Joint optimization allocation method of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection

Abstract

The present invention discloses a method for joint optimization and allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection, comprising the following steps: S1, constructing a scenario for asynchronous multi-target tracking in a heterogeneous multi-radar network; S2, constructing a predicted BCRLB matrix for target state estimation errors under non-ideal detection, and determining a metric for measuring the accuracy of asynchronous multi-target tracking; S3, establishing a joint optimization model for multi-domain resources in asynchronous multi-target tracking in a heterogeneous multi-radar network under non-ideal detection; and S4, solving the optimization model based on a four-step decomposition algorithm using a sequential quadratic programming algorithm and a cyclic minimization method, first solving the radar node selection problem, and then solving the optimization allocation problem of radiation power, dwell time, and signal bandwidth. The present invention effectively improves the radio frequency stealth performance of the heterogeneous multi-radar network.

Description

Technical Field

[0001] The present invention belongs to radar signal processing technology, and in particular relates to a method for joint optimization allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection. Background Art

[0002] Radar is known as the "eyes" of modern warfare, capable of detecting and tracking targets at all times and in all weather conditions. In the context of modern warfare, from the perspective of target detection performance, traditional single-base radars, limited by platform limitations, have limited radiation resources, making them incapable of completing their intended target detection missions and susceptible to interception and attack by enemy passive detection systems. From the perspective of large-scale strike capabilities, single-base radars also cannot meet the operational requirements of simultaneously striking multiple targets. However, compared to single-base radars, heterogeneous multi-radar network systems offer superior performance. These systems, composed of multiple radar networks with different operating systems, offer significant advantages in spatial multiplexing, waveform diversity, and anti-interference capabilities. Heterogeneous multi-radar networks achieve long-range multi-target detection by integrating multiple measurements from different radar nodes in the network. They possess strong distributed parallel perception and computing capabilities, superior robustness, and low mission error tolerance. Therefore, heterogeneous multi-radar networks hold broad application prospects in areas such as airspace surveillance, target detection, parameter estimation, and fire control. However, with the development of advanced materials and electronics, various advanced passive detection modes and systems have posed a significant threat to heterogeneous multi-radar networks, severely interfering with their battlefield survivability and penetration capabilities. Therefore, in this environment, heterogeneous multi-radar networks urgently need to utilize RF stealth technology to reduce the probability of being intercepted by enemy passive detection systems and improve their RF stealth performance.

[0003] RF radiation control technology is one of the key approaches to enabling radar systems to achieve a certain level of RF stealth capability. Radar systems must radiate the lowest possible energy while completing their assigned detection mission, tailored to different operational environments and operating modes. Currently, scholars at home and abroad have conducted extensive research on radar RF radiation control, achieving the goal of minimizing radiation resource consumption through adaptive optimization of radar emission parameters within the system. However, in actual combat, due to various uncertainties such as target radar cross section (RCS) fluctuations, electromagnetic attenuation, dense environmental clutter, and target echo signal attenuation, radar systems may not successfully detect all tracked targets. Missed detections may occur, resulting in a decrease in target detection performance during the tracking process. This situation is referred to as non-ideal detection. Therefore, rationally optimizing the allocation of multi-domain RF radiation resources within heterogeneous multi-radar networks under non-ideal detection to enhance the system's RF stealth performance is both urgent and necessary, and has important military applications.

[0004] Currently, there is a wealth of research on optimizing radar RF radiation resource management in multi-target tracking scenarios. However, most of this research focuses on synchronous multi-target tracking and fails to consider the impact of asynchronous multi-target tracking on radar systems, resulting in certain limitations. In summary, there is no existing method for jointly optimizing the allocation of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a method for joint optimization allocation of multi-domain resources of heterogeneous multi-radar networks under non-ideal detection, so as to improve the radio frequency stealth performance of heterogeneous multi-radar networks.

[0006] Technical solution: The method for joint optimization allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection of the present invention comprises the following steps:

[0007] S1. Construct a scenario for asynchronous multi-target tracking in a heterogeneous multi-radar network, establish a heterogeneous multi-radar network system scenario, target motion model, and asynchronous radar measurement model;

[0008] S2. Using radar node selection method, radar radiation power, radar dwell time and radar signal effective bandwidth as independent variables, construct the predicted BCRLB matrix of target state estimation error under non-ideal detection, and take the sum of the first and second elements on its diagonal as the measurement index of asynchronous multi-target tracking accuracy;

[0009] S3. Using the pre-set asynchronous multi-target tracking accuracy threshold and the system RF radiation resources as constraints, and minimizing the multi-domain resource consumption of each radar node in the system illuminating the target as the optimization goal, a multi-domain resource joint optimization model for asynchronous multi-target tracking in a heterogeneous multi-radar network under non-ideal detection is established.

[0010] S4. Solve the optimization model, specifically: based on the four-step decomposition algorithm of the sequential quadratic programming SQP algorithm and the cyclic minimization method, first simplify the optimization model into a function containing only the radar node selection constraints, and solve the radar node selection problem; secondly, by solving the radar nodes, simplify the optimization model, and perform an equivalent transformation on the objective function in the simplified optimization model to obtain three sub-optimization problems that optimize the radiation power resources, residence time resources, and signal bandwidth resources respectively, and solve the three sub-optimization problems separately to obtain the optimal control results of the radiation power, the optimal control results of the residence time, and the optimal control results of the signal bandwidth; finally, the optimal resource allocation result of asynchronous multi-target tracking of the heterogeneous multi-radar network system is obtained.

[0011] Furthermore, the heterogeneous multi-radar network system scenario established in step S1 is:

[0012] The heterogeneous multi-radar network system consists of M radar networks of different types and working independently. There are N m radar nodes, and the nth (n=1,2,…,N m The coordinates of the radar nodes are (x n,m ,y n,m ); radar nodes in different radar networks have different operating modes, the carrier frequencies of the signals transmitted by each radar node are the same or different, and for the same target, the initial sampling time and sampling interval of each radar node are the same or different; the following three types of radar networks and radiation resource constraints are defined:

[0013] (1) Centralized MIMO radar network: In a centralized MIMO radar network, the dwell time of all radar nodes illuminating the target is fixed, but the radiated power and transmitted signal bandwidth are different;

[0014] (2) Phased array radar network: The radar nodes in this radar network can adaptively rotate the beam to illuminate multiple targets. The radiation power of all radar nodes is fixed, but the dwell time and transmission signal bandwidth are different;

[0015] (3) Mechanical scanning radar network: The radar nodes in this radar network have fixed operating parameters, that is, all radar nodes illuminate the target with fixed radiation power, dwell time and transmission signal bandwidth.

