Beam assignment method and system for tracking multiple targets by networked radar against multiple jammers

Abstract

The application relates to a multi-target tracking beam allocation method and system of a networked radar against multiple jammers, wherein the method comprises the following steps: a model is established; a signal-to-interference-and-noise ratio of a receiving end of each radar node after step-by-step suppression of main lobe and side lobe interference is obtained, and a covariance matrix of target parameter estimation of the radar node is established; the covariance matrix of target parameter estimation of the radar node is calculated, and tracking results of the networked radar on each target are obtained; a posteriori Cramer-Rao lower bound is used to represent target tracking accuracy, a cost function of each target is established, a sum of the cost functions of all the targets is taken as a target function, and an adaptive scheduling multi-radar tracking beam optimization model is established by combining a radar beam constraint condition; and the adaptive scheduling multi-radar tracking beam optimization model is solved. The application provides a multi-target tracking beam allocation method and system of a networked radar against multiple jammers, and can effectively suppress interference and stably track targets throughout the whole process.

Description

Technical Field

[0001] This application relates to the field of electronic countermeasures and jamming technology, and in particular to a method and system for beam allocation of networked radar to track multiple targets against multiple jammers. Background Technology

[0002] Radar networking refers to connecting multiple radars of different types and locations through communication links, enabling unified management and data fusion processing to form an organic whole, thereby achieving more effective and comprehensive target detection and tracking. Furthermore, radar networking not only represents the fusion of detection information from individual radars but also the exchange, expansion, and optimization of their detection resources. The result is that the radar network system possesses richer anti-jamming resources: on the one hand, each node radar is equipped with anti-jamming measures, such as sidelobe cancellation and sidelobe concealment; on the other hand, multiple radars can coordinate to combat interference through information fusion. In addition to these two technical anti-jamming resources, networked radars also possess rich tactical operability, such as covert activation, feint activation, and scintillation transmission.

[0003] In existing technologies, when facing distributed coordinated jamming scenarios, radar networking, on the one hand, selects appropriate operating modes, radiation parameters, and anti-jamming measures for each node radar in real time based on jamming dynamics; on the other hand, it treats the networked radars as a whole to coordinate their anti-jamming efforts, thereby enhancing anti-jamming capabilities. However, when facing multiple jammers covering multiple targets' penetration, there are problems such as unreasonable beam allocation leading to low target tracking accuracy.

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

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

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

[0007] In a first aspect, this application provides a method for beam allocation in networked radar tracking multiple targets to counter multiple jammers, including:

[0008] Establish a multi-target tracking model for networked radar under multiple jammer backgrounds;

[0009] Obtain the signal-to-interference-plus-noise ratio (SIR) of each radar node receiver after step-by-step suppression of main and sidelobe interference, and establish the covariance matrix of the radar node for estimating target parameters.

[0010] By using global measurement fusion and extended Kalman filtering, the covariance matrix of the target parameters estimated by the radar nodes is calculated, and the tracking results of the networked radar for each target are obtained.

[0011] The target tracking accuracy is characterized by the posterior Cramerlow lower bound. 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, an adaptive scheduling multi-radar tracking beam optimization model is established.

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

[0013] In one possible implementation, the step of establishing a networked radar tracking multi-target model under a multi-jamming background includes:

[0014] Assume Q targets are moving at a constant velocity in the XOY plane, and the motion state of target q at time k is as follows: The equation of motion for target q is established as follows: Where F is the target state transition matrix, The target state transition matrix is ​​expressed as follows: (The noise is a zero-mean white Gaussian process.) ΔT is the sampling interval, and the covariance matrix is... κ q The noise intensity during the state transition process of the target q;

[0015] Assume a radar network system consists of one transmitting station and N receiving stations, tracks Q moving targets, and has M jammers to cover target penetration. The transmitting station is located at point p. t =[x t y t ] T The receiving station n is located at p rn =[x rn y rn ] T At time k, the target q is located

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

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

[0018]

[0019] in, For propagation loss, P t The transmission power of the launch station. and The reflection intensity, azimuth angle, propagation delay, and Doppler frequency of target q relative to receiving station n at time k are given by α. rn Let n be the receiving vector of receiving station n. M rn and d rn λ represents the number of array elements and the spacing of the receiving station n, respectively, and λ is the wavelength.

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

[0021]

[0022] in, To compensate for the propagation loss of interference signals, Let m be the transmission power of the jammer. and Let be the azimuth angle, propagation delay, and Doppler frequency of the jammer m relative to the receiving station n at time k, respectively.

[0023] In one possible implementation, the step of obtaining the signal-to-interference-plus-noise ratio (SNR) of each radar node receiver after stepwise suppression of main and sidelobe interference, and establishing the covariance matrix of the radar node for estimating target parameters, includes:

[0024] definition According to the received signal right and Perform maximum likelihood estimation when i = 1, 2. When i = 3 The received signal at receiver n is such that all interference enters the receiver from the sidelobe. For an interference that enters the receiver only from the main lobe of the receiving station n, and The received signal, The cardinality of the interference signal entering the receiver set from the main lobe. Assuming an interference source enters the receiver at station n from the main lobe and The received signal; in, Indicates residual interference and noise, w k，n Let n be the receiving weight vector of receiving station n;

[0025]

[0026] in,

[0027]

[0028] in, The pollution phase introduced for Doppler compensation, This represents 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 (SIR) of receiving station n at time k is in, The measurement noise follows a zero-mean Gaussian distribution. and Let be the angles between the transmitting station and the receiving station n relative to the target q at time k. covariance matrix for β 2 and T 2 These 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), then the measurement model can be expressed as:

[0030] In one possible implementation, when When interference enters the receiver at receiving station n from the sidelobe, it is suppressed by the radar's main lobe conformal capability and adaptive receiving beam. At that time, interference enters the receiver of receiving station n from the main lobe. Let θ be the angle difference between jammer m and target q relative to receiving station n at time k. 3dB This is the 3dB beamwidth of the receiving station n.

