Networking radar multi-target tracking beam allocation method and system for resisting multiple jammers

Abstract

The invention relates to a networking radar multi-target tracking beam allocation method and system for resisting multiple jammers, and the method comprises the steps: building a model; obtaining a signal to interference and noise ratio of each radar node receiving end after main lobe and side lobe interference step-by-step suppression, and establishing a covariance matrix of radar node estimation target parameters; calculating a covariance matrix of radar node estimation target parameters, and obtaining a tracking result of the networking radar on each target; representing target tracking precision through a posterior Cramer-Rao lower bound, establishing a cost function for each target, summing the cost functions of the targets as a target function, and establishing an adaptive scheduling multi-radar tracking beam optimization model in combination with radar beam constraint conditions; and solving the adaptive scheduling multi-radar tracking beam optimization model. The invention provides a networking radar tracking multi-target beam allocation method and system for resisting multiple jammers, which can effectively suppress interference and stably track targets in the whole process.

Description

Background Art

[0002] Radar networking refers to connecting multiple radars of different types and positions through communication links for unified management and data fusion processing, thus forming an organic whole to achieve more effective and comprehensive detection and tracking of targets. Moreover, radar networking not only represents the fusion of detection information of each radar, but also represents the exchange, expansion, and optimization of detection resources of each radar. As a result, the radar networking system has richer anti-jamming resources: on the one hand, each node radar is equipped with anti-jamming measures, such as sidelobe cancellation, sidelobe blanking, etc.; on the other hand, multiple radars can cooperate through information fusion to counter jamming. In addition to these two types of anti-jamming resources at the technical level, networked radars also have rich operability at the tactical level, such as stealthy startup, deceptive startup, and blinking emission.

[0003] In the prior art, in the face of a distributed cooperative jamming scenario, radar networking, on the one hand, selects appropriate operating modes, radiation parameters, and anti-jamming measures for each node radar in real time according to the jamming dynamics, and on the other hand, regards the networked radars as a whole to coordinate and work against jamming, thereby enhancing the anti-jamming ability. However, in the face of multiple jammers covering multiple targets to break through, there are problems such as unreasonable beam allocation, resulting in low target tracking accuracy.

[0004] Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions.

[0005] It should be noted that the information disclosed in the above background art section is only used to strengthen the understanding of the background of the present disclosure, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0006] The purpose of the embodiments of the present disclosure is to provide a method and system for beam allocation of a networked radar for tracking multiple targets against multiple jammers, thereby at least to a certain extent overcoming one or more problems caused by the limitations and defects of the related art.

[0007] In a first aspect, the present application provides a method for beam allocation of a networked radar for tracking multiple targets against multiple jammers, including:

[0008] Establish a model for a networked radar to track multiple targets under the background of multiple jammers;

[0009] Obtain the signal-to-interference-plus-noise ratio (SINR) of each radar node's receiving end after step-by-step suppression of main and sidelobe interference, and establish a covariance matrix of the estimated target parameters of the radar node;

[0010] Calculate the covariance matrix of the estimated target parameters of the radar node through global measurement fusion and extended Kalman filtering, and obtain the tracking result of the networked radar for each target;

[0011] Characterize the target tracking accuracy through the posterior Cramer-Rao lower bound, establish a cost function for each target, sum up the cost functions of each target as the objective function, and combine the radar beam constraint conditions to establish an adaptive scheduling multi-radar tracking beam optimization model;

[0012] Solve the adaptive scheduling multi-radar tracking beam optimization model to obtain the adaptive configuration result of the radar tracking beam.

[0013] In a possible implementation manner, the steps of establishing a multi-radar tracking multi-target model under the background of multiple jammers include:

[0014] Assume that Q targets are moving in a uniform straight line in the XOY plane, and the motion state of target q at time k is Establish the motion equation of target q as where F is the target state transition matrix, is a zero-mean white Gaussian process noise, and the expression of the target state transition matrix is ΔT is the sampling interval, and the covariance matrix is κ q is the noise intensity during the state transition process of target q;

[0015] Assume that a radar networking system includes one transmitting station and N receiving stations, tracks Q moving targets, and has M jammers to cover the target breakthrough. Among them, the transmitting station is located at p t =[x t , y t T , the receiving station n is located at p rn =[x rn , y rn T , and at time k, target q is located at

[0016] When the receiving station n tracks target q at time k, the superimposed signal of the echo, interference, and noise received by the receiving station n is y k，n (t)=x k，n (t)+r k，n (t)+n k，n (t), where x k,n (t) is the echo signal of target q received by the receiving station n at time k, r k,n (t) is the interference signal received by the receiving station n at time k, and n k,n (t) is the noise.

[0017] In a possible implementation manner, the echo signal of target q received by the receiving station n at time k is:

[0018] ​​

[0019] Among them, is the propagation loss, and P t is the transmission power of the transmitting station, and are respectively the reflection intensity, azimuth angle, propagation delay, and Doppler frequency of the target q relative to the receiving station n at time k. α rn is the receiving vector of the receiving station n, M rn and d rn are respectively the number of array elements and the interval of the receiving station n, and λ is the wavelength;

[0020] The interference signal received by the receiving station n at time k is:

[0021]

[0022] Among them, is the propagation loss of the interference signal, is the transmission power of the jammer m, and are respectively the azimuth angle, propagation delay, and Doppler frequency of the jammer m relative to the receiving station n at time k.

[0023] In a possible implementation manner, the step of obtaining the signal-to-interference-plus-noise ratio after step-by-step suppression of main and sidelobe interference at the receiving end of each radar node and establishing the covariance matrix for estimating the target parameters of the radar node includes:

[0024] Define According to the received signal For and Perform maximum likelihood estimation. When i = 1, 2, When i = 3, is the received signal when all interferences enter the receiver of the receiving station n from the sidelobes, is the received signal when one interference enters the receiver of the receiving station n only from the main lobe and ; is the cardinality of the set of receiving stations where the interference signal enters from the main lobe, is the received signal when one interference enters the receiver of the receiving station n from the main lobe and ; Among them, represents the remaining interference and noise, and w k，n is the receiving weight vector of the receiving station n;

[0025]

[0026] Among them,

[0027]

[0028] Among them, is the contaminated phase introduced for Doppler compensation, is the Doppler frequency difference between the received signal and the reference signal at the receiving station;

[0029] Obtain from the received signal and The signal-to-interference-plus-noise ratio of receiving station n at time k is Among them, The measurement noise of follows a Gaussian distribution with zero mean, and are the angles between the transmitting station and receiving station n with respect to target q at time k, respectively, Covariance matrix is β 2 and T 2 are the effective bandwidth and effective time width of the transmitted signal s0(t), respectively, If s0(f) is the Fourier transform of s0(t), the measurement model can be expressed as

[0030] In a possible implementation, when , the interference enters the receiver of receiving station n from the sidelobe and is suppressed by the adaptive receiving beam with the conformal ability of the main lobe of the radar. When , the interference enters the receiver of receiving station n from the main lobe, is the angle difference between jammer m and target q with respect to receiving station n at time k, θ 3dB is the 3dB beam width of receiving station n.

