Space-frequency aware networking radar power-time joint optimization method for multi-target tracking

Abstract

The application discloses a kind of space-frequency perception under the networking radar power time joint optimization method for multi-target tracking, comprising: S1, first for networking radar system to multi-target tracking scene, the state equation of moving target, radar observation model and interference model are established;S2, the expression of the Bayes Cramer-Rao lower bound BCRLB matrix that characterizes multi-target tracking accuracy is deduced;S3, with the upper limit of networking radar radiation resources and the interference energy that communication area can tolerate as constraint condition, with the trace of BCRLB matrix as optimization target, establish the networking radar power time joint optimization distribution model under space-frequency perception for multi-target tracking;S4, the joint optimization distribution model is solved using interior point method and cyclic minimum method.The application can adaptively dynamically optimize node selection and radiation resource allocation when networking radar multi-target tracking, so as to improve the multi-target tracking performance of networking radar.

Description

TECHNICAL FIELD

[0001] The present application relates to radar resource allocation technology, in particular to a space-frequency sensing based networked radar power-time joint optimization method for multi-target tracking. BACKGROUND

[0002] With the rapid increase of modern battlefield wireless radio frequency equipment and the widening of the working frequency spectrum, the traditional method for solving the radio frequency spectrum congestion of radar and wireless communication system has become more and more difficult to meet the actual demand. How to make radar system and other overlapping spectrum communication system work coordinately has become a hot topic. For such problems, we need to consider how to effectively improve the spectrum utilization rate, and how to effectively calculate and reduce the mutual interference between radar system and communication system when they share the same frequency spectrum.

[0003] At present, the existing research results involve radar transmission parameter optimization problem for multi-target tracking. Under the constraint condition of radar transmission parameter resource, the radar transmission parameter is optimized, which improves the tracking performance of networked radar system to a certain extent. However, the influence of mutual interference between radar system and communication system on multi-target tracking performance is not considered. SUMMARY

[0004] The purpose of the present application is to provide a space-frequency sensing based networked radar power-time joint optimization method for multi-target tracking, which optimizes radar node selection and transmission resource allocation to improve the multi-target tracking performance of networked radar while meeting the communication system tolerable interference energy threshold.

[0005] The space-frequency sensing based networked radar power-time joint optimization method for multi-target tracking of the present application comprises the following steps:

[0006] S1, first, considering a networked radar system composed of N radars in two-dimensional space, tracking multiple targets dispersedly deployed in space, establishing the state equation of moving target, radar observation model and interference model;

[0007] S2, deducing the Bayes Cramer-Rao lower bound (BCRLB) matrix expression representing the multi-target tracking accuracy;

[0008] S3, taking the networked radar radiation resource and the upper limit of the tolerable interference energy of the communication area as the constraint condition, taking the trace minimization of the BCRLB matrix as the optimization target, establishing a space-frequency sensing based networked radar power-time joint optimization distribution model for multi-target tracking;

[0009] S4, the node selection and radiation resource allocation of the multi-target tracking of the networked radar are adaptively and dynamically optimized, the interior point method and the cyclic minimum method are used to solve the power-time joint optimization distribution model of the networked radar for multi-target tracking under the space-frequency sensing.

[0010] Further, the state equation of the moving target established in step S1 is:

[0011]

[0012] wherein, represents the state vector of the qth moving target at the kth moment, represents the state vector of the qth moving target at the k-1th moment; F represents the state transition matrix of the qth moving target, and is represented as △T0 represents a sampling interval, represents a Kronecker product, I2 is a 2-order unit matrix; W represents a Gaussian process white noise with a mean of zero; q represents the qth moving target, and Q represents the number of moving targets.

[0013] Further, the radar observation model established in step S1 is:

[0014]

[0015] wherein, represents the measurement vector corresponding to the tracking of the qth moving target by the nth radar at the kth moment, represents a nonlinear observation function, represents a measurement noise vector subject to a zero-mean Gaussian distribution; is a binary variable, when represents that the qth moving target is tracked by the nth radar at the kth moment, when represents that the qth moving target is not tracked by the nth radar at the kth moment.

