CN110412534B - Networking radar multi-target tracking residence time optimization method based on radio frequency stealth - Google Patents

Networking radar multi-target tracking residence time optimization method based on radio frequency stealth Download PDF

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CN110412534B
CN110412534B CN201910728893.4A CN201910728893A CN110412534B CN 110412534 B CN110412534 B CN 110412534B CN 201910728893 A CN201910728893 A CN 201910728893A CN 110412534 B CN110412534 B CN 110412534B
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时晨光
仇伟
汪飞
李海林
周建江
夏伟杰
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Nanjing University of Aeronautics and Astronautics
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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
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/415—Identification of targets based on measurements of movement associated with the target
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention discloses a multi-target tracking residence time optimization method for a networking radar based on radio frequency stealth, which comprises the steps of constructing a Bayesian-Lame lower bound of a target state estimation error by taking a radar binary selection variable, radar residence time and transmitted signal bandwidth as independent variables, and taking the Bayesian-Lame lower bound as a measurement index of target tracking accuracy; on the basis, the prediction tracking precision of the target at the following moment, the data processing amount of the fusion center and the radar emission resource are taken as constraint conditions, the total residence time of the minimized networking radar system is taken as an optimization target, and parameters such as radar selection, residence time, emission signal bandwidth and the like in the multi-target tracking process are optimally designed. Therefore, the tracking precision of each target in the multi-target tracking process is met, the total residence time of the networking radar system is reduced to the maximum extent, and the radio frequency stealth performance of the networking radar system during multi-target tracking is improved.

Description

基于射频隐身的组网雷达多目标跟踪驻留时间优化方法Optimization method of dwell time for multi-target tracking in networked radar based on radio frequency stealth

技术领域Technical Field

本发明涉及雷达信号处理领域，特别是涉及基于射频隐身的组网雷达多目标跟踪驻留时间优化方法。The present invention relates to the field of radar signal processing, and in particular to a method for optimizing the dwell time of multi-target tracking of a networked radar based on radio frequency stealth.

背景技术Background Art

在现代电子战中，为了提高组网雷达系统的射频隐身性能，雷达辐射参数优化设计已得到了广泛关注。对于组网雷达系统而言，其发射参数动态可控，因此，可通过优化设计雷达发射参数来改善系统的目标探测跟踪能力，并提高组网雷达的射频隐身性能。从时间资源角度出发，减小各雷达发射波束在目标上的驻留时间是提高组网雷达系统射频隐身性能的重要措施。In modern electronic warfare, in order to improve the RF stealth performance of networked radar systems, the optimization design of radar radiation parameters has received extensive attention. For networked radar systems, their transmission parameters are dynamically controllable. Therefore, the target detection and tracking capability of the system can be improved by optimizing the design of radar transmission parameters, and the RF stealth performance of networked radars can be improved. From the perspective of time resources, reducing the residence time of each radar transmission beam on the target is an important measure to improve the RF stealth performance of networked radar systems.

然而，已有的研究成果虽然涉及组网雷达系统目标跟踪时的驻留时间优化问题，在保证给定目标跟踪精度以及雷达发射资源的条件下，对雷达选择、驻留时间进行联合优化设计，在一定程度上提升了组网雷达目标跟踪时的射频隐身性能。然而，已有研究成果都只针对单目标跟踪场景，且未考虑发射信号带宽对总驻留时间的影响，具有一定的局限性。However, although existing research results involve the optimization of dwell time during target tracking in a networked radar system, the radar selection and dwell time are jointly optimized under the conditions of ensuring given target tracking accuracy and radar transmission resources, which improves the RF stealth performance of networked radar target tracking to a certain extent. However, existing research results are only for single target tracking scenarios, and do not consider the impact of the transmission signal bandwidth on the total dwell time, which has certain limitations.

发明内容Summary of the invention

发明目的：本发明的目的是提供一种基于射频隐身的组网雷达多目标跟踪驻留时间优化方法，能够解决现有技术中存在的“只针对单目标跟踪场景，且未考虑发射信号带宽对总驻留时间的影响，具有一定的局限性”的技术问题。Purpose of the invention: The purpose of the present invention is to provide a method for optimizing the dwell time of multi-target tracking of a networked radar based on radio frequency stealth, which can solve the technical problem existing in the prior art that "it only targets single target tracking scenarios, and does not consider the influence of the transmission signal bandwidth on the total dwell time, and has certain limitations".

技术方案：本发明所述的基于射频隐身的组网雷达多目标跟踪驻留时间优化方法，包括以下步骤：Technical solution: The method for optimizing the dwell time of multi-target tracking of networked radar based on radio frequency stealth of the present invention comprises the following steps:

S1：针对组网雷达系统构建以雷达二元选择变量、雷达驻留时间和发射信号带宽为自变量的用于预测目标状态估计误差的贝叶斯克拉美-罗下界矩阵，将所述贝叶斯克拉美-罗下界矩阵作为目标跟踪精度的衡量指标；所述组网雷达系统包括N部两坐标相控阵雷达，所有雷达的空间、时间和频率都同步，在对多目标进行跟踪时，每部雷达只能接收并处理来自自身发射信号的目标回波，并且每个时刻每部雷达最多只能跟踪一个目标；S1: A Bayesian Cramer-Rao lower bound matrix for predicting target state estimation error is constructed for a networked radar system with radar binary selection variables, radar dwell time and transmission signal bandwidth as independent variables, and the Bayesian Cramer-Rao lower bound matrix is used as a measure of target tracking accuracy; the networked radar system includes N two-coordinate phased array radars, all of which are synchronized in space, time and frequency. When tracking multiple targets, each radar can only receive and process target echoes from its own transmission signal, and each radar can only track one target at most at each moment;

S2：以下一时刻目标的预测跟踪精度、融合中心的数据处理量和雷达发射资源为约束条件，以最小化组网雷达系统的总驻留时间为优化目标，建立基于射频隐身的组网雷达多目标跟踪驻留时间优化模型；S2: Taking the predicted tracking accuracy of the target at the next moment, the data processing capacity of the fusion center and the radar transmission resources as constraints, and minimizing the total dwell time of the networked radar system as the optimization goal, a networked radar multi-target tracking dwell time optimization model based on RF stealth is established;

S3：对所述组网雷达多目标跟踪驻留时间优化模型进行求解。S3: Solving the optimization model of the dwell time of multi-target tracking of the networked radar.