[0031] In a possible implementation, the step of calculating the covariance matrix of the radar node's estimated target parameters through global measurement fusion and extended Kalman filtering to obtain the tracking result of each target by the networked radar includes:

[0032] Stitch together the local measurements of multiple radars participating in tracking target q at time k to obtain the global measurement of target q at time k Among them, is the set of radars tracking target q at time k, represents the nth element of the set represents the cardinality of the set;

[0033] According to the measurement model, the global measurement model is obtained as wherein, the global measurement function is and the global covariance matrix is

[0034] The target state is estimated by the extended Kalman filter to obtain the target state estimation values at each moment and its covariance matrix

[0035] In a possible implementation manner, the step of estimating the target state by the extended Kalman filter to obtain the target state estimation values at each moment and its covariance matrix includes:

[0036] Sequential calculation is performed through the first formula, and the first formula is:

[0037] wherein, is the global measurement function with respect to the vector variable Jacobian matrix of, and is is also the function with respect to the vector variable Jacobian matrix of, defined as The first row elements of are respectively The second row elements of are respectively

[0038]

[0039] In a possible implementation manner, the step of characterizing the target tracking accuracy by the posterior Cramér-Rao lower bound, establishing a cost function for each target, summing the cost functions of each target as the objective function, and combining the radar beam constraint conditions to establish an adaptive scheduling multi-radar tracking beam optimization model includes:

[0040] The posterior Cramér-Rao lower bound is used as the characterization of the target tracking accuracy, and the posterior Cramér-Rao lower bound is wherein, represents all measurement values of target q at time k, is the Fisher information matrix about the target state,

[0041] According to the linear motion model of target q, it can be directly obtained that according to the linear motion model of the target, it can be directly obtained and making the observations of each radar on target q independent of each other, to obtain

[0042] Predictive value of zero process noise Replace Will Denote as The objective function is obtained;

[0043] Use To represent the radar beam allocation matrix, and use As a measure of target tracking accuracy, an adaptive scheduling multi-radar tracking beam optimization model is obtained

[0044] In a possible implementation manner, the step of solving the adaptive scheduling multi-radar tracking beam optimization model to obtain the radar tracking beam adaptive configuration result includes:

[0045] Solve the adaptive scheduling multi-radar tracking beam optimization model through the particle swarm optimization algorithm, and obtain the radar tracking beam adaptive configuration result by the particle with the optimal fitness value;

[0046] Solve the adaptive scheduling multi-radar tracking beam optimization model through the genetic algorithm, and obtain the radar tracking beam adaptive configuration result by selecting the individual with the highest fitness.

[0047] In a second aspect, the present application provides a multi-radar tracking multi-target beam allocation system for countering multiple jammers, which is used to execute the above-mentioned multi-radar tracking multi-target beam allocation method for countering multiple jammers. The system includes:

[0048] The first processing module is used to establish a multi-radar tracking multi-target model under the background of multiple jammers;

[0049] The second processing module is used to obtain the signal-to-interference-plus-noise ratio after the main and sidelobe interference is suppressed step by step at the receiving end of each radar node, and establish a covariance matrix of the estimated target parameters of the radar node;

[0050] The third processing module is used to calculate the covariance matrix of the estimated target parameters of the radar node through global measurement fusion and extended Kalman filtering, and obtain the tracking result of the multi-radar network for each target;

[0051] The fourth processing module is used to characterize the target tracking accuracy through the posterior Cramer-Rao lower bound, establish a cost function for each target, sum the cost functions of each target as the objective function, and combine the radar beam constraint conditions to establish an adaptive scheduling multi-radar tracking beam optimization model;

[0052] The fifth processing module is used to solve the adaptive scheduling multi-radar tracking beam optimization model to obtain the radar tracking beam adaptive configuration result.

[0053] The technical solution provided by the present application may include the following beneficial effects:

[0054] Since the main lobe interference requires multi-radar collaborative suppression, by using the method and system provided in this application, an optimization model can be established with the beam allocation matrix as the independent variable and the target tracking accuracy as the objective function, so as to determine the radars for collaborative countermeasure against the main lobe interference through beam allocation, thereby realizing effective interference suppression throughout the process and achieving stable tracking of the target.

[0055] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The accompanying drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present disclosure, and are used together with the specification to explain the principles of the present disclosure. Obviously, the accompanying drawings in the following description are only some embodiments of the present disclosure, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0057] Figure 1 A flowchart showing the beam allocation method for a networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of the present disclosure;

[0058] Figure 2 A schematic diagram of the scenario of a networked radar tracking multiple targets against multiple jammers in the beam allocation method for a networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of the present disclosure;

[0059] Figure 3 A detailed flowchart of the particle swarm optimization algorithm in the beam allocation method for a networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of the present disclosure;

[0060] Figure 4 A detailed flowchart of the genetic algorithm in the beam allocation method for a networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of the present disclosure;

[0061] Figure 5 A closed-loop framework diagram of the beam allocation method for a networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of the present disclosure;

[0062] Figure 6 A radar distribution and target trajectory diagram of the beam allocation method for a networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of the present disclosure;

[0063] Figure 7 A spatial distribution diagram of targets and jammers of the beam allocation method for a networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of the present disclosure;

[0064] Figure 8 Shows the radar 7 receiving beam pattern of the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0065] Figure 9 Shows the radar 7 matched filter output diagram of the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0066] Figure 10 Shows the radar 7 parameter estimation result diagram of the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0067] Figure 11 Shows the radar 2 receiving beam pattern of the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0068] Figure 12 Shows the radar 2 matched filter output diagram of the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0069] Figure 13 Shows the parameter estimation result diagram of the radar 2 after suppressing sidelobe interference in the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0070] Figure 14 Shows the parameter estimation result diagram of the radar 2 after suppressing sidelobe + main lobe interference in the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0071] Figure 15 Shows the PSO algorithm beam allocation scheme diagram of the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0072] Figure 16 Shows the GA algorithm beam allocation scheme diagram of the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0073] Figure 17 Shows the diagram of the change of PCRLB of each target throughout the process in the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0074] Figure 18 Shows the comparison diagram of the change of RMSE of each target throughout the process in the multi-target beam allocation method for a networked radar against multiple jammers in an exemplary embodiment of the present disclosure;

[0075] Figure 19Shows the structural diagram of a multi-radar tracking multi-target beam allocation system against multiple jammers in an exemplary embodiment of the present disclosure. Detailed implementation manners

[0076] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be more thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments.