[0016] Furthermore, the target motion model established in step S1, that is, the target motion state equation is expressed as:

[0017]

[0018] in, is the state vector of the qth target at the kth fusion sampling interval, is the state vector of the qth target at the k-1th fusion sampling interval, F is the state transfer matrix of the target, is the mean white Gaussian process noise;

[0019] The established asynchronous radar measurement model, that is, the measurement equation is:

[0020]

[0021] in, represents the measurement vector of the s-th measurement, represents the nonlinear observation function of the sth measurement, represents the error of the sth measurement, is a binary variable used to characterize the pairing index between radar nodes and targets in heterogeneous multi-radar networks. The expression is:

[0022]

[0023] Furthermore, the predicted BCRLB matrix of the target state estimation error under non-ideal detection in step S2 is The calculation formula is:

[0024]

[0025] in, is mean white Gaussian process noise The covariance matrix of ; F is the state transfer matrix of the target; is the inverse of the Bayesian information matrix; It is a binary variable used to characterize the pairing index between radar nodes and targets in heterogeneous multi-radar networks; is a binary variable used to characterize the detection of paired targets by the radar node within the kth fusion sampling interval; is the Jacobian matrix of the nonlinear observation function; is the error of the sth measurement The covariance matrix of In the i-th detection case, the heterogeneous multi-radar network has The probability that a radar node detects target q; M is the type of radar network in the heterogeneous multi-radar network system; N m is the number of radar nodes in the mth radar network; m=1,2,…,M; is the number of measurement information of target q by the nth radar node in the mth radar network within the kth fusion sampling interval; s is the sth measurement information; in the formula, the superscript T represents the transpose of the matrix, and the superscript -1 represents the inverse of the matrix;

[0026] The sum of the first and second elements on the diagonal represents the lower bound of the MSE of the predicted target position estimation, which is extracted as a measure of the accuracy of asynchronous multi-target tracking and expressed as:

[0027]

[0028] in, represents the transpose of the matrix consisting of the pairing indices of each radar node and target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix composed of the radiation power of each radar node illuminating the target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix consisting of the dwell time of each radar node illuminating the target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix consisting of the effective bandwidth of the target transmission signal measured by each radar node in the heterogeneous multi-radar network during the kth fusion sampling interval; express The first element on the diagonal; express The second element on the diagonal.

[0029] Furthermore, the multi-domain resource joint optimization model for asynchronous multi-target tracking in heterogeneous multi-radar networks under non-ideal detection established in step S3 is:

[0030]

[0031]

[0032] in, represents the transpose of the matrix consisting of the pairing indices of each radar node and target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix composed of the radiation power of each radar node illuminating the target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix consisting of the dwell time of each radar node illuminating the target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix composed of the effective bandwidth of the target transmission signal measured by each radar node in the heterogeneous multi-radar network within the kth fusion sampling interval; Q represents the number of targets; M is the type of radar network in the heterogeneous multi-radar network system; N m is the number of radar nodes in the mth radar network; It is a binary variable used to characterize the pairing index between radar nodes and targets in heterogeneous multi-radar networks; and They represent the normalized radiation power variable, residence time variable and signal bandwidth variable respectively. and They represent the power, time, and bandwidth upper limits of the nth radar node in the mth radar network respectively; η q represents the preset target q tracking accuracy threshold; ψ CMIMO represents the set of centralized MIMO radar network nodes in the heterogeneous multi-radar network; ψ PAR represents the set of phased array radar network nodes; ψ MSR Represents a collection of mechanical scanning radar network nodes; represents the radiated power of radar nodes in heterogeneous multi-radar networks; and They represent the lower and upper limits of the radiation power of radar nodes in heterogeneous multi-radar networks respectively; P PAR and P MSR denote the fixed radiated powers of the phased array radar network and the mechanically scanned radar network, respectively; Indicates the dwell time of the radar illuminating the target; and Respectively represent the lower and upper limits of the residence time; T CMIMO and T MSR denote the fixed dwell time of the centralized MIMO radar network and the mechanical scanning radar network, respectively; represents the effective bandwidth of the target q’s transmitted signal measured by the nth radar node in the mth radar network within the kth fusion sampling interval; β MSR Represents the fixed signal bandwidth of a mechanically scanned radar network; and They represent the lower and upper limits of the centralized MIMO radar network signal bandwidth respectively; and They represent the lower and upper limits of the phased array radar network signal bandwidth respectively; L max Indicates L max Radar nodes.

[0033] Furthermore, the specific method for solving the optimization model in step S4 is:

[0034] S41. Define three initial radiation power matrices respectively Dwell Time Matrix Sum signal bandwidth matrix Heterogeneous multi-radar network based on matrix and Allocate the corresponding radiation resources to each radar node for illumination; at the same time, the binary variable Relaxation The optimization model is simplified to a function containing only the radar node selection constraints, which can be expressed as:

[0035]

[0036]

[0037] The radar node selection coefficient matrix is ​​solved using the SQP algorithm Then, The coefficients in the are arranged in descending order, and the radar nodes corresponding to the coefficients are selected from high to low until the constraints are met. Finally, the pairing index of the selected radar node and the target is set to Set the pairing index of all unselected radar nodes and targets to That is, the radar node selection result is obtained

[0038] S42. By solving the radar node in step S41, the optimization model is simplified to:

[0039]

[0040]

[0041] By performing equivalent transformation on the objective function in the simplified optimization model, three sub-optimization problems are obtained, which are respectively optimizing the radiation power resource, the residence time resource and the signal bandwidth resource.

[0042] First, for the radiation power resource sub-optimization problem, the dwell time and signal bandwidth are fixed, and the SQP algorithm is used to solve the optimal radiation power control result when tracking the target. Second, for the dwell time resource sub-optimization problem, the signal bandwidth is fixed, and the obtained radiation power result is substituted into the dwell time resource sub-optimization problem, and the SQP algorithm is used to solve the optimal dwell time control result. Finally, the obtained radiation power and dwell time results are substituted into the signal bandwidth resource sub-optimization problem to obtain the optimal signal bandwidth control result.

