CN117970308A - Networking MIMO radar beam synthesis multi-target cognitive tracking method aiming at suppression interference - Google Patents

Abstract

The invention discloses a networking MIMO radar beam synthesis multi-target cognitive tracking method aiming at suppression interference, which comprises the steps of initializing networking MIMO radar system parameters, deducing enumeration PCRLB by enumerating target detection/omission conditions at all moments, designing a global multi-target tracking target function based on a service quality frame by combining radar-target allocation resource constraint and receiving-transmitting beam synthesis constraint, constructing a networking MIMO radar beam synthesis multi-target cognitive tracking problem aiming at suppression interference, solving an output beam synthesis optimization result by using a three-stage iterative decoupling solution method, and finally feeding back the beam synthesis optimization result to each radar to realize a global multi-target tracking task. The method disclosed by the invention considers the target detection conditions at all moments to deduce tracking PCRLB, has more accurate quantitative evaluation on tracking performance, can dynamically schedule MIMO radar synthesized wave beams in real time, forms a gain pattern with null, and meets the target tracking precision requirement while inhibiting the influence of suppression interference on target detection.

Description

Networking MIMO radar beam synthesis multi-target cognitive tracking method aiming at suppression interference

Technical Field

The invention belongs to the technical field of radar tracking, and particularly relates to a networking MIMO radar beam synthesis multi-target cognitive tracking method aiming at suppressing interference.

Background

The co-located MIMO radar consists of a plurality of closely spaced antennas, transmits a plurality of correlated or uncorrelated detection signals, and achieves waveform diversity superior to phased array radar. In the multi-beam mode, the co-located MIMO radar irradiates a time-varying number of focused beams in a power controllable mode through beam synthesis, and the multi-task such as target detection and multi-target tracking are completed. The adoption of multiple co-located MIMO radar networking, the capture of spatial diversity of radar cross sectional areas (RCS), enables the co-located MIMO radar network to have significant advantages over traditional single-station radar systems, such as multiplexing gain, electronic countermeasure capability. However, radar systems need to share limited system resources when performing multiple tasks. To maximize the potential of radar systems, such as multi-target tracking task performance, it is desirable to develop resource scheduling techniques.

Currently, resource scheduling techniques have been widely developed. However, most of the work is studied based on an ideal detection condition with a detection probability of 1, which has not been applied to an electromagnetic environment of gradually complicated. In practice, the electromagnetic environment in which radar operates is rich in various noise, clutter, suppression interference and rogue interference signals. Aiming at the multi-target tracking task of networking MIMO radar under multi-source suppression interference, the too optimistic detection assumption causes the derived tracking performance index to be mismatched with the actual tracking precision, thereby misleading the subsequent resource management and allocation operation and reducing the radar resource utilization efficiency. In addition, as the target echo signal is covered by the high-power noise signal under the multi-source suppression interference, the detection performance of the networking MIMO radar is affected and reduced. Therefore, it is desirable to derive an accurate quantization index to evaluate the accuracy of target tracking under multi-source hold-down interference and design an effective interference suppression strategy for multi-target cognitive tracking to reduce the impact of hold-down interference on radar tracking performance. Document "Joint beam selection and power allocation in cognitive collocated MIMO radar for potential guidance application under oppressive jamming,Digit.Signal Process.,vol.127,p.103579,2022" proposes a joint beam selection and power allocation strategy for potential guidance applications under the jamming environment, which effectively improves the number of tracked objects and tracking performance under the jamming environment. However, the method does not consider the influence of the suppression interference on the target detection and measurement extraction into a PCRLB (a posterior Cramer-Rao lower bound for accurately quantifying the target estimation accuracy under the suppression interference) derivation process and optimization model. The essence of system optimization is that more resources are distributed to radar nodes with excellent performance, task performance is improved by designing a multi-target cognitive tracking interference suppression strategy of the networking MIMO radar, and tracking performance improvement efficiency of the method is limited in practical application. Literature "A robust power allocation strategy based on benefit-cost ratio for multiple target guidance in the C-MIMO radar system under blanket jamming,EURASIP Journal on Advances in Signal Processing,48：1-19,2022" adopts interaction information between a target reflection signal and a path gain matrix as a performance criterion of target parameter estimation, and proposes a robust power allocation strategy of a co-located MIMO radar for multi-target guidance in a suppression interference environment, but the optimization strategy still does not consider the influence of suppression interference on a target detection and measurement model, and does not relate to the improvement of multi-target cognitive tracking performance through interference suppression strategies such as beam synthesis of the MIMO radar. From published literature, at present, no literature relates to deriving performance indexes of accurately quantifying target tracking precision under suppression interference, and a multi-target cognitive tracking strategy of a networking MIMO radar is not designed through a beam synthesis anti-interference technology, so that the aims of suppressing influence of interference signals on radar detection performance and meeting preset multi-target tracking precision requirements are fulfilled. Therefore, the networking MIMO radar beam synthesis multi-target cognitive tracking method for suppressing interference is researched to have certain application value.

Disclosure of Invention

In order to solve the technical problems, the invention provides a networking MIMO radar beam synthesis multi-target cognitive tracking method aiming at suppression interference, which effectively reduces the influence of the suppression interference on radar task performance and improves the overall target detection performance and multi-target tracking precision.

The invention adopts the technical scheme that: a networking MIMO radar beam synthesis multi-target cognitive tracking method aiming at suppression interference comprises the following specific steps:

S1, initializing networking MIMO radar system parameters;

s2, constructing a target detection matrix according to target detection conditions at each tracking moment based on the predicted target state;

S3, deriving enumeration PCRLB based on the step S2;

S4, combining radar-target allocation resource constraint and receiving-transmitting beam synthesis constraint, designing a global multi-target tracking objective function based on a service quality frame, and constructing a networking MIMO radar beam synthesis multi-target cognitive tracking problem aiming at suppressing interference;

S5, solving a feasible solution of the networking MIMO radar beam synthesis multi-target cognitive tracking problem aiming at suppressing interference by using a three-stage iterative decoupling solving method while meeting radar-target allocation resources and receiving-transmitting beam synthesis constraints, and outputting a beam synthesis optimizing result;

s6, synthesizing a receiving and transmitting beam pattern of each radar according to the radar-target allocation and receiving and transmitting beam synthesis optimization result;

s7, calculating target SINR under suppression interference, and obtaining the probability of detecting each target by the radar system;

S8, acquiring a target state at the current moment according to a target state equation of the radar system, constructing a measurement equation under suppression interference by combining target detection probability, and acquiring target measurement at the current moment;

S9, based on a centralized fusion rule, a global multi-target tracking result is obtained through extended Kalman filtering, and the global multi-target tracking result at the current moment is used as priori information together with priori detection information to guide networking MIMO radar beam synthesis multi-target cognitive tracking operation at the next moment.

Further, the step S1 specifically includes the following steps:

First, initializing networking MIMO radar system parameters, including:

Co-located MIMO radar position r ⁿ＝[xⁿ,yⁿ ], number N, number of transmit and receive array elements for each co-located MIMO radar N _a; at the kth tracking time, the number of beams B _n,k generated by each radar; number of targets Q _k, initial state of targets Target initial state bias obeys gaussian distribution/>Number M _k of supporting jammers, position of supporting jammers/>

Where q=1,..q _k denotes an index of a target, n=1,..n denotes an index of a radar,Representing the initial position of the target,/>Representing the initial speed of the target, (. Cndot.) ^T represents the transpose operation of the matrix,/>Representing the process noise covariance of the target q.