[0016] Further, the interference model in step S1 includes a radar interference model of a communication area and a communication area interference model of a radar, and specifically:

[0017] The radar interference model of the communication area established is:

[0018]

[0019] wherein, the superscript (·) H represents the conjugate transpose of a matrix; E n represents the interference covariance matrix of the communication area received by the radar n, M represents the number of communication areas, χ m,n represents the intensity coefficient of a transmission channel, T m,n represents the time-domain covariance matrix of the interference signal generated by the communication area m on the radar n, xC,m denotes the coordinate of the mth communication region, x R,n denotes the position coordinate of the radar n, denotes the azimuth angle between the communication region m and the radar n, denotes the radar half-wavelength steering vector;

[0020] The interference model of the radar to the communication region is:

[0021]

[0022] wherein, denotes the radar interference energy value received by the communication region m, Q denotes the number of moving targets, denotes the spatial distribution of the radar transmitted signal energy, s n = [s n (1), …, s n (L)] T denotes the waveform sequence with finite interval, is a binary variable, when denotes that the nth radar tracks the moving target q at the kth moment, when denotes that the nth radar does not track the moving target q at the kth moment; denotes the radar transmitted power of the radar n tracking the moving target q at the kth moment; Φ m,n denotes that:

[0023]

[0024] wherein, f L,m,n and f U,m,n respectively denote the upper limit and the lower limit of the frequency band covered by the communication region m and the radar n, T s denotes the signal sampling period, u and v respectively denote the row and column of Φ m,n .

[0025] Further, the expression of the BCRLB matrix of the target state estimation error at the kth moment in step S2 is:

[0026]

[0027] wherein, the superscript (·) T denotes the transpose of the matrix; the superscript (·) -1 denotes the inverse matrix of the matrix; U q is a Gaussian white noise matrix; F denotes the state transition matrix of the qth moving target; denotes the Bayesian information matrix of the target state at the k-1th moment; is a binary variable, when ​indicates that the nth radar tracks the moving target q at the kth moment, and indicates that the nth radar does not track the moving target q at the kth moment; indicates the Jacobian matrix at the kth moment; indicates the observation error covariance matrix at the kth moment;

[0028] The trace of the BCRLB matrix at the kth moment is used as a measurement index for representing the target tracking accuracy:

[0029]

[0030] Further, the power bandwidth resource joint optimization allocation model for the networked radar facing multi-target tracking under the space-frequency perception established in step S3 is:

[0031]

[0032] wherein, is a binary variable, when indicates that the nth radar tracks the moving target q at the kth moment, and indicates that the nth radar does not track the moving target q at the kth moment; indicates the dwell time of the radar n tracking the moving target q at the kth moment; indicates the radar transmit power of the radar n tracking the moving target q at the kth moment; Q indicates the number of moving targets; T min and T max respectively indicate the lower bound and the upper bound of the radar dwell time; P min and P max respectively indicate the lower bound and the upper bound of the radar transmit power; indicates the maximum value of the number of radar nodes allocated by the networked radar system when tracking each moving target at each moment; E max indicates the maximum radar interference energy value that can be tolerated by the communication area; T total indicates the sum of the dwell times of all radars irradiating a single moving target; P total indicates the sum of the transmit powers of all radars irradiating a single moving target.

[0033] Further, the model solving step in step S4 is:

[0034] (41) Set the initialization matrix of the radar transmit power and the dwell time respectively, and set the initial value of the transmit power and the dwell time for each radar node;

[0035] (42) Determine the tracked moving target, and take the transmit power and the dwell time allocation value of the moving target by the networked radar system at the previous moment as the initial value, and relax the binary variable to The weight coefficients of each radar node are calculated by using an interior point method, the weight coefficients are arranged in descending order to obtain A radar node selection method with different total number of nodes;

[0036] (43) For the different radar node selection methods in step (42), the radar transmit power resource allocation and the dwell time resource allocation are optimized to minimize the tracking error, and the transmit power and the dwell time priority are set to be the same in the optimization process, and the obtained The tracking error solutions are compared to obtain the minimum tracking error solution and the corresponding radar node selection scheme and radar resource allocation scheme;

[0037] (44) Jump to step (42) until the tracking error difference obtained twice is less than a set threshold, that is, the minimum tracking error of the networked radar tracking the moving target q at time k and the corresponding final radar node selection scheme and radar resource allocation scheme optimization allocation scheme are obtained;

[0038] (45) Remove the radar node selected in step (44), determine the next optimized moving target, and jump to step (42) until all moving target tracking schemes are optimized and allocated, that is, the optimal radar node selection scheme and radar power time allocation scheme of the networked radar tracking each moving target at time k are obtained.