[0077] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus their repeated description will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0078] In this example embodiment, a method for multi-radar tracking multi-target beam allocation against multiple jammers is first provided. This method can be applied to a terminal device, such as a mobile terminal like a mobile phone, a desktop computer, a personal digital assistant, a laptop computer, a tablet computer, a smart watch, etc. Referring to Figure 1 as shown, this method may include the following steps:

[0079] Step S100: Establish a multi-radar tracking multi-target model under the background of multiple jammers.

[0080] Step S200: Obtain the signal-to-interference-plus-noise ratio (SINR) of each radar node's receiving end after step-by-step suppression of main and sidelobe interferences, and establish the covariance matrix of the radar node's estimated target parameters.

[0081] Step S300: Calculate the covariance matrix of the radar node's estimated target parameters through global measurement fusion and extended Kalman filtering, and obtain the tracking results of the multi-radar for each target.

[0082] Step S400: Characterize the target tracking accuracy through the posterior Cramér-Rao lower bound, establish a cost function for each target, sum the cost functions of each target as the objective function, and establish an adaptive scheduling multi-radar tracking beam optimization model in combination with the radar beam constraint conditions.

[0083] Step S500: Solve the adaptive scheduling multi-radar tracking beam optimization model to obtain the adaptive configuration result of the radar tracking beam.

[0084] Through the above method, sidelobe interference can be independently suppressed by each node radar, and main lobe interference is suppressed through multi-radar cooperation. By establishing an optimization model with the beam allocation matrix as the independent variable and the target tracking accuracy as the objective function and solving it, the optimal beam allocation scheme is determined to achieve stable target tracking.

[0085] It should be noted that in step S300, calculating the covariance matrix of the estimated target parameters of the radar nodes is synchronized with obtaining the tracking results of the networked radars for each target. By calculating the covariance matrix of the estimated target parameters of the radar nodes, the error of the tracking results of the networked radars for each target is estimated, so as to guide the beam allocation during the next transmission.

[0086] Next, reference will be made to Figures 1 to 5 to describe each step of the above method in the exemplary embodiment in more detail.

[0087] In one embodiment, step S100 may include the following sub-steps:

[0088] Step S110: Assume that Q targets are moving in a straight line at a constant speed in the XOY plane. The motion state of target q at time k is Establish the motion equation of target q as where F is the target state transition matrix, is a zero-mean white Gaussian process noise, and the expression of the target state transition matrix is ΔT is the sampling interval, and the covariance matrix is κ q is the noise intensity during the state transition of target q.

[0089] Step S120: Assume that a radar networking system includes one transmitting station and N receiving stations, tracks Q moving targets, and has M jammers to cover the target penetration. Among them, the transmitting station is located at p t =[x t , y t T , the receiving station n is located at p rn =[x rn , y rn T , and at time k, target q is located at

[0090] Step S130: When the receiving station n tracks target q at time k, the superimposed signal of the echo, interference, and noise of target q received by the receiving station n is y k，n (t)=x k，n (t)+r k，n (t)+n k，n (t), where x k,n ​​$(t)$ is the echo signal of target $q$ received by receiving station $n$ at time $k$, $r$ k,n $(t)$ is the interference signal received by receiving station $n$ at time $k$, $n$ k,n $(t)$ is the noise.

[0091] It should be noted that, as Figure 2 shown, the transmitting station radiates omnidirectionally to cover the entire surveillance area. Each receiving station uses digital beamforming technology to form a narrow beam to track the target, and only one narrow beam can be formed at each moment, so only one target can be tracked. Assume that the transmitting station is located at $p$ t $=$ [$x$ t , $y$ t T The transmitted pulse train signal is: where $s(t)$ is the baseband signal, $T$ r is the pulse repetition interval, and $L$ is the number of pulses. Receiving station $n$ is located at $p$ rn $=$ [$x$ rn , $y$ rn T . Assume that at time $k$, target $q$ is located at Define to represent the (tracking) pairing relationship of receiving station $n$ to $Q$ targets at time $k$, represents that receiving station $n$ tracks target $q$ at time $k$, represents that receiving station $n$ does not track target $q$ at time $k$.

[0092] Furthermore, the echo signal of receiving station $n$ about target $q$ received at time $k$ is:

[0093]

[0094] where is the propagation loss, $P$ t is the transmitting power of the transmitting station, and are respectively the reflection intensity, azimuth angle, propagation delay and Doppler frequency of target $q$ relative to receiving station $n$ at time $k$, $\alpha$ rn is the receiving vector of receiving station $n$, $M$ rn and $d$ rn are respectively the number of array elements and the interval of receiving station $n$, and $\lambda$ is the wavelength;

[0095] The interference signal received by receiving station $n$ at time $k$ is:

[0096]

[0097] where is the propagation loss of the interference signal; is the transmit power of jammer m, and are respectively the azimuth angle, propagation delay, and Doppler frequency of jammer m relative to receiving station n at time k.

[0098] It should be noted that, among them, at time k, receiving station n tracks target q, that is and the position of jammer m at time k is The transmitted interference signal is r m (t).

