WO2022036733A1 - 面向低截获的组网雷达驻留时间与辐射功率联合优化方法 - Google Patents

面向低截获的组网雷达驻留时间与辐射功率联合优化方法 Download PDF

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WO2022036733A1
WO2022036733A1 PCT/CN2020/111323 CN2020111323W WO2022036733A1 WO 2022036733 A1 WO2022036733 A1 WO 2022036733A1 CN 2020111323 W CN2020111323 W CN 2020111323W WO 2022036733 A1 WO2022036733 A1 WO 2022036733A1
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radar
target
time
dwell time
radiation power
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时晨光
丁琳涛
王奕杰
周建江
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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
    • 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
    • G01S13/87—Combinations of radar systems, e.g. primary radar and secondary radar
    • 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
    • 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
    • G01S13/003—Bistatic radar systems; Multistatic radar systems
    • 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
    • G01S13/006—Theoretical aspects
    • 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
    • G01S7/03—Details of HF subsystems specially adapted therefor, e.g. common to transmitter and receiver
    • 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
    • G01S7/28—Details of pulse systems
    • G01S7/282—Transmitters
    • 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
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4004—Means for monitoring or calibrating of parts of a radar system
    • 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
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4052—Means for monitoring or calibrating by simulation of echoes
    • 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
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S2013/0236—Special technical features
    • G01S2013/0281—LPI, Low Probability of Intercept radar

Definitions

  • the invention relates to a radar signal processing technology, in particular to a low-interception-oriented networked radar dwell time and radiation power joint optimization method.
  • networked radar systems such as multi-static radar and multiple-input multiple-output radar have attracted extensive attention in academia.
  • networked radar systems have many potential advantages, such as superior waveform diversity gain, space diversity gain, and better target detection and tracking performance.
  • the first category is to improve the tracking accuracy of the target as much as possible under the constraints of the limited transmission resources of the networked radar system.
  • the second category is to minimize the radiation resource consumption of the networked radar system under the premise of meeting the target tracking accuracy requirements.
  • the purpose of the present invention is to provide a low-interception-oriented networked radar dwell time and radiation power joint optimization method.
  • the low-interception-oriented networking radar residence time and radiation power joint optimization method of the present invention includes the following steps:
  • step S1 a networked radar system composed of N rad monostatic phased array radars is considered to track a single target. These radars are dispersedly deployed in two-dimensional space and keep time, space, and frequency synchronization, and each A radar can only receive and process target echoes from its own transmitted signal.
  • step S2 is specifically:
  • ( ⁇ ) -1 represents the inverse operation of the matrix
  • k-1 ) is the Bayesian information matrix of the target
  • Predict the target state vector at time k at time k-1 where ( ⁇ ) T represents the transpose operation of the matrix or vector, and (x k
  • Q is the process noise covariance matrix, and its mathematical expression is:
  • ⁇ T 0 is the sampling interval, Indicates the matrix direct product operation, I 2 is the second-order unit matrix, r is the process noise intensity; F is the target state transition matrix, and its mathematical expression is:
  • (x i , y i ) are the position coordinates of the i-th radar in two-dimensional space;
  • k-1 is the measurement noise covariance matrix of the i-th radar, and its mathematical expression is:
  • c 3 ⁇ 10 8 m/s
  • ⁇ is the effective bandwidth of the radar transmit signal
  • ⁇ is the radar operating wavelength
  • ⁇ is the antenna aperture
  • k-1 is the prediction k of the i-th radar at time k-1
  • the target echo signal-to-noise ratio at time its mathematical expression is:
  • T d,i,k and P i,k are the dwell time and radiation power of the ith radar irradiated target at time k, respectively
  • T r is the repetition period of each radar pulse
  • G t and G r are the emission of each radar, respectively
  • ⁇ i is the radar cross section of the target relative to the i-th radar
  • G RP is the processing gain of the radar receiver
  • k 0 and T 0 are the Boltzmann constant and the noise temperature of each radar receiver, respectively
  • B r is the matched filter bandwidth of each radar receiver
  • F r is the noise coefficient of each radar receiver
  • k-1 is the predicted distance between the i-th radar at time k-1 and the target at time k, is the angle difference between the true azimuth of the target and the i-th radar transmit beam
  • ⁇ 3dB is the 3dB beam width of each radar antenna
  • k-1 is characterized by the trace of the predicted Bayesian Cramer-Rhodan lower bound matrix C k
  • Tr( ⁇ ) represents the trace operation of the matrix.