[0031] In one possible implementation, the step of calculating the covariance matrix of the target parameters estimated by the radar nodes through global measurement fusion and extended Kalman filtering to obtain the tracking results of the networked radar for each target includes:

[0032] By stitching together the local measurements from multiple radars that participate in tracking target q at time k, we obtain the global measurement of target q at time k. in, Let be the set of radars tracking target q at time k. Represents a set The nth element, Represents a set The cardinality;

[0033] Based on the aforementioned measurement model, the global measurement model is obtained as follows: Wherein, the global measurement function is The global covariance matrix is

[0034] The target state is estimated by extended Kalman filtering, and the target state estimates at each time step are obtained. and its covariance matrix

[0035] In one possible implementation, the target state is estimated by extended Kalman filtering to obtain the target state estimate at each time step. and its covariance matrix The steps include:

[0036] Sequential calculations are performed using the first formula, which is:

[0037] in, Global measurement function Regarding vector variables The Jacobian matrix is Also a function Regarding vector variables The Jacobian matrix is ​​defined as follows: The first row of elements are respectively The second row of elements are respectively

[0038]

[0039] In one possible implementation, the steps of characterizing target tracking accuracy through a posterior Cramer-Rao lower bound, establishing a cost function for each target, summing the cost functions of each target as the objective function, and combining radar beam constraints to establish an adaptive scheduling multi-radar tracking beam optimization model include:

[0040] The posterior Cramérós lower bound is used as a representation of target tracking accuracy. in, This represents all measurements of target q at time k. It is the Fisher information matrix about the target state.

[0041] Based on the linear motion model of the target q, we can directly obtain... And make the observations of target q by each radar independent of each other, thus obtaining

[0042] Predicted values ​​using zero process noise replace Will Represented as Obtain the objective function;

[0043] use Represent the radar beam assignment matrix, and use As a metric for target tracking accuracy, an adaptive scheduling multi-radar tracking beam optimization model is obtained.

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

[0045] The adaptive scheduling multi-radar tracking beam optimization model is solved by particle swarm optimization, and the adaptive configuration result of the radar tracking beam is obtained by obtaining the particle with the optimal fitness value.

[0046] The adaptive scheduling multi-radar tracking beam optimization model is solved using a genetic algorithm. By selecting the individual with the highest fitness, the adaptive configuration result of the radar tracking beam is obtained.

[0047] Secondly, this application provides a network radar tracking multi-target beam allocation system for countering multiple jammers, used to execute the aforementioned network radar tracking multi-target beam allocation method for countering multiple jammers, the system comprising:

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

[0049] The second processing module is used to obtain the signal-to-interference-plus-noise ratio (SINR) of each radar node receiver after step-by-step suppression of main and sidelobe interference, and to establish the covariance matrix of the radar node for estimating target parameters.

[0050] The third processing module is used to calculate the covariance matrix of the target parameters estimated by the radar nodes through global measurement fusion and extended Kalman filtering, so as to obtain the tracking results of the networked radar for each target.

[0051] The fourth processing module is used to characterize the target tracking accuracy through the posterior Cramerlow 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.

[0052] 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.

[0053] The technical solution provided in this application may include the following beneficial effects:

[0054] Since main lobe interference requires multi-radar coordinated suppression, the method and system provided in this application can establish an optimization model with the beam allocation matrix as the independent variable and the target tracking accuracy as the objective function. This model enables the radar to coordinately counteract main lobe interference by determining the beam allocation, thereby achieving effective interference suppression throughout the entire process and stable target tracking.

[0055] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0056] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0057] Figure 1 A flowchart illustrating a networked radar beam allocation method for tracking multiple targets against multiple jammers in an exemplary embodiment of this disclosure is shown.

[0058] Figure 2 This illustration shows a scenario of a networked radar tracking multiple targets under a multi-jamming background, illustrating the beam allocation method for countering multiple jammers in an exemplary embodiment of this disclosure.

[0059] Figure 3 A detailed flowchart of the particle swarm optimization algorithm for a networked radar tracking multi-target beam allocation method against multiple jammers in an exemplary embodiment of this disclosure is shown.

[0060] Figure 4 A detailed flowchart of the genetic algorithm for a networked radar beam allocation method for tracking multiple targets against multiple jammers, as shown in an exemplary embodiment of this disclosure, is provided.

[0061] Figure 5 This diagram illustrates a closed-loop framework of a networked radar beam allocation method for tracking multiple targets against multiple jammers, as shown in an exemplary embodiment of this disclosure.

[0062] Figure 6 The diagram illustrates the radar distribution and target trajectory of a networked radar beam allocation method for tracking multiple targets against multiple jammers, as shown in an exemplary embodiment of this disclosure.