[0099] In one embodiment, step S200 may include the following sub-steps:

[0100] Step S210: Define According to the received signal For and perform maximum likelihood estimation,

[0101] When i = 1, 2,

[0102]

[0103] When i = 3, is the received signal when all interferences enter the receiver of receiving station n from the sidelobes, is the received signal when one interference enters the receiver only from the main lobe of receiving station n and ; is the cardinality of the set of interference signals entering the receiving station from the main lobe, is the received signal when one interference enters the receiver of receiving station n from the main lobe and ;

[0104]

[0105] Among them, represents the residual interference and noise, w k，n is the receiving weight vector of receiving station n;

[0106]

[0107] Among them, Among them, is the contaminated phase introduced by Doppler compensation, is the Doppler frequency difference between the received signal of the receiving station and the reference signal.

[0108] Step S220: Obtain from the received signal and The signal-to-interference-plus-noise ratio (SINR) of receiving station n at time k is

[0109]

[0110] where the measurement noise of follows a zero-mean Gaussian distribution:

[0111] and are the angles between the transmitting station and receiving station n with respect to target q at time k, respectively covariance matrix is β 2 and T 2 are the effective bandwidth and effective time width of the transmitted signal s0(t), respectively S0(f) is the Fourier transform of s0(t), and the measurement model can be expressed as

[0112] It can be understood that before step S210, sidelobe interference suppression and mainlobe interference suppression need to be carried out separately for each radar node. Only after suppressing the interference can the signal-to-noise ratio and covariance matrix be calculated. First, sidelobe interference suppression is carried out through an adaptive beamformer with mainlobe conformal ability, and then multi-radar cooperation is used to suppress the mainlobe interference; among them, sidelobe interference suppression through an adaptive beamformer with mainlobe conformal ability is a common sidelobe interference suppression method in the prior art, and the method of suppressing the mainlobe interference through multi-radar cooperation can be implemented by the mainlobe interference suppression method described in the literature "Lei Zhang, Linghua Su, Dan Wang, Ying Luo, and Qun Zhang. Mainlobe Interference Suppression for Radar Network via RPCA-Based Covariance Matrix Reconstruction. IEEE SENSORS JOURNAL, VOL. 23, NO. 5, 1 MARCH 2023".

[0113] It should be noted that before estimating the target parameters, the interference signal needs to be suppressed first to improve the signal-to-interference-plus-noise ratio (SINR). According to whether the interference signal enters the receiver from the main beam of the radar, the interference can be divided into mainlobe interference and sidelobe interference. Assume that the receiving station can form a narrow beam to track the target, and let θ 3dB be the 3dB beam width of the receiving station, be the angle difference between jammer m and target q with respect to receiving station n at time k. When , if It is considered that interference m enters the receiver of receiving station n from the sidelobe. If It is considered that interference m enters the receiver of receiving station n from the main lobe. For sidelobe interference, the radar can suppress it by designing an adaptive receiving beam with the ability to maintain the main lobe shape. The requirement for maintaining the main lobe shape is because traditional adaptive beamforming methods are prone to causing distortion of the main beam, affecting the reception of the desired signal. Assuming that the minimum variance distortionless response (MVDR) criterion is used to design the receiving beam, the receiving weight vector can be expressed as where, R i+n is the interference + noise covariance matrix, and θ0 is the desired direction. To achieve main lobe shape preservation, R i+n does not contain the desired signal and main lobe interference. The Capon power spectrum can be used for integral reconstruction in the sidelobe region, and then assuming that the number of main lobe interferences received by receiving station n does not exceed 1, the interference suppression is divided into and where, and in represents the set of receiving stations where the interference signal enters from the main lobe, First, the beamforming method is used to suppress the sidelobe interference to obtain the received signal shown in Then, through range-Doppler compensation - covariance matrix reconstruction - time-domain constrained linear enhancement, the received signal shown in is obtained. The contaminated phase and Doppler frequency difference introduced by Doppler compensation are determined by the positions of jammer m and receiving station n; the symbol "≈" is used because the multi-radar cooperative processing gain may not be 1, is the time delay difference between the received signal of receiving station n and the reference signal, which is also determined by the positions of jammer m and receiving station n.

[0114] Furthermore, where, when , the interference enters the receiver of receiving station n from the sidelobe and is suppressed by the adaptive receiving beam with the main lobe shape preservation ability of the radar. When , the interference enters the receiver of receiving station n from the main lobe, is the angle difference between jammer m and target q relative to receiving station n at time k, and θ 3dB is the 3dB beam width of receiving station n.

[0115] In one embodiment, step S300 may include the following sub-steps:

[0116] Step S310: Concatenate the local measurements of multiple radars participating in tracking target q at time k to obtain the global measurement of target q at time k where, The set of radars tracking target q at time k denotes the set the nth element of denotes the set the cardinality of

[0117] Step S320: According to the measurement model, the global measurement model is obtained as where the global measurement function is and the global covariance matrix is

[0118] Step S330: Estimate the target state through the extended Kalman filter to obtain the target state estimation values at each time and its covariance matrix

[0119] Furthermore, the detailed process of Step S330 is as follows:

[0120] Sequential calculation is performed through the first formula, and the first formula is:

[0121] where is the global measurement function with respect to the vector variable the Jacobian matrix, which is also the function with respect to the vector variable the Jacobian matrix, defined as The first row elements of The second row elements of

[0122]

[0123] It should be noted that define as the set of radars tracking target q at time k. When multiple radars track target q simultaneously, i.e., information fusion is required.

[0124] In one embodiment, Step S400 may include the following sub-steps:

[0125] Step S410: Use the posterior Cramer-Rao lower bound (PCRLB) as the characterization of the target tracking accuracy. The posterior Cramer-Rao lower bound is

[0126]

[0127] where denotes all the measurement values of target q at time k, is the Fisher Information Matrix (FIM) regarding the target state,

[0128] Step S420: According to the linear motion model of target q, it can be directly obtained that according to the linear motion model of the target, it can be directly obtained and make the observations of each radar on target q independent of each other, obtaining

[0129] Step S430: Use the predicted value of zero process noise to replace and represent as to obtain the objective function.

[0130] Step S440: Use to represent the radar beam allocation matrix, and use as a measure of target tracking accuracy, obtaining the adaptive scheduling multi-radar tracking beam optimization model

[0131] It should be noted that in step S410 is because so it is further written as

[0132] In step S440, during the process of multiple jammers covering multiple targets to penetrate defenses, the receiving beam allocation method of the networked radar will affect the way the interference signal enters the receiver. For sidelobe interference, a single radar can use its inherent anti-jamming measures such as beamforming to suppress it. However, for main lobe interference, it is difficult for a single radar to effectively deal with it, and multi-radar cooperation is required. Therefore, the beam allocation method affects the interference suppression effect of each radar, and thus affects the target tracking accuracy. From the perspective of radar anti-jamming, the radar networking system should reasonably allocate tracking beams at each tracking moment to effectively suppress interference, and the interference suppression effect is demonstrated through target tracking accuracy.

