obtained in step S41, fix the aircraft speed and orientation angle parameters, set the optimization priority of the three variables of transmit power, dwell time and signal bandwidth to be the same, and use the SDP algorithm to optimize the allocation of radar transmit power, dwell time and signal bandwidth.

[0042] S43. Based on the radar node selection scheme and radar resource allocation scheme obtained in steps S41 and S42, the particle swarm algorithm is used to obtain the optimized results of the flight speed and heading angle of each carrier aircraft and the corresponding target tracking error value.

[0043] S44, jump to step S41 until the difference between two consecutive target tracking errors is less than the set threshold ε, that is, the radar node selection result, the flight parameter optimization result of each aircraft, and the radar radiation resource optimization allocation result when the airborne network radar tracks the moving target q at time k.

[0044] S45. Remove the radar node finally selected in step S44, determine the next moving target to be tracked, and jump to step S41 until the tracking schemes for all moving targets have been optimized and allocated. That is, obtain the radar node selection results, the flight parameter optimization results of each aircraft, and the radar radiation resource optimization allocation results when the airborne network radar tracks each moving target at time k.

[0045] The present invention provides a joint optimization system for airborne networked radar resource allocation and path planning under spectrum coexistence, comprising:

[0046] An airborne networked radar system, consisting of N airborne radars in two-dimensional space, is used to track multiple moving targets that are dispersed in space.

[0047] The model building module is used to establish the state equations of moving targets, the aircraft motion model, the radar observation model, and the interference model;

[0048] The metric determination module is used to derive the expression for the predictive Bayesian Cramé-Robber lower bound BCRLB matrix and to serve as a performance metric for multi-target tracking.

[0049] The optimization model building module is used to establish a joint optimization model of airborne network radar resource allocation and path planning under spectrum coexistence, with the maximum tolerable radar interference energy in the communication area and the total amount of airborne network radar radiation resources as constraints, and minimizing multi-target tracking BCRLB as the optimization objective.

[0050] The model solving module is used to perform adaptive joint dynamic optimization of radar node selection, radiation resource allocation, and aircraft path planning during multi-target tracking of airborne networked radar. It uses semidefinite programming algorithm, particle swarm optimization algorithm, and cyclic minimization algorithm to solve the joint optimization model of airborne networked radar resource allocation and path planning under spectrum coexistence.

[0051] The present invention provides a storage medium storing a computer program, which, when executed by at least one processor, implements the steps of the above-described method for joint optimization of airborne network radar resource allocation and path planning under spectrum coexistence.

[0052] Working principle and process:

[0053] This invention considers an airborne networked radar system consisting of N airborne radars in a two-dimensional space to track multiple moving targets deployed in a dispersed manner. First, the state equations of the moving targets, the aircraft motion model, and the radar observation model are established for the airborne networked radar tracking scenario. A BCRLB expression incorporating the radio frequency radiation parameters of each radar and the platform motion parameters is derived, serving as a metric for multi-target tracking accuracy. Then, with constraints including the tolerable radar interference energy of the communication base station and the total radiation resources of the airborne networked radar, and minimizing the trace of the BCRLB matrix as the optimization objective, a joint optimization model for airborne networked radar resource allocation and path planning under spectrum coexistence is established. Finally, the SDP algorithm, particle swarm optimization algorithm, and cyclic minimization algorithm are used to adaptively and dynamically optimize the airborne radar node selection, radiation resource allocation, and path planning. Solving the optimization model yields the optimal solutions for airborne radar node selection, radiation resource allocation, and path planning that achieve the highest multi-target tracking accuracy for the airborne networked radar, thereby improving multi-target tracking performance.

[0054] Beneficial effects: Compared with the prior art, the advantages of the present invention are: (1) By jointly optimizing the parameters such as radar node selection, radar radiation resources, flight orientation angle and speed of each aircraft in the process of multi-target tracking, the multi-target tracking accuracy of airborne network radar is effectively improved under the constraints of the radar interference energy threshold that the communication base station can tolerate and the total amount of radiation resources of airborne network radar. (2) The optimal radar node selection scheme, radar resource configuration and path planning scheme are realized, which effectively improves the multi-target tracking performance of airborne network radar. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method of the present invention;

[0056] Figure 2 A map showing the target's trajectory and the distribution of airborne networked radar;

[0057] Figure 3 The proposed algorithm is compared with other comparative algorithms for the objective 1 ARMSE.