  • step S3 the mathematical expression of the optimization objective function F k in step S3 is:
  • ⁇ and ⁇ are the weight coefficients of dwell time and radiation power, respectively
  • T d,i,k and P i,k are the dwell time and radiation power of the i-th radar irradiated target at time k, respectively
  • T d,min and T d,max are the lower and upper limits of the dwell time of each radar, respectively
  • P min and P max are the lower and upper limits of the radiated power of each radar, respectively
  • N rad is the number of monostatic phased array radars.
  • step S4 the target tracking accuracy satisfies the preset target tracking error threshold and the radiation resources of the networked radar system as constraints, and the optimization is to minimize the weighted sum of the residence time resources and radiation power resources of each radar irradiated target.
  • a joint optimization model of the low-interception-oriented networking radar dwell time and radiated power is established, as shown below:
  • F k is the weighted sum of the residence time resources and radiation power resources of each radar irradiation target, which is the optimization target
  • ⁇ and ⁇ are the weight coefficients of the residence time and radiation power, respectively
  • N rad represents the number of monostatic phased array radars
  • T d,i,k and P i,k are the dwell time and radiation power of the i-th radar irradiated target at time k, respectively
  • T d,min and T d,max are the lower and upper limit of the dwell time of each radar, respectively
  • P min and P max are the lower and upper limits of the radiated power of each radar respectively
  • k-1 is the target tracking accuracy
  • Q max is the preset target tracking error threshold.
  • step S5 the fmincon function in the MATLAB software is used to calculate and solve the joint optimization model of the low interception-oriented networking radar dwell time and radiated power, and the result is the optimal dwell time of the i-th radar at time k. and radiated power Among them, ( ) * represents the optimal value of the parameter.
  • the main task accomplished by the method of the present invention is to consider a networked radar system composed of multiple monostatic phased array radars to track a single target, and these radars are dispersedly deployed in a two-dimensional space And keep time, space, frequency synchronization, and each radar can only receive and process the target echo from its own transmitted signal.
  • the system radiation resources are the constraints, and the optimization goal is to minimize the weighted sum of the residence time resources and radiation power resources of each radar irradiated target.
  • the radio frequency radiation resource consumption of the network radar system is effectively improved, and its low interception performance is effectively improved.
  • the invention has the advantages that it can not only meet the preset target tracking accuracy performance requirements and the radiation resources of the networked radar system, but also can reduce the consumption of radio frequency radiation resources of the networked radar system, thereby improving its low interception performance.
  • the reason for this advantage is that the present invention adopts a low-intercept-oriented networked radar dwell time and radiation power joint optimization method.
  • Fig. 1 is a flow chart of the joint optimization method for the dwell time and radiated power of the networked radar for low interception;
  • Figure 2 is a diagram showing the relationship between the target movement trajectory and the geometric position of the networked radar
  • Fig. 3 is the distribution diagram of networked radar dwell time and radiated power
  • Figure 4 is a comparison curve of target tracking root mean square error under different methods
  • Figure 5 is the comparison curve between the total dwell time of the networked radar and the total radiated power under different methods
  • Figure 6 is a graph of the total residence time saving rate, total radiated power saving rate and optimization objective function reduction rate of the networked radar.
  • the present invention proposes a low-interception-oriented combined optimization method of networked radar residence time and radiation power, with target tracking accuracy satisfying a preset target tracking error threshold and networked radar system radiation resources as constraints
  • a low-interception-oriented networked radar residence time and radiation power joint optimization model is established, thereby reducing the networked radar.