[0133] In the adaptive scheduling multi-radar tracking beam optimization model, the constraint condition ensures that each radar can only track one target at each moment. When a single radar tracks multiple targets through multi-beamforming technology, it is possible that multiple interference signals enter the receiver from the main lobe of the radar, increasing the difficulty of main lobe interference suppression. By reasonably allocating the tracking beams of each receiving radar at each moment, the sum of the tracking accuracies of all targets can be maximized. Sidelobe interference can be independently suppressed by each node radar, while main lobe interference requires multi-radar cooperation to suppress. Therefore, beam allocation is equivalent to selecting appropriate anti-jamming measures for each radar to ensure that the networked radar effectively suppresses interference as a whole.

[0134] In one embodiment, step S500 may include the following sub-steps:

[0135] Step S510: Solve the adaptive scheduling multi-radar tracking beam optimization model through the particle swarm optimization algorithm, and obtain the radar tracking beam adaptive configuration result by obtaining the particle with the optimal fitness value.

[0136] Step S520: Solve the adaptive scheduling multi-radar tracking beam optimization model through the genetic algorithm, and obtain the radar tracking beam adaptive configuration result by selecting the individual with the highest fitness.

[0137] Among them, optionally, as Figure 3 shown, the detailed steps of step S510 are:

[0138] Initialize the particle swarm: Each particle is represented by an allocation matrix U k that satisfies the constraint conditions. For convenience of calculation, it can be converted into a vector. If represents a certain particle, then Randomly generate the initial position and velocity of the particle, where is the particle index.

[0139] Calculate the fitness: The fitness function is used to measure the quality of a candidate solution. In the PSO algorithm, the fitness function calculates a value based on the current state of the particle, and this value represents the degree to which the particle "fits" the problem in the solution space. In the model established in this paper, the objective function is non-negative, so it can be directly used as the fitness function of the particle.

[0140] Update the individual and global best: For each particle, record the best position it has experienced during the search process, that is, the individual best position pBest (i) , corresponding to the optimal fitness value of this particle; for the entire particle swarm, record the best position it has experienced during the search process, gBest, corresponding to the optimal fitness value among all particles.

[0141] Update the velocity and position: The velocity of each particle is updated according to the above formula, where ω is the inertia weight, used to control the influence degree of the particle velocity; c1 and c2 are learning factors; r1 and r2 are random numbers on [0,1], used to introduce randomness; gBest (i) is the best position of particle i; gBest is the global best position. After updating the velocity, the position of each particle is updated according to the following formula After the particle is updated, it is very likely that it does not satisfy the constraint conditions Therefore, constraint processing needs to be carried out again. The specific process is: First, decode the individual into the allocation matrix U k, then judge line by line. If the number of non-zero elements in a line is greater than 1, randomly retain one of them; if the number of non-zero elements in a line is zero, randomly select an element and assign it a value of 1; if the number of non-zero elements in a line is exactly 1, keep it unchanged.

[0142] Iteration and termination: Repeat updating the velocity and position of each particle, calculating the fitness until the iteration termination condition is reached, output the global best position gBest, and obtain the beam allocation matrix through decoding.

[0143] Optionally, as Figure 4 shown, the detailed steps of step S520 are as follows:

[0144] Determine the coding scheme: Convert the allocation matrix U k into a vector, where each element represents the pairing relationship between the radar and the target. The specific representation method can be seen in the PSO algorithm.

[0145] (2) Initialize the population: Randomly generate multiple individuals, and each individual is a linear representation of the allocation matrix U k that satisfies the constraint conditions, that is, a one-dimensional array.

[0146] (3) Calculate the fitness: The genetic algorithm judges the quality of an individual based on its fitness and determines the size of its genetic opportunity. In the model established in this paper, the objective function is non-negative, and the minimum value of the function is used as the objective function.

[0147] Therefore, can be used as the fitness of an individual.

[0148] (4) Selection operation: Select the next-generation population based on the fitness of individuals. Generally, it is required that individuals with higher fitness have a greater chance of being inherited to the next generation. In this paper, the roulette wheel selection mechanism is used to screen individuals with high fitness.

[0149] (5) Crossover operation: Exchange some chromosomes between two individuals with a certain probability to generate new individuals. In this paper, first pair adjacent individuals, and then randomly select the crossover point position, and exchange the genes of the two individuals after the crossover point.

[0150] (6) Mutation operation: Generate new genotypes by randomly modifying the genes of individuals to increase the population diversity. In this paper, the single-point mutation method is adopted. First, randomly select the mutation point position, and then invert the original gene at this mutation point, that is, 0 becomes 1 and 1 becomes 0. Note that when initializing the population, each individual is subject to the constraint conditions After generation, the individuals in the population still satisfy the constraint condition after the selection operation. However, after the crossover and mutation operations, some individuals are likely to no longer satisfy the constraint condition. Therefore, it is necessary to perform constraint processing on the individuals after the mutation operation. The specific process can be seen in the PSO algorithm. The above operations will reduce the individual diversity of the population.

[0151] (7) Iteration and termination: Repeat operations such as selection, crossover, and mutation until the termination condition is met, and output the individual with the highest fitness. After decoding, the beam allocation matrix is obtained.

[0152] In one embodiment, as Figure 5 shown is the closed-loop framework of the multi-target tracking method for a networked radar based on beam allocation. At time k, each node radar first uses an adaptive beamforming technique with main-lobe conformal ability to suppress sidelobe interference. If it still suffers from main-lobe interference, then the main-lobe interference is suppressed. Subsequently, the maximum likelihood estimation method is used to estimate from the interference-suppressed signal and then send it to the control center to splice into a global measurement An estimated value of the target state at the current moment is obtained through the EKF and the zero process noise prediction value of the target state at time k + 1 is calculated The is input into the resource optimization model, and the beam allocation matrix of the radar networking system at time k + 1 can be obtained. This process is looped to achieve the full-course tracking of multiple targets.