[0058] Figure 4 The proposed algorithm is compared with other comparative algorithms for the target 2ARMSE. Detailed Implementation

[0059] The structure and working process of the present invention will be further described below with reference to the accompanying drawings.

[0060] This invention considers an airborne networked radar system consisting of N airborne radars in a two-dimensional space to track multiple moving targets deployed in a dispersed manner. First, the state equations of the moving targets, the aircraft motion model, and the radar observation model are established for the airborne networked radar tracking scenario. A BCRLB expression incorporating the radio frequency radiation parameters of each radar and the platform motion parameters is derived, serving as a metric for multi-target tracking accuracy. Then, with constraints including the tolerable radar interference energy of the communication base station and the total radiation resources of the airborne networked radar, and minimizing the trace of the BCRLB matrix as the optimization objective, a joint optimization model for airborne networked radar resource allocation and path planning under spectrum coexistence is established. Finally, the SDP algorithm, particle swarm optimization algorithm, and cyclic minimization algorithm are used to adaptively and dynamically optimize the airborne radar node selection, radiation resource allocation, and path planning to improve multi-target tracking performance.

[0061] This invention, starting from actual combat scenarios, proposes a joint optimization method for airborne networked radar resource allocation and path planning under spectrum coexistence. Under the constraints of the radar interference energy threshold tolerable by communication base stations and the total radiation resources of airborne networked radars, the method aims to minimize the trace of the BCRLB matrix. It adaptively and dynamically optimizes airborne radar node selection, radiation resource allocation, and path planning, thereby improving the multi-target tracking performance of the networked radar. Figure 1 As shown, the joint optimization method for airborne network radar resource allocation and path planning under spectrum coexistence of the present invention includes the following steps:

[0062] S1. For multi-target tracking scenarios of airborne networked radar, establish the state equation of the moving target, the motion model of the carrier aircraft, the radar observation model, and the interference model.

[0063] Assume an airborne networked radar system consists of N airborne radars, where the position coordinates of the nth radar can be represented as x. R,n =(x R,n ,y R,n Let n = 1, 2, ..., N. Assuming the moving target is undergoing uniform linear motion, its state equation can be expressed as:

[0064]

[0065] in, This represents the state vector of the q-th moving target at time k; Let F represent the state vector of the q-th moving target at time k-1; let F represent the state transition matrix of the q-th target, which can be expressed as: △T0 represents the sampling interval; I represents the Kronecker product; I2 is the second-order identity matrix; W represents Gaussian white noise with zero mean; q represents the q-th moving target; Q represents the number of moving targets.

[0066] For an airborne radar performing a multi-target tracking mission, its trajectory is related to the aircraft's flight speed and heading angle. Assuming the aircraft's acceleration remains constant from time k-1 to time k, then the position coordinates x of the airborne radar n at time k are... n,k =(x n,k ,y n,k ), n=1,2,…,N can be represented as:

[0067]

[0068] Among them, v n,k θ represents the flight speed of aircraft n at time k; n,k This represents the orientation angle of aircraft n at time k.

[0069] This invention assumes that each radar can only track one target at any given time, and defines a binary variable here. This indicates that at time k, the airborne radar n tracks the moving target q; If the airborne radar n does not track the moving target q at time k, then the measurement model of radar n for target q at time k, i.e., the radar observation model, can be expressed as:

[0070]

[0071] in, This represents the measurement vector corresponding to the airborne radar n tracking the moving target q at time k; The nonlinear observation function can be expressed as:

[0072]

[0073] in, and Let represent the distance and azimuth of target q relative to radar n at time k, respectively; Represents the position coordinates of target q at time k; (x R,n ,y R,n () represents the position coordinates of radar n; Let represent the measurement noise vector that follows a zero-mean Gaussian distribution, and its covariance matrix is ​​expressed as:

[0074]

[0075] in, Let represent the measurement interference noise covariance matrix applied by the communication base station to radar n, where Let represent the radar transmit power of radar n tracking target q at time k; c represents the speed of light; This represents the transmitted waveform sequence of radar n; This represents the half-wavelength steering vector of radar n. The signal bandwidth of radar n tracking target q at time k is represented by λ and γ, respectively, representing the radar wavelength and antenna aperture. The signal-to-noise ratio of the echo from radar n tracking target q at time k can be expressed as:

[0076]

[0077] in, T represents the dwell time of radar n tracking target q at time k; r Indicates the pulse repetition period; G t Indicates the transmit antenna gain; G r Indicates the receiver antenna gain; G represents the radar cross-section of target q relative to airborne radar n; RP The signal represents the radar receiver processing gain; k is the Boltzmann constant; T o This indicates the noise temperature of the receiver; F represents the bandwidth of the matched filter of the airborne radar n to the target q receiver at time k; r This represents the noise figure of the radar receiver; θ represents the angular difference between the true azimuth of target q at time k and the direction of the radar beam transmitted at time n; 3dB This indicates the 3dB antenna beamwidth.

[0078] In a spectrum coexistence environment, mutual interference between airborne networked radar systems and communication base stations can affect the detection and tracking performance of the radar system and negatively impact the normal operation of the communication base stations. Therefore, this paper analyzes the mutual interference between radar and communication base stations. First, considering the interference from radar to communication base stations, this invention uses the joint spatial-frequency domain distribution of radar transmitted signal energy to characterize the interference intensity. The radar interference model for communication base stations is as follows:

[0079]

[0080] Where, x C,m Indicates the location coordinates of communication base station m; Indicates the spatial distribution of radar transmitted signal energy; s n =[s n (1),…,s n (L)α T Represents a waveform sequence with finite intervals; Φ represents the conjugate transpose of a waveform sequence with finite intervals; m,n It can be represented as:

[0081]

[0082] Among them, f U,m,n and f L,m,n represents the upper and lower bounds of the frequency band jointly covered by the communication area m and the airborne radar n, respectively; u and v represent the row and column numbers of the matrix, respectively; T s This indicates the signal sampling period.

[0083] The interference of a communication base station to a radar can be viewed as a combination of various randomly modulated signals. Assuming that the signal form can be approximated as a cyclically symmetric band-limited complex Gaussian sequence occupying a certain bandwidth, the time-domain covariance matrix T of the interference signal generated by the communication base station m to the radar n is defined. m,n for:

[0084]

[0085] Where, N m,n This represents the power spectral density intensity of the signal. Considering range attenuation and transmission loss, the interference noise exerted by the communication base station m on the radar n can be expressed as:

[0086]

[0087] Where, χ m,n Indicates the strength coefficient of the transmission channel; This represents the interference sequence generated by communication base station m within the radar frequency band n; Let m represent the azimuth angle between communication base station m and radar n. Assuming that the signals from each communication base station are orthogonal, the interference covariance matrix received by radar n from the communication base stations, i.e., the interference model of the communication base stations to the radar, can be expressed as:

[0088]

[0089] in, Let M represent the interference covariance matrix received by airborne radar n from communication base stations; M represents the number of communication base stations. This represents the half-wavelength steering vector of airborne radar n; x represents the conjugate transpose of the half-wavelength steering vector of airborne radar n; R,n This represents the position coordinates of radar n.

[0090] S2. Under the condition of unbiased parameter estimation, BCRLB provides a lower bound for the mean square error of moving target tracking and is often used as a performance indicator for networked radar tracking of moving targets. To effectively solve the problem of optimizing the configuration of radar radio frequency radiation parameters and platform motion parameters, this invention derives a BCRLB expression that includes each radar radio frequency radiation parameter and platform motion parameter, and uses this as a measure of multi-target tracking accuracy. The specific calculation steps are as follows:

[0091] The expression for the k-time BCRLB matrix of the target state estimation error is:

[0092]

[0093] Among them, the superscript (·) T Indicates the transpose of a matrix; superscript (·) -1 U represents the inverse matrix of a matrix; q The matrix is ​​Gaussian white noise. The Bayesian information matrix represents the target q state at time k-1; This represents the observation error covariance matrix at time k; Represents the nonlinear observation function The Jacobian matrix.