[0039] In another embodiment of the application, the space-frequency sensing networked radar power time joint optimization system for multi-target tracking includes:

[0040] A target tracking and data acquisition module for acquiring the motion state of multiple targets and establishing a motion target state method, a radar observation model and an interference model;

[0041] A multi-target tracking accuracy calculation module for using a Bayesian Cramer-Rao lower bound (BCRLB) matrix to represent multi-target tracking accuracy;

[0042] A model construction module for establishing a networked radar power time joint optimization model for multi-target tracking under space-frequency sensing, with the networked radar radiation resources and the communication area tolerable interference energy as constraint conditions and the trace of the BCRLB matrix as the optimization target;

[0043] A model solving module for adaptively and dynamically optimizing the node selection and radiation resource allocation of the networked radar multi-target tracking, and solving the optimization model by using an interior point method and a cyclic minimum method.

[0044] An apparatus device comprising a memory and a processor, wherein:

[0045] The memory is used to store a computer program capable of running on the processor;

[0046] a processor configured to execute the steps of the method when the computer program is run by the processor.

[0047] A storage medium having stored thereon a computer program which, when executed by at least one processor, implements the steps of the method.

[0048] Working principle and working process:

[0049] The present application considers a networked radar system composed of N radars in two-dimensional space, and tracks multiple targets dispersedly deployed in space. First, the state equation and observation model of the moving target in the networked radar tracking scene are established, and the BCRLB matrix expression is derived, and the trace of the matrix is taken as the measurement index of the target tracking accuracy. Then, taking the tolerable interference energy of the networked radar radiation resources and the communication area as the constraint condition, and taking the trace of the BCRLB matrix as the optimization target, a networked radar power and time joint optimization allocation model is established. Finally, the interior point method and the cyclic minimum method are used to solve the optimization model. Through solving the optimization model, the optimal solution of the node selection, the transmission power and the residence time distribution of the multiple target tracking accuracy is obtained under the constraint condition of satisfying the upper limit of the total radiation power of the radar and the tolerable interference energy of the communication area.

[0050] Advantages: Compared with the prior art, the advantages of the present application are: (1) by jointly optimizing the node selection distribution of the networked radar tracking moving target and the networked radar transmission power and residence time parameters in the multiple target tracking process, the multiple target tracking accuracy of the networked radar is maximized under the constraint condition of satisfying the upper limit of the total radiation resources of the networked radar and the tolerable interference energy of the communication area. (2) The optimal radar power and time distribution and radar node selection scheme are realized, and the multiple target tracking performance of the networked radar is effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 Flow chart of the networked radar power and time joint optimization method for multiple target tracking under space-frequency perception;

[0052] Figure 2 Distribution diagram of multiple target motion trajectories and networked radars;

[0053] Figure 3 Radar node selection and power and time distribution results of the networked radar tracking moving target 1;

[0054] Figure 4 Radar node selection and power and time distribution results of the networked radar tracking moving target 2;

[0055] Figure 5 ARMSE comparison of the proposed algorithm and other comparative algorithms. DETAILED DESCRIPTION

[0056] The structure and working process of the application will be further described below with reference to the drawings.

[0057] Firstly, the application considers a networked radar system composed of N radars in two-dimensional space, and tracks multiple moving targets dispersedly deployed in space; secondly, a Bayesian Cramer-Rao Lower Bound (BCRLB) expression representing the tracking accuracy of multiple targets is derived; on this basis, a networked radar power-time joint optimization allocation model is established, with the tolerable interference energy of networked radar radiation resources and communication areas as constraint conditions and the trace of the BCRLB matrix as the optimization objective, to adaptively and dynamically optimize the node selection and radiation resource allocation of networked radars in multiple target tracking, so as to improve the performance of multiple target tracking.

[0058] The application proposes a networked radar power-time joint optimization method for multiple target tracking under space-frequency sensing, starting from actual combat scenarios, to adaptively and dynamically optimize the node selection and radiation resource allocation of networked radars in multiple target tracking under the constraint conditions of satisfying the upper limit of tolerable interference energy of networked radar radiation resources and communication areas, so as to improve the performance of multiple target tracking of networked radars. Figure 1 As shown in the figure, the networked radar power-time joint optimization method for multiple target tracking under space-frequency sensing of the application includes the following steps:

[0059] S1, first, for the multiple target tracking scene of the networked radar system, the state equation of the moving target, the radar observation model and the interference model are established. The state vector of the qth moving target at time k can be expressed as wherein, and represent the position and velocity of the qth moving target at time k, respectively, and Q represents the number of moving targets. Assuming that the target moves at a constant speed in a straight line, the state equation of the moving target can be expressed as:

[0060]

[0061] wherein, represents the state vector of the qth moving target at time k-1, F represents the state transition matrix of the qth moving target, and can be expressed as △T0 represents the sampling interval, denotes the Kronecker product, I2 is a 2nd order identity matrix. W denotes a Gaussian process white noise with zero mean, whose covariance matrix U q may be expressed as:

[0062]

[0063] where r q denotes the process noise intensity.