进一步，所述步骤S1中的贝叶斯克拉美-罗下界矩阵根据式(1)得到：Further, the Bayesian Cramer-Rao lower bound matrix in step S1 is obtained according to formula (1):

Figure BDA0002159858160000021
Figure BDA0002159858160000021

式(1)中，

Figure BDA0002159858160000022
为第k个时刻、第q个目标的贝叶斯克拉美-罗下界矩阵，
Figure BDA0002159858160000023
为第k个时刻、第q个目标的预测贝叶斯信息矩阵；
Figure BDA0002159858160000024
为第k个时刻、第q个目标的预测状态向量，其中
Figure BDA0002159858160000025
为第k个时刻、第q个目标的预测位置，
Figure BDA0002159858160000026
为第k个时刻、第q个目标的预测位置的横坐标，
Figure BDA0002159858160000027
为第k个时刻、第q个目标的预测位置的纵坐标，
Figure BDA0002159858160000028
为第k个时刻、第q个目标的预测运动速度，
Figure BDA0002159858160000029
为第k个时刻、第q个目标的预测运动速度的横坐标分量，
Figure BDA00021598581600000210
为第k个时刻、第q个目标的预测运动速度的纵坐标分量；Wq为第q个目标过程噪声的方差，F为目标状态转移矩阵，
Figure BDA00021598581600000211
为第k-1个时刻、第q个目标的贝叶斯信息矩阵，
Figure BDA00021598581600000212
为第k个时刻、第q个目标的状态向量；
Figure BDA00021598581600000213
为第k个时刻、第i个雷达的雷达二元选择变量，
Figure BDA00021598581600000214
时表示第k个时刻、第i个雷达对第q个目标进行照射，
Figure BDA00021598581600000215
时表示第k个时刻、第i个雷达不对第q个目标进行照射；
Figure BDA00021598581600000216
为
Figure BDA00021598581600000217
的雅克比矩阵，
Figure BDA00021598581600000218
为第k个时刻、第i个雷达对第q个目标的非线性量测函数，N为雷达的总数，
Figure BDA00021598581600000219
为第k个时刻、第i个雷达对第q个目标的量测噪声的预测协方差矩阵。In formula (1),
Figure BDA0002159858160000022
is the Bayesian Cramer-Rao lower bound matrix for the k-th moment and the q-th target,
Figure BDA0002159858160000023
is the predicted Bayesian information matrix of the k-th moment and the q-th target;
Figure BDA0002159858160000024
is the predicted state vector of the kth moment and the qth target, where
Figure BDA0002159858160000025
is the predicted position of the qth target at the kth moment,
Figure BDA0002159858160000026
is the horizontal coordinate of the predicted position of the qth target at the kth moment,
Figure BDA0002159858160000027
is the ordinate of the predicted position of the qth target at the kth moment,
Figure BDA0002159858160000028
is the predicted motion speed of the qth target at the kth moment,
Figure BDA0002159858160000029
is the horizontal coordinate component of the predicted motion speed of the qth target at the kth moment,
Figure BDA00021598581600000210
is the ordinate component of the predicted motion speed of the qth target at the kth moment; Wq is the variance of the qth target process noise, F is the target state transfer matrix,
Figure BDA00021598581600000211
is the Bayesian information matrix of the k-1th moment and the qth target,
Figure BDA00021598581600000212
is the state vector of the kth moment and the qth target;
Figure BDA00021598581600000213
is the radar binary selection variable for the i-th radar at the k-th moment,
Figure BDA00021598581600000214
When means that at the kth moment, the i-th radar illuminates the q-th target,
Figure BDA00021598581600000215
When means that at the kth moment, the i-th radar does not illuminate the q-th target;
Figure BDA00021598581600000216
for
Figure BDA00021598581600000217
The Jacobian matrix of
Figure BDA00021598581600000218
is the nonlinear measurement function of the ith radar to the qth target at the kth moment, N is the total number of radars,
Figure BDA00021598581600000219
is the predicted covariance matrix of the measurement noise of the ith radar on the qth target at the kth moment.

进一步，所述式(1)中，Wq通过式(2)得到：Furthermore, in the formula (1), Wq is obtained by formula (2):

Figure BDA0002159858160000031
Figure BDA0002159858160000031

式(2)中，

Figure BDA0002159858160000032
为第q个目标的过程噪声强度，T为目标跟踪采样间隔。In formula (2),
Figure BDA0002159858160000032
is the process noise intensity of the qth target, and T is the target tracking sampling interval.

进一步，所述式(1)中，

Figure BDA0002159858160000033
通过式(3)得到：Furthermore, in the formula (1),
Figure BDA0002159858160000033
Through formula (3), we can get:

Figure BDA0002159858160000034
Figure BDA0002159858160000034

式(3)中，

Figure BDA0002159858160000035
为第k个时刻、第q个目标的先验信息的预测Fisher信息矩阵，
Figure BDA0002159858160000036
为第k个时刻、第i个雷达对第q个目标的量测数据的Fisher信息矩阵。In formula (3),
Figure BDA0002159858160000035
is the predicted Fisher information matrix of the prior information of the k-th moment and the q-th target,
Figure BDA0002159858160000036
is the Fisher information matrix of the measurement data of the qth target by the ith radar at the kth moment.

进一步，所述

Figure BDA0002159858160000037
通过式(4)得到：Further, the
Figure BDA0002159858160000037
Through formula (4), we can get:

Figure BDA0002159858160000038
Figure BDA0002159858160000038

式(4)中，

Figure BDA0002159858160000039
表示对
Figure BDA00021598581600000310
求期望。In formula (4),
Figure BDA0002159858160000039
Express
Figure BDA00021598581600000310
Seek expectations.

进一步，所述

Figure BDA00021598581600000311
通过式(5)得到：Further, the
Figure BDA00021598581600000311
Through formula (5), we can get:

Figure BDA00021598581600000312
Figure BDA00021598581600000312

式(5)中，

Figure BDA00021598581600000313
为
Figure BDA00021598581600000314
的估计均方误差，
Figure BDA00021598581600000315
为第k个时刻、第i个雷达与第q个目标之间的预测距离，
Figure BDA00021598581600000316
为
Figure BDA00021598581600000317
的估计均方误差，
Figure BDA00021598581600000318
为第k个时刻、第i个雷达对第q个目标的预测方向角。In formula (5),
Figure BDA00021598581600000313
for
Figure BDA00021598581600000314
The estimated mean square error of
Figure BDA00021598581600000315
is the predicted distance between the i-th radar and the q-th target at the k-th moment,
Figure BDA00021598581600000316
for
Figure BDA00021598581600000317
The estimated mean square error of
Figure BDA00021598581600000318
is the predicted direction angle of the qth target by the ith radar at the kth moment.

进一步，所述

Figure BDA00021598581600000319
和
Figure BDA00021598581600000320
通过式(6)得到：Further, the
Figure BDA00021598581600000319
and
Figure BDA00021598581600000320
Through formula (6), we can get:

Figure BDA00021598581600000321
Figure BDA00021598581600000321

式(6)中，

Figure BDA0002159858160000041
为第k个时刻、第i个雷达对第q个目标的发射信号的有效带宽，c＝3×108m/s为光速，λ为雷达工作波长，γ为天线孔径，
Figure BDA0002159858160000042
为第k个时刻、第i个雷达对第q个目标照射的预测回波信噪比。In formula (6),
Figure BDA0002159858160000041
is the effective bandwidth of the transmitted signal of the i-th radar to the q-th target at the k-th moment, c = 3 × 10 8 m/s is the speed of light, λ is the radar operating wavelength, γ is the antenna aperture,
Figure BDA0002159858160000042
is the predicted echo signal-to-noise ratio of the qth target illuminated by the ith radar at the kth moment.