[0043] S43: Remove the radar node and target q selected in step S41, specify the next tracking target, and repeat steps S41 and S42 until all tracking targets are assigned corresponding radar nodes and multi-domain RF radiation resources;

[0044] S44, using a cyclic minimization method, repeating steps S41 to S43 until the difference between the objective function values ​​of two consecutive iterations is less than a preset fixed value, stopping the iteration, and obtaining a final optimal resource allocation result for asynchronous multi-target tracking in a heterogeneous multi-radar network system;

[0045] The optimal control result of radiation power obtained Optimal residence time control results Optimal control results of signal bandwidth Respectively replace the steps in step S41 and That is, they are used as the initial transmission parameters for radar node selection and joint optimization allocation of multi-domain resources in the next fusion sampling interval.

[0046] Furthermore, the three sub-optimization problems of optimizing radiation power resources, dwell time resources, and signal bandwidth resources are:

[0047] The sub-optimization problem of optimizing the radiated power resources is:

[0048]

[0049]

[0050] The sub-optimization problem for optimizing residence time resources is:

[0051]

[0052]

[0053] The sub-optimization problem of optimizing signal bandwidth resources is:

[0054]

[0055] The present invention proposes a method for joint optimization allocation of multi-domain resources of heterogeneous multi-radar networks under non-ideal detection. The main task of this method is to consider a heterogeneous multi-radar network system in two-dimensional space. The system consists of multiple radar networks of different types and working independently, and simultaneously tracks multiple targets deployed in space. Secondly, the BCRLB expression characterizing the accuracy of asynchronous multi-target tracking under non-ideal detection is derived; on this basis, with minimizing the multi-domain resource consumption of each radar node in the system illuminating the target as the optimization goal, and with the pre-set asynchronous target tracking accuracy threshold and the system RF radiation resources as constraints, a multi-domain resource joint optimization model of heterogeneous multi-radar networks based on asynchronous multi-target tracking under non-ideal detection is established, and the parameters such as radar node selection method, radiation power, dwell time and signal transmission bandwidth are adaptively and dynamically optimized to achieve the purpose of improving the RF stealth performance of the heterogeneous multi-radar network.

[0056] In another embodiment of the present invention, a system for joint optimization and allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection includes:

[0057] Heterogeneous multi-radar network system building module, used to build scenarios for asynchronous multi-target tracking in heterogeneous multi-radar networks, establish heterogeneous multi-radar network system scenarios, target motion models, and asynchronous radar measurement models;

[0058] The measurement index calculation module is used to construct the predicted BCRLB matrix of target state estimation error under non-ideal detection using radar node selection method, radar radiation power, radar dwell time and radar signal effective bandwidth as independent variables. The sum of the first and second elements on its diagonal is taken as the measurement index of asynchronous multi-target tracking accuracy.

[0059] The optimization model building module is used to establish a multi-domain resource joint optimization model for asynchronous multi-target tracking in a heterogeneous multi-radar network under non-ideal detection, using the pre-set asynchronous multi-target tracking accuracy threshold and the system's RF radiation resources as constraints and minimizing the multi-domain resource consumption of each radar node in the system illuminating the target as the optimization goal.

[0060] The optimization model solving module is used for a four-step decomposition algorithm based on the sequential quadratic programming (SQP) algorithm and the cyclic minimization method. First, the optimization model is simplified into a function containing only radar node selection constraints, and the radar node selection problem is solved; secondly, by solving the radar nodes, the optimization model is simplified, and the objective function in the simplified optimization model is equivalently transformed to obtain three sub-optimization problems for optimizing radiation power resources, residence time resources, and signal bandwidth resources respectively. The three sub-optimization problems are solved separately to obtain the optimal control results of radiation power, residence time, and signal bandwidth; finally, the optimal resource allocation result of asynchronous multi-target tracking in a heterogeneous multi-radar network system is obtained.

[0061] In yet another embodiment of the present invention, a device includes a memory and a processor, wherein:

[0062] a memory for storing computer programs capable of running on the processor;

[0063] The processor is configured to, when running the computer program, execute the steps of the above-mentioned method for joint optimization allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection.

[0064] In yet another embodiment of the present invention, a storage medium stores a computer program, which, when executed by at least one processor, implements the steps of the above-mentioned method for joint optimization allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection.

[0065] Beneficial effects: Compared with the existing technology, the method for joint optimization allocation of multi-domain resources of heterogeneous multi-radar networks under non-ideal detection of the present invention jointly optimizes parameters such as radar node selection method, radar radiation power, radar dwell time and radar signal effective bandwidth in the asynchronous multi-target tracking process, thereby maximizing the RF stealth performance of the heterogeneous multi-radar network while meeting the pre-set asynchronous target tracking accuracy threshold and the constraints of the system RF radiation resources. The reason for this advantage is that the method of the present invention constructs a predicted BCRLB matrix of target state estimation error under non-ideal detection with radar node selection mode, radar radiation power, radar dwell time and radar signal effective bandwidth as independent variables, and takes the sum of the first and second elements on its diagonal as the measurement index of asynchronous multi-target tracking accuracy; on this basis, taking the system's RF radiation resources and the given asynchronous multi-target tracking accuracy threshold as constraints, and minimizing the multi-domain resource consumption of each radar node in the system illuminating the target as the optimization goal, a multi-domain resource joint optimization model of heterogeneous multi-radar network based on asynchronous multi-target tracking under non-ideal detection is established, and the radar node selection, radiation power, dwell time and signal transmission bandwidth are adaptively optimized to achieve the purpose of improving the RF stealth performance of heterogeneous multi-radar network. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 Flow chart of the method of the present invention;

[0067] Figure 2 is the asynchronous radar measurement model of target q at the kth fusion sampling interval;

[0068] Figure 3 Flowchart of the solution method for the optimization model;

[0069] Figure 4 Distribution of heterogeneous multi-radar networks and multi-target motion trajectories;

[0070] Figure 5 Radar node selection and multi-domain resource allocation diagram for target 1;

[0071] Figure 6 Radar node selection and multi-domain resource allocation diagram for target 2;

[0072] Figure 7 Comparison of the total radiated power of the five algorithms under different detection probabilities;

[0073] Figure 8 Comparison of the total residence time of the five algorithms under different detection probabilities;

[0074] Figure 9 Comparison of the total signal bandwidth of the five algorithms under different detection probabilities;

[0075] Figure 10 ARMSE comparison chart of target 1 and target 2 under different detection probabilities. DETAILED DESCRIPTION

[0076] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0077] Based on actual combat scenarios, this paper proposes a method for joint optimization allocation of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection. Under the constraints of pre-set asynchronous target tracking accuracy threshold and system RF radiation resources, the optimization goal is to minimize the multi-domain resource consumption of each radar node in the system to illuminate the target. Parameters such as radar node selection method, radiation power, dwell time, and signal transmission bandwidth are adaptively and dynamically optimized to improve the RF stealth performance of the heterogeneous multi-radar network. Firstly, a heterogeneous multi-radar network system is assumed to exist in two-dimensional space. The system consists of multiple radar networks of different types and working independently, and tracks multiple targets dispersed in space simultaneously. Secondly, the Bayesian Cramér-Rao Lower Bound (BCRLB) expression for the accuracy of asynchronous multi-target tracking under non-ideal detection is derived. On this basis, with minimizing the multi-domain resource consumption of each radar node in the system illuminating the target as the optimization goal, and with the pre-set asynchronous target tracking accuracy threshold and the system RF radiation resources as constraints, a multi-domain resource joint optimization model for heterogeneous multi-radar networks based on asynchronous multi-target tracking under non-ideal detection is established. The parameters such as radar node selection method, radiation power, dwell time and signal transmission bandwidth are adaptively and dynamically optimized to achieve the purpose of improving the RF stealth performance of the heterogeneous multi-radar network.