[0094] This invention uses the trace of the predicted BCRLB matrix as a metric to characterize the accuracy of multi-target tracking:

[0095]

[0096] Where trace(·) represents the trace operation of a matrix; This represents the predicted state vector of target q at time k; This represents the set of radar node selection parameters; and These represent the sets of radar transmit power, dwell time, and signal bandwidth, respectively; v k and θ k Let K represent the set of flight speeds and heading angles of each aircraft at time k.

[0097] S3. To effectively improve the target tracking accuracy, radio frequency resource utilization, and combat effectiveness of radar detection systems, this invention addresses the multi-target tracking resource allocation problem under spectrum coexistence. It establishes a joint optimization model for airborne network radar resource allocation and path planning under spectrum coexistence, with constraints including the tolerable radar interference energy of communication base stations and the total radiation resources of airborne network radars, and minimizing the trace of the BCRLB matrix as the optimization objective.

[0098] The joint optimization model for airborne networked radar resource allocation and path planning under spectrum coexistence established in this invention is shown in equation (13):

[0099]

[0100]

[0101] in, This represents the predicted state vector of target q at time k; ν represents the dwell time of radar n tracking target q at time k; min and νmax θ represents the minimum and maximum flight speed of the aircraft, respectively; max Indicates the maximum turning angle of the aircraft; T min and T max These represent the lower and upper bounds of the radar dwell time, respectively; P min and P max These represent the lower and upper bounds of the radar transmit power, respectively; β min and β max These represent the lower and upper bounds of the radar signal bandwidth, respectively. E represents the number of radar nodes allocated to the networked radar system at each moment when tracking each moving target; max This indicates the maximum radar interference energy that a communication base station can tolerate. This indicates that at time k, each radar tracks at most one moving target; T total P represents the sum of the dwell times of all radars illuminating a single moving target; total β represents the sum of the transmitted power of all radars illuminating a single moving target. total It represents the sum of the bandwidths of all radar signals illuminating a single moving target.

[0102] S4. The optimization model (13) is a non-convex, nonlinear optimization problem containing five variables: radar node selection, transmit power, dwell time, aircraft speed, and heading angle. This invention decomposes the optimization model (13) into multiple sub-convex problems, uses the SDP algorithm and particle swarm optimization algorithm to solve the convex problems, and combines the cyclic minimum method to adaptively and jointly optimize the flight parameters of each aircraft and the radar radiation resource parameters. The specific solution steps are as follows:

[0103] S41. Determine the moving target to be tracked, set the initial values ​​of the transmit power, dwell time, and signal bandwidth of each radar node at time k, and fix the speed and heading angle parameters of the carrier aircraft. (This involves a binary variable...) relaxation The SDP algorithm is used to calculate the weight coefficient of each radar node, and the node with the largest weight coefficient is selected. Each radar node performs target tracking and sets its weighting coefficient. The remaining radar node weighting coefficients

[0104] S42. Based on the radar node selection scheme obtained in step S41, fix the aircraft speed and orientation angle parameters, set the optimization priority of the three variables of transmit power, dwell time and signal bandwidth to be the same, and use the SDP algorithm to optimize the allocation of radar transmit power, dwell time and signal bandwidth.

[0105] S43. Based on the radar node selection scheme and radar resource allocation scheme obtained in steps S41 and S42, the particle swarm algorithm is used to obtain the optimized results of the flight speed and heading angle of each carrier aircraft and the corresponding target tracking error value.

[0106] S44, jump to step S41, until the difference between two consecutive target tracking errors is less than the set threshold ε, then the radar node selection result, the flight parameter optimization result of each aircraft, and the radar radiation resource optimization allocation result when the airborne networking radar tracks the moving target q at time k can be obtained.