Then, the update time t _k =0 is initialized, the time index is denoted as k=0, and the state of the initialization target q is as followsSetting a Fisher Information Matrix (FIM)/>, at the initial timeSetting an initial time radar-target allocation variable/>And the transmit and receive patterns/>, of all radars

At the kth (k is greater than or equal to 1), for a scene of N radar tracking Q _k targets, the radar-target matching matrix expression is as follows:

Wherein, The b-th beam representing radar n is assigned to track target q; the kronecker symbol expression is as follows:

Then, the transmit-receive beam weight matrix of the N radars, that is, the transmit-receive beam pattern expression of the networking MIMO radar system is as follows:

Wherein, Representing the transmission pattern weight matrix of radar n,/>Representing a transmission pattern weight matrix of the N radars; /(I)A reception pattern weight matrix representing radar n,/>Representing a receive pattern weight matrix for N radars.

Further, the step S2 is as follows:

enumerating the detection condition of each radar to each target at all times (0, k) at the current time k (k is greater than or equal to 1), using an observable binary variable To describe whether the radar n detects the target q, the expression is as follows:

Wherein, Indicating that radar n detected target q,/>The radar N is indicated to miss the target q, and the N radars form 2 ^kN detection matrices at the time k.

For the qth target, during the kth tracking frame, N binary variables may form i=2 ^kN target detection/omission matrices, where the ith matrix is:

Wherein, The detection of the target q by the radar n at the tracking time k in the ith target detection/omission matrix is shown.

Finally, obtaining a target detection matrix

Further, the step S3 specifically includes the following steps:

Is provided with Representing target q based on measurement vector/>Target state/>Given a specific target detection/omission matrix/>The following inequality holds:

Wherein, Representation of target state/>And its related measurement/>Is/are the desired operator of (1)Expressed as matrix/>FIM, which is a condition, is specifically expressed as follows:

Wherein, FIM representing a priori information; /(I)Representing the state of the target q at the time k; b _n,k denotes the number of beams that radar n synthesizes at time k; /(I)As in formula (2), represents a beam selection identifier,/>Indicating that radar n is allocated to b-th beam tracking target q, otherwise,/>Data information FIM representing the radar n versus the target q; f represents a target state transition matrix,/>Representing a desired operation based on a target state,/>Representing a nonlinear measurement function/>Is a jacobian matrix of (c).

Then the condition PCRLB of the q-th target is expressed as a conditionIs the inverse of (3):

Then according to the target detection probability at the current tracking moment Detection matrix/>The occurrence probability expression of (2) is:

finally, taking the expectation of equation (8) yields enumerated PCRLB:

further, the step S4 specifically includes the following steps:

using first PCRLB based on enumeration and following the quality of service framework, the overall utility function is designed, and then the task utility function design expression for the q-th objective is as follows:

Wherein, PCRLB,/>, representing a position estimate of the target qPCRLB matrix representing target q,/>Then the j-th diagonal element of the enumeration PCRLB matrix is represented,/>Representing the tracking performance requirement of target q.

Then, summing utility functions of all target tracking tasks, and establishing a global multi-target tracking target function as follows:

Wherein, PCRLB set vectors representing all targets; eta _k represents the set of tracking performance requirements for all targets, and/>

The angle space can be divided into B _n,k main lobe beam grids, M _k null grids and the rest C _s auxiliary lobe direction grids by converting the continuous domain of the angle theta epsilon [0,180 DEG ] of the radar system observation area into a group of discrete angle grids. The discrete angular grid of beams, nulls, and side lobes are represented as:

Wherein, Respectively representing the arrival angles of the main lobe and the side lobe directions,/>The arrival angle in the m direction of the jammer at radar n is shown.

Finally, the networking MIMO radar beam forming multi-target cognitive tracking problem for the suppressed interference can be expressed as:

Wherein, Representing the radar quantity allocated to the target q by the radar system at the moment k, and N _max represents the radar quantity of the radar system which is allocated to track the target q at most in each tracking interval; b _max denotes the number of beams that can be generated at maximum per radar due to the limitation of the antenna array capacity; b 'represents a b' th beam other than b; /(I)Representing the transmit beam pattern of radar n,Representing the transmitting gain of the radar n in the m direction of the jammer; /(I)Representing the trace of the covariance matrix of the transmitted signal, which is the transmitted power of the radar in the MIMO radar; (. ^H) represents a conjugate transpose operation of the matrix; gamma ^null denotes a gain threshold value of the null direction set in advance; /(I)A received beam pattern representing the b-th beam of radar n,/>Representing the receiving gain of the b-th beam of the radar n in the m direction of the jammer,/>Representing the receive gain of the b-th beam of radar n in the unmatched target q-direction.

Further, the step S5 specifically includes the following steps:

s51, fixing an isotropic receiving and transmitting beam pattern, and solving a radar-target allocation sub-optimization problem;

if the elements of the transmit and receive weight matrices of the co-located MIMO radar are averaged, then The representation, and the resulting transmit and receive beam patterns are isotropic.

The optimization problem in formula (14) can be translated into the following:

Wherein the radar-target allocation constraints are taken Then use/>Substitution/>The integer programming is converted to a semi-definite programming of continuous variables between 0 and 1.

And then adopting Zoutendijk a feasible direction method to realize a suboptimal scheme, and if all variables of the radar-target allocation are integer solutions, considering that the original problem is solved, and terminating the algorithm. Otherwise, continuing to solve in the scoreThe element with the largest value is selected and set/>Until the beam resources of all the radars satisfy the constraint of equation (15).

Finally, a suboptimal radar-target allocation result is obtained

S52, according to the obtained radar-target distribution resultDeriving a convex approximation model of a non-convex optimization problem based on a first-order Taylor expansion convex approximation method, and sequentially solving a transmit-receive beam synthesis sub-optimization problem of each radar;

decomposing the multi-radar beam synthesis optimization problem into a plurality of single-radar beam synthesis optimization problems, wherein the method comprises the following steps of:

Wherein, Representing the transmit weight matrix of the remaining radars except for radar n, i.e. the un-optimized result/>Or an optimized weight matrix/>

And replacing the original objective function and constraint by using a first-order Taylor expansion of the non-convex function, and iteratively solving the non-convex problem. At the moment of obtaining the transmission weight matrix of all the selected radarsThe remaining receive beam pattern optimization sub-problem can then be expressed as:

Wherein, Representing the receive weight matrix of the remaining radars except radar n. Then, solving a receiving weight matrix/>, by adopting an iterative convex approximation method based on first-order Taylor expansion

S53, taking the minimum global multi-target tracking performance as a target, and obtaining a beam dynamic synthesis result based on the previous iterationAnd (3) solving a radar receiving and transmitting weight matrix by loop iteration until a loop stopping condition is met, and outputting a radar-target allocation and receiving and transmitting beam synthesis optimization result/>Then executing step S6, otherwise, continuing executing step S52;

wherein, the circulation stop conditional expression is as follows:

Wherein, Representing a jth round-robin global multi-target tracking objective function,Representing a suboptimal transmit-receive beam weight matrix obtained in a jth cycle; epsilon represents a preset threshold value for controlling the final tracking accuracy.

