CN107728139B - Phased array radar networking system resource management method based on multi-target tracking - Google Patents

Phased array radar networking system resource management method based on multi-target tracking Download PDF

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CN107728139B
CN107728139B CN201710816710.5A CN201710816710A CN107728139B CN 107728139 B CN107728139 B CN 107728139B CN 201710816710 A CN201710816710 A CN 201710816710A CN 107728139 B CN107728139 B CN 107728139B
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CN107728139A (en
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易伟
王祥丽
付月
黎明
孔令讲
李雯
翟博文
袁野
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
    • G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
    • G01S13/726—Multiple target tracking
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0408—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas using two or more beams, i.e. beam diversity

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Abstract

The invention discloses a multi-target tracking-based phased array radar networking system resource management method, belongs to the technical field of phased array radar networking resource management, and relates to multi-target tracking. The method comprises the steps of firstly researching a topological structure between a radar network and a target, and analyzing the influence of different angles and space diversity gains of the multi-phased array radar network on the signal to noise ratio of an echo in a multi-beam working mode. And then, on the premise that the tracking precision of each target meets a preset requirement, the beam direction and the beam residence time of each radar are optimized, so that the total residence time of the radar networking beams for tracking is minimum. Due to the fact that the target position, the angle, the RCS and the radar networking space diversity gain are different, the requirement of each target on system resources for maintaining preset tracking precision is changed, and the problem that a plurality of targets cannot be effectively tracked is caused, and the purpose that the ordered tracking of a plurality of targets by a system is completed while resources are saved is achieved.

Description

Phased array radar networking system resource management method based on multi-target tracking
Technical Field
The invention belongs to the technical field of phased array radar networking resource management, and relates to multi-target tracking, and the research of a beam and dwell time resource joint management technology of a multi-radar system in a multi-target tracking mode.
Background
The phased array radar is an important radar widely researched and developed at present, and because the wave beam can be pointed at will and can be changed from microsecond to hundred microseconds in a short time, the phased array radar has the advantages of multiple functions, multiple targets, high self-adaptive capacity, great flexibility and the like. The phased array radar is combined with a computer control technology, and relevant working parameters and working modes of the radar can be adaptively changed to adapt to the external changing working environment, such as changing the shape of an antenna beam, the beam residence time, the power distribution and the like. Therefore, the management of phased array radar resources according to the external environment has wide research value.
In a target tracking and observation radar network including a plurality of phased array radars, there are resource management problems, in addition to a time resource management problem, a space resource (radar allocation) management problem, which is a so-called sensor allocation problem. Therefore, for the networking tracking system composed of phased array radars, the resource management problem includes not only the management of beam pointing and residence time, but also the correspondence problem between the sensor and the target (which radars track which targets). In the document 'multi-target tracking distributed MIMO radar transceiver station joint selection optimization algorithm, radar report, 2017,6(1): 73-80', an author constructs station selection as a Boolean programming problem, relaxes the Boolean programming problem into a semi-positive programming problem, and then obtains an approximate optimal solution of joint selection by using a block coordinate descent iteration method. In the document "Variable Dwell Time Task Scheduling for multifunctionality Radar, IEEE TASE,2014,11(2):463 and 472." after the residence Time is quantified based on tasks, an effective heuristic Scheduling method is provided, so that a Radar system can complete more tasks in a Time axis range, but the method aims at macroscopic Task management of the system and has an unobvious effect on the problem that multi-target tracking is completed by consuming less resources as much as possible.
Disclosure of Invention
The invention aims to research and design a multi-target tracking-based phased array radar networking resource management method aiming at the defects in the background art, and solves the problems that when a phased array radar networking tracks a plurality of targets in a multi-beam working mode, system resources are wasted and a plurality of targets cannot be effectively tracked due to the fact that the positions, angles, RCS and radar space diversity gains of the targets are different, and the requirements of the targets on phased array radar networking beams and residence time for maintaining preset tracking accuracy are changed.