[0107] S45. Remove the radar node finally selected in step S44, determine the next moving target to be tracked, and jump to step S41 until the tracking schemes for all moving targets have been optimized and allocated. Then, the radar node selection results, the flight parameter optimization results of each carrier aircraft, and the radar radiation resource optimization allocation results when the networked radar tracks each moving target at time k can be obtained.

[0108] S5. Simulation Results:

[0109] The relevant simulation parameter settings in this embodiment of the invention are shown in Table 1 below:

[0110] Table 1 Airborne Networked Radar Parameter Settings

[0111]

[0112] Consider an airborne networked radar system consisting of N=6 airborne radars, all with identical transmission parameters. The system needs to simultaneously track Q=2 targets. Target 1 has an initial position of [-80, 20] km and flies at a constant speed of [150, 260] m / s; Target 2 has an initial position of [80, 60] km and flies at a constant speed of [-150, -260] m / s. There are M=2 communication base stations within the radar detection area, with their center positions at [-15, 20] km and [25, 60] km respectively. The maximum tolerable interference energy threshold for each communication base station is set to E. max =4.2J. The sampling interval of the networked radar is ΔT = 3s, and the tracking duration is 150s. The target trajectory and the distribution map of the airborne networked radar are shown below. Figure 2 As shown.

[0113] The average root mean square error (ARMSE) for target tracking is defined as follows:

[0114]

[0115] Where, N MC For the number of Monte Carlo experiments, Let N be the estimated position of the target obtained in the nth Monte Carlo experiment. MC =100. Figure 3 and Figure 4 A comparison of the proposed algorithm with other comparative algorithms, such as ARMSE, is presented. As can be seen from the figures, this invention effectively reduces multi-target tracking errors and improves the multi-target tracking performance of airborne networked radar systems in environments with coexisting spectrum.

[0116] The innovative aspects of this invention are:

[0117] 1. Assume several targets are dispersed on a two-dimensional plane, and an airborne networked radar system consisting of N airborne radars with limited total radiation resources tracks these targets. For this scenario of airborne networked radar tracking multiple targets, we construct the state equations of the moving targets, the aircraft motion model, the radar measurement model, and the interference model. We derive the BCRLB matrix expression, which includes airborne radar radio frequency radiation resource parameters (i.e., the set of radar node selection parameters, radar transmit power, and dwell time) and platform flight parameters (i.e., the set of flight speeds and heading angles of each aircraft), and use this as a metric for measuring the multi-target tracking accuracy of the airborne networked radar.

[0118] 2. Under the constraints of the tolerable radar interference energy of communication base stations and the total radiation resources of airborne network radar, and with the optimization objective of minimizing the trace of the BCRLB matrix, a joint optimization model for airborne network radar resource allocation and path planning under spectrum coexistence is established. Finally, the SDP algorithm, particle swarm optimization algorithm, and cyclic minimization algorithm are used to solve this optimization model. By solving this optimization model, the optimal solutions for airborne radar node selection, radiation resource allocation, and path planning that achieve the highest multi-target tracking accuracy are obtained under the constraints of the tolerable radar interference energy threshold of communication base stations and the total radiation resources of airborne network radar.