[0063] Figure 7 This diagram illustrates the spatial distribution of targets and jammers in a networked radar tracking multi-target beam allocation method for countering multiple jammers, as shown in an exemplary embodiment of this disclosure.

[0064] Figure 8 The radar 7 receiving beam pattern shows the beam distribution method for a networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of this disclosure.

[0065] Figure 9 A radar 7 matched filter output diagram showing the beam allocation method for tracking multiple targets in a networked radar against multiple jammers in an exemplary embodiment of this disclosure;

[0066] Figure 10 A diagram showing the radar parameter estimation results of the networked radar tracking multi-target beam allocation method for countering multiple jammers in an exemplary embodiment of this disclosure;

[0067] Figure 11 The radar 2 receiving beam pattern shows the beam distribution method for a networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of this disclosure;

[0068] Figure 12 The radar 2 matched filter output diagram shows the beam allocation method for tracking multiple targets with a networked radar in an exemplary embodiment of the present disclosure to counter multiple jammers;

[0069] Figure 13 A diagram showing the parameter estimation results of radar 2 after suppressing sidelobe interference in the beam allocation method for networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of this disclosure;

[0070] Figure 14 The diagram shows the parameter estimation results of radar 2 after suppressing sidelobe and mainlobe interference in the beam allocation method for networked radar tracking multiple targets against multiple jammers in an exemplary embodiment of the present disclosure.

[0071] Figure 15 A diagram illustrating the beam allocation scheme of the PSO algorithm in the networked radar tracking multi-target beam allocation method for countering multiple jammers in an exemplary embodiment of this disclosure is shown.

[0072] Figure 16 This diagram illustrates the beam allocation scheme of the GA algorithm in the networked radar tracking multi-target beam allocation method for countering multiple jammers in an exemplary embodiment of this disclosure.

[0073] Figure 17 This diagram illustrates the full-range PCRLB variation of each target in the networked radar tracking multi-target beam allocation method for countering multiple jammers in an exemplary embodiment of this disclosure.

[0074] Figure 18A comparison diagram showing the changes in the total RMSE of each target throughout the course of the networked radar tracking multi-target beam allocation method for countering multiple jammers in an exemplary embodiment of this disclosure is shown.

[0075] Figure 19 This diagram illustrates the structure of a networked radar tracking multi-target beam allocation system for countering multiple jammers, as shown in an exemplary embodiment of this disclosure. Detailed Implementation

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

[0077] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some 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, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0078] This example implementation first provides a method for beam allocation in networked radar tracking of multiple targets to counter multiple jammers. This method can be applied to a terminal device, such as a mobile terminal like a mobile phone, desktop computer, personal digital assistant, laptop, tablet, or smartwatch. (Reference) Figure 1 As shown, the method may include the following steps:

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

[0080] Step S200: Obtain the signal-to-interference-plus-noise ratio (SIR) of each radar node receiver after step-by-step suppression of main and sidelobe interference, and establish the covariance matrix of the radar node for estimating target parameters.

[0081] Step S300: Calculate the covariance matrix of the target parameters estimated by the radar nodes through global measurement fusion and extended Kalman filtering, and obtain the tracking results of the networked radar for each target.

[0082] Step S400: Characterize the target tracking accuracy by 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 constraints to establish an adaptive scheduling multi-radar tracking beam optimization model.

[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] Using the above method, sidelobe interference can be suppressed independently by each node radar, while mainlobe interference can be suppressed through multi-radar collaborative suppression. By establishing and solving an optimization model with the beam allocation matrix as the independent variable and the target tracking accuracy as the objective function, the optimal beam allocation scheme can be determined, thereby achieving stable target tracking.

[0085] It should be noted that in step S300, the calculation of the covariance matrix of the radar node's estimated target parameters is performed simultaneously with the acquisition of the tracking results of the networked radar for each target. By calculating the covariance matrix of the radar node's estimated target parameters, the error of the networked radar's tracking results for each target is estimated, thereby guiding the beam allocation during the next transmission.

[0086] Below, we will refer to Figures 1 to 5 The steps of the method described above in this example embodiment will be explained in more detail.

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

[0088] Step S110: Assume that Q targets are moving at a constant velocity in the XOY plane, and the motion state of target q at time k is as follows: The equation of motion for target q is established as follows: Where F is the target state transition matrix, The target state transition matrix is ​​expressed as follows: (The noise is a zero-mean white Gaussian process.) ΔT is the sampling interval, and the covariance matrix is... κ q Let be the noise intensity during the state transition process of the target q.

[0089] Step S120: Assume a radar network system contains one transmitting station and N receiving stations, tracks Q moving targets, and has M jammers to cover target penetration. 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 At time k, the target q is located

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

[0091] It should be noted that, as Figure 2 As shown, the transmitting station radiates omnidirectionally, covering the entire monitoring area. Each receiving station uses digital beamforming technology to form a narrow beam to track the target, and can only form one narrow beam at any given time, thus only one target can be tracked. Assume 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 L is the pulse repetition interval, and L is the number of pulses. The receiving station n is located at p. rn =[x rn y rn ] T Assume that at time k, target q is located at... definition Let this represent the (tracking) pairing relationship between receiving station n and Q targets at time k. This indicates that at time k, receiving station n tracks target q. This indicates that at time k, receiving station n does not track target q.