The solution of the invention is: the method comprises the steps of firstly researching a topological structure between a radar network and a target, and analyzing the influence of different angles and space diversity gains of the multi-phased array radar network on the signal to noise ratio of an echo in a multi-beam working mode. And then, on the premise that the tracking precision of each target meets a preset requirement, the beam direction and the beam residence time of each radar are optimized, so that the total residence time of the radar networking beams for tracking is minimum. Aiming at the problem, a conversion algorithm is provided, the algorithm firstly gives a fixed residence time value to each target, selects a plurality of radars with rich data information to track the target, determines the beam direction, converts the original non-convex problem into a convex problem, and then distributes the residence time of each selected radar beam according to the preset tracking precision of each target, thereby finally realizing the distribution of the phased array radar networking system resources. And finally, tracking the multiple targets by the radar networking by adopting an extended Kalman filtering algorithm according to the target observation model. The method effectively solves the problem of the change of the demand of different targets on radar resources for maintaining the preset tracking threshold, thereby realizing reasonable matching between the system resources and the targets, and completing the ordered tracking of a plurality of targets while saving resources.
The invention provides a multi-target tracking-based phased array radar networking system resource management method, which comprises the following steps:
step 1: determining the topological structures and managed resource variables of the radar and the target;
a radar network consisting of M phased array radars, the M-th radar being located at (x)m,ym) M is 1,2, …, M, Q targets are widely distributed in a monitoring area, and the radar system tracks the targets, and each target is assumed to move at a constant speedThe initial position and velocity of the target q are respectively
Figure GDA0002620952850000021
And
Figure GDA0002620952850000022
then at the kth tracking instant the position and velocity of the target q are respectively
Figure GDA0002620952850000023
And
Figure GDA0002620952850000024
at time k, each radar may transmit BmA beam of waves having
Figure GDA0002620952850000025
Selecting a beam for target tracking, wherein each beam can only track one target at each tracking moment, and introducing a binary variable because whether the beam of the radar m is used for tracking the target q cannot be determined
Figure GDA0002620952850000026
Figure GDA0002620952850000027
In order to maintain the tracking of the target, at each tracking moment, the radar beam needs to transmit a certain amount of pulses to the target to acquire target information, and if the beam of the radar m at the moment k transmits a series of repeated cycles with a period of TpriA pulse signal, and
Figure GDA0002620952850000028
the pulse irradiates on the target q, and the residence time of the radar beam on the target is
Figure GDA0002620952850000029
Figure GDA00026209528500000210
Indicating the number of pulses, TpriThe pulse repetition period is represented, so that the beam pointing direction and the residence time of the radar system are controlled; thus, the managed resource variables are determined: 1. number of beams used for tracking per radar per time instant
Figure GDA00026209528500000211
2. How each target chooses which radar beam to illuminate from, 3. dwell time of beam illumination from different radars
Figure GDA00026209528500000212
Dividing;
step 2: establishing a resource optimization model;
the target q moves at a constant speed, and the state at the moment k is as follows:
Figure GDA00026209528500000213
then the dynamic equation and the target measurement equation from radar m are respectively:
Figure GDA0002620952850000031
wherein, FkRepresenting state transition matrix, process noise
Figure GDA0002620952850000032
Is a mean of zero and a variance of Qq,k-1White Gaussian noise of (1), measurement
Figure GDA0002620952850000033
Measuring noise for range and angle information of target and radar extracted from echo signal
Figure GDA0002620952850000034
Is zero mean and variance of
Figure GDA0002620952850000035
The white gaussian noise of (a) is,
Figure GDA0002620952850000036
representing a measurement and the variance is related to the echo signal-to-noise ratio;
for convenience of the following description, two sets of variables are defined, the beam selection variable Φ at time kk＝[Φ1,k,…,Φq,k,…,ΦQ,k]TAnd a dwell time variable Δ Tk＝[T1,k,…,Tq,k,…,TQ,k]TWherein
Figure GDA0002620952850000037
representing the illumination of the target q by all the radars,
Figure GDA0002620952850000038
representing the residence time of all radar pairs on the target q, the relationship is as follows:
Figure GDA0002620952850000039