Claims

1. A joint optimization method for airborne networked radar resource allocation and path planning under spectrum coexistence, characterized in that, Includes the following steps: S1. Based on the multi-target tracking scenario of airborne network radar, establish the state equation of the moving target, the motion model of the carrier aircraft, the radar observation model, and the interference model; S2. Derive the expression for the predictive Bayesian Cramé-Robber lower bound BCRLB matrix as a performance metric for multi-target tracking. S3. Using the maximum tolerable radar interference energy in the communication area and the total radiation resources of airborne network radar as constraints, and minimizing the multi-target tracking (BCRLB) as the optimization objective, a joint optimization model for airborne network radar resource allocation and path planning under spectrum coexistence is established; the expression is: ； in, Indicate target exist The predicted state vector value at time 1; Represents a binary variable; express Airborne radar Tracking target The transmission power; Indicates in Time Radar Tracking target Duration of stay; Indicates in Time Radar Tracking target The signal bandwidth; express Time Carrier Flight speed; express Time Carrier Orientation angle; express Time Carrier Orientation angle; This represents the set of radar node selection parameters; , and These represent the radar transmit power, dwell time, and signal bandwidth, respectively. and They represent The set of flight speeds and heading angles of each aircraft at any given moment; Indicates communication base station Position coordinates; Indicates the number of moving targets; Indicates the number of airborne radars; and These represent the minimum and maximum flight speeds of the aircraft, respectively. Indicates the maximum turning angle of the aircraft; and These represent the lower and upper bounds of the radar dwell time, respectively. and These represent the lower and upper bounds of the radar's transmit power, respectively. and These represent the lower and upper bounds of the radar signal bandwidth, respectively. This indicates the number of radar nodes allocated to the networked radar system at each moment when tracking each moving target; This indicates the maximum radar interference energy that a communication base station can tolerate. express Each airborne radar can track a maximum of one moving target at any given time; This represents the sum of the dwell times of all radars illuminating a single moving target; This represents the sum of the transmitted power of all radars illuminating a single moving target. It represents the sum of the bandwidths of all radar signals illuminating a single moving target; S4. Adaptive joint dynamic optimization is performed on radar node selection, radiation resource allocation, and aircraft path planning for multi-target tracking in airborne networked radar. The joint optimization model for airborne networked radar resource allocation and path planning under spectrum coexistence is solved using a semidefinite programming algorithm, a particle swarm optimization algorithm, and a cyclic minimization algorithm. The model solution steps are as follows: S41. Determine the moving target to be tracked and set... Initial values ​​of transmit power, dwell time, and signal bandwidth for each radar node at any given time, with fixed parameters for the aircraft's speed and heading angle, are used to calculate the binary variables. relaxation The SDP algorithm is used to calculate the weight coefficient of each radar node, and the node with the largest weight coefficient is selected. Each radar node performs target tracking and sets its weighting coefficient. The remaining radar node weighting coefficients ; S42. Based on the radar node selection scheme obtained in step S41, fix the aircraft speed and orientation angle parameters, set the optimization priority of the three variables of transmit power, dwell time and signal bandwidth to be the same, and use the SDP algorithm to optimize the allocation of radar transmit power, dwell time and signal bandwidth. S43. Based on the radar node selection scheme and radar resource allocation scheme obtained in steps S41 and S42, the particle swarm algorithm is used to obtain the optimized results of the flight speed and heading angle of each carrier aircraft and the corresponding target tracking error value. S44, Jump to step S41, until the difference between two consecutive target tracking errors is less than the set threshold. That is, to obtain Airborne networked radar tracks moving targets at all times The results of radar node selection, optimization of flight parameters for each aircraft, and optimization allocation of radar radiation resources at that time. S45. Remove the radar node finally selected in step S44, determine the next moving target to track, and jump to step S41 until the tracking scheme for all moving targets has been optimized and assigned, thus obtaining the desired result. The results of radar node selection, flight parameter optimization, and radar radiation resource optimization allocation for each aircraft when the airborne network radar tracks various moving targets.

2. The joint optimization method for airborne networked radar resource allocation and path planning under spectrum coexistence as described in claim 1, characterized in that, The state equation of the moving target established in step S1 is: ； in, express Time of the first The state vector of a moving target; express Time of the first The state vector of a moving target; Indicates the first The state transition matrix of each objective is represented as follows: , Indicates the sampling interval; Indicates the Kronecker product; It is a second-order identity matrix; This represents Gaussian white noise with zero mean. Indicates the first One sporting goal, Indicates the number of moving targets.

3. The joint optimization method for airborne networked radar resource allocation and path planning under spectrum coexistence as described in claim 1, characterized in that, The aircraft motion model established in step S1 is as follows: ； in, express Time Carrier Position coordinates; express Time Carrier Position coordinates; express Time Carrier Flight speed; express Time Carrier Flight speed; express Time Carrier Orientation angle; express Time Carrier Orientation angle; Indicates the sampling interval.