  • the RF radiation resource consumption of the system effectively improves its low intercept performance.
  • the low-interception-oriented networking radar residence time and radiation power joint optimization method of the present invention includes the following steps:
  • N rad monostatic phased array radars to track a single target. These radars are dispersed in two-dimensional space and keep time, space and frequency synchronization, and each radar can only receive and process The target echo from its own transmitted signal.
  • ( ⁇ ) -1 represents the inverse operation of the matrix
  • k-1 ) is the Bayesian information matrix of the target
  • Predict the target state vector at time k at time k-1 where ( ⁇ ) T represents the transpose operation of the matrix or vector, and (x k
  • Q is the process noise covariance matrix, and its mathematical expression is:
  • ⁇ T 0 is the sampling interval, Indicates the matrix direct product operation, I 2 is the second-order unit matrix, r is the process noise intensity; F is the target state transition matrix, and its mathematical expression is:
  • (x i , y i ) are the position coordinates of the i-th radar in two-dimensional space;
  • k-1 is the measurement noise covariance matrix of the i-th radar, and its mathematical expression is:
  • c 3 ⁇ 10 8 m/s
  • ⁇ is the effective bandwidth of the radar transmit signal
  • ⁇ is the radar operating wavelength
  • ⁇ is the antenna aperture
  • k-1 is the prediction k of the i-th radar at time k-1
  • the target echo signal-to-noise ratio at time its mathematical expression is:
  • T d,i,k and P i,k are the dwell time and radiation power of the ith radar irradiated target at time k, respectively
  • T r is the repetition period of each radar pulse
  • G t and G r are the emission of each radar, respectively
  • ⁇ i is the radar cross section of the target relative to the i-th radar
  • G RP is the processing gain of the radar receiver
  • k 0 and T 0 are the Boltzmann constant and the noise temperature of each radar receiver, respectively
  • B r is the matched filter bandwidth of each radar receiver
  • F r is the noise coefficient of each radar receiver
  • k-1 is the predicted distance between the i-th radar at time k-1 and the target at time k
  • ⁇ 3dB is the 3dB beam width of each radar antenna.
  • Equation (1) the predicted Bayesian Kramer-Roe lower bound matrix of the estimation error of the target motion state can be obtained, and its mathematical expression is:
  • k-1 is characterized by the trace of the predicted Bayesian Cramer-Rhodan lower bound matrix C k
  • Tr( ⁇ ) represents the trace operation of the matrix.
  • ⁇ and ⁇ are the weight coefficients of the dwell time and radiated power, respectively
  • T d,min and T d,max are the lower and upper limits of the dwell time of each radar, respectively
  • P min and P max are the radiated power of each radar, respectively.
  • the target tracking accuracy satisfies the preset target tracking error threshold and the radiation resources of the networked radar system as constraints, and the optimization goal is to minimize the weighted sum of the residence time resources and radiation power resources of each radar irradiated target.
  • the combined optimization model of the networked radar dwell time and radiated power is as follows:
  • Q max is a preset target tracking error threshold.
  • the fmincon function in MATLAB software can be used to calculate and solve, and the result is the optimal dwell time of the ith radar at time k and radiated power Among them, ( ) * represents the optimal value of the parameter.
  • the radar cross section of the target relative to each radar is set to 1m 2 .
  • Figure 2 shows the relationship between the target trajectory and the geometric position of the networked radar. It can be seen from Fig. 2 that the method proposed in the present invention can track the target well.
  • Fig. 3 shows the distribution diagram of networked radar dwell time and radiated power.
  • the networked radar will preferentially select the radar with a closer distance to the target and a better relative position to illuminate the target; at the same time, more residence time resources and radiation Power resources will be allocated to radars that are far away from the target and have poor relative positions, so as to ensure that the total RF radiation resource consumption of the networked radar system is minimized.