进一步，所述

Figure BDA0002159858160000043
通过式(7)得到：Further, the
Figure BDA0002159858160000043
Through formula (7), we can get:

Figure BDA0002159858160000044
Figure BDA0002159858160000044

式(7)中，

Figure BDA0002159858160000045
为第k个时刻、第i个雷达对第q个目标照射的驻留时间，Trpt为雷达的脉冲重复周期，Pt为雷达的发射功率，Gt为雷达发射天线的增益，Gr为雷达接收天线的增益，GRP为雷达接收机的处理增益，To为雷达接收机的噪声温度，Frad为雷达接收机的噪声系数，kB为玻尔兹曼常数，σq为第q个目标的雷达散射截面，
Figure BDA0002159858160000046
为第k个时刻针对第q个目标的第i个雷达的接收机中匹配滤波器的带宽，
Figure BDA0002159858160000047
为第q个目标的真实方位角与第i个雷达对第q个目标的波束指向角之间的角度差，θ3dB是3dB发射天线和接收天线波束宽度。In formula (7),
Figure BDA0002159858160000045
is the dwell time of the ith radar irradiating the qth target at the kth moment, T rpt is the pulse repetition period of the radar, P t is the transmit power of the radar, G t is the gain of the radar transmit antenna, G r is the gain of the radar receive antenna, G RP is the processing gain of the radar receiver, T o is the noise temperature of the radar receiver, F rad is the noise coefficient of the radar receiver, k B is the Boltzmann constant, σ q is the radar scattering cross section of the qth target,
Figure BDA0002159858160000046
is the bandwidth of the matched filter in the receiver of the ith radar for the qth target at the kth moment,
Figure BDA0002159858160000047
is the angle difference between the true azimuth of the qth target and the beam pointing angle of the ith radar to the qth target, and θ 3dB is the 3dB beamwidth of the transmitting antenna and the receiving antenna.

进一步，所述

Figure BDA0002159858160000048
通过式(8)得到：Further, the
Figure BDA0002159858160000048
Through formula (8), we can get:

Figure BDA0002159858160000049
Figure BDA0002159858160000049

式(8)中，

Figure BDA00021598581600000410
为第k个时刻、第i个雷达与第q个目标之间的预测距离，
Figure BDA00021598581600000411
为第k个时刻、第i个雷达对第q个目标的预测方向角，(xi,yi)为第i个雷达的位置坐标，xi为第i个雷达的横坐标，yi为第i个雷达的纵坐标。In formula (8),
Figure BDA00021598581600000410
is the predicted distance between the i-th radar and the q-th target at the k-th moment,
Figure BDA00021598581600000411
is the predicted direction angle of the ith radar to the qth target at the kth moment, ( xi , yi ) is the position coordinate of the ith radar, xi is the horizontal coordinate of the ith radar, and yi is the vertical coordinate of the ith radar.

进一步，所述步骤S2中，组网雷达多目标跟踪驻留时间优化模型如式(9)所示：Furthermore, in step S2, the optimization model of the dwell time of the networked radar multi-target tracking is shown in formula (9):

Figure BDA0002159858160000051
Figure BDA0002159858160000051

式(9)中，

Figure BDA0002159858160000052
为第k个时刻、第i个雷达对第q个目标的发射信号的有效带宽，Q为目标的总数，
Figure BDA0002159858160000053
为第k个时刻、第i个雷达对第q个目标照射的驻留时间，
Figure BDA0002159858160000054
为矩阵
Figure BDA0002159858160000055
第1行第1列的元素，
Figure BDA0002159858160000056
为矩阵
Figure BDA0002159858160000057
第3行第3列的元素，Fmax为各目标位置估计均方误差下界的阈值，
Figure BDA0002159858160000058
为第k个时刻雷达传输到融合中心的数据总量，
Figure BDA0002159858160000059
为第k个时刻、第i个雷达需要传输至融合中心并且与第q个目标相关的数据量，ρ≥1为过采样系数，V为给定观测区域的面积，c＝3×108m/s为光速，
Figure BDA00021598581600000510
为第k个时刻、第i个雷达对第q个目标的发射信号的有效带宽，ε为融合中心的数据处理率，βmin为发射信号带宽的下限，βmax为发射信号带宽的上限，
Figure BDA00021598581600000511
为雷达照射目标驻留时间的上限，
Figure BDA00021598581600000512
为雷达照射目标驻留时间的下限，M≤N。In formula (9),
Figure BDA0002159858160000052
is the effective bandwidth of the transmission signal of the i-th radar to the q-th target at the k-th moment, Q is the total number of targets,
Figure BDA0002159858160000053
is the dwell time of the ith radar irradiating the qth target at the kth moment,
Figure BDA0002159858160000054
For the matrix
Figure BDA0002159858160000055
The element at row 1 and column 1,
Figure BDA0002159858160000056
For the matrix
Figure BDA0002159858160000057
The element in the 3rd row and 3rd column, F max is the threshold of the lower bound of the mean square error of each target position estimation,
Figure BDA0002159858160000058
is the total amount of data transmitted from the radar to the fusion center at the kth moment,
Figure BDA0002159858160000059
is the amount of data related to the qth target that the ith radar needs to transmit to the fusion center at the kth moment, ρ≥1 is the oversampling coefficient, V is the area of the given observation area, c＝3×10 8 m/s is the speed of light,
Figure BDA00021598581600000510
is the effective bandwidth of the transmitted signal of the i-th radar to the q-th target at the k-th moment, ε is the data processing rate of the fusion center, β min is the lower limit of the transmitted signal bandwidth, β max is the upper limit of the transmitted signal bandwidth,
Figure BDA00021598581600000511
is the upper limit of the target dwell time of the radar,
Figure BDA00021598581600000512
is the lower limit of the target illumination dwell time of the radar, M≤N.

有益效果：本发明公开了一种基于射频隐身的组网雷达多目标跟踪驻留时间优化方法，构建了以雷达二元选择变量、雷达驻留时间和发射信号带宽为自变量的目标状态估计误差的贝叶斯克拉美-罗下界，并将其作为目标跟踪精度的衡量指标；在此基础上，以下一时刻目标的预测跟踪精度、融合中心的数据处理量以及雷达发射资源为约束条件，以最小化组网雷达系统的总驻留时间为优化目标，对多目标跟踪过程中雷达选择、驻留时间和发射信号带宽等参数进行优化设计。这样既满足了多目标跟踪过程中各目标的跟踪精度，而且最大限度地减小了组网雷达系统的总驻留时间，提升了组网雷达系统多目标跟踪时的射频隐身性能。Beneficial effects: The present invention discloses a method for optimizing the dwell time of multi-target tracking of networked radar based on radio frequency stealth, constructs a Bayesian Cramer-Rao lower bound of the target state estimation error with radar binary selection variables, radar dwell time and transmission signal bandwidth as independent variables, and uses it as a measure of target tracking accuracy; on this basis, the predicted tracking accuracy of the target at the next moment, the data processing volume of the fusion center and the radar transmission resources are used as constraints, and the total dwell time of the networked radar system is minimized as the optimization goal, and the parameters such as radar selection, dwell time and transmission signal bandwidth in the multi-target tracking process are optimized. In this way, the tracking accuracy of each target in the multi-target tracking process is met, and the total dwell time of the networked radar system is minimized to the maximum extent, and the radio frequency stealth performance of the networked radar system during multi-target tracking is improved.