[0064] The present application assumes that only one moving target can be tracked by each radar at each time. Here, a binary variable is defined. denotes that the nth radar tracks the moving target q at time k, and denotes that the nth radar does not track the moving target q at time k. Therefore, the radar observation model of the moving target q by radar n at time k can be expressed as:

[0065]

[0066] where, denotes the measurement vector corresponding to the moving target q tracked by radar n at time k, denotes a nonlinear observation function, which can be expressed as:

[0067]

[0068] where, and denote the range and azimuth angle of the moving target q relative to radar n at time k, respectively, (x R,n , y R,n ) denotes the position coordinates of radar n, denotes a measurement noise vector subject to a zero-mean Gaussian distribution.

[0069] In the space-frequency sensing environment, the radar and communication areas will interfere with each other's normal work. Here, the mutual interference of the two is analyzed. First, consider the interference of the communication area on the radar. Such interference can be regarded as a combination of multiple random modulated signals. According to the central limit theorem, it is assumed that the signal form can be approximately expressed as a circularly symmetric band-limited complex Gaussian sequence occupying a certain bandwidth. The power spectral density (Power Spectral Density, PSD) Θ m,n (f) shows uniform characteristics in the working passband range of the radar, that is:

[0070]

[0071] where N m,n denotes the PSD intensity, f L,m,n and f U,m,nrespectively represent the upper bound and lower bound of the nth radar and the mth communication region coverage frequency band. The time-domain covariance matrix T of the signal generated by the communication region m to the radar n is defined m,n may be represented as:

[0072]

[0073] T m,n The element of the u-th row and the v-th column of T is the autocorrelation function of the corresponding signal delay, which is also the inverse discrete Fourier transform of the PSD, T s denotes the signal sampling period. Assuming that the signals between the communication regions are orthogonal, the interference covariance matrix received by the radar n from the communication region is, that is, the interference model of the communication region to the radar can be represented as:

[0074]

[0075] wherein, denotes the azimuth angle between the communication region m and the radar n, and the superscript (·) H denotes the conjugate transpose of the matrix; E n denotes the interference covariance matrix received by the radar n from the communication region, M denotes the number of communication regions, χ m,n denotes the intensity coefficient of the transmission channel, T m,n denotes the time-domain covariance matrix of the interference signal generated by the communication region m to the radar n, x C,m denotes the position coordinates of the mth communication region, x R,n denotes the position coordinates of the radar n, denotes the radar half-wavelength steering vector.

[0076] From equation (6), if the mth communication region and the nth radar do not cover the spectrum, it can be considered that f U,m,n -f L,m,n = 0, and the corresponding interference intensity is 0, f U,m,n -f L,m,n The greater the value is, the stronger the interference energy is.

[0077] The interference of the radar to the communication region when tracking the moving target is time-varying and related to the moving target. The present application uses the joint spatial and spectral distribution of the radar transmission signal energy to represent the interference intensity, and the interference model of the radar to the communication region can be represented as:

[0078]

[0079] wherein, denotes the radar interference energy value received by the communication region m; denotes the radar transmission power of the radar n tracking the moving target q at the kth moment; denotes the spatial distribution of the radar transmitted signal energy, i.e.

[0080]

[0081] wherein, denotes the azimuth angle between the communication area m and the radar n, A denotes the number of radar array elements, denotes the tracking angle of the radar n to the moving target q, denotes the angle between the moving target q and the initial position; Φ m,n The u-th row and v-th column of the matrix S can be expressed as:

[0082]

[0083] s n = [s n (1),…,s n (L)] T denotes a waveform sequence with finite interval, L denotes the discrete sampling number, denotes the conjugate transpose of s n ;

[0084] S2, the BCRLB matrix is derived, and the trace of the matrix is calculated as a measurement index of the target tracking accuracy, and the specific calculation steps are as follows:

[0085] The trace of the BCRLB matrix at time k is used as a measurement index of the target tracking accuracy:

[0086]