Further, the step S6 specifically includes the following steps:

In the tracking stage, if the array element of the radar n is calibrated, the mathematical expression of the transmit beam pattern is:

Where a _n (θ) represents the transmit steering vector, which depends on the geometry of the array. The expression a _n (θ) is as follows:

Wherein f _c denotes the carrier frequency, Representing the delay of signal transmission from the nth _a antennas to the target q:

Where d=λ/2 denotes the spatial distance between the two antennas, λ denotes the wavelength, c denotes the speed of light, Representing the distance between radar n and target q.

The receive beam pattern mathematical expression of radar n is:

Wherein b _n(θ)＝a_n (θ) represents the received steering vector, an Representing the receive beam weight matrix for the b-th beam of radar n.

Further, the step S7 specifically includes the following steps:

in the interference suppression environment, the SINR of the target is the ratio of the target echo power to the interference power, and the calculation formula is as follows:

Where ρ _N,k represents the background noise power, The target echo power and the interference signal power received by the radar n are respectively represented by the following expressions:

Wherein, Representing the total transmit power of radar n,/>Representing the target RCS,/>Is the transmitting interference power of the jammer m,/>Is the polarization mismatch loss of the jammer m,/>Is the distance between radar n and jammer m.

In a suppressed interference environment, the radar examination azimuth and the signals in the range resolution unit are set to determine the presence of the target q. A test is set to detect the presence or absence of the qth object over the monitored area. The test expression is as follows:

Wherein, Representing the magnitude squared output of the matched filter. In the test equation (25), the setting H ₀ indicates that the target q is not present in the monitored area, and the echo is composed of only noise and interference signals. Setting H ₁ indicates that there is a target q in the monitored area and that the echo is a combination of noise, interference signal and target signal.

According to the nomann-pearson criterion, the probability expression of detection of the target q by the radar n is as follows:

Where V _T represents the detection threshold.

Further, the step S8 specifically includes the following steps:

The set target motion model follows a linear Constant Velocity (CV) model expressed as:

Wherein F represents a target state transition matrix, Representing process noise, set to have covariance matrix/>Is a zero-mean gaussian noise of:

where T ₀ denotes the interval between two consecutive tracking frames, r _q denotes the intensity of process noise, and I ₂ denotes the identity matrix with dimension 2.

Under the hold-down interference, the radar collects/loses measurement data with a certain probability. The measured value of the q-th target acquired by the n-th radar is as follows:

Wherein, Representing measurement noise,/>The detection probability of the radar n to the target q is represented; h _n (·) represents a nonlinear function,/>And:

further, the step S9 specifically includes the following steps:

Setting allocation The q-th target is tracked by a radar, and the centralized measurement set of the q-th target in the fusion center can be expressed as:

Wherein, Representing the measured quantity of the target q at the fusion center; /(I)Represents the/>, of the target q at the fusion centerAnd (5) measuring.

Then, the posterior density of the target is calculated according to the bayesian rule, and the posterior density of the q-th target is set to be approximately gaussian as follows:

Where N (x; m, B) represents a Gaussian distribution with a parameter of x, the mean value is m, and the covariance is B. Posterior Density The mean and covariance of (a) are:

Wherein, And/>Representing the mean and covariance of the predictions,/>Residual error representing Kalman gain and effective measurement, respectively,/>Representing a local approximation of the metrology function based on state prediction.

The state of the target q at time k can be estimated asThe global multi-target tracking result is/>

If the selected radar is affected by the hold-down disturbance, no valid measurements of target q can be collected (i.e) The prior probability density predicted at time k-1 is used to approximate the target posterior density as follows:

In the state prediction stage, the prior probability density is calculated by taking the target posterior density as prior information, namely:

Wherein,

And finally, taking one-step prediction of the global multi-target tracking result at the current moment in the formula (36) as priori information and priori detection information to guide networking MIMO radar beam forming multi-target cognitive tracking operation at the next moment.

The invention has the beneficial effects that: the method comprises the steps of initializing networking MIMO radar system parameters, deducing enumeration PCRLB by enumerating target detection/omission conditions at all moments, combining radar-target allocation resource constraint and receiving-transmitting beam synthesis constraint, designing a global multi-target tracking target function based on a service quality framework, constructing a networking MIMO radar beam synthesis multi-target cognitive tracking problem aiming at suppression interference, solving an output beam synthesis optimization result by using a three-stage iterative decoupling solution method, and finally feeding back the beam synthesis optimization result to each radar to realize a global multi-target tracking task. The method provided by the invention can accurately evaluate the target tracking performance under the suppression interference, realize the dynamic synthesis of networking MIMO radar beams under the online multi-source suppression interference, quickly and effectively obtain the networking MIMO radar multi-target cognitive tracking result, inhibit the influence of the suppression interference on the radar detection performance, and improve the multi-target tracking precision. Compared with the existing target tracking performance index, the method considers the target detection conditions at all moments to deduce tracking PCRLB, and the quantitative evaluation of the tracking performance is more accurate; compared with the existing multi-target cognitive tracking method, the method provided by the invention can reduce the influence of suppression interference on a radar system while increasing the target direction gain through the dynamic synthesis operation of the receiving and transmitting beam, so that the method can be well adapted to complex electromagnetic countermeasure environment, and effectively improve the target detection performance and multi-target tracking precision of the radar system; the method can realize the online multi-target cognitive tracking requirement, and the proposed three-stage iterative decoupling solving method can rapidly obtain the networking MIMO radar beam dynamic synthesis result under the multi-source suppression interference, so that the method can respond to the complex and changeable requirements in real time.

Drawings

Fig. 1 is a flowchart of a networking MIMO radar beam forming multi-target cognitive tracking method for suppressing interference according to the present invention.

Fig. 2 is a schematic diagram of multiple targets tracking by a networking MIMO radar under multi-source suppression interference in an embodiment of the present invention.

Fig. 3 is a schematic diagram of a networking MIMO radar and a target motion track under multi-source suppression interference in an embodiment of the present invention.

Fig. 4 is a target tracking accuracy diagram of a networking MIMO radar beam forming multi-target cognitive tracking method aiming at interference suppression in the embodiment of the present invention.

Fig. 5 is a target tracking accuracy chart of a conventional multi-target cognitive tracking method for performance comparison in an embodiment of the present invention.

Fig. 6 is a graph of target tracking accuracy of a near-range radar-target allocation and uniform gain beam dynamic synthesis method for performance comparison in an embodiment of the invention.

Fig. 7 is a graph showing the comparison of target detection probabilities of three multi-target cognitive tracking methods according to an embodiment of the present invention.

Fig. 8 is a radar-target allocation result of a networking MIMO radar beam synthesis multi-target cognitive tracking method for suppressing interference according to an embodiment of the present invention.

Fig. 9 is a diagram of transmit and receive beam patterns of the selected radar of frame 5 according to an embodiment of the present invention.

Fig. 10 is a diagram of transmit and receive beam patterns of a selected radar of frame 15 according to an embodiment of the present invention.

Fig. 11 is a diagram of transmit and receive beam patterns of a selected radar of a 25 th frame according to an embodiment of the present invention.

Detailed Description

The method of the present invention will be further described with reference to the accompanying drawings and examples.