[0153] Furthermore, in this exemplary embodiment, a simulation experiment of a multi-target tracking beam allocation method for a networked radar against multiple jammers is also provided. The effectiveness of the proposed method for a networked radar against multiple jammers based on beam allocation is verified through simulation experiments in a specific scenario.

[0154] In the simulation, the spatial distribution of the radars and the movement trajectories of the targets and jammers are as Figure 6 shown. The radar transmitting station is located at [0,0] km, and the receiving stations are located at [30,30] km, [0,30] km, [30,15] km, [30,5] km, [15,0] km, [10,0] km, [20,30] km, and [10,30] km respectively. The initial states of the targets and jammers are shown in Tables 1 and 2 respectively, and other necessary simulation parameters are shown in Table 3. It is assumed that the radar transmits LFM signals and the jammers transmit noise-like interference signals, and the signal parameters are consistent with those in the simulation of Chapter 3. From the setting of the spatial distribution parameters of the targets and jammers, it can be seen that the spatial positions of two jammers are very close to those of two targets respectively. Therefore, it can be considered that the echo of these two targets must be accompanied by main-lobe interference signals. According to the radar wavelength, the number of receiving array elements, and the interval, the 3dB beam width of the radar is approximately 3°. It is assumed that the networked radar accurately obtains the real-time positions of the jammers through interference source cross-location. Therefore, the positions of the jammers can be considered as known quantities.

[0155] Table 1 Target Initial State

[0156]

[0157]

[0158] Table 2 Jammer Initial State

[0159]

[0160] Table 3 Radar-related Parameters

[0161]

[0162] First, verify the interference suppression effect. Assume that when k = 13, the target and the jammer are respectively in the Figure 7 shown positions. The system allocates tracking radar 7 to target 5 and tracking radars 2 and 8 to target 2.

[0163] For target 5, assume it is located at the center of the main beam of radar 7, i.e., the 0° direction. According to the spatial distribution of radar 7, target 5, and four jammers, the directions of the interference signals can be calculated as -32.2767°, -22.1970°, -2.0048°, and -48.7776° respectively. The angular differences between these interference signals and the target echo are all greater than, so it is considered that the interference signals all enter the receiver of radar 7 from the sidelobe direction. Figure 8 shows the adaptive receiving beam pattern of radar 7 at this moment. It can be seen that the receiving beam forms nulls of -30.38 dB, -31.67 dB, -25.55 dB, and -31.57 dB respectively in the four interference directions. Figure 6 .8 then shows the result of radar 7 using adaptive beamforming to suppress sidelobe interference. From Figure 9 it can be seen that after adaptive beamforming, the interference power level drops significantly and the target can be effectively detected. Figure 10 then shows the parameter estimation result in the range-Doppler plane, which is relatively close to the actual value (39.6021 km, 92.5663 Hz) of the range-Doppler frequency of target 5 relative to radar 7 at the current moment, indicating that sidelobe interference suppression improves the accuracy of target parameter estimation.

[0164] For target 2, assuming it is located at the center of the main beam of Radar 2, the signals of three jammers will enter the receiver of Radar 2 from -9.0180°, 3.0875°, and -2.8813° respectively. These interferences can be considered as sidelobe interferences. In addition, the signal of one jammer enters the receiver of Radar 2 from the main lobe along with the target echo. After reconstructing the (sidelobe) interference plus noise covariance matrix, an adaptive receiving beam with the ability to maintain the main lobe shape can be constructed, and its pattern is as shown in Figure 11 . It can be seen that the receiving beam forms nulls of -27.07dB, -22.62dB, and -23.01dB in the three interference directions respectively, while the main lobe is undistorted, ensuring the complete reception of the target echo (and main lobe interference). When only using adaptive beamforming to suppress sidelobe interference, the output of its matched filtering is shown by the Figure 12 gray line. It can be seen that the target is still completely submerged in the (main lobe) interference and cannot be effectively detected. The range-Doppler estimation result is shown in Figure 13 . At this time, there are large errors in the parameter estimation values. Radar 8 undergoes the same sidelobe interference suppression process. Since Radar 2 and Radar 8 receive the main lobe interference signals from the same jammer, the TDCLE method proposed in Chapter 3 can be used to jointly suppress the main lobe interference. Taking Radar 2 as the reference station, after range-Doppler compensation, covariance matrix reconstruction, and linear enhancement, the signal output by Radar 2 is shown by the Figure 12 blue line. It can be seen that after local sidelobe interference suppression and multi-radar collaborative main lobe interference suppression, the interference has been significantly filtered out and the target can be effectively detected. The final parameter estimation result is shown in Figure 14 . It can be seen that the parameter estimation result is relatively close to the true value of the range-Doppler frequency of target 2 relative to Radar 2 (36.2352km, -67.1675Hz), indicating that the radar assigned to this target can effectively suppress interference and improve the accuracy of parameter estimation.

[0165] Secondly, the tracking effectiveness is verified. As shown in Figures 15 - 16 , the beam allocation schemes solved by the PSO algorithm and the GA algorithm are given respectively. During the solution process, the particle swarm and population size are both 50, and the maximum number of iterations is 100 times. For comparison, it is assumed that a random number generator (RNG) randomly assigns tracking targets to the system at each tracking moment. At this time, each radar can still suppress sidelobe interference, but it is unknown whether the main lobe interference can be suppressed.

[0166] As shown in Figure 17 , the variation of the PCRLB of each target throughout the process under three beam allocation schemes is given. Since the initial FIM of each target is set to Q q , so for all targets, we have As can be seen from the figure, as the tracking time increases, the tracking accuracy of each target gradually improves. In addition, the beam allocation schemes given by the PSO algorithm and the GA algorithm have similar performances, and their performances on targets other than target 3 are significantly better than those of the RNG scheme, indicating that reasonable optimization of beam allocation can give play to the advantages of the radar networking system and effectively cope with multiple jammers.

[0167] However Figure 17 only shows the calculated or predicted tracking accuracy, and the actual tracking accuracy represented by RMSE is as Figure 18 shown. The definition of RMSE is the same as that in Chapter 2, and the number of Monte Carlo trials N MC = 1000. During the tracking process, there may be a situation where the system does not allocate a tracking radar to a certain target at a certain moment. At this time, the target state estimate value can be replaced by the zero process noise prediction value of the previous moment, that is and the covariance matrix estimate value can be expressed as Because the system cannot continuously not allocate a tracking radar to a certain target, the tracking situation of this target will not deteriorate seriously. As Figure 18 can be seen, for target 1 and target 4, the tracking accuracy provided by the PSO scheme is better than that of the GA scheme and the RNG scheme; for target 2, 5 and 6, the tracking accuracies of the PSO scheme and the GA scheme are similar and better than that of the RNG scheme; a special case occurs in target 3, and the tracking accuracy provided by the RNG scheme for it is better than those of the two optimization schemes. Generally speaking, the two optimization schemes can provide higher tracking accuracy, which once again verifies the effectiveness of the method of using beam allocation by networking radars to counter multiple jammers.