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

[0093]

[0094] in, For propagation loss, P t The transmission power of the launch station. and The reflection intensity, azimuth angle, propagation delay, and Doppler frequency of target q relative to receiving station n at time k are given by α. rn Let n be the receiving vector of receiving station n. M rn and d rnλ represents the number of array elements and the spacing of the receiving station n, respectively, and λ is the wavelength.

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

[0096]

[0097] in, This is the propagation loss of the interference signal; Let m be the transmission power of the jammer. and Let be the azimuth angle, propagation delay, and Doppler frequency of the jammer m relative to the receiving station n at time k, respectively.

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

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

[0100] Step S210: Definition According to the received signal right and Perform maximum likelihood estimation.

[0101] When i = 1, 2

[0102]

[0103] When i = 3 The received signal at receiver n is such that all interference enters the receiver from the sidelobe. For an interference that enters the receiver only from the main lobe of the receiving station n, and The received signal, The cardinality of the interference signal entering the receiver set from the main lobe. Assuming an interference source enters the receiver at station n from the main lobe and The received signal;

[0104]

[0105] in, Indicates residual interference and noise, w k，n Let n be the receiving weight vector of receiving station n;

[0106]

[0107] in, in, The pollution phase introduced for Doppler compensation, This represents the Doppler frequency difference between the received signal and the reference signal at the receiving station.

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

[0109]

[0110] in, The measurement noise follows a zero-mean Gaussian distribution:

[0111] and The angles between the transmitting station and the receiving station n and the target q at time k are respectively. covariance matrix for β 2 and T 2 These 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] Understandably, before step S210, sidelobe interference suppression and main lobe interference suppression need to be performed on each radar node separately. Only after the interference is suppressed can the signal-to-noise ratio and covariance matrix be calculated. First, sidelobe interference suppression is performed using an adaptive beamforming method with main lobe shape preservation capability, and then main lobe interference suppression is performed through multi-radar collaboration. Among these methods, sidelobe interference suppression using an adaptive beamforming method with main lobe shape preservation capability is a commonly used sidelobe interference suppression method in the prior art. The method of main lobe interference suppression through multi-radar collaboration can be implemented using the main lobe 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 interference signals must be suppressed before estimating target parameters to improve the signal-to-interference-plus-noise ratio (SINR). Interference can be categorized into mainlobe interference and sidelobe interference based on whether the interference signal enters the receiver from the radar's main beam. Assuming the receiving station can form a narrow beam to track the target, and letting θ... 3dB The 3dB beamwidth of the receiving station Let be the angular difference between the jammer m and the target q relative to the receiving station n at time k. At that time, if Then it is assumed that the interference m enters the receiver of receiving station n from the sidelobe. It is assumed 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 main lobe conformance. Main lobe conformance is required because traditional adaptive beamforming methods easily cause main beam distortion, affecting the reception of the desired signal. Assuming the receiving beam is designed using the Minimum Variance Distortionless Response (MVDR) criterion, the receiving weight vector can be expressed as... Among them, R i+n It is the interference + noise covariance matrix, and θ0 is the desired direction. To achieve main lobe conformal, R... i+n Without the desired signal and main lobe interference, the Capon power spectrum can be integrated and reconstructed in the sidelobe region. Then, assuming that the number of main lobe interferences received by receiver n does not exceed 1, the interference suppression is divided into... and in, and In This represents the set of receiving stations from which the interference signal enters through the main lobe. First, beamforming methods are used to suppress sidelobe interference to obtain... The received signal shown is then subjected to range Doppler compensation, covariance matrix reconstruction, and time-domain constrained linear enhancement to obtain... The received signal shown shows that the contamination phase and Doppler frequency difference introduced by Doppler compensation are determined by the positions of the jammer m and the receiving station n; "≈" is used because the multi-radar cooperative processing gain may not be 1. It is the time delay difference between the received signal at receiving station n and the reference signal, which is also determined by the positions of jammer m and receiving station n.

[0114] Furthermore, among them, when When interference enters the receiver at receiving station n from the sidelobe, it is suppressed by the radar's main lobe conformal capability and adaptive receiving beam. At that time, interference enters the receiver of receiving station n from the main lobe. Let θ be the angle difference between jammer m and target q relative to receiving station n at time k.3dB This is the 3dB beamwidth of the receiving station n.

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

[0116] Step S310: Segment the local measurements from multiple radars tracking target q at time k to obtain the global measurement of target q at time k. in, Let be the set of radars tracking target q at time k. Represents a set The nth element, Represents a set The base number.

[0117] Step S320: Based on the measurement model, obtain the global measurement model as follows: Wherein, the global measurement function is The global covariance matrix is

[0118] Step S330: Estimate the target state using an extended Kalman filter to obtain the target state estimates at each time step. and its covariance matrix

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

[0120] Sequential calculations are performed using the first formula, which is:

[0121] in, Global measurement function Regarding vector variables The Jacobian matrix is Also a function Regarding vector variables The Jacobian matrix is ​​defined as follows: The first row of elements are respectively The second row of elements are respectively

[0122]

[0123] It should be noted that the definition Let K be the set of radars tracking target q at time k. When multiple radars simultaneously track target q, i.e. At that time, 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 a characterization of target tracking accuracy, wherein the posterior Cramer-Rao lower bound is...

[0126]

[0127] in, This represents all measurements of target q at time k. It is the Fisher Information Matrix (FIM) concerning the target state.