As shown in fig. 1, the method for multi-target cognitive tracking by networking MIMO radar beam synthesis for suppressing interference according to the present invention comprises the following specific steps:

S1, initializing networking MIMO radar system parameters;

s2, constructing a target detection matrix according to target detection conditions at each tracking moment based on the predicted target state;

S3, deriving enumeration PCRLB based on the step S2;

S4, combining radar-target allocation resource constraint and receiving-transmitting beam synthesis constraint, designing a global multi-target tracking objective function based on an quality of service (OoS) framework, and constructing a networking MIMO radar beam synthesis multi-target cognitive tracking problem aiming at suppression interference;

S5, solving a feasible solution of the networking MIMO radar beam synthesis multi-target cognitive tracking problem aiming at suppressing interference by using a three-stage iterative decoupling solving method while meeting radar-target allocation resources and receiving-transmitting beam synthesis constraints, and outputting a beam synthesis optimizing result;

s6, synthesizing a receiving and transmitting beam pattern of each radar according to the radar-target allocation and receiving and transmitting beam synthesis optimization result;

s7, calculating target SINR under suppression interference, and obtaining the probability of detecting each target by the radar system;

S8, acquiring a target state at the current moment according to a target state equation of the radar system, constructing a measurement equation under suppression interference by combining target detection probability, and acquiring target measurement at the current moment;

S9, based on a centralized fusion rule, a global multi-target tracking result is obtained through extended Kalman filtering, and the global multi-target tracking result at the current moment is used as priori information together with priori detection information to guide networking MIMO radar beam synthesis multi-target cognitive tracking operation at the next moment.

In this embodiment, the step S1 is specifically as follows:

First, initializing networking MIMO radar system parameters, including:

Co-located MIMO radar position r ⁿ＝[xⁿ,yⁿ ], number N, number of transmit and receive array elements for each co-located MIMO radar N _a; at the kth tracking time, the number of beams B _n,k generated by each radar; number of targets Q _k, initial state of targets Target initial state bias obeys gaussian distribution/>Number M _k of supporting jammers, position of supporting jammers/>

Where q=1,..q _k denotes an index of a target, n=1,..n denotes an index of a radar,Representing the initial position of the target,/>Representing the initial speed of the target, (. Cndot.) ^T represents the transpose operation of the matrix,/>Representing the process noise covariance of the target q.

As shown in fig. 2, in this embodiment, a multi-source suppression interference networking MIMO radar tracking is schematically shown.

As shown in fig. 3, the networking MIMO radar system in this embodiment is composed of n=12 radars, tracks Q _k =3 widely separated targets, and performs tasks such as formation detection and burst prevention on the M _k =2 interference machine isotropic emission high-power suppression interference support targets. The initial states of the target and jammer are shown in table 1. The radar detection area is divided into two areas, different target tracking precision requirements are set in each area, the area 1 is 40m, and the area 2 is 60m. The interval T ₀ = 1s between two consecutive tracking instants is set and the nulling gain of the radar for the interference direction is set to y ^null = -60dB.

TABLE 1

	Location (km)	Speed (m/s)
			Target 1	(180,80)	(-300,-100)
Target 2	(180,60)	(-300,-100)
			Target 3	(180,40)	(-300,-100)
Jammer 1	(145,85)	(-150,-250)
			Jammer 2	(145,45)	(-150,-250)

Then, the update time t _k =0 is initialized, the time index is denoted as k=0, and the state of the initialization target q is as followsSetting a Fisher Information Matrix (FIM)/>, at the initial timeSetting an initial time radar-target allocation variable/>And the transmit and receive patterns/>, of all radars

At the kth (k is greater than or equal to 1), for a scene of N radar tracking Q _k targets, the radar-target matching matrix expression is as follows:

Wherein, The b-th beam representing radar n is assigned to track target q; the kronecker symbol expression is as follows:

Then, the transmit-receive beam weight matrix of the N radars, that is, the transmit-receive beam pattern expression of the networking MIMO radar system is as follows:

Wherein, Representing the transmission pattern weight matrix of radar n,/>Representing a transmission pattern weight matrix of the N radars; /(I)A reception pattern weight matrix representing radar n,/>Representing a receive pattern weight matrix for N radars.

In this embodiment, the step S2 is specifically as follows:

enumerating the detection condition of each radar to each target at all times (0, k) at the current time k (k is greater than or equal to 1), using an observable binary variable To describe whether the radar n detects the target q, the expression is as follows:

Wherein, Indicating that radar n detected target q,/>The radar N is indicated to miss the target q, and the N radars form 2 ^kN detection matrices at the time k.

For the qth target, during the kth tracking frame, N binary variables may form i=2 ^kN target detection/omission matrices, where the ith matrix is:

Wherein, The detection of the target q by the radar n at the tracking time k in the ith target detection/omission matrix is shown.

Finally, obtaining a target detection matrix

In this embodiment, the step S3 is specifically as follows:

Is provided with Representing target q based on measurement vector/>Target state/>Given a specific target detection/omission matrix/>The following inequality holds:

Wherein, Representation of target state/>And its related measurement/>For the linear dynamic model and the nonlinear measurement model in this embodiment,/>Expressed as matrix/>FIM, which is a condition, is specifically expressed as follows:

Wherein, FIM representing a priori information; /(I)Representing the state of the target q at the time k; b _n,k denotes the number of beams that radar n synthesizes at time k; /(I)As in formula (2), represents a beam selection identifier,/>Indicating that radar n is allocated to b-th beam tracking target q, otherwise,/>Data information FIM representing the radar n versus the target q; f represents a target state transition matrix,/>Representing a desired operation based on a target state,/>Representing a nonlinear measurement function/>Is a jacobian matrix of (c).

Then the condition PCRLB of the q-th target is expressed as a conditionIs the inverse of (3):

Then according to the target detection probability at the current tracking moment Detection matrix/>The occurrence probability expression of (2) is:

statistically, each target detection/omission matrix is based on the independence assumption of measurement noise Is a sample of an independent event. Thus, the enumeration-based PCRLB calculation follows the principle of the full probability theorem; finally, taking the expectation of equation (8) yields enumerated PCRLB:

In this embodiment, the step S4 is specifically as follows:

mathematically, networking MIMO radar beam dynamic synthesis and multi-target cognitive tracking for suppressed interference can be expressed as a problem of optimizing some system-level utility function under configuration constraints. Therefore, the design of utility functions has a crucial meaning for the multi-objective cognitive tracking problem. The present embodiment uses the prediction-based enumeration PCRLB as a performance index for single-target tracking problems under multi-source suppression interference, as it can be Provides an accurate lower bound for target state estimation errors in an incomplete detection scenario. Here, since different targets have different priorities and threats, etc., they are considered to have unique tracking accuracy requirements. Using enumeration-based PCRLB, and following the quality of service framework, an overall utility function is designed to reflect the effectiveness of the multi-objective tracking task. The task utility function design expression for the q-th target is as follows:

Wherein, PCRLB,/>, representing a position estimate of the target qPCRLB matrix representing target q,/>Then the j-th diagonal element of the enumeration PCRLB matrix is represented,/>Representing the tracking performance requirement of target q.

Then, summing utility functions of all target tracking tasks, and establishing a global multi-target tracking target function as follows:

Wherein, PCRLB set vectors representing all targets; eta _k represents the set of tracking performance requirements for all targets, and/>

For the convenience of experiment and analysis, the continuous domain of the angle theta epsilon [0,180 DEG ] of the radar system observation area is converted into a group of discrete angle grids, so that the angle space can be divided into B _n,k main lobe beam grids, M _k null grids and the rest C _s side lobe direction grids. The discrete angular grid of beams, nulls, and side lobes are represented as:

Wherein, Respectively representing the arrival angles of the main lobe and the side lobe directions,/>The arrival angle in the m direction of the jammer at radar n is shown.