附图说明BRIEF DESCRIPTION OF THE DRAWINGS

图1为本发明具体实施方式中基于非线性规划的遗传算法的流程图；FIG1 is a flow chart of a genetic algorithm based on nonlinear programming in a specific implementation manner of the present invention;

图2为本发明具体实施方式中多目标运动轨迹与组网雷达空间分布图；FIG2 is a diagram showing the motion trajectories of multiple targets and the spatial distribution of networked radars in a specific embodiment of the present invention;

图3为本发明具体实施方式中目标1的雷达选择与信号带宽分配图；FIG3 is a radar selection and signal bandwidth allocation diagram of target 1 in a specific embodiment of the present invention;

图4为本发明具体实施方式中目标2的雷达选择与信号带宽分配图；FIG4 is a diagram of radar selection and signal bandwidth allocation for target 2 in a specific embodiment of the present invention;

图5为本发明具体实施方式中目标1的雷达选择与驻留时间分配图；FIG5 is a radar selection and dwell time allocation diagram of target 1 in a specific embodiment of the present invention;

图6为本发明具体实施方式中目标2的雷达选择与驻留时间分配图；FIG6 is a radar selection and dwell time allocation diagram of target 2 in a specific embodiment of the present invention;

图7为本发明具体实施方式中不同算法下多目标跟踪误差对比图；FIG7 is a comparison diagram of multi-target tracking errors under different algorithms in a specific embodiment of the present invention;

图8为本发明具体实施方式中不同算法下组网雷达系统总驻留时间对比图。FIG8 is a comparison chart of the total dwell time of a networked radar system under different algorithms in a specific implementation manner of the present invention.

具体实施方式DETAILED DESCRIPTION

本具体实施方式公开了一种基于射频隐身的组网雷达多目标跟踪驻留时间优化方法，包括以下步骤：This specific embodiment discloses a method for optimizing the dwell time of multi-target tracking of a networked radar based on radio frequency stealth, comprising the following steps:

S1：针对组网雷达系统构建以雷达二元选择变量、雷达驻留时间和发射信号带宽为自变量的用于预测目标状态估计误差的贝叶斯克拉美-罗下界矩阵，将所述贝叶斯克拉美-罗下界矩阵作为目标跟踪精度的衡量指标；所述组网雷达系统包括N部两坐标相控阵雷达，所有雷达的空间、时间和频率都同步，在对多目标进行跟踪时，每部雷达只能接收并处理来自自身发射信号的目标回波，并且每个时刻每部雷达最多只能跟踪一个目标；S1: A Bayesian Cramer-Rao lower bound matrix for predicting target state estimation error is constructed for a networked radar system with radar binary selection variables, radar dwell time and transmission signal bandwidth as independent variables, and the Bayesian Cramer-Rao lower bound matrix is used as a measure of target tracking accuracy; the networked radar system includes N two-coordinate phased array radars, all of which are synchronized in space, time and frequency. When tracking multiple targets, each radar can only receive and process target echoes from its own transmission signal, and each radar can only track one target at most at each moment;

S2：以下一时刻目标的预测跟踪精度、融合中心的数据处理量和雷达发射资源为约束条件，以最小化组网雷达系统的总驻留时间为优化目标，建立基于射频隐身的组网雷达多目标跟踪驻留时间优化模型；S2: Taking the predicted tracking accuracy of the target at the next moment, the data processing capacity of the fusion center and the radar transmission resources as constraints, and minimizing the total dwell time of the networked radar system as the optimization goal, a networked radar multi-target tracking dwell time optimization model based on RF stealth is established;

S3：对所述组网雷达多目标跟踪驻留时间优化模型进行求解。S3: Solving the optimization model of the networked radar multi-target tracking dwell time.

步骤S1中的贝叶斯克拉美-罗下界矩阵根据式(1)得到：The Bayesian Cramer-Rao lower bound matrix in step S1 is obtained according to formula (1):

Figure BDA0002159858160000061
Figure BDA0002159858160000061

式(1)中，

Figure BDA0002159858160000062
为第k个时刻、第q个目标的贝叶斯克拉美-罗下界矩阵，
Figure BDA0002159858160000071
为第k个时刻、第q个目标的预测贝叶斯信息矩阵；
Figure BDA0002159858160000072
为第k个时刻、第q个目标的预测状态向量，其中
Figure BDA0002159858160000073
为第k个时刻、第q个目标的预测位置，
Figure BDA0002159858160000074
为第k个时刻、第q个目标的预测位置的横坐标，
Figure BDA0002159858160000075
为第k个时刻、第q个目标的预测位置的纵坐标，
Figure BDA0002159858160000076
为第k个时刻、第q个目标的预测运动速度，
Figure BDA0002159858160000077
为第k个时刻、第q个目标的预测运动速度的横坐标分量，
Figure BDA0002159858160000078
为第k个时刻、第q个目标的预测运动速度的纵坐标分量；Wq为第q个目标过程噪声的方差，F为目标状态转移矩阵，
Figure BDA0002159858160000079
为第k-1个时刻、第q个目标的贝叶斯信息矩阵，
Figure BDA00021598581600000710
为第k个时刻、第q个目标的状态向量；
Figure BDA00021598581600000711
为第k个时刻、第i个雷达的雷达二元选择变量，
Figure BDA00021598581600000712
时表示第k个时刻、第i个雷达对第q个目标进行照射，
Figure BDA00021598581600000713
时表示第k个时刻、第i个雷达不对第q个目标进行照射；
Figure BDA00021598581600000714
为
Figure BDA00021598581600000715
的雅克比矩阵，
Figure BDA00021598581600000716
为第k个时刻、第i个雷达对第q个目标的非线性量测函数，N为雷达的总数，
Figure BDA00021598581600000717
为第k个时刻、第i个雷达对第q个目标的量测噪声的预测协方差矩阵。In formula (1),
Figure BDA0002159858160000062
is the Bayesian Cramer-Rao lower bound matrix for the k-th moment and the q-th target,
Figure BDA0002159858160000071
is the predicted Bayesian information matrix of the k-th moment and the q-th target;
Figure BDA0002159858160000072
is the predicted state vector of the kth moment and the qth target, where
Figure BDA0002159858160000073
is the predicted position of the qth target at the kth moment,
Figure BDA0002159858160000074
is the horizontal coordinate of the predicted position of the qth target at the kth moment,
Figure BDA0002159858160000075
is the ordinate of the predicted position of the qth target at the kth moment,
Figure BDA0002159858160000076
is the predicted motion speed of the qth target at the kth moment,
Figure BDA0002159858160000077
is the horizontal coordinate component of the predicted motion speed of the qth target at the kth moment,
Figure BDA0002159858160000078
is the ordinate component of the predicted motion speed of the qth target at the kth moment; Wq is the variance of the qth target process noise, F is the target state transfer matrix,
Figure BDA0002159858160000079
is the Bayesian information matrix of the k-1th moment and the qth target,
Figure BDA00021598581600000710
is the state vector of the kth moment and the qth target;
Figure BDA00021598581600000711
is the radar binary selection variable for the i-th radar at the k-th moment,
Figure BDA00021598581600000712
When means that at the kth moment, the i-th radar illuminates the q-th target,
Figure BDA00021598581600000713
When means that at the kth moment, the i-th radar does not illuminate the q-th target;
Figure BDA00021598581600000714
for
Figure BDA00021598581600000715
The Jacobian matrix of
Figure BDA00021598581600000716
is the nonlinear measurement function of the ith radar to the qth target at the kth moment, N is the total number of radars,
Figure BDA00021598581600000717
is the predicted covariance matrix of the measurement noise of the ith radar on the qth target at the kth moment.