[0128] Step S420: Based on the linear motion model of the target q, the following can be directly obtained. And make the observations of target q by each radar independent of each other, thus obtaining

[0129] Step S430: Predict values ​​using zero process noise replace Will Represented as The objective function is obtained.

[0130] Step S440: Use Represent the radar beam assignment matrix, and use As a metric for target tracking accuracy, an adaptive scheduling multi-radar tracking beam optimization model is obtained.

[0131] It should be noted that in step S410 for because Therefore, further writing

[0132] In step S440, during the multi-target penetration process covered by multiple jammers, the beam allocation method of the networked radars affects how the jamming signal enters the receiver. For sidelobe jamming, a single radar can suppress it using its inherent anti-jamming measures such as beamforming. However, for mainlobe jamming, a single radar is insufficient to effectively counter it, requiring coordinated countermeasures from multiple radars. Therefore, the beam allocation method affects the jamming suppression effect of each radar, thus impacting target tracking accuracy. From the perspective of radar anti-jamming, the radar network system should rationally allocate the tracking beam at each tracking moment to effectively suppress jamming; the jamming suppression effect is reflected in the target tracking accuracy.

[0133] In the adaptive scheduling multi-radar tracking beam optimization model, the constraints are... To ensure that each radar can only track one target at any given time, when a single radar tracks multiple targets using multi-beamforming technology, multiple interference signals may enter the receiver from the radar's main lobe, increasing the difficulty of main lobe interference suppression. By rationally allocating the tracking beams of each receiving radar at each time moment, the sum of tracking accuracy for all targets is maximized. Sidelobe interference can be suppressed independently by each node radar, while main lobe interference requires coordinated suppression by multiple radars. Therefore, beam allocation is equivalent to selecting appropriate anti-interference measures for each radar, ensuring that the networked radars effectively suppress 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 using the particle swarm optimization algorithm, and obtain the adaptive configuration result of the radar tracking beam by obtaining the particle with the optimal fitness value.

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

[0137] Among them, optional, such as Figure 3 As shown, the detailed steps of step S510 are as follows:

[0138] Initialize the particle swarm: Each particle is assigned a distribution matrix U that satisfies the constraints. k This indicates that, for ease of calculation, it can be converted into a vector. If using... To represent a certain particle, then The initial position and velocity of the randomly generated particles are the particle index.

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

[0140] Update individual and global best: For each particle, record the best position it experiences during the search process, i.e., the individual best position pBest. (i) This corresponds to the optimal fitness value of the particle; for the particle swarm as a whole, record the best position gBest that it experiences during the search process, which corresponds to the optimal fitness value among all particles.

[0141] Update speed and location: The velocities of each particle are updated according to the above formula, where ω is the inertia weight, used to control the degree of influence of particle velocity; c1 and c2 are learning factors; r1 and r2 are random numbers in [0,1], used to introduce randomness; gBest (i) `i` is the optimal position for particle `i`; `gBest` is the globally optimal position. After updating the velocity, the positions of each particle are updated using the following formula: The updated particles may not meet the constraints. Therefore, further constraint processing is required. The specific process is as follows: First, decode the individual into an allocation matrix U. k Then, each row is judged. If the number of non-zero elements in the row is greater than 1, one element is randomly retained. If the number of non-zero elements in the row is zero, an element is randomly selected and assigned the value 1. If the number of non-zero elements in the row is exactly 1, it remains unchanged.

[0142] Iteration and Termination: For each particle, its velocity and position are repeatedly updated, and its fitness is calculated until the iteration termination condition is met. The global best position gBest is output and decoded to obtain the beam assignment matrix.

[0143] Among them, optional, such as Figure 4 As shown, the detailed steps of step S520 are as follows:

[0144] Determine the encoding scheme: Assign the matrix U k This is converted into a vector, where each element represents the pairing relationship between the radar and the target. See the PSO algorithm for the specific representation.

[0145] (2) Population initialization: Randomly generate multiple individuals, each of which is an allocation matrix U that satisfies the constraints. k The linear representation of is a one-dimensional array.

[0146] (3) Fitness Calculation: The genetic algorithm determines the quality of an individual based on its fitness and thus its chance of inheritance. In the model established in this paper, the objective function is non-negative, and the minimum value of the function is the objective function.

[0147] Therefore it is usable Fitness as an individual.

[0148] (4) Selection operation: The next generation of the population is selected based on the fitness of individuals. Generally, individuals with higher fitness are required to have a greater chance of passing on their genes to the next generation. This paper uses the roulette wheel selection mechanism to select individuals with high fitness.

[0149] (5) Crossover operation: A new individual is generated by exchanging a portion of the chromosomes between two individuals with a certain probability. In this paper, two adjacent individuals are first paired up, and then the crossover point is randomly selected to exchange the genes of the two individuals after the crossover point.

[0150] (6) Mutation Operation: New genotypes are generated by randomly modifying the genes of individuals, increasing population diversity. This paper uses the single-point mutation method. First, a mutation point is randomly selected, and then the original gene at that mutation point is inverted, i.e., 0 becomes 1, and 1 becomes 0. Note that each individual is initialized according to the constraints. After generation and selection, individuals in the population may still satisfy the constraint. However, after crossover and mutation, some individuals may no longer satisfy the constraint. Therefore, constraint processing is needed after mutation; the specific process is described in the PSO algorithm. These operations reduce the diversity of the population.