[0087] The Bayesian information matrix of the target state at time k is combined The expression of the BCRLB matrix of the target state estimation error at time k is:

[0088]

[0089] wherein, the superscript (·) T denotes the transpose of the matrix; the superscript (·) -1 denotes the inverse matrix of the matrix; U q is a Gaussian white noise matrix; denotes the inverse matrix of the Bayesian information matrix of the target state at time k-1; denotes the Jacobian matrix at time k; denotes the observation error covariance matrix at time k, the observation error covariance matrix at time k is expressed by formula (13) as:

[0090]

[0091] wherein, This represents the measurement interference noise covariance matrix imposed on radar n by the communication area. This represents the transmitted waveform sequence of radar n. Let represent the half-wavelength steering vector of radar n. Let c represent the speed of light, and β represent... n,k Let λ represent the transmitted signal bandwidth of radar n at time k, and γ represent the radar wavelength and antenna aperture, respectively. The signal-to-noise ratio (SNR) of the echo from radar n tracking moving target q at time k can be expressed as:

[0092]

[0093] in, T represents the dwell time of radar n tracking moving target q at time k. r The pulse signal repetition period, G represents the radar transmit power of radar n tracking moving target q at time k. t G represents the transmit antenna gain. r Indicates the receiving antenna gain. G represents the radar cross section (RCS) of the target q observed by radar n. RP This represents the receiver processing gain, where K is the Boltzmann constant, and T... o This indicates the noise temperature of the receiver. F represents the bandwidth of the receiver's matched filter when radar n tracks moving target q at time k. r This represents the noise figure of the receiver. θ represents the angular difference between the true azimuth of the moving target q at time k and the direction of the radar beam transmitted by n. 3dB This indicates the 3dB antenna beamwidth.

[0094] S3. Establish a joint optimization allocation model for power and time of networked radars for multi-target tracking under space-frequency sensing:

[0095] With constraints on the radiation resources of networked radar and the upper limit of the tolerable interference energy in the communication area, and with the optimization objective of minimizing the trace of the BCRLB matrix, a joint optimization allocation model for the power and time of networked radar for multi-target tracking under space-frequency sensing is established, as shown in the equation:

[0096]

[0097] Among them, T min and T max P represents the lower and upper bounds of the radar dwell time, respectively. min and P max These represent the lower and upper bounds of the radar transmit power, respectively. denotes the maximum value of the number of radar nodes allocated by the networked radar system to track each moving target at each time instant, E max denotes the maximum radar interference energy value that the communication area can tolerate, T total denotes the sum of the residence time of all radars irradiating a single moving target, P total denotes the sum of the transmission power of all radars irradiating a single moving target.

[0098] S4, the interior point method and the cyclic minimum method are used to solve the optimization model (15). The specific solving steps are as follows:

[0099] S41, the initial matrix of the radar transmission power and residence time is set respectively, and the initial value of the transmission power and residence time is set for each radar node;

[0100] S42, the moving target to be tracked is determined, the transmission power and residence time allocation value of the networked radar system to the target at the previous time instant is taken as the initial value, and the binary variable is relaxed to The interior point method is used to calculate the weight coefficient of each radar node, the weight coefficients are arranged in descending order, and the radar node selection mode with different node selection total numbers is obtained.

[0101] S43, for different radar node selection modes in step S42, the radar transmission power resource allocation and residence time resource allocation are optimized with the minimum tracking error as the target, and the transmission power and residence time priority is set to be the same in the optimization process. The obtained tracking error solutions are compared, and the minimum tracking error solution and the corresponding radar node selection scheme and radar resource allocation scheme are obtained;

[0102] S44, step S42 is jumped to, until the tracking error difference obtained for two consecutive times is less than a set threshold value, and the minimum tracking error of the networked radar tracking the moving target q at the k time instant and the corresponding final radar node selection scheme and radar resource allocation scheme optimization allocation scheme are obtained.

[0103] S45, the radar node finally selected in step S44 is removed, the next optimized moving target is determined, step S42 is jumped to, and until all the moving target tracking schemes are optimized and allocated, the optimal radar node selection scheme and radar power time allocation scheme of the networked radar tracking each moving target at the k time instant are obtained.