[0078] like Figure 1 As shown, the present invention provides a method for joint optimization allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection, comprising the following steps:

[0079] 1. Construct a scenario for asynchronous multi-target tracking in a heterogeneous multi-radar network. Establish a heterogeneous multi-radar network system scenario, target motion model, and asynchronous radar measurement model. The specific steps are as follows:

[0080] Assume that there is a heterogeneous multi-radar network system in two-dimensional space, which consists of M radar networks of different types and working independently. There are N radar networks in the mth (m=1,2,…,M) radar network. m radar nodes, and the nth (n=1,2,…,N m The coordinates of the radar nodes are (x n,m ,y n,m Since the radar nodes in different radar networks have different working modes, the carrier frequencies of the signals transmitted by each radar node may be different. For the target q, their initial sampling time is and sampling interval It may also be different. Based on this, the following three types of radar networks and radiation resource constraints are defined:

[0081] (1) Centralized Multiple-Input Multiple-Output (MIMO) radar network: In a centralized MIMO radar network, all radar nodes have a fixed dwell time on the target, but the radiated power and transmitted signal bandwidth are different;

[0082] (2) Phased Array Radar Network: Radar nodes in this radar network can adaptively rotate their beams to illuminate multiple targets. Based on this, the radiation power of the radar nodes in this radar network is fixed, but the dwell time and the transmitted signal bandwidth are different;

[0083] (3) Mechanical scanning radar network: The radar nodes in this radar network have fixed operating parameters, that is, all radar nodes illuminate the target with fixed radiation power, dwell time and transmission signal bandwidth.

[0084] In addition, it is assumed that there are Q independent targets moving in a uniform linear motion in the surveillance area of ​​the heterogeneous multi-radar network system, and the initial position of target q (q = 1, 2, ..., Q) is The movement speed is

[0085] Assume that the fusion sampling interval of the heterogeneous multi-radar network system is T fusion , and the kth fusion sampling interval is (t k-1 ,t k ], then T fusion =t k -t k-1 Assume that the state vector of the qth target at the kth fusion sampling interval is in{·} T represents the transpose operation of the matrix. Then the motion state equation of the target can be expressed as:

[0086]

[0087] Where F is the state transition matrix of the target, which can be described as:

[0088]

[0089] Where I2 represents the second-order identity matrix, Indicates the matrix direct product operation. Represents zero-mean white Gaussian process noise, whose covariance matrix It can be calculated as:

[0090]

[0091] Where σ represents the process noise intensity of the target.

[0092] Define a binary variable To characterize the pairing index of radar nodes and targets in heterogeneous multi-radar networks, the expression is:

[0093]

[0094] Assume that the number of measurement information of target q by the nth radar node in the mth radar network in the kth fusion sampling interval is Among them, The arrival time of the measurement information is The asynchronous measurement model of target q at the kth fusion sampling interval is as follows: Figure 2 Therefore, in the kth fusion sampling interval (t k-1 ,t k ], combined with radar node-target pairing indicators The equation for the sth measurement can be obtained as:

[0095]

[0096] in, represents the measurement vector of the s-th measurement, represents the nonlinear observation function of the sth measurement. The calculation formula can be written as:

[0097]

[0098] in, and They represent the actual distance and azimuth between the nth radar node in the mth radar network and the target q at the sth measurement. and Respectively indicate the arrival time The horizontal and vertical coordinates of the target q at time . Represents the error of the sth measurement, and its covariance matrix The distance and azimuth are independent of each other and can be expressed as:

[0099]

[0100] in, and They represent the variance of the target q range and azimuth measurement errors, respectively, and they are both related to the echo signal-to-noise ratio of the target in the fusion sampling interval:

[0101]

[0102] in, represents the echo signal-to-noise ratio of a single pulse radiated by target q from the sth measurement of the nth radar node in the mth radar network within the kth fusion sampling interval, represents the effective bandwidth of the signal transmitted by the sth radar node in the mth radar network to the target q within the kth fusion sampling interval, B NN Represents the beam width of the radar receiving antenna. It can be seen that the radar transmit signal bandwidth affects its measurement error of the target distance. Under the condition of other parameters being the same, the wider the signal bandwidth, the smaller the distance measurement noise variance. More specifically, the echo signal-to-noise ratio The expression is:

[0103]

[0104] in, represents the dwell time of the radar illuminating the target, T r is the radar pulse repetition period, Indicates the radiation power of the radar illuminating the target, G t and G r are the radar transmitting antenna gain and receiving antenna gain respectively, represents the RCS of target q relative to the nth radar node in the mth radar network, λ represents the radar wavelength, G RP represents the radar receiver processing gain, k B and T are the Boltzmann constant and radar receiver noise temperature, respectively. r represents the radar receiver matched filter bandwidth, F r is the radar receiver noise figure.

[0105] Based on the above analysis, four groups of vectors are defined as follows:

[0106]

[0107] in, and Both The matrix of .