[0151] (7) Iteration and Termination: Repeat the selection, crossover, mutation and other operations until the termination condition is met, output the individual with the highest fitness, and obtain the beam assignment matrix after decoding.

[0152] In one embodiment, such as Figure 5 The diagram shows the closed-loop framework of a network radar multi-target tracking method based on beam allocation. At time k, each node radar first employs adaptive beamforming technology with main lobe conformal capability to suppress sidelobe interference. If main lobe interference still occurs, it is then suppressed. Subsequently, the maximum likelihood estimation method is used to estimate the signal from the interference-suppressed signal. Then it is sent to the control center to be pieced together into a global measurement. The estimated state of the target at the current moment is obtained through EKF. The zero-process noise prediction value of the target state at time k+1 is calculated. Will By inputting the resource optimization model, the beam allocation matrix of the radar network system at time k+1 can be obtained. Repeating this process enables full-range tracking of multiple targets.

[0153] Furthermore, this example embodiment also provides a simulation experiment of a network radar beam allocation method for tracking multiple targets against multiple jammers. The effectiveness of the proposed beam allocation-based network radar method for countering multiple jammers is verified through simulation experiments in a specific scenario.

[0154] The spatial distribution of the radar and the motion trajectories of the target and jammer in the simulation are as follows: Figure 6As 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 target and the jammer 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 an LFM signal, and the jammer transmits a noise-like interference signal, with signal parameters consistent with the simulation in Chapter 3. From the spatial distribution parameters of the target and the jammer, it can be seen that two jammers are spatially very close to the two targets, therefore, it can be considered that the echoes of these two targets must be accompanied by main lobe interference signals. Based on the radar wavelength, the number of receiving array elements, and the spacing, the radar's 3dB beamwidth can be calculated to be approximately 3°. Assuming that the networked radar accurately obtains the real-time position of the jammer through cross-location of the interference sources, the jammer position can be considered a known quantity.

[0155] Table 1 Initial State of the Target

[0156]

[0157]

[0158] Table 2 Initial State of the Jammer

[0159]

[0160] Table 3 Radar-related parameters

[0161]

[0162] First, the interference suppression effect is verified. It is assumed that when k=13, the target and the jammer are respectively at... Figure 7 At the location shown, the system assigns tracking radar 7 to target 5 and tracking radars 2 and 8 to target 2.

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

[0164] For target 2, assuming it is located at the center of radar 2's main beam, signals from three jammers will enter radar 2's receiver from -9.0180°, 3.0875°, and -2.8813° respectively. These jammer signals can be considered sidelobe jamming. Additionally, a jammer signal will accompany the target echo from the main lobe into radar 2's receiver. After reconstructing the (sidelobe) jamming plus noise covariance matrix, an adaptive receiving beam with main lobe conformal capability can be constructed, as shown in the following pattern. Figure 11 As shown in the diagram, the receiving beam forms nulls of -27.07dB, -22.62dB, and -23.01dB in the three interference directions, respectively, while the main lobe remains undistorted, ensuring complete reception of the target echo (and main lobe interference). When only adaptive beamforming is used to suppress sidelobe interference, its matched filter output is shown in the diagram. Figure 12 The gray lines indicate that the target is completely obscured by interference (in the main lobe) and cannot be effectively detected. The distance Doppler estimation results are shown below. Figure 13 At this point, the parameter estimation values ​​have a large error. Radar 8 undergoes the same sidelobe interference suppression process. Since Radar 2 and Radar 8 receive mainlobe interference signals from the same jammer, the TDCLE method proposed in Chapter 3 can be used to collaboratively suppress mainlobe interference. Taking Radar 2 as the reference station, after undergoing range Doppler compensation, covariance matrix reconstruction, and linear enhancement, the signal output by Radar 2 is shown below. Figure 12 The blue line indicates that after local sidelobe interference suppression and multi-radar collaborative mainlobe interference suppression, the interference has been significantly filtered out, and the target can be effectively detected. The final parameter estimation results are shown below. Figure 14 As can be seen, the parameter estimation results are quite close to the true value of the distance-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 effectiveness of the tracking needs to be verified, such as... Figure 15-16Beam assignment schemes obtained using the PSO and GA algorithms are presented, with a particle swarm size of 50 and a maximum number of iterations of 100 for both algorithms. For comparison, it is assumed that a random number generator (RNG) randomly assigns a target to the system at each tracking time. In this case, each radar can still suppress sidelobe interference, but it is unknown whether mainlobe interference can be suppressed.

[0166] like Figure 17 The changes in PCRLB for each target throughout the entire beam assignment process are presented under three beam assignment schemes. Since the initial FIM for each target is set to Q... q Therefore, it applies to all targets. As shown in the figure, the tracking accuracy of each target gradually improves with increasing tracking time. Furthermore, the beam allocation schemes proposed by the PSO and GA algorithms exhibit similar performance, and the PSO algorithm significantly outperforms the RNG scheme on all targets except target 3. This demonstrates that optimizing beam allocation can leverage the advantages of a radar network system and effectively counter multiple jammers.