[0104] The embodiment of the application also provides a space-frequency sensing networked radar power time joint optimization system for multi-target tracking, which comprises:

[0105] A target tracking and data acquisition module is configured to acquire motion states of multiple targets and establish a state method, a radar observation model and an interference model of the moving targets;

[0106] A multi-target tracking precision calculation module is configured to represent multi-target tracking precision by using a Bayesian Cramer-Rao lower bound (BCRLB) matrix;

[0107] A model construction module is configured to establish a networking radar power-time joint optimization model for multi-target tracking under space-frequency sensing by taking the networking radar radiation resources and the tolerable interference energy of the communication area as constraint conditions and minimizing the trace of the BCRLB matrix as an optimization target.

[0108] A model solving module is configured to adaptively and dynamically optimize node selection and radiation resource allocation of the networking radar in multi-target tracking and solve the optimization model by using an interior point method and a cyclic minimum method.

[0109] The application further provides a device apparatus comprising a memory and a processor, wherein:

[0110] The memory is configured to store a computer program capable of running on the processor.

[0111] The processor is configured to execute the steps of the networking radar power-time joint optimization method for multi-target tracking under space-frequency sensing when running the computer program and achieve the technical effects consistent with the above method.

[0112] The application further provides a storage medium having a computer program stored thereon, wherein the computer program is executed by at least one processor to implement the steps of the networking radar power-time joint optimization method for multi-target tracking under space-frequency sensing and achieve the technical effects consistent with the above method.

[0113] Simulation results:

[0114] The simulation parameters in the embodiments of the application are shown in Table 1 as follows:

[0115] Table 1 Simulation parameter settings

[0116]

[0117] Consider a networking radar system composed of N=6 position-fixed radars, the positions of each radar are known, and the radar transmission parameters are all the same. The networking radar system needs to track Q=2 moving targets simultaneously, the initial position of the moving target 1 is [-70, 0] km, and the moving target 1 flies at a constant speed of [900, 400] m / s; the initial position of the moving target 2 is [70, 80] km, and the moving target 2 flies at a constant speed of [-900, -400] m / s. There are M=2 communication areas in the radar detection area, for example, Figure 1As shown, the center positions of the two communication areas are [50, 50] km and [-40, 50] km respectively, and the maximum interference energy threshold tolerated by the communication area is set to E max = 4.5 J. The sampling interval of the networked radar is △T = 3 s, and the tracking duration is 150 s.

[0118] The multi-target motion trajectory and the networked radar distribution diagram are as shown in Figure 2 As shown in (a) and (b) of FIG. 8, the radar node selection and power-time allocation results of the networked radar in tracking the moving target 1 are as shown in Figure 3 As shown in (a) and (b) of FIG. 9, the radar node selection and power-time allocation results of the networked radar in tracking the moving target 2 are as shown in Figure 4 As shown in (a) and (b) of FIG. 9, it can be seen from the figure that the networked radar system will select the radar node selection mode and resource allocation mode that does not exceed the threshold E max and has the minimum tracking error according to the real-time position of the moving target 1. For the moving target 2, the networked radar node selection will be affected by the node selection of the moving target 1, and it is not always possible to select the node allocation mode with the minimum tracking error at the current moment. In order to minimize the tracking error, three radar nodes need to be selected to track the target at the same time at multiple time instants.

[0119] The average root mean square error (ARMSE) of target tracking is defined as:

[0120]

[0121] wherein N MC is the number of Monte Carlo experiments, represents the number of radiations of the networked radar to the moving target q in the n th Monte Carlo experiment, is the target estimated position obtained in the n th Monte Carlo experiment. Herein, N MC = 100. Figure 5 The ARMSE comparison of the algorithm and other comparative algorithms is given. As can be seen from Figure 5 , the algorithm can effectively reduce the multi-target tracking error and improve the multi-target tracking performance of the networked radar system in the spatial-frequency sensing environment compared with other algorithms.

[0122] In conclusion, the application assumes that several moving targets are scattered and arranged on a two-dimensional plane, and a networked radar system composed of N radars with limited total radiation resources tracks the targets. In view of the scenario of tracking multiple targets by the networked radar, a state equation of the moving targets, a radar observation model and an interference model are constructed, an expression of a BCRLB matrix is derived, and a trace of the matrix is taken as a measurement index of target tracking accuracy. A networked radar power-time joint optimization allocation model is established by taking the radiation resources of the networked radar and tolerable interference energy of a communication area as constraint conditions and minimizing the trace of the BCRLB matrix as an optimization target. Finally, the optimization model is solved by using an interior point method and a cyclic minimum method. Through solving the optimization model, an optimal solution of node selection, transmission power and residence time allocation is obtained under the constraint conditions of satisfying the upper limit of the total radar radiation power and the tolerable interference energy of the communication area, so that the multiple target tracking accuracy is the highest.