[0108] 2. Using radar node selection method, radar radiation power, radar dwell time, and radar signal effective bandwidth as independent variables, a predicted BCRLB matrix of target state estimation error under non-ideal detection is constructed. The sum of the first and second elements on its diagonal is taken as the measurement index of asynchronous multi-target tracking accuracy. The specific calculation steps are as follows:

[0109] Since BCRLB provides a lower bound for the mean square error (MSE) of unbiased parameter estimates, it is reasonable to use it as a criterion for tracking performance. The predicted Bayesian information matrix (BIM) under an ideal detection environment can be described as:

[0110]

[0111] in, Represents the Jacobian matrix of the nonlinear observation function. The BCRLB of asynchronous multi-target tracking error under ideal detection environment is obtained by inverting BIM, and the expression is:

[0112]

[0113] However, in non-ideal detection environments, radar nodes in a heterogeneous multi-radar network may not be able to successfully detect all tracked targets, and there may be cases of missed detection. Therefore, the following binary variable is defined to represent the detection status of the radar node for the paired target in the kth fusion sampling interval:

[0114]

[0115] Coexistence in heterogeneous multi-radar networks radar nodes. Therefore, in each fusion sampling interval, we can get detection situations, describing them as:

[0116]

[0117] in, It represents the i-th detection situation of target q by the multi-radar network in the k-th fusion sampling interval. Assume that in the i-th detection situation, the heterogeneous multi-radar network has A radar node detects target q, and the probability of this happening can be calculated as:

[0118]

[0119] in, represents the detection probability of target q by the nth radar node in the mth radar network within the kth fusion sampling interval. In fact, the detection probability of a target by different radar nodes may be different, which is related to parameters such as the target RCS and the distance between the radar node and the target. To simplify the subsequent derivation and calculation, It is considered as a constant in the whole tracking process. Combining Equations (11)-(15), the predicted BCRLB of asynchronous multi-target tracking error in non-ideal detection environment can be calculated as:

[0120]

[0121] in, is the inverse of the Bayesian information matrix.

[0122] The sum of the first and second elements on the diagonal represents the lower bound of the MSE of the predicted target position estimate. Therefore, it can be extracted as a measure of the accuracy of asynchronous multi-target tracking, expressed as:

[0123]

[0124] 3. Establish a joint optimization model for multi-domain resources in heterogeneous multi-radar networks under non-ideal detection:

[0125] Taking the preset asynchronous multi-target tracking accuracy threshold and the system RF radiation resources as constraints, and minimizing the multi-domain resource consumption of each radar node in the system to illuminate the target as the optimization goal, a multi-domain resource joint optimization model for asynchronous multi-target tracking in heterogeneous multi-radar networks under non-ideal detection is established, as shown in Equation (18):

[0126]

[0127] in, and They represent the normalized radiation power variable, residence time variable and signal bandwidth variable respectively, and They represent the power, time, and bandwidth upper limits of the nth radar node in the mth radar network respectively; η q represents the preset target q tracking accuracy threshold; ψ CMIMO represents the set of centralized MIMO radar network nodes in the heterogeneous multi-radar network; ψ PAR represents the set of phased array radar network nodes; ψ MSR Represents a collection of mechanical scanning radar network nodes; and They represent the lower and upper limits of the radiation power of radar nodes in heterogeneous multi-radar networks respectively; P PAR and P MSR denote the fixed radiated powers of the phased array radar network and the mechanically scanned radar network, respectively; and Respectively represent the lower and upper limits of the residence time; T CMIMO and T MSR denote the fixed dwell time of the centralized MIMO radar network and the mechanical scanning radar network, respectively; β MSR Represents the fixed signal bandwidth of a mechanically scanned radar network; and They represent the lower and upper limits of the centralized MIMO radar network signal bandwidth respectively; and They represent the lower and upper limits of the phased array radar network signal bandwidth respectively; Indicates that each radar node can track at most one target in the kth fusion sampling interval. Denotes the fixed allocation L of the kth fusion sampling interval heterogeneous multi-radar network max radar nodes to track a single target.

[0128] 4. Due to is a binary variable, so the optimization model of formula (18) is a non-convex optimization problem with four variables. For non-convex optimization problems, the results obtained by using the exhaustive search method are relatively accurate, but the solution process is very cumbersome. However, if some intelligent algorithms such as ant colony algorithm are used to solve the problem, it cannot meet the real-time requirements. Based on this, the present invention proposes a four-step decomposition algorithm based on the Sequential Quadratic Programming (SQP) algorithm and the cyclic minimum method, which first solves the radar node selection problem, and then solves the optimization allocation problem of radiation power, residence time and signal bandwidth, such as Figure 3 The specific steps are as follows:

[0129] (1) Define three initial radiation power matrices respectively Dwell Time Matrix Sum signal bandwidth matrix Heterogeneous multi-radar network based on matrix and The corresponding radiation resources are allocated to each radar node for illumination. At the same time, the binary variable Relaxation Equation (18) can be simplified to a function containing only the radar node selection constraints, as shown in Equation (19):

[0130]

[0131] Among them, Q is the target number.

[0132] The optimization model described by formula (19) is a convex problem. Therefore, the SQP algorithm can be used to solve the radar node selection coefficient matrix: Then, The coefficients in the are arranged in descending order, and the radar nodes corresponding to the coefficients are selected from high to low until the constraints are met. Finally, the pairing index of the selected radar node and the target is set to Set the pairing index of all unselected radar nodes and targets to You can get the radar node selection result

[0133] (2) By solving the radar node in step (1), equation (18) can be simplified to:

[0134]

[0135] By performing an equivalent transformation on the objective function in the optimization model (20), we can obtain three sub-optimization problems for optimizing radiation power resources, residence time resources, and signal bandwidth resources respectively:

[0136]

[0137]

[0138]

[0139] First, solve the radiation power according to equation (21). and The value of the dwell time and signal bandwidth is fixed. At this time, the optimization model (21) is a convex problem, and the SQP algorithm is still used to solve it. Based on this, the optimal control result of the radiation power when tracking the target q can be obtained. Secondly, solve the residence time according to equation (22). and Fixed radiation power and signal bandwidth, the SQP algorithm is also used to solve the optimal control result of residence time. Finally, the radiation power and dwell time results are obtained and Substituting into formula (23), we can get the optimal control result of signal bandwidth

[0140] (3) Remove the radar node and target q selected in step (1), specify the next tracking target, and repeat steps (1) and (2) until all tracking targets are assigned corresponding radar nodes and multi-domain RF radiation resources.

[0141] (4) Using the cyclic minimization method, repeat steps (1) to (3) until the difference between the objective function values ​​of two consecutive iterations is less than a preset fixed value, stop the iteration, and obtain the final optimal resource allocation result for asynchronous multi-target tracking in heterogeneous multi-radar network system. In addition, the obtained and Replace the steps in (1) and That is, they are used as the initial transmission parameters for radar node selection and joint optimization allocation of multi-domain resources in the next fusion sampling interval.