[0168] Furthermore, as Figure 19 shown, in the embodiment of the present example, a networking radar tracking multi-target beam allocation system for countering multiple jammers is also provided, which is used to execute the networking radar tracking multi-target beam allocation method for countering multiple jammers as described above. The system includes:

[0169] A first processing module, configured to establish a networking radar tracking multi-target model under the background of multiple jammers;

[0170] A second processing module, configured to obtain the signal-to-interference-plus-noise ratio after step-by-step suppression of main and sidelobe interferences at the receiving end of each radar node, and establish a covariance matrix for estimating target parameters of the radar node;

[0171] A third processing module, configured to calculate the covariance matrix for estimating target parameters of the radar node through global measurement fusion and extended Kalman filtering, and obtain the tracking result of the networking radar for each target;

[0172] The fourth processing module is used to characterize the target tracking accuracy by the posterior Cramer-Rao lower bound, establish a cost function for each target, sum up the cost functions of each target as the objective function, and establish an adaptive scheduling multi-radar tracking beam optimization model in combination with the radar beam constraint conditions;

[0173] The fifth processing module is used to solve the adaptive scheduling multi-radar tracking beam optimization model to obtain the adaptive configuration result of the radar tracking beam.

[0174] Regarding the device in the above embodiments, the specific manners in which each module performs operations have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0175] It should be noted that although several modules or units of the device for action execution are mentioned in the above detailed description, such a division is not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of the two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units. The components shown as modules or units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of the present disclosure. Those of ordinary skill in the art can understand and implement it without creative work.

[0176] In an exemplary embodiment of the present disclosure, an electronic device is further provided. The electronic device may include a processor and a memory for storing executable instructions of the processor. Wherein, the processor is configured to execute the steps of the method for allocating multi-target beams of a networking radar for countering multiple jammers in any one of the above embodiments by executing the executable instructions.

[0177] Those skilled in the art can understand that various aspects of the present invention can be implemented as a system, a method, or a program product. Therefore, various aspects of the present invention can be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or an implementation combining hardware and software aspects, which can be collectively referred to as "circuit", "module", or "system" here.

[0178] Through the description of the above embodiments, those skilled in the art can easily understand that the exemplary embodiments described herein can be implemented by software or by a combination of software and necessary hardware. Therefore, the technical solution according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, including several instructions to enable a computing device (which can be a personal computer, a server, or a network device, etc.) to execute the above multi-jammer-resistant networked radar tracking multi-target beam allocation method according to the embodiments of the present disclosure.

[0179] In an exemplary embodiment of the present disclosure, there is also provided a computer storage medium, on which a computer program is stored, and when the program is executed by, for example, a processor, the steps of the multi-jammer-resistant networked radar tracking multi-target beam allocation method described in any one of the above embodiments can be implemented.

[0180] In some possible implementation manners, various aspects of the present invention can also be implemented in the form of a computer program product, which includes a computer program or instruction. When the computer program product runs on a terminal device, the computer program code or instruction is used to cause the terminal device to execute the steps according to various exemplary embodiments of the present invention described in the above multi-jammer-resistant networked radar tracking multi-target beam allocation method part of this specification.

[0181] The above program product can be written in any combination of one or more programming languages for programming code to perform the operations of the present invention. The programming languages include object-oriented programming languages - such as Java, C++, etc., and also include conventional procedural programming languages - such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's device, executed as an independent software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user's computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computing device (for example, by using an Internet service provider to connect through the Internet).

[0182] The computer software product can be stored in a computer storage medium, which includes read-only memory (ROM), random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), one-time programmable read-only memory (OTPROM), electrically-erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc memories, magnetic disk memories, magnetic tape memories, or any other medium that is computer-readable and can be used to carry or store data.

[0183] Those skilled in the art will readily conceive of other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include known common general knowledge or conventional technical means in the technical field not disclosed in the present disclosure. The specification and examples are only to be considered as exemplary, and the true scope and spirit of the present disclosure are pointed out by the appended claims.

Claims

1. A beam allocation method for tracking multiple targets by a networked radar against multiple jammers, characterized in that: include: Establish a model for networked radar tracking multiple targets under the background of multiple jammers; Obtain the signal-to-interference-noise ratio of each radar node receiving end after the main sidelobe interference is suppressed step by step, and establish the covariance matrix of the radar node to estimate the target parameters; Through global measurement fusion and extended Kalman filtering, the covariance matrix of the radar node estimated target parameters is calculated, and the tracking results of each target by the networked radar are obtained; The target tracking accuracy is characterized by the posterior Cramer-Rao lower bound, and a cost function is established for each target. The sum of the cost functions of each target is used as the objective function. Combined with the radar beam constraint conditions, an adaptive scheduling multi-radar tracking beam optimization model is established. Solve the adaptive scheduling multi-radar tracking beam optimization model to obtain the radar tracking beam adaptive configuration result.

2. The method for tracking multiple targets by a networked radar against multiple jammers according to claim 1 is characterized in that: The steps of establishing a networked radar tracking multi-target model under a multi-jammer background include: Assume that Q targets are moving in a uniform linear motion in the XOY plane, and the motion state of target q at time k is The motion equation of the target q is established as Among them, is the target state transfer matrix, is zero-mean white Gaussian process noise, and the expression of the target state transfer matrix is: ΔT is the sampling interval, and the covariance matrix is k q is the noise intensity during the target q state transition; Assume that a radar network system contains one transmitting station and N receiving stations, tracking Q moving targets, and has M jammers to cover the target penetration, where the transmitting station is located at p t =[x t ,y t ] T , the receiving station n is located at p rn =[x rn ,y rn ] T , the target q at time k is located When receiving station n tracks target q at time k, the superposition signal of the echo, interference and noise received by receiving station n is y k，n (t) = x k，n (n(t)+r k， n (t)+n k，n (t), where x k,n (t) is the echo signal of target q received by receiving station n at time k, r k,n (t) is the interference signal received by receiving station n at time k, n k,n (t) is the noise.