the Bayes Cramer-Rao bound provides a lower bound for the minimum Mean Square Error (MSE) of the target state estimation, and has certain predictability; therefore, the bayesian clar-merome boundary is adopted as a criterion of tracking performance, and the expression is as follows:
Figure GDA00026209528500000310
Figure GDA00026209528500000311
representing the bayesian clarmeo bound,
Figure GDA00026209528500000312
representing target states
Figure GDA00026209528500000313
The bayesian information matrix of (a) is:
Figure GDA00026209528500000314
wherein,
Figure GDA00026209528500000315
a fisher information matrix representing the target prior information,
Figure GDA00026209528500000316
the fisher information matrix of data from radar m at time k for target q,
Figure GDA00026209528500000317
a Jacobian determinant representing target measurements versus target states;
Figure GDA00026209528500000318
the inverse of the measured variance is represented,
Figure GDA00026209528500000319
the mathematical expectation operation is expressed, because the diagonal elements of the target bayesian clar-merome boundary can reflect the lower bound of the estimation variance of each component of the target state vector, and the following formula is taken as the index of each target tracking precision:
Figure GDA00026209528500000320
wherein, CCRLB(1,1) and CCRLB(3,3) respectively representing a first component and a third component on a diagonal of the Bayesian Cramer-Lo boundary;
the optimization purpose is determined as follows: in a radar networking formed by phased array radars, radar beam pointing and beam residence time are reasonably distributed, and all target tracking accuracy is ensured to meet a preset requirement etaqMinimizing the dwell time of all beams for tracking; the objective function is thus
Figure GDA0002620952850000041
Combining beams
Figure GDA0002620952850000042
And residence time
Figure GDA0002620952850000043
Constraining, and establishing an optimization problem model as follows:
Figure GDA0002620952850000044
wherein: the first constraint represents that each target needs to meet its predetermined tracking accuracy ηq(ii) a The second constraint indicates that the beam variable is a binary variable consisting of 0 and 1; the third constraint represents the total number of beams used by the radar m for tracking at time k, considering that the radar beams are to perform not only tracking but also searching in the monitored area
Figure GDA00026209528500000413
Requiring less than the total number of beams B formed by the radarm(ii) a The fourth constraint indicates that if the predicted tracking performance of a target is good, beam irradiation from all radars may not be required to satisfy the predetermined tracking accuracy, and a subset of the radar numbers is needed, so the number of wave numbers L on the target q at time k isq,kNot greater than the total number M of radars; a fifth constraint indicates that the dwell time does not exist if the target is not illuminated by the beam; the sixth constraint indicates that the residence time exists, but it is not arbitrary and also requires that an upper and lower bound be satisfied, the upper bound being
Figure GDA0002620952850000045
Lower boundary is
Figure GDA0002620952850000046
The seventh constraint represents an upper time limit for tracking for each radar of
Figure GDA0002620952850000047
And step 3: a beam and residence time distribution strategy of the radar networking is provided, beam pointing is distributed based on radar data information, and then resource distribution is realized according to an algorithm for distributing residence time based on an optimization theory to obtain a distribution result;
step 3.1: time k, in order to represent the respective radar data information
Figure GDA0002620952850000048
Given a fixed time within a constraint range for each radar beam, i.e. assuming
Figure GDA0002620952850000049
Data information from each radar for target q is calculated
Figure GDA00026209528500000410
Then, the matrix is obtained
Figure GDA00026209528500000411
Trace of
Figure GDA00026209528500000412
Figure GDA0002620952850000051
Wherein: tr [. to]Indicating an operation of determining a trace of a matrix
Figure GDA0002620952850000052
And to
Figure GDA0002620952850000053
The elements of (2) are sorted from large to small, and the classification result is as follows:
Figure GDA0002620952850000054
wherein:
Figure GDA0002620952850000055
representing trace ordering results and each resultIn the position of Iq,kIndicating the location of each result;
Figure GDA0002620952850000056
representing a sort operation;
step 3.2: let the number L of wave numbers on the target q at time k q,k0, for i-1, 2, … M,
step 3.2.1,
Figure GDA0002620952850000057
Wherein, Iq,k(i) Representation matrix Iq,kThe (c) th variable of (a),
Figure GDA0002620952850000058
denotes a dwell time of TfixFrom radar I on time target qq,k(i) The fischer information matrix of the data of (a),
Figure GDA0002620952850000059
representing the sum of bayesian information matrices from i radars on target q,
Figure GDA00026209528500000510
denotes a dwell time of TfixThe bayesian cramer-pero boundary on the time target q,
Figure GDA00026209528500000511