Claims

1. A joint power-time optimization method for networked radars in multi-target tracking under space-frequency sensing, characterized in that, Includes the following steps: S1. First, consider a networked radar system consisting of N radars in a two-dimensional space to track multiple targets that are dispersed in space, and establish the state equation, radar observation model and interference model of the moving targets. S2. Derive the expression for the Bayesian Cramé-Robber lower bound (BCRLB) matrix characterizing the accuracy of multi-target tracking; S3. Using the radiation resources of the networked radar and the upper limit of the tolerable interference energy in the communication area as constraints, and minimizing the trace of the BCRLB matrix as the optimization objective, a joint power-time optimization allocation model for networked radar under space-frequency sensing and multi-target tracking is established; the model expression is: in, As a metric to characterize target tracking accuracy, For a binary variable, when The time indicates that at time k, the nth radar tracks the moving target q. The time indicates that at time k, the nth radar did not track the moving target q; This represents the dwell time of radar n tracking moving target q at time k; T represents the radar transmit power of radar n tracking moving target q at time k; Q represents the number of moving targets; ... min and T max These represent the lower and upper bounds of the radar dwell time, respectively; P min and P max These represent the lower and upper bounds of the radar's transmit power, respectively. This represents the maximum number of radar nodes allocated to the networked radar system at any given moment when tracking each moving target; x C,m E represents the coordinates of the m-th communication region; max T represents the maximum radar interference energy that the communication area can tolerate. total P represents the sum of the dwell times of all radars illuminating a single moving target; total This represents the sum of the transmitted power of all radars illuminating a single moving target; S4. Adaptive dynamic optimization of node selection and radiation resource allocation for multi-target tracking of networked radar is performed. The interior point method and the cyclic minimum method are used to solve the joint optimization allocation model of power and time of networked radar for multi-target tracking under space frequency sensing.

2. The method for joint optimization of power and time of networked radar for multi-target tracking under space-frequency sensing according to claim 1, characterized in that, The state equation of the moving target established in step S1 is: in, Let represent the state vector of the q-th moving target at time k. Let F represent the state vector of the q-th moving target at time k-1; let F represent the state transition matrix of the q-th moving target, denoted as: ΔT0 represents the sampling interval. I² represents the Kronecker product, I² is the second-order identity matrix; W represents Gaussian white noise with zero mean; q represents the q-th moving target, and Q represents the number of moving targets.

3. The method for joint optimization of power and time of networked radar for multi-target tracking under space-frequency sensing according to claim 1, characterized in that, The radar observation model established in step S1 is as follows: in, This represents the measurement vector at time k when radar n tracks moving target q. Represents a nonlinear observation function. This represents a measurement noise vector that follows a zero-mean Gaussian distribution. For a binary variable, when The time indicates that at time k, the nth radar tracks the moving target q. The time indicates that at time k, the nth radar did not track the moving target q.

4. The method for joint optimization of power and time of networked radar for multi-target tracking under space-frequency sensing according to claim 1, characterized in that, The interference model in step S1 includes an interference model of the communication area to the radar and an interference model of the radar to the communication area, specifically: The established interference model for the radar in the communication area is as follows: Among them, the superscript (·) H E represents the conjugate transpose of a matrix; n This represents the interference covariance matrix received by radar n from the communication area, where M represents the number of communication areas, and χ represents the number of communication areas. m,n T represents the strength coefficient of the transmission channel. m,n Let x represent the time-domain covariance matrix of the interference signal generated by communication area m on radar n. C,m Let x represent the coordinates of the m-th communication region. R,n This represents the position coordinates of radar n. This represents the azimuth angle between the communication area m and the radar n. This represents the radar half-wavelength steering vector; The radar interference model for the communication area is as follows: in, Q represents the radar interference energy received by the communication area m, and Q represents the number of moving targets. s represents the spatial distribution of radar transmitted signal energy. n =[s n (1),...,s n (L)] T This represents a waveform sequence with finite intervals. For a binary variable, when The time indicates that at time k, the nth radar tracks the moving target q. The time indicates that at time k, the nth radar did not track the moving target q; Φ represents the radar transmit power at time k when radar n tracks moving target q; m,n Represented as: Among them, f L,m,n and f U,m,n T represents the upper and lower bounds of the communication area m and radar n's coverage frequency band, respectively. s This represents the signal sampling period, where u and v represent Φ respectively. m,n The rows and columns.