式(1)中，Wq通过式(2)得到：In formula (1), W q is obtained by formula (2):

Figure BDA00021598581600000718
Figure BDA00021598581600000718

式(2)中，

Figure BDA00021598581600000719
为第q个目标的过程噪声强度，T为目标跟踪采样间隔。In formula (2),
Figure BDA00021598581600000719
is the process noise intensity of the qth target, and T is the target tracking sampling interval.

式(1)中，

Figure BDA00021598581600000720
通过式(3)得到：In formula (1),
Figure BDA00021598581600000720
Through formula (3), we can get:

Figure BDA00021598581600000721
Figure BDA00021598581600000721

式(3)中，

Figure BDA00021598581600000722
为第k个时刻、第q个目标的先验信息的预测Fisher信息矩阵，
Figure BDA0002159858160000081
为第k个时刻、第i个雷达对第q个目标的量测数据的Fisher信息矩阵。In formula (3),
Figure BDA00021598581600000722
is the predicted Fisher information matrix of the prior information of the k-th moment and the q-th target,
Figure BDA0002159858160000081
is the Fisher information matrix of the measurement data of the qth target by the ith radar at the kth moment.

Figure BDA0002159858160000082
通过式(4)得到：
Figure BDA0002159858160000082
Through formula (4), we can get:

Figure BDA0002159858160000083
Figure BDA0002159858160000083

式(4)中，

Figure BDA0002159858160000084
表示对
Figure BDA0002159858160000085
求期望。In formula (4),
Figure BDA0002159858160000084
Express
Figure BDA0002159858160000085
Seek expectations.

Figure BDA0002159858160000086
通过式(5)得到：
Figure BDA0002159858160000086
Through formula (5), we can get:

Figure BDA0002159858160000087
Figure BDA0002159858160000087

式(5)中，

Figure BDA0002159858160000088
为
Figure BDA0002159858160000089
的估计均方误差，
Figure BDA00021598581600000810
为第k个时刻、第i个雷达与第q个目标之间的预测距离，
Figure BDA00021598581600000811
为
Figure BDA00021598581600000812
的估计均方误差，
Figure BDA00021598581600000813
为第k个时刻、第i个雷达对第q个目标的预测方向角。In formula (5),
Figure BDA0002159858160000088
for
Figure BDA0002159858160000089
The estimated mean square error of
Figure BDA00021598581600000810
is the predicted distance between the i-th radar and the q-th target at the k-th moment,
Figure BDA00021598581600000811
for
Figure BDA00021598581600000812
The estimated mean square error of
Figure BDA00021598581600000813
is the predicted direction angle of the qth target by the ith radar at the kth moment.

Figure BDA00021598581600000814
和
Figure BDA00021598581600000815
通过式(6)得到：
Figure BDA00021598581600000814
and
Figure BDA00021598581600000815
Through formula (6), we can get:

Figure BDA00021598581600000816
Figure BDA00021598581600000816

式(6)中，

Figure BDA00021598581600000817
为第k个时刻、第i个雷达对第q个目标的发射信号的有效带宽，c＝3×108m/s为光速，λ为雷达工作波长，γ为天线孔径，
Figure BDA00021598581600000818
为第k个时刻、第i个雷达对第q个目标照射的预测回波信噪比。In formula (6),
Figure BDA00021598581600000817
is the effective bandwidth of the transmitted signal of the i-th radar to the q-th target at the k-th moment, c = 3 × 10 8 m/s is the speed of light, λ is the radar operating wavelength, γ is the antenna aperture,
Figure BDA00021598581600000818
is the predicted echo signal-to-noise ratio of the qth target illuminated by the ith radar at the kth moment.

Figure BDA00021598581600000819
通过式(7)得到：
Figure BDA00021598581600000819
Through formula (7), we can get:

Figure BDA00021598581600000820
Figure BDA00021598581600000820

式(7)中，

Figure BDA00021598581600000821
为第k个时刻、第i个雷达对第q个目标照射的驻留时间，Trpt为雷达的脉冲重复周期，Pt为雷达的发射功率，Gt为雷达发射天线的增益，Gr为雷达接收天线的增益，GRP为雷达接收机的处理增益，To为雷达接收机的噪声温度，Frad为雷达接收机的噪声系数，kB为玻尔兹曼常数，σq为第q个目标的雷达散射截面，
Figure BDA0002159858160000091
为第k个时刻针对第q个目标的第i个雷达的接收机中匹配滤波器的带宽，
Figure BDA0002159858160000092
为第q个目标的真实方位角与第i个雷达对第q个目标的波束指向角之间的角度差，θ3dB是3dB发射天线和接收天线波束宽度。In formula (7),
Figure BDA00021598581600000821
is the dwell time of the ith radar irradiating the qth target at the kth moment, T rpt is the pulse repetition period of the radar, P t is the transmit power of the radar, G t is the gain of the radar transmit antenna, G r is the gain of the radar receive antenna, G RP is the processing gain of the radar receiver, T o is the noise temperature of the radar receiver, F rad is the noise coefficient of the radar receiver, k B is the Boltzmann constant, σ q is the radar scattering cross section of the qth target,
Figure BDA0002159858160000091
is the bandwidth of the matched filter in the receiver of the ith radar for the qth target at the kth moment,
Figure BDA0002159858160000092
is the angle difference between the true azimuth of the qth target and the beam pointing angle of the ith radar to the qth target, and θ 3dB is the 3dB beamwidth of the transmitting antenna and the receiving antenna.

Figure BDA0002159858160000093
通过式(8)得到：
Figure BDA0002159858160000093
Through formula (8), we can get:

Figure BDA0002159858160000094
Figure BDA0002159858160000094

式(8)中，

Figure BDA0002159858160000095
为第k个时刻、第i个雷达与第q个目标之间的预测距离，
Figure BDA0002159858160000096
为第k个时刻、第i个雷达对第q个目标的预测方向角，(xi,yi)为第i个雷达的位置坐标，xi为第i个雷达的横坐标，yi为第i个雷达的纵坐标。In formula (8),
Figure BDA0002159858160000095
is the predicted distance between the i-th radar and the q-th target at the k-th moment,
Figure BDA0002159858160000096
is the predicted direction angle of the ith radar to the qth target at the kth moment, ( xi , yi ) is the position coordinate of the ith radar, xi is the horizontal coordinate of the ith radar, and yi is the vertical coordinate of the ith radar.