Finally, the networking MIMO radar beam forming multi-target cognitive tracking problem for the suppressed interference can be expressed as:

Wherein, Representing the radar quantity allocated to the target q by the radar system at the moment k, and N _max represents the radar quantity of the radar system which is allocated to track the target q at most in each tracking interval; b _max denotes the number of beams that can be generated at maximum per radar due to the limitation of the antenna array capacity; b 'represents a b' th beam other than b; /(I)Representing the transmit beam pattern of radar n,Representing the transmitting gain of the radar n in the m direction of the jammer; /(I)Representing the trace of the covariance matrix of the transmitted signal, which is the transmitted power of the radar in the MIMO radar; (. ^H) represents a conjugate transpose operation of the matrix; gamma ^null denotes a gain threshold value of the null direction set in advance; /(I)A received beam pattern representing the b-th beam of radar n,/>Representing the receiving gain of the b-th beam of the radar n in the m direction of the jammer,/>Representing the receive gain of the b-th beam of radar n in the unmatched target q-direction.

The first bracketed constraint in the optimization problem (14) is the constraint on the allocation of resources to radar-targets, which are: the maximum number of tracking beams synthesized by the radar at the same time is limited; the radar-target beam matching variable is a discrete variable; each radar is allocated one wave beam at most to track the same target; the radar system allocates a maximum of N _max radars to track the same target within each tracking interval. The second bracketed constraint in the optimization problem (14) is the constraint on the radar emission pattern, which is: the gain in the null direction is lower than a pre-designed threshold y ^null; the transmit weight matrix must satisfy the trace constraint. The third bracketed constraint in the optimization problem (14) is the constraint on the radar reception pattern, giving the null constraints in the interference direction and the non-matching target direction, respectively.

In this embodiment, the step S5 is specifically as follows:

The optimization problem (14) involves an optimization search of three coupled variables, namely the integer variable U _k of the radar-target assignment and the transmit and receive weight matrix Is a continuous value variable of (a). The optimization problem (14) is a high-dimensional non-convex optimization problem, since the forward nature of the second order gradient of the objective function cannot be guaranteed. Currently, shan Lei for optimal scheduling of array resources remains an open research problem. For the problem of optimizing and scheduling array resources of a multi-radar system, a feasible solution is difficult to find. In order to design a computationally feasible optimization method, the present embodiment decomposes the multiple variable coupling joint optimization problem of the optimization problem (14) into a three-stage iterative optimization process.

S51, fixing an isotropic receiving and transmitting beam pattern, and solving a radar-target allocation sub-optimization problem;

if the elements of the transmit and receive weight matrices of the co-located MIMO radar are averaged, then The representation, and the resulting transmit and receive beam patterns are isotropic.

The optimization problem in formula (14) can be translated into the following:

Wherein the radar-target allocation constraints are taken Then use/>Substitution/>The integer programming is converted to a semi-definite programming of continuous variables between 0 and 1.

However, this relaxation optimization problem remains a non-convex problem because PCRLB based on enumeration is non-convex. The solution of the relaxation problem (15) is a lower bound to the solution of the original problem (14) because the feasible set of relaxation problems contains the feasible set of original problems.

For the non-convex problem, a Zoutendijk feasible direction method (ZMFD) is adopted to realize a suboptimal scheme, and if all variables of radar-target allocation are integer solutions, the original problem is considered to be solved, and the algorithm is terminated. Otherwise, continuing to solve in the scoreThe element with the largest value is selected and set/>Until the beam resources of all the radars satisfy the constraint of equation (15).

Finally, a suboptimal radar-target allocation result is obtained

S52, according to the obtained radar-target distribution resultDeriving a convex approximation model of a non-convex optimization problem based on a first-order Taylor expansion convex approximation method, and sequentially solving a transmit-receive beam synthesis sub-optimization problem of each radar;

given the radar-target allocation results, it is still necessary to decompose and solve the transmit and receive weight matrices sequentially. Due to the high dimensionality of the multi-radar system array resource optimization problem, it is difficult to quickly and efficiently get a viable solution. In addition, the receiving and transmitting weight variables among different radars are not strongly coupled, so that the multi-radar beam synthesis optimization problem is decomposed into a plurality of single-radar beam synthesis optimization problems, and the method specifically comprises the following steps:

Wherein, Representing the transmit weight matrices of the remaining radars except for radar n, which may be the result of non-optimization, i.e./>May also be an optimized weight matrix/>

Since both the PCRLB and output filter energy constraints based on enumeration are non-convex, the sub-optimization problem (16) remains non-convex. The non-convex multiplier alternate direction method (NCADMM) can be used to solve the non-convex beam optimization problem because it can converge to the KKT point. However, the method is influenced by the penalty factor and the initialization value, and the convergence speed and the quality of the solution cannot be guaranteed.

Therefore, the first-order taylor expansion of the non-convex function is utilized to replace the original objective function and constraint, and the non-convex problem is solved iteratively. At the moment of obtaining the transmission weight matrix of all the selected radarsThe remaining receive beam pattern optimization sub-problem can then be expressed as:

Wherein, Representing the receive weight matrix of the remaining radars except radar n. Then, solving a receiving weight matrix/>, by adopting an iterative convex approximation method based on first-order Taylor expansion

Similar to the transmit beam pattern optimization problem (16), the objective function is also non-convex. Finally, solving a receiving weight matrix by adopting an iterative convex approximation method based on first-order Taylor expansion

S53, taking the minimum global multi-target tracking performance as a target, and obtaining a beam dynamic synthesis result based on the previous iterationAnd (3) solving a radar receiving and transmitting weight matrix by loop iteration until a loop stopping condition is met, and outputting a radar-target allocation and receiving and transmitting beam synthesis optimization result/>Then executing step S6, otherwise, continuing executing step S52;

wherein, the circulation stop conditional expression is as follows:

Wherein, Representing a jth round-robin global multi-target tracking objective function,Representing a suboptimal transmit-receive beam weight matrix obtained in a jth cycle; epsilon represents a preset threshold value for controlling the final tracking accuracy.

In this embodiment, the step S6 is specifically as follows:

In the tracking stage, if the array element of the radar n is calibrated, the mathematical expression of the transmit beam pattern is:

Where a _n (θ) represents the transmit steering vector, which depends on the geometry of the array. The expression a _n (θ) is as follows:

/>

Wherein f _c denotes the carrier frequency, Representing the delay of signal transmission from the nth _a antennas to the target q:

Where d=λ/2 denotes the spatial distance between the two antennas, λ denotes the wavelength, c denotes the speed of light, Representing the distance between radar n and target q.

The receive beam pattern mathematical expression of radar n is:

Wherein b _n(θ)＝a_n (θ) represents the received steering vector, an Representing the receive beam weight matrix for the b-th beam of radar n.

In this embodiment, the step S7 is specifically as follows:

in the interference suppression environment, the SINR of the target is the ratio of the target echo power to the interference power, and the calculation formula is as follows:

Where ρ _N,k represents the background noise power, The target echo power and the interference signal power received by the radar n are respectively represented by the following expressions:

Wherein, Representing the total transmit power of radar n,/>Representing the target RCS,/>Is the transmitting interference power of the jammer m,/>Is the polarization mismatch loss of the jammer m,/>Is the distance between radar n and jammer m.

In a suppressed interference environment, the radar examination azimuth and the signals in the range resolution unit are set to determine the presence of the target q. A test is set to detect the presence or absence of the qth object over the monitored area. The test expression is as follows:

Wherein, Representing the magnitude squared output of the matched filter. In the test equation (25), the setting H ₀ indicates that the target q is not present in the monitored area, and the echo is composed of only noise and interference signals. Setting H ₁ indicates that there is a target q in the monitored area and that the echo is a combination of noise, interference signal and target signal.