5. The method for joint optimization of power and time of networked radar for multi-target tracking under space-frequency sensing according to claim 1, characterized in that, The BCRLB matrix of the target state estimation error at time k in step S2 The expression is: Among them, the superscript (·) T Indicates the transpose of a matrix; superscript (·) -1 U represents the inverse matrix of a matrix; q The variable is a Gaussian white noise matrix; F represents the state transition matrix of the q-th moving target. The Bayesian information matrix represents the target state at time k-1; For a binary variable, when The time indicates that at time k, the nth radar tracks the moving target q. The time indicates that at time k, the nth radar did not track the moving target q; Denotes the Jacobian matrix at time k; Let k represent the observation error covariance matrix at time k; The trace of the BCRLB matrix at time k is used as a metric to characterize the target tracking accuracy.

6. The method for joint optimization of power and time of networked radar for multi-target tracking under space-frequency sensing according to claim 1, characterized in that, The model solution steps in step S4 are as follows: (41) Set the initialization matrices for radar transmit power and dwell time respectively, and set the initial values ​​for transmit power and dwell time for each radar node; (42) Determine the moving target to be tracked. Use the transmission power and dwell time allocation values ​​of the networked radar system for the moving target at the previous moment as initial values, and then use the binary variables... relaxation The weighting coefficients of each radar node are calculated using the interior-point method, and these weighting coefficients are then sorted in descending order to obtain... Radar node selection methods with different total number of nodes; (43) For different radar node selection methods in step (42), with the goal of minimizing tracking error, optimize the allocation of radar transmit power resources and dwell time resources, and set transmit power and dwell time to have the same priority during the optimization process. By comparing the tracking error solutions, the minimum tracking error solution and the corresponding radar node selection scheme and radar resource allocation scheme are obtained; (44) Jump to step (42) until the difference between the tracking errors obtained in two consecutive times is less than the set threshold, that is, the minimum tracking error of the network radar tracking the moving target q at time k and the corresponding final radar node selection scheme and radar resource allocation scheme optimization allocation scheme are obtained. (45) Remove the radar node finally selected in step (44), determine the next optimized moving target, and jump to step (42) until all moving target tracking schemes have been optimized and allocated, that is, obtain the optimal radar node selection scheme and radar power time allocation scheme for the network radar to track each moving target at time k.

7. A networked radar power-time joint optimization system for multi-target tracking under space-frequency sensing, characterized in that, include: The target tracking and data acquisition module is used to collect the motion status of multiple targets and establish the motion target status method, radar observation model and interference model; A multi-target tracking accuracy calculation module is used to characterize the multi-target tracking accuracy using the Bayesian Cramé-Robber lower bound BCRLB matrix. The model building module is used to establish a joint power-time optimization model for networked radar tracking under space-frequency sensing, with networked radar radiation resources and tolerable interference energy in the communication area as constraints, and minimizing the trace of the BCRLB matrix as the optimization objective. The model expression is as follows: in, As a metric to characterize target tracking accuracy, For a binary variable, when The time indicates that at time k, the nth radar tracks the moving target q. The time indicates that at time k, the nth radar did not track the moving target q; This represents the dwell time of radar n tracking moving target q at time k; T represents the radar transmit power of radar n tracking moving target q at time k; Q represents the number of moving targets; ... min and T max These represent the lower and upper bounds of the radar dwell time, respectively; P min and P max These represent the lower and upper bounds of the radar's transmit power, respectively. This represents the maximum number of radar nodes allocated to the networked radar system at any given moment when tracking each moving target; x C,m E represents the coordinates of the m-th communication region; max T represents the maximum radar interference energy that the communication area can tolerate. total P represents the sum of the dwell times of all radars illuminating a single moving target; total This represents the sum of the transmitted power of all radars illuminating a single moving target; The model solving module adaptively and dynamically optimizes node selection and radiation resource allocation for multi-target tracking in networked radar, and solves the optimization model using the interior point method and the cyclic minimum method.

8. A device, characterized in that, Includes memory and processor, wherein: Memory is used to store computer programs that can run on a processor; A processor, configured to, while running the computer program, execute the steps of the network radar power-time joint optimization method for multi-target tracking under air-frequency sensing as described in any one of claims 1-6.

9. A storage medium, characterized in that, The storage medium stores a computer program, which, when executed by at least one processor, implements the steps of the network radar power-time joint optimization method for multi-target tracking under air-frequency sensing as described in any one of claims 1-6.

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