4. The joint optimization method for airborne networked radar resource allocation and path planning under spectrum coexistence as described in claim 1, characterized in that, The radar observation model established in step S1 is as follows: ； in, express Airborne radar Tracking moving targets The corresponding measurement vector; Represents a nonlinear observation function; This represents a measurement noise vector that follows a zero-mean Gaussian distribution. Indicates in Airborne radar For moving targets Track; Indicates in Airborne radar Untracked moving target .

5. The joint optimization method for airborne networked radar resource allocation and path planning under spectrum coexistence as described in claim 1, characterized in that, The interference model established in step S1 includes the radar interference model to the communication base station and the communication base station interference model to the radar. The radar interference model for communication base stations is as follows: ； in, Represents a binary variable; express Airborne radar Tracking target The transmission power; Indicates communication base station Position coordinates; Indicates the number of moving targets; This indicates the spatial distribution of radar transmitted signal energy; Represents a waveform sequence with finite intervals; This represents the conjugate transpose of a waveform sequence with finite intervals. Represented as: ； in, and Representing communication areas and airborne radar Together they cover the upper and lower boundaries of the frequency band; and These represent the row number and column number of the matrix, respectively. Indicates the signal sampling period; The interference model of a communication base station to radar is as follows: ； in, Indicates airborne radar The interference covariance matrix received from the communication base station; Indicates the number of communication base stations; Indicates the strength coefficient of the transmission channel; Indicated by communication base station radar The time-domain covariance matrix of the generated interference signal; Indicates airborne radar The half-wavelength steering vector; Indicates airborne radar The conjugate transpose of the half-wavelength steering vector; Indicates radar The location coordinates.

6. The joint optimization method for airborne networked radar resource allocation and path planning under spectrum coexistence as described in claim 1, characterized in that, In step S2 Momentary Goal The expression for the BCRLB matrix is: ； in, express Momentary Goal The Bayesian information matrix of the state; express Momentary Goal The inverse of the Bayesian information matrix of the state; The matrix is ​​Gaussian white noise. Indicates the first The state transition matrix of each objective. Indicates the first Transpose of the state transition matrix of each objective; Represents a binary variable; Represents the nonlinear observation function The Jacobian matrix; express The covariance matrix of observation errors at any given time; The trace of the predicted BCRLB matrix is ​​used as a metric to characterize the performance of multi-target tracking. ； in, This represents the trace operation of a matrix; Indicate target exist The predicted state vector value at time 1; This represents the set of radar node selection parameters; , and These represent the radar transmit power, dwell time, and signal bandwidth, respectively. and They represent The set of flight speeds and heading angles of each aircraft at any given time.

7. A system for the joint optimization method of airborne networked radar resource allocation and path planning under spectrum coexistence as described in any one of claims 1 to 6, characterized in that, include: Airborne networked radar system, which consists of two-dimensional space It consists of an airborne radar system used to track multiple moving targets that are dispersed in space; The model building module is used to establish the state equations of moving targets, the aircraft motion model, the radar observation model, and the interference model; The metric determination module is used to derive the expression for the predictive Bayesian Cramé-Robber lower bound BCRLB matrix and to serve as a performance metric for multi-target tracking. The optimization model building module is used to establish a joint optimization model of airborne network radar resource allocation and path planning under spectrum coexistence, with the maximum tolerable radar interference energy in the communication area and the total amount of airborne network radar radiation resources as constraints, and minimizing multi-target tracking BCRLB as the optimization objective. The model solving module is used to perform adaptive joint dynamic optimization of radar node selection, radiation resource allocation, and aircraft path planning during multi-target tracking of airborne networked radar. It uses semidefinite programming algorithm, particle swarm optimization algorithm, and cyclic minimization algorithm to solve the joint optimization model of airborne networked radar resource allocation and path planning under spectrum coexistence.

8. A storage medium, characterized in that, The storage medium stores a computer program, which, when executed by at least one processor, implements the steps of the joint optimization method for airborne network radar resource allocation and path planning under spectrum coexistence as described in any one of claims 1-6.

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