  • RMSE Root Mean Square Error
  • N MC is the number of Monte Carlo experiments
  • (x k , y k ) is the real position of the target at time k
  • It is the estimated position of the target at time k obtained in the nth Monte Carlo experiment.
  • set N MC 500.
  • the present invention uses the residence time and radiation power uniform distribution algorithm (hereinafter referred to as "uniform distribution algorithm") as a comparison algorithm to verify the advantages of the proposed method in the present invention.
  • Figure 4 shows the comparison curve of target tracking root mean square error under different methods. It can be seen from FIG. 4 that the method proposed in the present invention can better meet the requirements of target tracking accuracy.
  • Figure 5 shows the comparison curve of the total dwell time and total radiated power of the networked radar under different methods.
  • Figure 5(a) shows the comparison curve of the total dwell time of the networked radar under different methods.
  • Figure 5(b) The comparison curves of the total radiated power of the networked radars under different methods are shown. It can be seen from Fig. 5 that, compared with the uniform allocation algorithm, the method proposed in the present invention can significantly reduce the consumption of the total residence time resource and total radiation power resource of the networked radar under the condition that the target tracking accuracy is similar, and improve the Low interception performance of the system.
  • Fig. 6 shows a graph of the total residence time saving rate, total radiated power saving rate and optimization objective function reduction rate of the networked radar, wherein Fig. 6(a) shows a graph of the total residence time saving rate of the networked radar, Fig.
  • FIG. 6(b) shows the diagram of the total radiation power saving rate of the networked radar
  • Fig. 6(c) shows the diagram of the reduction rate of the optimization objective function of the networked radar. It can be seen from Fig. 6 that, compared with the uniform distribution algorithm, the method proposed in the present invention not only effectively reduces the consumption of radio frequency radiation resources of the networked radar system, but also reduces the optimization objective function value, thereby improving the performance of the networked radar system. Low interception performance.
  • the present invention considers a networked radar system composed of multiple monostatic phased array radars to track a single target. These radars are dispersedly deployed in two-dimensional space and keep time, space and frequency synchronization, and each radar can only receive and Processes the target echo from its own transmit signal.
  • the system radiation resource is the constraint condition