[0142] Another embodiment of the present invention is a system for joint optimization and allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection, comprising:

[0143] Heterogeneous multi-radar network system building module, used to build scenarios for asynchronous multi-target tracking in heterogeneous multi-radar networks, establish heterogeneous multi-radar network system scenarios, target motion models, and asynchronous radar measurement models;

[0144] The measurement index calculation module is used to construct the predicted BCRLB matrix of target state estimation error under non-ideal detection using radar node selection method, radar radiation power, radar dwell time and radar signal effective bandwidth as independent variables. The sum of the first and second elements on its diagonal is taken as the measurement index of asynchronous multi-target tracking accuracy.

[0145] The optimization model building module is used to establish a multi-domain resource joint optimization model for asynchronous multi-target tracking in a heterogeneous multi-radar network under non-ideal detection, using the pre-set asynchronous multi-target tracking accuracy threshold and the system's RF radiation resources as constraints and minimizing the multi-domain resource consumption of each radar node in the system illuminating the target as the optimization goal.

[0146] The optimization model solving module is used for a four-step decomposition algorithm based on the sequential quadratic programming (SQP) algorithm and the cyclic minimization method. First, the optimization model is simplified into a function containing only radar node selection constraints, and the radar node selection problem is solved; secondly, by solving the radar nodes, the optimization model is simplified, and the objective function in the simplified optimization model is equivalently transformed to obtain three sub-optimization problems for optimizing radiation power resources, residence time resources, and signal bandwidth resources respectively. The three sub-optimization problems are solved separately to obtain the optimal control results of radiation power, residence time, and signal bandwidth; finally, the optimal resource allocation result of asynchronous multi-target tracking in a heterogeneous multi-radar network system is obtained.

[0147] According to another embodiment of the present invention, a device includes a memory and a processor, wherein:

[0148] a memory for storing computer programs capable of running on the processor;

[0149] The processor is configured to, when running the computer program, execute the steps of the above-mentioned method for joint optimization allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection, and achieve the technical effects described in the above-mentioned method.

[0150] Yet another embodiment of the present invention provides a storage medium having a computer program stored thereon. When the computer program is executed by at least one processor, the computer program implements the steps of the above-mentioned method for joint optimization allocation of multi-domain resources in a heterogeneous multi-radar network under non-ideal detection, and can achieve the technical effects described in the above-mentioned method.

[0151] 5. Simulation results

[0152] The relevant simulation parameter settings are shown in Table 1 below:

[0153] Table 1 Simulation parameter settings

[0154]

[0155] Suppose there is a heterogeneous multi-radar network system consisting of M = 3 radar networks in two-dimensional space. Radar network 1 is a centralized MIMO radar network with N1 = 5 radar nodes; radar network 2 is a phased array radar network with N2 = 5 radar nodes; and radar network 3 is a mechanical scanning radar network with N3 = 2 radar nodes. Furthermore, within the surveillance area of ​​the heterogeneous multi-radar network, there are Q = 2 targets. Target 1 has an initial position of (50, 0) km and is flying at a constant speed of (-600, 230) m / s. Target 2 has an initial position of (-50, -17) km and is flying at a constant speed of (570, -220) m / s. Assuming the entire target tracking process lasts 150 seconds, the initial sampling time and sampling interval for each radar node are shown in Table 2.

[0156] Table 2 Initial sampling time and sampling interval of each radar node

[0157]

[0158] The flowchart of the joint optimization allocation method of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection is as follows: Figure 1 As shown in the figure, the distribution of heterogeneous multi-radar networks and the trajectory of multiple targets are as follows: Figure 4 As shown, the detection probability The radar node selection and multi-domain resource allocation diagram of target 1 are as follows: Figure 5 As shown in (a) to (c), the detection probability The radar node selection and multi-domain resource allocation diagram of target 2 is as follows: Figure 6 As shown in (a) to (c), it can be seen from the figure that the distance between the target and the radar node, the initial sampling time of the radar node, and the sampling interval will affect the radar node selection method and the multi-domain resource optimization allocation result. The heterogeneous multi-radar network will give priority to illuminating the target by radar nodes that are closer to the target, have a better relative position, and have a higher number of sampling times within the fusion sampling interval.

[0159] In order to better illustrate the improvement of the algorithm proposed in this invention on the RF stealth performance of heterogeneous multi-radar networks and the impact of changes in detection probability on RF stealth performance, this invention uses the node random selection algorithm, power time uniform allocation algorithm, bandwidth uniform allocation algorithm and the algorithm proposed in this invention during synchronous target tracking as comparisons to prove the superiority of the algorithm proposed in this invention. Figure 7 As shown in (a) to (c), the total residence time of the five algorithms under different detection probabilities is compared. Figure 8 As shown in (a) to (c), the total signal bandwidth comparison of the five algorithms under different detection probabilities is as follows: Figure 9 As shown in (a) to (c) in the figure. Two conclusions can be drawn from the figure: (1) As the detection probability of non-ideal detection conditions decreases from 0.9 to 0.7, the detection environment of asynchronous multi-target tracking in heterogeneous multi-radar networks gradually becomes worse. Therefore, heterogeneous multi-radar networks require more and more radiation power, dwell time and signal bandwidth to ensure the preset asynchronous multi-target tracking accuracy, at the cost of the system's RF stealth performance deteriorating; (2) Under different detection probability conditions, compared with the other four comparison algorithms, the total radiation power, total dwell time and total signal bandwidth consumption of the heterogeneous multi-radar network obtained by the algorithm proposed in this invention are lower, which can effectively improve its RF stealth performance.

[0160] The average root mean square error (ARMSE) is defined to calculate the target tracking accuracy of the kth fusion sampling interval. The calculation formula can be expressed as:

[0161]

[0162] Among them, N MC is the number of Monte Carlo experiments. In the simulation of the present invention, N MC =100. is the estimated target position obtained in the nth Monte Carlo experiment, It represents the number of radiations of the heterogeneous multi-radar network to the target q in the lth Monte Carlo experiment. Figure 10 (I) and (II) show the ARMSE comparison diagrams of target 1 and target 2 under different detection probabilities. As can be seen from the figure, under different detection probabilities, the tracking accuracy errors of target 1 and target 2 obtained by the five algorithms are relatively close, and are slightly higher than η q , maintained at the same level.