步骤S2中，组网雷达多目标跟踪驻留时间优化模型如式(9)所示：In step S2, the optimization model of the dwell time of networked radar multi-target tracking is shown in formula (9):

Figure BDA0002159858160000097
Figure BDA0002159858160000097

式(9)中，

Figure BDA0002159858160000098
为第k个时刻、第i个雷达对第q个目标的发射信号的有效带宽，Q为目标的总数，
Figure BDA0002159858160000099
为第k个时刻、第i个雷达对第q个目标照射的驻留时间，
Figure BDA0002159858160000101
为矩阵
Figure BDA0002159858160000102
第1行第1列的元素，
Figure BDA0002159858160000103
为矩阵
Figure BDA0002159858160000104
第3行第3列的元素，Fmax为各目标位置估计均方误差下界的阈值，
Figure BDA0002159858160000105
为第k个时刻雷达传输到融合中心的数据总量，
Figure BDA0002159858160000106
为第k个时刻、第i个雷达需要传输至融合中心并且与第q个目标相关的数据量，ρ≥1为过采样系数，V为给定观测区域的面积，c＝3×108m/s为光速，
Figure BDA0002159858160000107
为第k个时刻、第i个雷达对第q个目标的发射信号的有效带宽，ε为融合中心的数据处理率，βmin为发射信号带宽的下限，βmax为发射信号带宽的上限，
Figure BDA0002159858160000108
为雷达照射目标驻留时间的上限，
Figure BDA0002159858160000109
为雷达照射目标驻留时间的下限，M≤N。In formula (9),
Figure BDA0002159858160000098
is the effective bandwidth of the transmission signal of the i-th radar to the q-th target at the k-th moment, Q is the total number of targets,
Figure BDA0002159858160000099
is the dwell time of the ith radar irradiating the qth target at the kth moment,
Figure BDA0002159858160000101
For the matrix
Figure BDA0002159858160000102
The element at row 1 and column 1,
Figure BDA0002159858160000103
For the matrix
Figure BDA0002159858160000104
The element in the 3rd row and 3rd column, F max is the threshold of the lower bound of the mean square error of each target position estimation,
Figure BDA0002159858160000105
is the total amount of data transmitted from the radar to the fusion center at the kth moment,
Figure BDA0002159858160000106
is the amount of data related to the qth target that the ith radar needs to transmit to the fusion center at the kth moment, ρ≥1 is the oversampling coefficient, V is the area of the given observation area, c＝3×10 8 m/s is the speed of light,
Figure BDA0002159858160000107
is the effective bandwidth of the transmitted signal of the i-th radar to the q-th target at the k-th moment, ε is the data processing rate of the fusion center, β min is the lower limit of the transmitted signal bandwidth, β max is the upper limit of the transmitted signal bandwidth,
Figure BDA0002159858160000108
is the upper limit of the target dwell time of the radar,
Figure BDA0002159858160000109
is the lower limit of the target illumination dwell time of the radar, M≤N.

对于式(9)所示的模型采用两步分解法和基于非线性规划的遗传算法进行求解，求解过程如下：The model shown in formula (9) is solved by using a two-step decomposition method and a genetic algorithm based on nonlinear programming. The solution process is as follows:

(a)首先，针对第q个目标对于一种给定的满足约束条件

Figure BDA00021598581600001010
的雷达分配方式，式(9)可以改写为只含有变量
Figure BDA00021598581600001011
和
Figure BDA00021598581600001012
的形式。另外，假设融合中心处理每个目标的相关数据量相等，以保证所有目标都拥有足够的信息量，式(9)可以化简为：(a) First, for the qth objective, for a given constraint condition
Figure BDA00021598581600001010
Radar allocation method, equation (9) can be rewritten as containing only variables
Figure BDA00021598581600001011
and
Figure BDA00021598581600001012
In addition, assuming that the fusion center processes the same amount of relevant data for each target to ensure that all targets have sufficient information, formula (9) can be simplified as:

Figure BDA00021598581600001013
Figure BDA00021598581600001013

式中，βtotal为照射单个目标的所有雷达发射信号带宽和。Where β total is the sum of the bandwidths of all radar transmit signals illuminating a single target.

(b)其次，由于式(10)是一个非凸、非线性约束优化问题，采用基于非线性规划的遗传算法对其进行求解。基于非线性规划的遗传算法流程图如图1所示。其中，种群初始化模块根据求解问题初始化种群，适应度值计算模块根据适应度函数计算种群中染色体的适应度值，选择、交叉和变异为遗传算法的搜索算子，N为固定值，当进化次数为N的倍数时，则采用非线性寻优的方法加快进化，非线性寻优利用当前染色体值采用函数fminimax寻找问题的局部最优值。(b) Secondly, since formula (10) is a non-convex, nonlinear constrained optimization problem, a genetic algorithm based on nonlinear programming is used to solve it. The flowchart of the genetic algorithm based on nonlinear programming is shown in Figure 1. Among them, the population initialization module initializes the population according to the problem to be solved, the fitness value calculation module calculates the fitness value of the chromosome in the population according to the fitness function, selection, crossover and mutation are the search operators of the genetic algorithm, N is a fixed value, when the number of evolutions is a multiple of N, the nonlinear optimization method is used to accelerate the evolution, and the nonlinear optimization uses the current chromosome value to use the function fminimax to find the local optimal value of the problem.

(c)最后，根据通过基于非线性规划的遗传算法得到的各目标在指定雷达分配方式下的雷达选择、驻留时间和发射信号带宽值，选取使得组网雷达系统总驻留时间最小的雷达选择

Figure BDA0002159858160000111
驻留时间
Figure BDA0002159858160000112
和发射信号带宽
Figure BDA0002159858160000113
作为模型的最优解。(c) Finally, based on the radar selection, dwell time, and transmit signal bandwidth values of each target under the specified radar allocation mode obtained by the genetic algorithm based on nonlinear programming, the radar selection that minimizes the total dwell time of the networked radar system is selected.
Figure BDA0002159858160000111
Dwell time
Figure BDA0002159858160000112
and transmit signal bandwidth
Figure BDA0002159858160000113
as the optimal solution of the model.

假设组网雷达系统中的雷达个数为N＝6，目标个数为Q＝2，且各雷达的工作参数均相同。其余参数设置如表1所示。Assume that the number of radars in the networked radar system is N = 6, the number of targets is Q = 2, and the operating parameters of each radar are the same. The remaining parameter settings are shown in Table 1.