[0167] and Figure 17 Only the calculated or predicted tracking accuracy is shown; the actual tracking accuracy, expressed in RMSE, is as follows: Figure 18 As shown, the definition of RMSE is the same as in Chapter 2, and the number of Monte Carlo trials N is... MC =1000. During the tracking process, there may be a moment when the system does not assign a tracking radar to a certain target. In this case, the target state estimate can be replaced by the zero-process noise prediction value from the previous moment, i.e. The covariance matrix estimate can be expressed as: Because the system cannot continuously fail to allocate tracking radar to a target, the tracking situation for that target will not deteriorate significantly. Figure 18 As can be seen, for targets 1 and 4, the PSO scheme provides better tracking accuracy than the GA and RNG schemes; for targets 2, 5, and 6, the PSO and GA schemes have similar tracking accuracy, and the PSO scheme is better than the RNG scheme; the special case occurs for target 3, where the RNG scheme provides better tracking accuracy than the two optimized schemes. Overall, the two optimized schemes still provide higher tracking accuracy, which once again verifies the effectiveness of the networked radar's beam allocation method for countering multiple jammers.

[0168] Furthermore, such as Figure 19 As shown, this example embodiment also provides a networked radar tracking multi-target beam allocation system for countering multiple jammers, used to execute the above-described networked radar tracking multi-target beam allocation method for countering multiple jammers. The system includes:

[0169] The first processing module is used to establish a multi-target tracking model of a networked radar under the background of multiple jammers;

[0170] The second processing module is used to obtain the signal-to-interference-plus-noise ratio (SINR) of each radar node receiver after step-by-step suppression of main and sidelobe interference, and to establish the covariance matrix of the radar node for estimating target parameters.

[0171] The third processing module is used to calculate the covariance matrix of the target parameters estimated by the radar nodes through global measurement fusion and extended Kalman filtering, so as to obtain the tracking results of the networked radar for each target.

[0172] The fourth processing module is used to characterize the target tracking accuracy through the posterior Cramerlow 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.

[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 apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0175] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of 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. Components shown as modules or units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the disclosed solution according to actual needs. Those skilled in the art can understand and implement this without any inventive effort.

[0176] In an exemplary embodiment of this disclosure, an electronic device is also provided, which may include a processor and a memory for storing executable instructions of the processor. The processor is configured to perform the steps of the network radar tracking multi-target beam allocation method for countering multiple jammers described in any of the above embodiments by executing the executable instructions.

[0177] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: entirely hardware implementations, entirely software implementations (including firmware, microcode, etc.), or implementations combining hardware and software aspects, collectively referred to herein as “circuits,” “modules,” or “systems.”

[0178] Through the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this 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, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, or network device, etc.) to execute the above-described method for networked radar tracking of multiple targets against multiple jammers according to the embodiments of this disclosure.

[0179] In an exemplary embodiment of this disclosure, a computer storage medium is also provided, on which a computer program is stored, which, when executed by, for example, a processor, can implement the steps of the network radar tracking multi-target beam allocation method for countering multiple jammers as described in any of the above embodiments.

[0180] In some possible implementations, various aspects of the present invention can also be implemented as a computer program product comprising a computer program or instructions which, when run on a terminal device, cause the terminal device to perform the steps described in the section on the method for beam allocation of networked radar for tracking multiple targets against multiple jammers described in this specification, according to various exemplary embodiments of the present invention.

[0181] The aforementioned program products can be written in any combination of one or more programming languages ​​to perform the operations of this invention. These programming languages ​​include object-oriented programming languages—such as Java and C++—and conventional procedural programming languages—such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone 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 cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0182] The computer software product may be stored in a computer storage medium, including 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 storage, disk storage, magnetic tape storage, or any other computer-readable medium capable of carrying or storing data.

[0183] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A method for beam allocation in networked radar to track multiple targets against multiple jammers, characterized in that, include: Establish a multi-target tracking model for networked radar under multiple jammer backgrounds; including: Assume Q targets are moving at a constant velocity in the XOY plane. q exist k The motion state at time t is Establish goals q The equation of motion is ,in, Let be the target state transition matrix. For zero-mean white Gaussian process noise, the expression for the target state transition matrix is: , Let be the sampling interval, and let the covariance matrix be... , For the goal q Noise intensity during state transition; Assume a radar network system includes one transmitting station and N One receiving station, tracking Q There are several moving targets, and they have M Several jammers provide cover for the target's penetration, with the launch station located at... Receiving station n lie in , k Momentary Goal q lie in ; when k Time Receiving Station n For the target q During tracking, the receiving station n Received target q The superimposed signal of echo, interference, and noise is , where x k,n ( t (receiving station) n in k Constantly received information about the target q The echo signal, r k,n ( t (receiving station) n in k Interference signal received at any time, n k,n ( t () represents noise; Obtain the signal-to-interference-plus-noise ratio (SIR) of each radar node receiver after stepwise suppression of main and sidelobe interference, and establish the covariance matrix of the radar node's estimated target parameters; including: definition According to the received signal right and Perform maximum likelihood estimation. when i When =1,2, ， when i When =3, ; To ensure all interference enters the receiving station from the sidelobe. n The received signal of the receiver For there is interference only from the receiving station n The main lobe enters the receiver and The received signal, The cardinality of the interference signal entering the receiver set from the main lobe. Assuming an interference source enters the receiver at station n from the main lobe and The received signal; ， in, , , This indicates residual interference and noise. Let n be the receiving weight vector of receiving station n; ， in, , ; ， in, ; The pollution phase introduced for Doppler compensation, This represents the Doppler frequency difference between the received signal and the reference signal at the receiving station. Obtain from the received signal and , k Time Receiving Station n The signal-to-interference-plus-noise ratio is ;in, The measurement noise follows a zero-mean Gaussian distribution. , and They are respectively k Time transmission station and receiving station n For the target q The included angle ; covariance matrix for , and Transmitted signals Effective bandwidth and effective time bandwidth, , yes The Fourier transform of the model can then be expressed as: ; By using global measurement fusion and extended Kalman filtering, the covariance matrix of the target parameters estimated by the radar nodes is calculated, and the tracking results of the networked radar for each target are obtained. The target tracking accuracy is characterized by the posterior Cramer-Rao lower bound. A cost function is established for each target, and the sum of the cost functions for each target is used as the objective function. Combined with radar beam constraints, an adaptive scheduling multi-radar tracking beam optimization model is established, including: The posterior Cramérós lower bound is used as a representation of target tracking accuracy. , in, express k Always on the target q All measurements, It is the Fisher information matrix about the target state. ; According to the goal q The linear motion model can be directly obtained from the linear motion model of the target. ; and enable each radar to target the target q The observations are independent of each other, and thus... ; Predicted values ​​using zero process noise replace ,Will Represented as Thus, the objective function is obtained; use Represent the radar beam assignment matrix, and use As a metric for target tracking accuracy, an adaptive scheduling multi-radar tracking beam optimization model is obtained. ; Solve the adaptive scheduling multi-radar tracking beam optimization model to obtain the adaptive configuration result of the radar tracking beam.