[0163] The working principle and working process of the invention are as follows:

[0164] The present invention considers a heterogeneous multi-radar network system in a two-dimensional space, which is composed of multiple radar networks of different types and working independently, and performs asynchronous tracking on multiple targets dispersedly deployed in the two-dimensional space. For this scenario of asynchronous multi-target tracking in heterogeneous multi-radar networks, first, the radar node selection method, radar radiation power, radar dwell time and radar signal effective bandwidth are used as independent variables to construct a predicted BCRLB matrix of target state estimation error under non-ideal detection, and the sum of the first and second elements on its diagonal is taken as a measure of the accuracy of asynchronous multi-target tracking; then, with minimizing the multi-domain resource consumption of each radar node in the system illuminating the target as the optimization goal, and with the pre-set asynchronous target tracking accuracy threshold and the system RF radiation resources as constraints, a multi-domain resource joint optimization model for asynchronous multi-target tracking in heterogeneous multi-radar networks under non-ideal detection is established; finally, the SQP algorithm and the cyclic minimization method are used to solve the optimization model. By solving the optimization model, a radar node selection method is obtained that improves the RF stealth performance of the heterogeneous multi-radar network system while meeting the pre-set asynchronous target tracking accuracy threshold and the system RF radiation resources. Radar radiated power Radar dwell time and the effective bandwidth of the radar signal is the optimal solution of the model.

Claims

1. A method for joint optimization allocation of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection, characterized by: The following steps are involved: S1. Construct a scenario for asynchronous multi-target tracking in a heterogeneous multi-radar network, establish a heterogeneous multi-radar network system scenario, target motion model, and asynchronous radar measurement model; S2. Using radar node selection method, radar radiation power, radar dwell time and radar signal effective bandwidth as independent variables, construct the predicted BCRLB matrix of target state estimation error under non-ideal detection, and take the sum of the first and second elements on its diagonal as the measurement index of asynchronous multi-target tracking accuracy; S3. Using the pre-set asynchronous multi-target tracking accuracy threshold and the system RF radiation resources as constraints, and minimizing the multi-domain resource consumption of each radar node in the system illuminating the target as the optimization goal, a multi-domain resource joint optimization model for asynchronous multi-target tracking in a heterogeneous multi-radar network under non-ideal detection is established. S4. Solve the optimization model, specifically: based on the four-step decomposition algorithm of the sequential quadratic programming (SQP) algorithm and the cyclic minimization method, first simplify the optimization model into a function containing only the radar node selection constraints, and solve the radar node selection problem; secondly, by solving the radar nodes, simplify the optimization model, and perform an equivalent transformation on the objective function in the simplified optimization model to obtain three sub-optimization problems that optimize the radiation power resources, residence time resources, and signal bandwidth resources respectively, and solve the three sub-optimization problems respectively to obtain the optimal control results of the radiation power, the optimal control results of the residence time, and the optimal control results of the signal bandwidth; finally, the optimal resource allocation result of asynchronous multi-target tracking of the heterogeneous multi-radar network system is obtained.

2. The method for joint optimization allocation of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection according to claim 1 is characterized in that: The heterogeneous multi-radar network system scenario established in step S1 is: The heterogeneous multi-radar network system consists of M radar networks of different types and working independently. There are N m radar nodes, and the coordinates of the nth radar node in the mth radar network are (x n,m ,y n,m ); where m = 1, 2, ..., M and n = 1, 2, ..., N m , the radar nodes in different radar networks have different working modes, the carrier frequencies of the signals transmitted by each radar node are the same or different, and for the same target, the initial sampling time and sampling interval of each radar node are the same or different; the following three types of radar networks and radiation resource constraints are defined: (1) Centralized MIMO radar network: In a centralized MIMO radar network, the dwell time of all radar nodes illuminating the target is fixed, but the radiated power and transmitted signal bandwidth are different; (2) Phased array radar network: The radar nodes in this radar network can adaptively rotate the beam to illuminate multiple targets. The radiation power of all radar nodes is fixed, but the dwell time and transmission signal bandwidth are different; (3) Mechanical scanning radar network: The radar nodes in this radar network have fixed operating parameters, that is, all radar nodes illuminate the target with fixed radiation power, dwell time and transmission signal bandwidth.

3. The method for joint optimization allocation of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection according to claim 1 is characterized in that: The target motion model established in step S1, that is, the target motion state equation is expressed as: in, is the state vector of the qth target at the kth fusion sampling interval, is the state vector of the qth target at the k-1th fusion sampling interval, F is the state transfer matrix of the target, is the mean white Gaussian process noise; The established asynchronous radar measurement model, that is, the measurement equation is: in, represents the measurement vector of the s-th measurement, represents the nonlinear observation function of the sth measurement, represents the error of the sth measurement, is a binary variable used to characterize the pairing index between radar nodes and targets in heterogeneous multi-radar networks. The expression is:

4. The method for joint optimization allocation of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection according to claim 1 is characterized in that: The predicted BCRLB matrix of the target state estimation error under non-ideal detection in step S2 The calculation formula is: in, is mean white Gaussian process noise The covariance matrix of ; F is the state transfer matrix of the target; is the inverse of the Bayesian information matrix; It is a binary variable used to characterize the pairing index between radar nodes and targets in heterogeneous multi-radar networks; is a binary variable used to characterize the detection of paired targets by the radar node within the kth fusion sampling interval; is the Jacobian matrix of the nonlinear observation function; is the error of the sth measurement The covariance matrix of In the i-th detection case, the heterogeneous multi-radar network has The probability that a radar node detects target q; M is the type of radar network in the heterogeneous multi-radar network system; N m is the number of radar nodes in the mth radar network; m=1,2,…,M; is the number of measurement information of target q by the nth radar node in the mth radar network within the kth fusion sampling interval; s is the sth measurement information; in the formula, the superscript T represents the transpose of the matrix, and the superscript -1 represents the inverse of the matrix; The sum of the first and second elements on the diagonal represents the lower bound of the MSE of the predicted target position estimation, which is extracted as a measure of the accuracy of asynchronous multi-target tracking and expressed as: in, represents the transpose of the matrix consisting of the pairing indices of each radar node and target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix composed of the radiation power of each radar node illuminating the target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix consisting of the dwell time of each radar node illuminating the target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix consisting of the effective bandwidth of the target transmission signal measured by each radar node in the heterogeneous multi-radar network during the kth fusion sampling interval; express The first element on the diagonal; express The second element on the diagonal.