3. The method for tracking multiple targets by a networked radar against multiple jammers according to claim 2 is characterized in that: The echo signal about target q received by the receiving station n at time k is: in, is the propagation loss, P t is the transmitting power of the transmitting station, and are respectively the reflection intensity, azimuth, propagation delay and Doppler frequency of target q relative to receiving station n at time k, α rn is the receiving vector of receiving station n, M rn and d rn are the number and spacing of array elements at receiving station n, respectively, and λ is the wavelength; The interference signal received by the receiving station n at time k is: in, is the propagation loss of the interference signal; is the transmission power of jammer m, and are respectively the azimuth, propagation delay and Doppler frequency of the jammer m relative to the receiving station n at time k.

4. The method for beam allocation of multi-target networked radar tracking against multiple jammers according to claim 3 is characterized in that: The step of obtaining the signal to noise ratio of each radar node receiving end after the main sidelobe interference is suppressed step by step, and establishing the covariance matrix of the radar node estimating the target parameter includes: definition According to the received signal right and Perform maximum likelihood estimation. When i=1,2, When i=3, is the received signal of the receiver at receiving station n when all interference enters from the side lobes, For an interference that enters the receiver only from the main lobe of receiving station n and The received signal, is the cardinality of interference signals entering the receiving station set from the main lobe, There is an interference from the main lobe into the receiver of receiving station n and The received signal; in, represents the residual interference and noise, w k，n is the receiving weight vector of receiving station n; in, in, The contamination phase introduced for Doppler compensation, is the Doppler frequency difference between the received signal at the receiving station and the reference signal; Get from the received signal and The signal-to-interference-to-noise ratio of receiving station n at time k is in, The measurement noise of follows a zero-mean Gaussian distribution, and are the angles between the transmitting station and the receiving station n and the target q at time k Covariance matrix for β 2 and T 2 are the effective bandwidth and effective time width of the transmitted signal s0(t), S0(f) is the Fourier transform of s0(t), then the measurement model can be expressed as 5. The beam allocation method for tracking multiple targets by a networked radar against multiple jammers according to claim 4 is characterized in that: when When the interference enters the receiver of receiving station n from the side lobe, it is suppressed by the adaptive receiving beam of the radar's main lobe conformal capability. When the interference enters the receiver of receiving station n from the main lobe, the main lobe interference is suppressed by multi-radar cooperation. is the angle difference between the jammer m and the target q relative to the receiving station n at time k, θ 3dB is the 3dB beamwidth of receiving station n.

6. The beam allocation method for tracking multiple targets by a networked radar against multiple jammers according to claim 4 is characterized in that: The step of calculating the covariance matrix of the radar node estimated target parameters through global measurement fusion and extended Kalman filtering to obtain the tracking result of each target by the networked radar includes: The local measurements of multiple radars participating in tracking target q at time k are stitched together to obtain the global measurement of target q at time k. in, is the set of radars tracking target q at time k, Representing a collection The nth element of Representing a collection The cardinality of According to the measurement model, the global measurement model is obtained as follows: Among them, the global measurement function is The global covariance matrix is The target state is estimated by extending the Kalman filter to obtain the estimated value of the target state at each moment. and its covariance matrix 7. The beam allocation method for tracking multiple targets by a networked radar against multiple jammers according to claim 6 is characterized in that: The target state is estimated by using the extended Kalman filter to obtain the target state estimation value at each moment. and its covariance matrix The steps include: The sequential calculation is performed by the first formula, which is: in, is the global measurement function About vector variables The Jacobian matrix of Also a function About vector variables The Jacobian matrix of The first row elements of The second row elements of 8. The beam allocation method for tracking multiple targets by a networked radar against multiple jammers according to claim 1, characterized in that: The steps of characterizing the target tracking accuracy by the posterior Cramer-Rao lower bound, establishing a cost function for each target, summing the cost functions of each target as the objective function, and establishing an adaptive scheduling multi-radar tracking beam optimization model in combination with radar beam constraints include: The posterior Cramer-Rao lower bound is used as the representation of target tracking accuracy. The posterior Cramer-Rao lower bound is in, represents all measured values ​​of the target q at time k, is the Fisher information matrix about the target state, According to the linear motion model of the target q, we can directly get And make the observation of target q by each radar independent of each other, we can get Predicting values ​​with zero process noise replace Will Expressed as Get the objective function; use represents the radar beam allocation matrix, and is represented by As a measure of target tracking accuracy, the adaptive scheduling multi-radar tracking beam optimization model is obtained 9. The method for beam allocation of multi-target networked radar tracking against multiple jammers according to claim 1 is characterized in that: The step of solving the adaptive scheduling multi-radar tracking beam optimization model to obtain the radar tracking beam adaptive configuration result includes: The adaptive scheduling multi-radar tracking beam optimization model is solved by a particle swarm algorithm, and the radar tracking beam adaptive configuration result is obtained by obtaining particles with the optimal fitness value; The adaptive scheduling multi-radar tracking beam optimization model is solved by a genetic algorithm, and the radar tracking beam adaptive configuration result is obtained by selecting the individual with the highest fitness.

10. A networked radar tracking multi-target beam allocation system against multiple jammers, characterized in that: The system is used to execute the beam allocation method for tracking multiple targets by a networked radar against multiple jammers as claimed in any one of claims 1 to 9, and the system comprises: The first processing module is used to establish a model for tracking multiple targets by a networked radar under a multi-jammer background; The second processing module is used to obtain the signal-to-interference-noise ratio of each radar node receiving end after the main sidelobe interference is suppressed step by step, and to establish a covariance matrix of the radar node to estimate the target parameters; The third processing module is used to calculate the covariance matrix of the radar node estimated target parameters through global measurement fusion and extended Kalman filtering, and obtain the tracking result of each target by the networked radar; The fourth processing module is used to characterize the target tracking accuracy through the posterior Cramer-Rao lower bound, establish a cost function for each target, sum the cost functions of each target as the objective function, and establish an adaptive scheduling multi-radar tracking beam optimization model in combination with radar beam constraints; The fifth processing module is used to solve the adaptive scheduling multi-radar tracking beam optimization model to obtain the radar tracking beam adaptive configuration result.

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