denotes a dwell time of TfixTracking performance index of the time target q;
step 3.2.2, mixing
Figure GDA00026209528500000512
And a tracking threshold ηqIn contrast, if
Figure GDA00026209528500000513
Then
Figure GDA00026209528500000514
Returning to the step 3.2.1; up to
Figure GDA00026209528500000515
Or i reaches M, and the cycle stops;
step 3.2.3, mixing
Figure GDA00026209528500000516
And a tracking threshold ηqIn contrast, if
Figure GDA00026209528500000517
Then
Figure GDA00026209528500000518
Returning to the step 3.2.1; up to
Figure GDA00026209528500000519
Or i reaches M, the cycle stops, the size of i at the moment is recorded, and L is enabledq,k＝i；
Step 3.3: for each radar M being 1,2, …, M, the total beam amount used for tracking by each radar at the moment is calculated
Figure GDA00026209528500000520
If it is
Figure GDA00026209528500000521
Then this time
Figure GDA00026209528500000522
Counting the total beam quantity L of each targetq,kObtaining the data from radar I on target qq,k(i) Beam selection result of (2):
Figure GDA00026209528500000523
wherein Iq,k(1:Lq,k) Representation matrix Iq,kFront L ofq,kA variable;
obtaining a wave beam selection result phi from all radars on the target q at the moment k through the steps 3.1-3.3q,k，Φq,kRepresenting the beam selection results from all radars on target q, is a plurality of scalars
Figure GDA0002620952850000061
A vector of components and having Lq,kEach beam is selected to track target q, for Φq,kSequencing to obtain sequenced beam variable gammaq,k：
[Υq,k]＝sort(Φq,k,'descend′) (10)
The beam on the final target q can be written as:
Figure GDA0002620952850000062
and only Lq,kThe individual beams need to illuminate the target q, so the Bayesian information matrix can be written as
Figure GDA0002620952850000063
Wherein:
Figure GDA0002620952850000064
representing the origin from radar I on target qq,k(i) Beam dwell time of (a);
when the beam allocation is complete, the optimization problem (6) is transformed into the following form:
Figure GDA0002620952850000065
solving the formula (12) by a gradient projection method to obtain residence time distribution delta Tk(ii) a Although the residence time value obtained by the method is optimal, the value is any value between the upper limit and the lower limit, and the residence time is
Figure GDA0002620952850000066
Can only be an integer multiple of the pulse repetition period, so by rounding off, the dwell time is approximated as an integer multiple of the pulse repetition period, denoted
Figure GDA0002620952850000067
Finally, the multi-radar system wave beam and residence time distribution result based on multi-target tracking at each tracking moment is obtained
Figure GDA0002620952850000068
The invention provides a multi-target tracking-based phased array radar networking resource management method, which is used for analyzing the influence of different angles and space diversity gains on echo signal-to-noise ratios of different targets in a multi-beam working mode of a multi-phased array radar networking. Then, an optimization problem which ensures the tracking precision of each target and simultaneously reduces the resource consumption of a phased array radar networking system is established, aiming at the target, a fixed residence time value is given to each target, a plurality of radars with rich data information are selected to track the target, a conversion algorithm which is used for converting the original non-convex problem into the convex problem after the beam pointing direction is established, then the residence time of each selected radar beam is distributed according to the preset tracking precision of each target, the distribution algorithm of the phased array radar networking system resources is finally realized, and finally, the tracking of the phased array radar networking system on multiple targets is realized by adopting an extended Kalman filtering algorithm according to a target observation model. The method has the advantages of effectively solving the problem that when a plurality of radars execute a plurality of tracking tasks, due to different target positions, angles, RCS and radar networking space diversity gains, the requirement of each target on system resources for maintaining preset tracking precision is changed, so that a plurality of targets cannot be effectively tracked, and realizing the ordered tracking of the system on the plurality of targets while saving the resources.
Drawings
Fig. 1 is a flow chart of radar networking beam and dwell time joint management based on multi-target tracking.
Fig. 2 is a schematic diagram of a multi-beam operating mode of a multi-radar system.
FIG. 3 is a plot of target track versus radar position.
Fig. 4 is the number of pulses on target 1 for each radar.
Fig. 5 is the number of pulses on the target 2 for each radar.
Fig. 6 is the number of pulses on the target 3 for each radar.
Fig. 7 is the number of pulses on the target 4 for each radar.
Fig. 8 is the time each radar is used for tracking.
FIG. 9 is a comparison of total trace consumption times based on the methods herein and a traditional greedy algorithm.