表1仿真参数设置Table 1 Simulation parameter settings

Figure BDA0002159858160000114
Figure BDA0002159858160000114

目标1的初始位置为(-100,-10)km，以速度(1300,530)m/s匀速飞行，目标2的初始位置为(100,90)km，以速度(-1300,-530)m/s匀速飞行，两个目标的过程噪声强度均为15。假设机载雷达组网采样间隔T＝3s，跟踪过程持续时间为150s。驻留时间的最大值为

Figure BDA0002159858160000115
最小值等于雷达脉冲重复周期Tr。雷达发射信号带宽的最大值为βmax＝1.9MHz，最小值βmin＝0.1MHz。预先设定的跟踪精度阈值为Fmax＝30m。The initial position of target 1 is (-100, -10) km, and it flies at a constant speed of (1300, 530) m/s. The initial position of target 2 is (100, 90) km, and it flies at a constant speed of (-1300, -530) m/s. The process noise intensity of both targets is 15. Assume that the airborne radar network sampling interval T = 3s, and the tracking process duration is 150s. The maximum dwell time is
Figure BDA0002159858160000115
The minimum value is equal to the radar pulse repetition period Tr . The maximum value of the radar transmission signal bandwidth is β max =1.9MHz, and the minimum value is β min =0.1MHz. The preset tracking accuracy threshold is F max =30m.

多目标运动轨迹与组网雷达空间分布图如图2所示，目标1的雷达选择与信号带宽分配图如图3所示，目标2的雷达选择与信号带宽分配图如图4所示，目标1的雷达选择与驻留时间分配图如图5所示，目标2的雷达选择与驻留时间分配图如图6所示。从图2至图6中可以看出，在目标跟踪过程中，随着目标的运动，组网雷达系统会优先选择与目标距离较近的雷达对该目标进行照射；同时，雷达发射信号带宽和驻留时间倾向于分配给所选的距离目标较远的雷达，从而保证组网雷达系统的总驻留时间最短。The motion trajectory of multiple targets and the spatial distribution of networked radars are shown in Figure 2, the radar selection and signal bandwidth allocation diagram of target 1 is shown in Figure 3, the radar selection and signal bandwidth allocation diagram of target 2 is shown in Figure 4, the radar selection and dwell time allocation diagram of target 1 is shown in Figure 5, and the radar selection and dwell time allocation diagram of target 2 is shown in Figure 6. It can be seen from Figures 2 to 6 that in the target tracking process, as the target moves, the networked radar system will give priority to the radar that is closer to the target to illuminate the target; at the same time, the radar transmission signal bandwidth and dwell time tend to be allocated to the selected radar that is farther away from the target, so as to ensure that the total dwell time of the networked radar system is the shortest.

不同算法下多目标跟踪误差对比如图7所示，其中，目标跟踪均方根误差(RootMean Square Error,RMSE)定义为：The comparison of multi-target tracking errors under different algorithms is shown in Figure 7, where the target tracking root mean square error (RMSE) is defined as:

Figure BDA0002159858160000121
Figure BDA0002159858160000121

式中，NMC为蒙特卡洛实验次数，

Figure BDA0002159858160000122
为第n次蒙特卡洛实验时得到的目标估计位置，此处，设NMC＝100。从图2和图7中可以看出，所提算法能够较好地满足所有目标的跟踪精度要求。Where N MC is the number of Monte Carlo experiments,
Figure BDA0002159858160000122
is the estimated position of the target obtained in the nth Monte Carlo experiment, and here, N MC = 100. It can be seen from Figures 2 and 7 that the proposed algorithm can better meet the tracking accuracy requirements of all targets.

不同算法下组网雷达系统的总驻留时间对比如图8所示。从图8中可以看出，相比于带宽均匀分配算法法，所提算法法使得组网雷达系统具有更短的总驻留时间，从而进一步提升了组网雷达多目标跟踪时的射频隐身性能。The comparison of the total dwell time of the networked radar system under different algorithms is shown in Figure 8. As can be seen from Figure 8, compared with the bandwidth uniform allocation algorithm, the proposed algorithm enables the networked radar system to have a shorter total dwell time, thereby further improving the RF stealth performance of the networked radar during multi-target tracking.

由上述仿真结果可知，基于射频隐身的组网雷达多目标跟踪驻留时间优化方法，可在满足下一时刻目标预测跟踪精度、融合中心数据处理量以及雷达发射资源约束的条件下，自适应地优化调整多目标跟踪过程中雷达选择、驻留时间和发射信号带宽等参数，最小化组网雷达系统的总驻留时间，有效提升了组网雷达系统多目标跟踪时的射频隐身性能。From the above simulation results, it can be seen that the optimization method of the dwell time of multi-target tracking of networked radar based on RF stealth can adaptively optimize and adjust the parameters such as radar selection, dwell time and transmission signal bandwidth in the multi-target tracking process under the conditions of satisfying the target prediction and tracking accuracy at the next moment, the data processing volume of the fusion center and the radar transmission resource constraints, minimize the total dwell time of the networked radar system, and effectively improve the RF stealth performance of the networked radar system during multi-target tracking.

Claims (8)