Taking SWERLING I-type targets as an example, according to the noman-pearson criterion, the probability expression of detection of target q by radar n is as follows:

/>

Where V _T represents the detection threshold.

In this embodiment, the step S8 is specifically as follows:

The set target motion model follows a linear Constant Velocity (CV) model expressed as:

Wherein F represents a target state transition matrix, Representing process noise, set to have covariance matrix/>Is a zero-mean gaussian noise of:

where T ₀ denotes the interval between two consecutive tracking frames, r _q denotes the intensity of process noise, and I ₂ denotes the identity matrix with dimension 2.

Under the hold-down interference, the radar collects/loses measurement data with a certain probability. The measured value of the q-th target acquired by the n-th radar is as follows:

Wherein, Representing measurement noise,/>The detection probability of the radar n to the target q is represented; h _n (·) represents a nonlinear function,/>And:

in this embodiment, the step S9 is specifically as follows:

Since Q _k targets are far apart and each transmit/receive beam is focused, the multi-target tracking task can be divided into multiple independent single-target tracking sub-tasks. The amount of measurement data collected by the radar system is uncertain in each frame. This is because under the suppression of interference, the radars are allocated to The probability of acquiring a measure of the target q is shown in equation (29).

Setting allocationThe q-th target is tracked by a radar, and the centralized measurement set of the q-th target in the fusion center can be expressed as:

Wherein, Representing the measured quantity of the target q at the fusion center; /(I)Represents the/>, of the target q at the fusion centerAnd (5) measuring.

Then, the posterior density of the target is calculated according to the bayesian rule, and the posterior density of the q-th target is set to be approximately gaussian as follows:

/>

Where N (x; m, B) represents a Gaussian distribution with a parameter of x, the mean value is m, and the covariance is B. Posterior Density The mean and covariance of (a) are:

Wherein, And/>Representing the mean and covariance of the predictions,/>Residual error representing Kalman gain and effective measurement, respectively,/>Representing a local approximation of the metrology function based on state prediction.

The state of the target q at time k can be estimated asThe global multi-target tracking result is/>

If the selected radar is affected by the hold-down disturbance, no valid measurements of target q can be collected (i.e) The prior probability density predicted at time k-1 is used to approximate the target posterior density as follows:

In the state prediction stage, the prior probability density is calculated by taking the target posterior density as prior information, namely:

Wherein,

And finally, taking one-step prediction of the global multi-target tracking result at the current moment in the formula (36) as priori information and priori detection information to guide networking MIMO radar beam forming multi-target cognitive tracking operation at the next moment.

The embodiment also provides two comparative resource scheduling strategies, namely a traditional multi-target cognitive tracking method (reference method 1) of the networking MIMO radar in a multi-beam mode, namely the co-located MIMO radar generates multi-focusing beams with controllable power to lock targets, but the synthesized beams do not generate nulls in the direction of an interference source. Another is a beam dynamic synthesis method (reference method 2) for near-range radar-target allocation and uniform gain beam dynamic synthesis, i.e., a beam dynamic synthesis method for near-pair radar-target relationship while generating nulls in the direction of the interferer.

Fig. 4-6 show graphs comparing tracking performance of the method of the present invention, a conventional multi-target cognitive tracking method, and a near range radar-target allocation and uniform gain beam dynamic synthesis method, respectively. Fig. 7 shows a comparison of detection probabilities for three strategies. As can be seen from fig. 4, in frame 17, frame 22 and frame 24, the tracking PCRLB of the three objects decreases from 60m to 40m, respectively, as the three objects move from region 2 to region 1, respectively. The method of the invention promotes all targets to reach the precision requirement, so that the performance precision of the multi-target tracking task is kept stable under the multi-source suppression interference. In addition, all root mean square error curves obtained by the method of the invention can approach the corresponding PCRLB in the whole tracking process. In connection with fig. 7, the target detection performance of the method of the present invention is significantly improved, and the target detection probability is kept at a high level, about 1. This clearly verifies the effectiveness of the proposed strategy of the present invention to perform multi-objective tracking tasks under multi-source suppression interference.

In the conventional multi-target cognitive tracking method of fig. 5, PCRLB of all targets cannot meet the corresponding tracking accuracy requirement because no nulls are generated in the interference direction to mitigate the impact of interference on target tracking. In particular, tracking PCRLB of the target 3 tends to diverge. And the detection probability of all targets obtained by the traditional multi-target cognitive tracking method is very low as the target tracking result is consistent. The detection probability of the final target 3 is always kept between 0.2 and 0.6.

In fig. 6, the target tracking PCRLB obtained by the near-range radar-target allocation and uniform gain beam dynamic synthesis method suppresses interference by beam synthesis with nulls, and finally shows a convergence trend. Compared with the traditional resource perception strategy, the short-range radar-target allocation and uniform gain beam pattern synthesis strategy has better detection performance on all targets, and the detection probability is about 0.6-0.8. However, PCRLB cannot meet the tracking accuracy requirement in the whole tracking process. In summary, compared with the traditional multi-target cognitive tracking method, the near range radar-target allocation and uniform gain beam dynamic synthesis method, the method provided by the invention has better detection performance and tracking precision under multi-source suppression interference.

Fig. 8 shows the radar-target allocation results achieved by the method of the present invention, and fig. 9-11 show the transmit and receive beam patterns for the 5 th, 15 th, and 25 th frames, respectively, of the selected radar. Wherein, fig. 9 (a) - (d) are transmit and receive beam patterns of selected radars numbered 9, 10, 11, and 12, respectively, in frame 5; FIGS. 10 (a) - (d) are transmit and receive beam patterns for selected radars numbered 3, 4, 10 and 11, respectively, in frame 15; fig. 11 (a) - (d) are transmit and receive beam patterns for selected radars numbered 4, 9, 10 and 12, respectively, in frame 25.

As can be seen from fig. 8, the radars 1 and 6-8 are rarely assigned target tracking tasks. The method is characterized in that the angles of the targets and the jammers are similar to those of the radars, so that main lobe interference can be effectively avoided when the radars are avoided during resource allocation, and the overall performance of multi-target tracking is improved. In addition, since each radar can track at most two targets, the number of radars selected per frame is also different, which is consistent with fig. 9-11. For each selected co-located MIMO radar, the optimized transmit and receive beams can adaptively aim the main lobe at a specified target direction. I.e. the power gain at azimuth angles of the specified target is significantly higher than at other azimuth angles. Therefore, the power resources can be concentrated on the target, so that the resource utilization rate is improved, and finally the task performance is improved. In addition, a null with a depth greater than y ^null = -60dB is formed at the angle of arrival of the jammer relative to the active radar, thereby mitigating the impact of the active radar from the squelch disturbance and enhancing the battlefield viability of the radar system. For the receive beam pattern, gain nulls are also formed in the direction of the radar mismatch target to avoid mutual interference between the radar signals.