Detailed Description
The following presents a specific embodiment of the present invention in terms of a MATLAB simulation example.
Since the number of pulses is directly proportional to the beam dwell time, the present invention will reflect the dwell time in terms of the number of pulses.
Step 1: studying the topology of radar and target and establishing the variables of the managed resources
The system parameters are initialized, given radar position and target initial state as shown in tables 1 and 2, respectively. Selecting a beam pointing phi in view of operabilitykAnd a residence time Δ TkIs a variable of the current resource management.
TABLE 1 radar position
Figure GDA0002620952850000071
TABLE 2 target initial State
Figure GDA0002620952850000072
Step 2: establishment of resource optimization model
And (3) introducing a Bayesian Claritrol bound, deriving a tracking accuracy criterion formula (5) according to the Bayesian Claritrol bound, and establishing an optimization problem by combining beam and dwell time constraints as shown in a formula (6).
And step 3: providing a beam and residence time distribution strategy of the radar networking system to obtain a distribution result
Giving resource optimization model parameters: pulse repetitionPeriod Tpri1ms, transmission power Pav＝2e4w, total time for tracking per tracking time TtrackConstraint of beam dwell time 0.005T, 0.4strack≤ΔTq,k≤0.9TtrackD, tracking threshold eta1:Q＝[0.027,0.027,0.027,0.027]TAnd the noise of the target process is consistent in the tracking process. Obtaining a resource allocation result according to the proposed beam selection and dwell time allocation algorithm
Figure GDA0002620952850000081
Fig. 4, 5, 6 and 7 are beam and dwell allocation results for targets 1,2, 3 and 4, respectively. Fig. 8 is the total time consumption of each radar in this tracking. By showing the effectiveness of the invention, a traditional greedy algorithm is compared with the method provided by the invention, and the time consumption graph for tracking the two methods is shown in fig. 9, so that the method provided by the invention saves more resources, and saves about 25% of resources compared with the greedy algorithm.
Step four: method for realizing multi-target tracking by adopting extended Kalman filtering algorithm
Allocating the resource to the result
Figure GDA0002620952850000082
And substituting the target dynamic model and the measurement model (2) to obtain a measurement noise covariance and an echo signal-to-noise ratio, and then obtaining the state estimation of the target according to the prediction and update processes of target tracking. The actual and estimated trajectories of the target are shown in fig. 3.
According to the specific implementation mode of the invention, compared with the greedy algorithm for allocating resources, the method can reduce the resource consumption of the phased array radar system for tracking tasks on the premise of ensuring the tracking precision of all targets, and approximately saves 25% of resources.

Claims (1)

1. A multi-target tracking based resource management method for a phased array radar networking system comprises the following steps:
step 1: determining the topological structures and managed resource variables of the radar and the target;
a radar network consisting of M phased array radars, the M-th radar being located at (x)m,ym) M is 1,2, …, M, Q targets are widely distributed in a monitoring area, the radar system tracks the targets, and assuming that each target moves at a constant speed, the initial position and the speed of the target Q are respectively
Figure FDA0002620952840000011
And
Figure FDA0002620952840000012
q is 1, …, Q, and at the kth tracking time, the position and velocity of the target Q are respectively
Figure FDA0002620952840000013
And
Figure FDA0002620952840000014
at time k, each radar may transmit BmA beam of waves having
Figure FDA0002620952840000015
Selecting a beam for target tracking, wherein each beam can only track one target at each tracking moment, and introducing a binary variable because whether the beam of the radar m is used for tracking the target q cannot be determined
Figure FDA0002620952840000016
Figure FDA0002620952840000017
In order to maintain the tracking of the target, at each tracking moment, the radar beam needs to transmit a certain amount of pulses to the target to acquire target information, and if the beam of the radar m at the moment k transmits a series of repeated cycles with a period of TpriPulse of lightA signal, and is provided with
Figure FDA0002620952840000018
The pulse irradiates on the target q, and the residence time of the radar beam on the target is
Figure FDA0002620952840000019
Figure FDA00026209528400000110