5. The method for joint optimization allocation of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection according to claim 1 is characterized in that: The multi-domain resource joint optimization model for asynchronous multi-target tracking in heterogeneous multi-radar networks under non-ideal detection established in step S3 is: in, represents the transpose of the matrix consisting of the pairing indices of each radar node and target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix composed of the radiation power of each radar node illuminating the target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix consisting of the dwell time of each radar node illuminating the target in the heterogeneous multi-radar network within the kth fusion sampling interval; represents the transpose of the matrix composed of the effective bandwidth of the target transmission signal measured by each radar node in the heterogeneous multi-radar network within the kth fusion sampling interval; Q represents the number of targets; M is the type of radar network in the heterogeneous multi-radar network system; N m is the number of radar nodes in the mth radar network; It is a binary variable used to characterize the pairing index between radar nodes and targets in heterogeneous multi-radar networks; and They represent the normalized radiation power variable, residence time variable and signal bandwidth variable respectively. and They represent the power, time, and bandwidth upper limits of the nth radar node in the mth radar network respectively; η q represents the preset target q tracking accuracy threshold; ψ CMIMO represents the set of centralized MIMO radar network nodes in the heterogeneous multi-radar network; ψ PAR represents the set of phased array radar network nodes; ψ MSR Represents a collection of mechanical scanning radar network nodes; represents the radiated power of radar nodes in heterogeneous multi-radar networks; and They represent the lower and upper limits of the radiation power of radar nodes in heterogeneous multi-radar networks respectively; P PAR and P MSR denote the fixed radiated powers of the phased array radar network and the mechanically scanned radar network, respectively; Indicates the dwell time of the radar illuminating the target; and Respectively represent the lower and upper limits of the residence time; T CMIMO and T MSR denote the fixed dwell time of the centralized MIMO radar network and the mechanical scanning radar network, respectively; represents the effective bandwidth of the target q’s transmitted signal measured by the nth radar node in the mth radar network within the kth fusion sampling interval; β MSR Represents the fixed signal bandwidth of a mechanically scanned radar network; and They represent the lower and upper limits of the centralized MIMO radar network signal bandwidth respectively; and They represent the lower and upper limits of the phased array radar network signal bandwidth respectively; L max Indicates L max Radar nodes.

6. The method for joint optimization allocation of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection according to claim 5 is characterized in that: The specific method for solving the optimization model in step S4 is: S41. Define three initial radiation power matrices respectively Dwell Time Matrix Sum signal bandwidth matrix Heterogeneous multi-radar network based on matrix and Allocate the corresponding radiation resources to each radar node for illumination; at the same time, the binary variable Relaxation The optimization model is simplified to a function containing only the radar node selection constraints, which can be expressed as: The radar node selection coefficient matrix is ​​solved using the SQP algorithm Then, The coefficients in the are arranged in descending order, and the radar nodes corresponding to the coefficients are selected from high to low until the constraints are met. Finally, the pairing index of the selected radar node and the target is set to Set the pairing index of all unselected radar nodes and targets to That is, the radar node selection result is obtained S42. By solving the radar node in step S41, the optimization model is simplified to: By performing equivalent transformation on the objective function in the simplified optimization model, three sub-optimization problems are obtained, which are respectively optimizing the radiation power resource, the residence time resource and the signal bandwidth resource. First, for the radiation power resource sub-optimization problem, the dwell time and signal bandwidth are fixed, and the SQP algorithm is used to solve the optimal radiation power control result when tracking the target. Second, for the dwell time resource sub-optimization problem, the signal bandwidth is fixed, and the obtained radiation power result is substituted into the dwell time resource sub-optimization problem, and the SQP algorithm is used to solve the optimal dwell time control result. Finally, the obtained radiation power and dwell time results are substituted into the signal bandwidth resource sub-optimization problem to obtain the optimal signal bandwidth control result. S43: Remove the radar node and target q selected in step S41, specify the next tracking target, and repeat steps S41 and S42 until all tracking targets are assigned corresponding radar nodes and multi-domain RF radiation resources; S44, using a cyclic minimization method, repeating steps S41 to S43 until the difference between the objective function values ​​of two consecutive iterations is less than a preset fixed value, stopping the iteration, and obtaining a final optimal resource allocation result for asynchronous multi-target tracking in a heterogeneous multi-radar network system; The optimal control result of radiation power obtained Optimal residence time control results Optimal control results of signal bandwidth Respectively replace the steps in step S41 and That is, they are used as the initial transmission parameters for radar node selection and joint optimization allocation of multi-domain resources in the next fusion sampling interval.

7. The method for joint optimization allocation of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection according to claim 6 is characterized in that: The three sub-optimization problems for optimizing radiation power resources, dwell time resources, and signal bandwidth resources are: The sub-optimization problem of optimizing the radiated power resources is: The sub-optimization problem for optimizing residence time resources is: The sub-optimization problem of optimizing signal bandwidth resources is:

8. A multi-domain resource joint optimization allocation system for heterogeneous multi-radar networks under non-ideal detection, characterized by: include: Heterogeneous multi-radar network system building module, used to build scenarios for asynchronous multi-target tracking in heterogeneous multi-radar networks, establish heterogeneous multi-radar network system scenarios, target motion models, and asynchronous radar measurement models; The measurement index calculation module is used to construct the predicted BCRLB matrix of target state estimation error under non-ideal detection using radar node selection method, radar radiation power, radar dwell time and radar signal effective bandwidth as independent variables. The sum of the first and second elements on its diagonal is taken as the measurement index of asynchronous multi-target tracking accuracy. The optimization model building module is used to establish a multi-domain resource joint optimization model for asynchronous multi-target tracking in a heterogeneous multi-radar network under non-ideal detection, using the pre-set asynchronous multi-target tracking accuracy threshold and the system's RF radiation resources as constraints and minimizing the multi-domain resource consumption of each radar node in the system illuminating the target as the optimization goal. The optimization model solving module is used for a four-step decomposition algorithm based on the sequential quadratic programming (SQP) algorithm and the cyclic minimization method. First, the optimization model is simplified into a function containing only radar node selection constraints, and the radar node selection problem is solved; secondly, by solving the radar nodes, the optimization model is simplified, and the objective function in the simplified optimization model is equivalently transformed to obtain three sub-optimization problems for optimizing radiation power resources, residence time resources, and signal bandwidth resources respectively. The three sub-optimization problems are solved separately to obtain the optimal control results of radiation power, residence time, and signal bandwidth; finally, the optimal resource allocation result of asynchronous multi-target tracking in a heterogeneous multi-radar network system is obtained.

9. A device, characterized in that: comprising a memory and a processor, wherein: a memory for storing computer programs capable of running on the processor; A processor, configured to, when running the computer program, execute the steps of the method for joint optimization allocation of multi-domain resources of a heterogeneous multi-radar network under non-ideal detection according to any one of claims 1 to 7.

10. 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 method for joint optimization allocation of multi-domain resources of a heterogeneous multi-radar network under non-ideal detection as claimed in any one of claims 1 to 7.

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