In summary, the method provided by the invention accurately evaluates the target tracking performance under the suppression interference, realizes the dynamic synthesis of networking MIMO radar beams under the on-line multi-source suppression interference, rapidly and effectively obtains the networking MIMO radar multi-target cognitive tracking result, suppresses the influence of the suppression interference on the radar detection performance, and improves the multi-target tracking precision. Compared with the existing target tracking performance index, the tracking PCRLB deduced by the method considers the target detection condition at all moments, and the quantitative evaluation of the tracking performance is more accurate; compared with the existing multi-target cognitive tracking method, the method provided by the invention can reduce the influence of suppression interference on a radar system while increasing the target direction gain through the dynamic synthesis operation of the receiving and transmitting beam, so that the method can be well adapted to complex electromagnetic countermeasure environment, and effectively improve the target detection performance and multi-target tracking precision of the radar system; the method can realize the online multi-target cognitive tracking requirement, and the proposed three-stage iterative decoupling solving method can rapidly obtain the networking MIMO radar beam dynamic synthesis result under the multi-source suppression interference, so that the method can respond to the complex and changeable requirements in real time.

Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.

Claims (10)

1. A networking MIMO radar beam synthesis multi-target cognitive tracking method aiming at suppression interference comprises the following specific steps:

S1, initializing networking MIMO radar system parameters;

s2, constructing a target detection matrix according to target detection conditions at each tracking moment based on the predicted target state;

S3, deriving enumeration PCRLB based on the step S2;

S4, combining radar-target allocation resource constraint and receiving-transmitting beam synthesis constraint, designing a global multi-target tracking objective function based on a service quality frame, and constructing a networking MIMO radar beam synthesis multi-target cognitive tracking problem aiming at suppressing interference;

S5, solving a feasible solution of the networking MIMO radar beam synthesis multi-target cognitive tracking problem aiming at suppressing interference by using a three-stage iterative decoupling solving method while meeting radar-target allocation resources and receiving-transmitting beam synthesis constraints, and outputting a beam synthesis optimizing result;

s6, synthesizing a receiving and transmitting beam pattern of each radar according to the radar-target allocation and receiving and transmitting beam synthesis optimization result;

s7, calculating target SINR under suppression interference, and obtaining the probability of detecting each target by the radar system;

S8, acquiring a target state at the current moment according to a target state equation of the radar system, constructing a measurement equation under suppression interference by combining target detection probability, and acquiring target measurement at the current moment;

S9, based on a centralized fusion rule, a global multi-target tracking result is obtained through extended Kalman filtering, and the global multi-target tracking result at the current moment is used as priori information together with priori detection information to guide networking MIMO radar beam synthesis multi-target cognitive tracking operation at the next moment.

2. The method for multi-target cognitive tracking by combining networking MIMO radar beam synthesis for suppressing interference according to claim 1, wherein the step S1 is specifically as follows:

First, initializing networking MIMO radar system parameters, including:

Co-located MIMO radar position r ⁿ＝[xⁿ,yⁿ ], number N, number of transmit and receive array elements for each co-located MIMO radar N _a; at the kth tracking time, the number of beams B _n,k generated by each radar; number of targets Q _k, initial state of targets Target initial state bias obeys gaussian distribution/>Number M _k of supporting jammers, position of supporting jammers/>

Where q=1,..q _k denotes an index of a target, n=1,..n denotes an index of a radar,Representing the initial position of the target,/>Representing the initial speed of the target, (. Cndot.) ^T represents the transpose operation of the matrix,/>A process noise covariance representing a target q;

Then, the update time t _k =0 is initialized, the time index is denoted as k=0, and the state of the initialization target q is as follows Setting a Fisher Information Matrix (FIM)/>, at the initial timeSetting an initial time radar-target allocation variable/>And the transmit and receive patterns/>, of all radars

At the kth (k is greater than or equal to 1), for a scene of N radar tracking Q _k targets, the radar-target matching matrix expression is as follows:

Wherein, The b-th beam representing radar n is assigned to track target q; the kronecker symbol expression is as follows:

Then, the transmit-receive beam weight matrix of the N radars, that is, the transmit-receive beam pattern expression of the networking MIMO radar system is as follows:

Wherein, Representing the transmission pattern weight matrix of radar n,/>Representing a transmission pattern weight matrix of the N radars; /(I)A reception pattern weight matrix representing radar n,/>Representing a receive pattern weight matrix for N radars.

3. The method for multi-target cognitive tracking by combining networking MIMO radar beam synthesis for interference suppression according to claim 1, wherein the step S2 is as follows:

enumerating the detection condition of each radar to each target at all times (0, k) at the current time k (k is greater than or equal to 1), using an observable binary variable To describe whether the radar n detects the target q, the expression is as follows:

Wherein, Indicating that radar n detected target q,/>The radar N miss targets q are represented, and N radars form 2 ^kN detection matrixes at the moment k;

For the qth target, during the kth tracking frame, N binary variables may form i=2 ^kN target detection/omission matrices, where the ith matrix is:

Wherein, The detection condition of the radar n to the target q at the tracking moment k in the ith target detection/omission matrix is shown;

finally, obtaining a target detection matrix

4. The method for multi-target cognitive tracking by combining networking MIMO radar beam synthesis for suppressing interference according to claim 1, wherein the step S3 is specifically as follows:

Is provided with Representing target q based on measurement vector/>Target state/>Given a specific target detection/omission matrix/>The following inequality holds:

Wherein, Representation of target state/>And its related measurement/>Is/are the desired operator of (1)Expressed in matrixFIM, which is a condition, is specifically expressed as follows:

Wherein, FIM representing a priori information; /(I)Representing the state of the target q at the time k; b _n,k denotes the number of beams that radar n synthesizes at time k; /(I)As in formula (2), represents a beam selection identifier,/>Indicating that radar n is allocated to b-th beam tracking target q, otherwise,/> Data information FIM representing the radar n versus the target q; f represents a target state transition matrix,/>Representing a desired operation based on a target state,/>Representing a nonlinear measurement function/>Jacobian matrix of (a);

then condition PCRLB of the q-th target is expressed as condition FIM Is the inverse of (3):

Then according to the target detection probability at the current tracking moment Detection matrix/>The occurrence probability expression of (2) is:

finally, taking the expectation of equation (8) yields enumerated PCRLB:

5. The method for multi-target cognitive tracking by combining networking MIMO radar beam synthesis for suppressing interference according to claim 1, wherein the step S4 is specifically as follows:

using first PCRLB based on enumeration and following the quality of service framework, the overall utility function is designed, and then the task utility function design expression for the q-th objective is as follows:

Wherein, PCRLB,/>, representing a position estimate of the target qPCRLB matrix representing target q,/>Then the j-th diagonal element of the enumeration PCRLB matrix is represented,/>Representing the tracking performance requirement of the target q;

Then, summing utility functions of all target tracking tasks, and establishing a global multi-target tracking target function as follows:

Wherein, PCRLB set vectors representing all targets; eta _k represents the set of tracking performance requirements for all targets, and/>

The continuous domain of the angle theta epsilon [0,180 DEG ] of the observation area of the radar system is converted into a group of discrete angle grids, so that the angle space can be divided into B _n,k main lobe beam grids, M _k null grids and the rest C _s auxiliary lobe direction grids; the discrete angular grid of beams, nulls, and side lobes are represented as:

Wherein, Respectively representing the arrival angles of the main lobe and the side lobe directions,/>Representing the arrival angle of the jammer m direction at the radar n;

finally, the networking MIMO radar beam forming multi-target cognitive tracking problem for the suppressed interference can be expressed as:

Wherein, Representing the radar quantity allocated to the target q by the radar system at the moment k, and N _max represents the radar quantity of the radar system which is allocated to track the target q at most in each tracking interval; b _max denotes the number of beams that can be generated at maximum per radar due to the limitation of the antenna array capacity; b 'represents a b' th beam other than b; /(I)Representing the transmit beam pattern of radar n,/>Representing the transmitting gain of the radar n in the m direction of the jammer; /(I)Representing the trace of the covariance matrix of the transmitted signal, which is the transmitted power of the radar in the MIMO radar; (. ^H) represents a conjugate transpose operation of the matrix; gamma ^null denotes a gain threshold value of the null direction set in advance; /(I)A received beam pattern representing the b-th beam of radar n,/>Representing the receiving gain of the b-th beam of the radar n in the m direction of the jammer,/>Representing the receive gain of the b-th beam of radar n in the unmatched target q-direction.