Indicating the number of pulses, TpriThe pulse repetition period is represented, so that the beam pointing direction and the residence time of the radar system are controlled; thus, the managed resource variables are determined: 1. number of beams used for tracking per radar per time instant
Figure FDA00026209528400000111
2. How each target chooses which radar beam to illuminate from, 3. dwell time of beam illumination from different radars
Figure FDA00026209528400000112
Dividing;
step 2: establishing a resource optimization model;
the target q moves at a constant speed, and the state at the moment k is as follows:
Figure FDA00026209528400000113
then the dynamic equation and the target measurement equation from radar m are respectively:
Figure FDA00026209528400000114
wherein, FkRepresenting state transition matrix, process noise
Figure FDA00026209528400000115
Is a mean of zero and a variance of Qq,k-1White Gaussian noise of (1), measurement
Figure FDA00026209528400000116
Measuring noise for range and angle information of target and radar extracted from echo signal
Figure FDA00026209528400000117
Is zero mean and variance of
Figure FDA00026209528400000118
The white gaussian noise of (a) is,
Figure FDA00026209528400000119
representing a measurement and the variance is related to the echo signal-to-noise ratio;
for convenience of the following description, two sets of variables are defined, the beam selection variable Φ at time kk＝[Φ1,k,…,Φq,k,…,ΦQ,k]TAnd a dwell time variable Δ Tk＝[T1,k,…,Tq,k,…,TQ,k]TWherein
Figure FDA00026209528400000120
representing the illumination of the target q by all the radars,
Figure FDA0002620952840000021
representing the residence time of all radar pairs on the target q, the relationship is as follows:
Figure FDA0002620952840000022
the Bayes Cramer-Rao bound provides a lower bound for the minimum Mean Square Error (MSE) of the target state estimation, and has certain predictability; therefore, the bayesian clar-merome boundary is adopted as a criterion of tracking performance, and the expression is as follows:
Figure FDA0002620952840000023
Figure FDA0002620952840000024
representing the bayesian clarmeo bound,
Figure FDA0002620952840000025
representing target states
Figure FDA0002620952840000026
The bayesian information matrix of (a) is:
Figure FDA0002620952840000027
wherein,
Figure FDA0002620952840000028
a fisher information matrix representing the target prior information,
Figure FDA0002620952840000029
the fisher information matrix of data from radar m at time k for target q,
Figure FDA00026209528400000210
a Jacobian determinant representing target measurements versus target states;
Figure FDA00026209528400000211
the inverse of the measured variance is represented,
Figure FDA00026209528400000212
the mathematical expectation operation is expressed, because the diagonal elements of the target bayesian clar-merome boundary can reflect the lower bound of the estimation variance of each component of the target state vector, and the following formula is taken as the index of each target tracking precision:
Figure FDA00026209528400000213
wherein, CCRLB(1,1) and CCRLB(3,3) respectively representing a first component and a third component on a diagonal of the Bayesian Cramer-Lo boundary;
the optimization purpose is determined as follows: in a radar networking formed by phased array radars, radar beam pointing and beam residence time are reasonably distributed, and all target tracking accuracy is ensured to meet a preset requirement etaqMinimizing the dwell time of all beams for tracking; the objective function is thus
Figure FDA00026209528400000214
Combining beams
Figure FDA00026209528400000215
And residence time
Figure FDA00026209528400000216
Constraining, and establishing an optimization problem model as follows:
Figure FDA0002620952840000031
wherein: the first constraint represents that each target needs to meet its predetermined tracking accuracy ηq(ii) a The second constraint indicates that the beam variable is a binary variable consisting of 0 and 1; the third constraint represents the total number of beams used by the radar m for tracking at time k, considering that the radar beams are to perform not only tracking but also searching in the monitored area
Figure FDA00026209528400000313
Requiring less than the total number of beams B formed by the radarm(ii) a The fourth constraint indicates that if the predicted tracking performance of a target is better, it may not require beam shots from all radars for it to meet the predetermined tracking accuracy, since one subset of the number of radars is neededHere, the number of wave numbers L on the target q at the time kq,kNot greater than the total number M of radars; a fifth constraint indicates that the dwell time does not exist if the target is not illuminated by the beam; the sixth constraint indicates that the residence time exists, but it is not arbitrary and also requires that an upper and lower bound be satisfied, the upper bound being