1. The method for optimizing the multi-target tracking residence time of the networking radar based on the radio frequency stealth is characterized by comprising the following steps of: the method comprises the following steps:
s1: constructing a Bayesian Clary-Rous lower bound matrix which takes a radar binary selection variable, radar residence time and transmitted signal bandwidth as independent variables and is used for predicting target state estimation errors aiming at a networking radar system, and taking the Bayesian Clary-Rous lower bound matrix as a measurement index of target tracking accuracy; the networking radar system comprises N two-coordinate phased array radars, the space, time and frequency of all the radars are synchronous, when a plurality of targets are tracked, each radar can only receive and process target echoes from self-emitted signals, and each radar can only track one target at most at each moment;
the bayesian krame-luo lower bound matrix is obtained according to equation (1):
Figure FDA0003987500260000011
in the formula (1), the reaction mixture is,
Figure FDA0003987500260000012
a Bayesian Classman-Luo lower bound matrix for the kth time, qth objective, <' > is based on>
Figure FDA0003987500260000013
A prediction Bayesian information matrix for the kth moment and the qth target;
Figure FDA0003987500260000014
Is the predicted state vector of the qth target at the kth time instant, in which->
Figure FDA0003987500260000015
For the predicted position of the qth object at the kth time instant>
Figure FDA0003987500260000016
Is the abscissa of the predicted position of the kth time point, the qth object>
Figure FDA0003987500260000017
As the ordinate of the predicted position of the qth object at the kth time,
Figure FDA0003987500260000018
for the predicted movement speed of the kth, qth object at a time instant>
Figure FDA0003987500260000019
For the abscissa component of the predicted movement speed of the qth object at the kth time instant, it is determined whether a reference value is greater than or equal to>
Figure FDA00039875002600000110
The ordinate component of the predicted movement speed of the qth target at the kth time; w is a group of q For the variance of the qth target process noise, F is the target state transition matrix, based on>
Figure FDA00039875002600000111
A Bayesian information matrix for the kth-1 time, qth object, <' >>
Figure FDA00039875002600000112
The state vector of the kth moment and the qth target is obtained;
Figure FDA00039875002600000113
Binary selection of variables for the radar at the kth time instant, i-th radar>
Figure FDA00039875002600000114
Time means the kth time, the ith radar irradiates the qth target and gets it->
Figure FDA00039875002600000115
The time indicates that the kth time and the ith radar do not irradiate the qth target;
Figure FDA00039875002600000116
Is->
Figure FDA00039875002600000117
The jacobian matrix of (a) is,
Figure FDA00039875002600000118
a non-linear measurement function of the ith radar to the qth target at the kth time, N is the total number of radars, and->
Figure FDA00039875002600000119
A prediction covariance matrix of the measured noise of the ith radar to the qth target at the kth moment;
s2: the method comprises the following steps that the predicted tracking precision of a target at the next moment, the data processing amount of a fusion center and radar emission resources are used as constraint conditions, the total residence time of a minimized networking radar system is used as an optimization target, and a networking radar multi-target tracking residence time optimization model based on radio frequency stealth is established;
the networking radar multi-target tracking residence time optimization model is shown as formula (9):
Figure FDA0003987500260000021
in the formula (9), the reaction mixture is,
Figure FDA0003987500260000022
the effective bandwidth of the signal transmitted by the ith radar to the qth target for the kth time, Q being the total number of targets, and->
Figure FDA0003987500260000023
For the dwell time of the qth target illumination by the ith radar at the kth time instant, <' >>
Figure FDA0003987500260000024
Is a matrix->
Figure FDA0003987500260000025
Row 1, column 1 element->
Figure FDA0003987500260000026
Is a matrix->
Figure FDA0003987500260000027
Element of row 3, column 3, F max Estimate a threshold value of the lower bound of the mean square error for each target position, <' >>
Figure FDA0003987500260000028
For the sum of data transmitted by the radar to the fusion center at the k-th time instant, the value is greater than>
Figure FDA0003987500260000029
The data volume which needs to be transmitted to the fusion center and is related to the qth target for the ith moment and the ith radar, rho is more than or equal to 1 and is an oversampling coefficient, V is the area of a given observation area, and c =3 × 10 8 m/s is the speed of light, and>
Figure FDA00039875002600000210
effective bandwidth of a transmitted signal of the ith radar to the qth target at the kth moment, wherein epsilon is data processing rate of a fusion center and beta min For the lower limit of the bandwidth of the transmitted signal, beta max For upper limit of the bandwidth of the transmitted signal>
Figure FDA00039875002600000211
For upper bounds on radar exposure target dwell times>
Figure FDA00039875002600000212
The lower limit of the residence time of the radar irradiated target is set, and M is less than or equal to N;
s3: and solving the networking radar multi-target tracking residence time optimization model.
2. The radio frequency stealth-based networking radar multi-target tracking residence time optimization method according to claim 1, characterized in that: in the formula (1), W q Obtained by the formula (2):
Figure FDA0003987500260000031
in the formula (2), the reaction mixture is,
Figure FDA0003987500260000032
and T is the process noise intensity of the qth target, and T is the target tracking sampling interval.
3. The radio frequency stealth-based networking radar multi-target tracking residence time optimization method according to claim 1, characterized in that: in the formula (1), the reaction mixture is,
Figure FDA0003987500260000033
obtained by the formula (3): />
Figure FDA0003987500260000034
In the formula (3), the reaction mixture is,
Figure FDA0003987500260000035
a prediction Fisher information matrix of the prior information of the kth time and the qth target,
Figure FDA0003987500260000036
and the Fisher information matrix is the measured data of the kth radar to the qth target at the kth moment.
4. According to the claimsSolving 3 the multi-target tracking residence time optimization method for the networking radar based on the radio frequency stealth is characterized in that: the above-mentioned
Figure FDA0003987500260000037
Obtained by the formula (4):
Figure FDA0003987500260000038
in the formula (4), the reaction mixture is,
Figure FDA0003987500260000039
represents a pair->
Figure FDA00039875002600000310
And (4) making the expectation.
5. The method for optimizing the multi-target tracking residence time of the networking radar based on the radio frequency stealth as claimed in claim 3, wherein: the above-mentioned
Figure FDA00039875002600000311
Obtained by the formula (5):
Figure FDA00039875002600000312
in the formula (5), the reaction mixture is,
Figure FDA00039875002600000313
is->
Figure FDA00039875002600000314
In the mean square error of the evaluation of>
Figure FDA00039875002600000315
For the predicted distance between the kth time, the ith radar and the qth target>
Figure FDA00039875002600000316
Is->
Figure FDA00039875002600000317
In the mean square error of the evaluation of>
Figure FDA00039875002600000318
And predicting the direction angle of the ith radar to the qth target at the kth moment.
6. The radio frequency stealth-based networking radar multi-target tracking residence time optimization method according to claim 5, characterized in that: the above-mentioned
Figure FDA0003987500260000041
And &>
Figure FDA0003987500260000042
Obtained by the formula (6):
Figure FDA0003987500260000043
in the formula (6), the reaction mixture is,
Figure FDA0003987500260000044
c =3 × 10 for the effective bandwidth of the transmitted signal of the ith radar to the qth target at the kth time 8 m/s is the speed of light, lambda is the radar operating wavelength, gamma is the antenna aperture, and/or>
Figure FDA0003987500260000045
And predicting the signal-to-noise ratio of the echo irradiated by the ith radar to the qth target at the kth moment.
7. The method for optimizing the multi-target tracking residence time of the networking radar based on the radio frequency stealth as claimed in claim 6,the method is characterized in that: the above-mentioned
Figure FDA0003987500260000046
Obtained by the formula (7):
Figure FDA0003987500260000047
in the formula (7), the reaction mixture is,
Figure FDA0003987500260000048
the dwell time of the irradiation of the qth target by the ith radar at the kth time, T rpt For the pulse repetition period of the radar, P t Is the transmission power of radar, G t Gain for radar transmitting antenna, G r Gain of radar receiving antenna, G RP For processing gain, T, of radar receivers o As noise temperature of radar receiver, F rad Is the noise figure, k, of the radar receiver B Is Boltzmann constant, σ q Is the radar cross section of the qth target>
Figure FDA0003987500260000049
The bandwidth of the matched filter in the receiver of the i-th radar for the q-th target at the k-th instant is->
Figure FDA00039875002600000410
Is the angle difference between the true azimuth of the qth target and the beam pointing angle of the ith radar to the qth target, θ 3dB Is the 3dB transmit and receive antenna beamwidth.
8. The method for optimizing the multi-target tracking residence time of the networking radar based on the radio frequency stealth as claimed in claim 1, wherein: the described
Figure FDA00039875002600000411
Obtained by the formula (8):
Figure FDA0003987500260000051
in the formula (8), the reaction mixture is,
Figure FDA0003987500260000052
for the predicted distance between the kth time, the ith radar and the qth target>
Figure FDA0003987500260000053
Predicting direction angle of the ith radar to the qth target for the kth time, (x) i ,y i ) Is the position coordinate, x, of the ith radar i Is the abscissa, y, of the ith radar i The ordinate of the ith radar. />
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