6. The method for multi-target cognitive tracking by combining networking MIMO radar beam synthesis for suppressing interference according to claim 1, wherein the step S5 is specifically as follows:

s51, fixing an isotropic receiving and transmitting beam pattern, and solving a radar-target allocation sub-optimization problem;

if the elements of the transmit and receive weight matrices of the co-located MIMO radar are averaged, then Representing, and the resulting transmit and receive beam patterns are isotropic;

The optimization problem in formula (14) can be translated into the following:

Wherein the radar-target allocation constraints are taken Then use/>Substitution/>Converting the integer programming into a semi-definite programming of continuous variables between 0 and 1;

Then adopting Zoutendijk feasible direction method to implement suboptimal scheme, if all variables of radar-target allocation are integer solutions, then considering original problem to be solved, and stopping algorithm; otherwise, continuing to solve in the score Selecting the element with the largest value, settingUntil the beam resources of all the radars satisfy the constraint of equation (15);

Finally, a suboptimal radar-target allocation result is obtained

S52, according to the obtained radar-target distribution resultDeriving a convex approximation model of a non-convex optimization problem based on a first-order Taylor expansion convex approximation method, and sequentially solving a transmit-receive beam synthesis sub-optimization problem of each radar;

decomposing the multi-radar beam synthesis optimization problem into a plurality of single-radar beam synthesis optimization problems, wherein the method comprises the following steps of:

Wherein, Representing the transmit weight matrix of the remaining radars except for radar n, i.e. the un-optimized result/>Or an optimized weight matrix/>

Using a first-order Taylor expansion of the non-convex function to replace the original objective function and constraint, and iteratively solving the non-convex problem; at the moment of obtaining the transmission weight matrix of all the selected radarsThe remaining receive beam pattern optimization sub-problem can then be expressed as:

Wherein, Representing a receiving weight matrix of the other radars except the radar n; then, solving a receiving weight matrix/>, by adopting an iterative convex approximation method based on first-order Taylor expansion

S53, taking the minimum global multi-target tracking performance as a target, and obtaining a beam dynamic synthesis result based on the previous iterationAnd (3) solving a radar receiving and transmitting weight matrix by loop iteration until a loop stopping condition is met, and outputting a radar-target allocation and receiving and transmitting beam synthesis optimization result/>Then executing step S6, otherwise, continuing executing step S52;

wherein, the circulation stop conditional expression is as follows:

Wherein, Representing a jth round-robin global multi-target tracking objective function,Representing a suboptimal transmit-receive beam weight matrix obtained in a jth cycle; epsilon represents a preset threshold value for controlling the final tracking accuracy.

7. The method for multi-target cognitive tracking by combining networking MIMO radar beam synthesis for interference suppression according to claim 1, wherein the step S6 is specifically as follows:

In the tracking stage, if the array element of the radar n is calibrated, the mathematical expression of the transmit beam pattern is:

Where a _n (θ) represents the emission steering vector, which depends on the geometry of the array; the expression a _n (θ) is as follows:

Wherein f _c denotes the carrier frequency, Representing the delay of signal transmission from the nth _a antennas to the target q:

Where d=λ/2 denotes the spatial distance between the two antennas, λ denotes the wavelength, c denotes the speed of light, Representing the distance between radar n and target q;

The receive beam pattern mathematical expression of radar n is:

Wherein b _n(θ)＝a_n (θ) represents the received steering vector, an Representing the receive beam weight matrix for the b-th beam of radar n.

8. The method for multi-target cognitive tracking by combining networking MIMO radar beam synthesis for interference suppression according to claim 1, wherein the step S7 is specifically as follows:

in the interference suppression environment, the SINR of the target is the ratio of the target echo power to the interference power, and the calculation formula is as follows:

Where ρ _N,k represents the background noise power, The target echo power and the interference signal power received by the radar n are respectively represented by the following expressions:

Wherein, Representing the total transmit power of radar n,/>Representing the target RCS,/>Is the transmit interference power of the jammer m,Is the polarization mismatch loss of the jammer m,/>Is the distance between the radar n and the jammer m;

under the condition of suppressing interference, setting a radar checking azimuth angle and signals in a distance resolution unit to determine the existence of a target q; a check is set to detect the presence or absence of the qth object in the entire monitored area; the test expression is as follows:

Wherein, Representing the magnitude squared output of the matched filter; in the test formula (25), H ₀ is set to indicate that the target q is not present in the monitored area, and the echo is composed of only noise and interference signals; setting H ₁ to indicate that a target q exists in the monitoring area, and the echo is a combination of noise, interference signals and target signals;

according to the nomann-pearson criterion, the probability expression of detection of the target q by the radar n is as follows:

Where V _T represents the detection threshold.

9. The method for multi-target cognitive tracking by combining networking MIMO radar beam synthesis for suppressing interference according to claim 1, wherein the step S8 is specifically as follows:

The set target motion model follows a linear Constant Velocity (CV) model expressed as:

Wherein F represents a target state transition matrix, Representing process noise, set to have covariance matrix/>Is a zero-mean gaussian noise of:

Wherein T ₀ represents the interval between two consecutive tracking frames, r _q represents the intensity of process noise, I ₂ represents an identity matrix with dimension 2;

Under suppression interference, the radar acquires/loses measurement data with a certain probability; the measured value of the q-th target acquired by the n-th radar is as follows:

Wherein, Representing measurement noise,/>The detection probability of the radar n to the target q is represented; h _n (·) represents a nonlinear function,/>And:

10. The method for multi-target cognitive tracking by combining networking MIMO radar beam synthesis for suppressing interference according to claim 1, wherein the step S9 is specifically as follows:

Setting allocation The q-th target is tracked by a radar, and the centralized measurement set of the q-th target in the fusion center can be expressed as:

Wherein, Representing the measured quantity of the target q at the fusion center; /(I)Represents the/>, of the target q at the fusion centerMeasuring the number of the measurement units;

then, the posterior density of the target is calculated according to the bayesian rule, and the posterior density of the q-th target is set to be approximately gaussian as follows:

wherein, N (x; m, B) represents Gaussian distribution with parameter x, mean value is m, covariance is B; posterior Density The mean and covariance of (a) are:

Wherein, And/>Representing the mean and covariance of the predictions,/>Residual error representing Kalman gain and effective measurement, respectively,/>Representing a local approximation of the metrology function based on state prediction;

the state of the target q at time k can be estimated as The global multi-target tracking result is/>

If the selected radar is affected by the hold-down disturbance, no valid measurements of target q can be collected (i.e) The prior probability density predicted at time k-1 is used to approximate the target posterior density as follows:

In the state prediction stage, the prior probability density is calculated by taking the target posterior density as prior information, namely:

Wherein,

And finally, taking one-step prediction of the global multi-target tracking result at the current moment in the formula (36) as priori information and priori detection information to guide networking MIMO radar beam forming multi-target cognitive tracking operation at the next moment.