Figure FDA0002620952840000032
Lower boundary is
Figure FDA0002620952840000033
The seventh constraint represents an upper time limit for tracking for each radar of
Figure FDA0002620952840000034
And step 3: a beam and residence time distribution strategy of the radar networking is provided, beam pointing is distributed based on radar data information, and then resource distribution is realized according to an algorithm for distributing residence time based on an optimization theory to obtain a distribution result;
step 3.1: time k, in order to represent the respective radar data information
Figure FDA0002620952840000035
Given a fixed time within a constraint range for each radar beam, i.e. assuming
Figure FDA0002620952840000036
Data information from each radar for target q is calculated
Figure FDA0002620952840000037
Then, the matrix is obtained
Figure FDA0002620952840000038
Trace of
Figure FDA0002620952840000039
Figure FDA00026209528400000310
Wherein: tr [. to]Indicating an operation of determining a trace of a matrix
Figure FDA00026209528400000311
And to
Figure FDA00026209528400000312
The elements of (2) are sorted from large to small, and the classification result is as follows:
Figure FDA0002620952840000041
wherein:
Figure FDA0002620952840000042
indicating the trace-ordering results and where each result is located, Iq,kIndicating the location of each result;
Figure FDA0002620952840000043
representing a sort operation;
step 3.2: let the number L of wave numbers on the target q at time kq,k0, for i-1, 2, … M,
step 3.2.1,
Figure FDA0002620952840000044
Wherein, Iq,k(i) Representation matrix Iq,kThe (c) th variable of (a),
Figure FDA0002620952840000045
denotes a dwell time of TfixFrom radar I on time target qq,k(i) The fischer information matrix of the data of (a),
Figure FDA0002620952840000046
representing the sum of bayesian information matrices from i radars on target q,
Figure FDA0002620952840000047
denotes a dwell time of TfixThe bayesian cramer-pero boundary on the time target q,
Figure FDA0002620952840000048
denotes a dwell time of TfixTracking performance index of the time target q;
step 3.2.2, mixing
Figure FDA0002620952840000049
And a tracking threshold ηqIn contrast, if
Figure FDA00026209528400000410
Then
Figure FDA00026209528400000411
Returning to the step 3.2.1; up to
Figure FDA00026209528400000412
Or i reaches M, and the cycle stops;
step 3.2.3, mixing
Figure FDA00026209528400000413
And a tracking threshold ηqIn contrast, if
Figure FDA00026209528400000414
Then
Figure FDA00026209528400000415
Returning to the step 3.2.1; up to
Figure FDA00026209528400000416
Or i reaches M, the cycle stops, recording i at that timeSize, order Lq,k＝i；
Step 3.3: for each radar M being 1,2, …, M, the total beam amount used for tracking by each radar at the moment is calculated
Figure FDA00026209528400000417
If it is
Figure FDA00026209528400000418
Then this time
Figure FDA00026209528400000419
Counting the total beam quantity L of each targetq,kObtaining the data from radar I on target qq,k(i) Beam selection result of (2):
Figure FDA00026209528400000420
wherein Iq,k(1:Lq,k) Representation matrix Iq,kFront L ofq,kA variable;
obtaining a wave beam selection result phi from all radars on the target q at the moment k through the steps 3.1-3.3q,k，Φq,kRepresenting the beam selection results from all radars on target q, is a plurality of scalars
Figure FDA00026209528400000421
A vector of components and having Lq,kEach beam is selected to track target q, for Φq,kSequencing to obtain sequenced beam variable gammaq,k：
[Υq,k]＝sort(Φq,k,'descend′) (10)
The beam on the final target q can be written as:
Figure FDA0002620952840000051
and only Lq,kThe individual beams need to illuminate the target q, so the Bayesian information matrix can be written as
Figure FDA0002620952840000052
Wherein:
Figure FDA0002620952840000053
representing the origin from radar I on target qq,k(i) Beam dwell time of (a);
when the beam allocation is complete, the optimization problem (6) is transformed into the following form:
Figure FDA0002620952840000054
solving the formula (12) by a gradient projection method to obtain residence time distribution delta Tk(ii) a Although the residence time value obtained by the method is optimal, the value is any value between the upper limit and the lower limit, and the residence time is
Figure FDA0002620952840000055
Can only be an integer multiple of the pulse repetition period, so by rounding off, the dwell time is approximated as an integer multiple of the pulse repetition period, denoted
Figure FDA0002620952840000056
Finally, the multi-radar system wave beam and residence time distribution result based on multi-target tracking at each tracking moment is obtained
Figure FDA0002620952840000057
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