2. The method for beam allocation in networked radar tracking of multiple targets to counter multiple jammers according to claim 1, characterized in that, The receiving station n in k Constantly received information about the target q The echo signal is: ； in, For propagation loss, P t The transmission power of the launch station. , , and The target q exist k Time relative to receiving station n The reflection intensity, azimuth angle, propagation delay, and Doppler frequency, For receiving station n The received vector, , and Receiving stations n The number of array elements and the interval, It is the wavelength; The receiving station n in k The interference signal received at any given time is: ； in, This is the propagation loss of the interference signal; jammer m The transmission power, , and Interference machine m exist k Time relative to receiving station n The azimuth angle, propagation delay, and Doppler frequency.

3. The method for beam allocation in networked radar tracking of multiple targets to counter multiple jammers according to claim 2, characterized in that, when At that time, interference enters the receiving station from the sidelobe. n The receiver, through the radar's main lobe conformal capability, adaptively suppresses the received beam. At that time, interference entered the receiving station from the main lobe. n The receiver, through multi-radar collaboration, suppresses main lobe interference. for k Time jammer m With the goal q Relative to the receiving station n angular difference, For receiving station n 3dB beamwidth.

4. The method for beam allocation in networked radar tracking of multiple targets to counter multiple jammers according to claim 2, characterized in that, The step of calculating the covariance matrix of the target parameters estimated by the radar nodes through global measurement fusion and extended Kalman filtering, and obtaining the tracking results of the networked radar for each target, includes: Will k Constantly participate in tracking the target q Multiple radar local measurement stitches were obtained k Always on the target q Global measurement , ,in, for k Track the target at all times q A collection of radars, Represents a set The n One element, Represents a set The cardinality; Based on the aforementioned measurement model, the global measurement model is obtained as follows: The global measurement function is: The global covariance matrix is ； The target state is estimated by extended Kalman filtering, and the target state estimates at each time step are obtained. and its covariance matrix .

5. The method for beam allocation in networked radar tracking of multiple targets to counter multiple jammers according to claim 4, characterized in that, The target state is estimated by extended Kalman filtering to obtain the target state estimate at each time step. and its covariance matrix The steps include: Sequential calculations are performed using the first formula, which is: ;in, Global measurement function Regarding vector variables The Jacobian matrix is , Also a function Regarding vector variables The Jacobian matrix is ​​defined as follows: , The first row of elements are respectively , The second row of elements are respectively 。 6. The method for beam allocation in networked radar tracking multiple targets to counter multiple jammers according to claim 1, characterized in that, The steps for solving the adaptive scheduling multi-radar tracking beam optimization model to obtain the adaptive configuration result of the radar tracking beam include: The adaptive scheduling multi-radar tracking beam optimization model is solved by particle swarm optimization, and the adaptive configuration result of the radar tracking beam is obtained by obtaining the particle with the optimal fitness value. The adaptive scheduling multi-radar tracking beam optimization model is solved using a genetic algorithm. By selecting the individual with the highest fitness, the adaptive configuration result of the radar tracking beam is obtained.

7. A networked radar beam distribution system for tracking multiple targets and countering multiple jammers, characterized in that, The system is used to execute the network radar tracking multi-target beam allocation method for countering multiple jammers as described in any one of claims 1 to 6, the system comprising: The first processing module is used to establish a multi-target tracking model of a networked radar under the background of multiple jammers; The second processing module is used to obtain the signal-to-interference-plus-noise ratio of each radar node receiver after step-by-step suppression of main and sidelobe interference, and to establish the covariance matrix of the radar node to estimate the target parameters. The third processing module is used to calculate the covariance matrix of the target parameters estimated by the radar nodes through global measurement fusion and extended Kalman filtering, so as to obtain the tracking results of the networked radar for each target. The fourth processing module is used to characterize the target tracking accuracy through the posterior Cramerlow 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 adaptive configuration result of the radar tracking beam.

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