  • the optimization goal is to minimize the residence time resource and the weighted sum of the radiation power resource of each radar irradiated target at each moment. Reduce the RF radiation resource consumption of the networked radar system and effectively improve its low interception performance.
  • the interior point method is used to solve the above optimization model, and the joint optimal allocation of the networked radar residence time and radiation power can be obtained. result.

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  • Radar, Positioning & Navigation (AREA)
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Abstract

面向低截获的组网雷达驻留时间与辐射功率联合优化方法，包括S1、确定组网雷达系统架构及其任务；S2、以各雷达驻留时间和辐射功率为自变量，构造目标状态估计误差的预测贝叶斯克拉美-罗下界矩阵，取预测贝叶斯克拉美-罗下界矩阵的迹作为目标跟踪精度的衡量指标；S3、以k时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和Fk为优化目标函数；S4、建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型；S5、利用内点法对面向低截获的组网雷达驻留时间与辐射功率联合优化模型进行求解。降低了组网雷达系统的射频辐射资源消耗，有效提升了其低截获性能。

Description

面向低截获的组网雷达驻留时间与辐射功率联合优化方法 技术领域
本发明涉及雷达信号处理的技术，具体涉及面向低截获的组网雷达驻留时间与辐射功率联合优化方法。
背景技术
近年来，组网雷达系统如多基地雷达和多输入多输出雷达等引起了学术界的广泛关注。与传统的单基地雷达系统相比，组网雷达系统具有诸多潜在优势，如优越的波形分集增益、空间分集增益和更好的目标检测跟踪性能等。
对于组网雷达系统在目标跟踪下的资源分配问题，国内外学者提出了一系列资源分配管理方法，目的是充分地利用系统潜力，提升系统性能。根据优化目标，这些方法可以分为两类。第一类是在组网雷达系统有限的发射资源约束下，尽可能的提高目标的跟踪精度。第二类是在满足目标跟踪精度要求的前提下，最小化组网雷达系统的辐射资源消耗。
在现代作战环境中，随着无源探测设备的广泛使用，低截获技术是组网雷达系统必须着重考虑的问题。然而，现有技术中尚未有面向低截获的组网雷达驻留时间与辐射功率联合优化方法。
发明内容
发明目的：本发明的目的是提供一种面向低截获的组网雷达驻留时间与辐射功率联合优化方法。
技术方案：本发明的面向低截获的组网雷达驻留时间与辐射功率联合优化方法，包括以下步骤：
S1、确定组网雷达系统架构及其任务；
S2、以各雷达驻留时间和辐射功率为自变量，构造目标状态估计误差的预测贝叶斯克拉美-罗下界矩阵，取预测贝叶斯克拉美-罗下界矩阵的迹作为目标跟踪精度的衡量指标；
S3、以k时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和F k为优化目标函数；
S4、建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型；
S5、利用内点法对面向低截获的组网雷达驻留时间与辐射功率联合优化模型进行求解。
进一步的，步骤S1中考虑有N rad部单基地相控阵雷达构成的组网雷达系统对单目标进行跟踪，这些雷达分散部署于二维空间中并保持时间、空间、频率同步，且每部雷达只能接收并处理来自自身发射信号的目标回波。
进一步的，步骤S2具体为：
目标的贝叶斯信息矩阵计算表达式为：
Figure PCTCN2020111323-appb-000001
其中，(·) -1表示矩阵的逆运算，J(X k|k-1)为目标的贝叶斯信息矩阵；
Figure PCTCN2020111323-appb-000002
为k-1时刻预测k时刻的目标状态向量，其中，(·) T表示矩阵或矢量的转置运算，(x k|k-1,y k|k-1)表示k-1时刻预测k时刻的目标位置，
Figure PCTCN2020111323-appb-000003
表示k-1时刻预测k时刻的目标运动速度，N rad表示单基地相控阵雷达的数量；Q为过程噪声协方差矩阵，其数学表达式为：
Figure PCTCN2020111323-appb-000004
其中，ΔT 0为采样间隔，
Figure PCTCN2020111323-appb-000005
表示矩阵直积运算，I 2为2阶单位矩阵，r为过程噪声强度；F为目标状态转移矩阵，其数学表达式为：
Figure PCTCN2020111323-appb-000006
Figure PCTCN2020111323-appb-000007
为第i部雷达量测函数g i(X k|k-1)的雅克比矩阵，其中，
Figure PCTCN2020111323-appb-000008
表示对目标状态向量X k|k-1求一阶偏导，第i部雷达量测函数g i(X k|k-1)的数学表达式为：
Figure PCTCN2020111323-appb-000009
其中，(x i,y i)为第i部雷达在二维空间中的位置坐标；ψ i,k|k-1为第i部雷达的量测噪声协方差矩阵，其数学表达式为：
Figure PCTCN2020111323-appb-000010
其中，
Figure PCTCN2020111323-appb-000011
为k-1时刻预测k时刻的目标距离量测误差，
Figure PCTCN2020111323-appb-000012
为k-1时刻预测k时刻的目标方位角量测误差，其数学表达式分别为：
Figure PCTCN2020111323-appb-000013
Figure PCTCN2020111323-appb-000014
其中，c＝3×10 8m/s，β为雷达发射信号有效带宽，λ为雷达工作波长，γ为天线孔径，SNR i,k|k-1为第i部雷达k-1时刻预测k时刻的目标回波信噪比，其数学表达式为：
Figure PCTCN2020111323-appb-000015
其中，T d,i,k和P i,k分别为k时刻第i部雷达照射目标的驻留时间和辐射功率，T r为各雷达脉冲重复周期，G t和G r分别为各雷达发射天线增益和接收天线增益，σ i为目标相对第i部雷达的雷达散射截面，G RP为雷达接收机处理增益，k 0和T 0分别为玻尔兹曼常数和各雷达接收机噪声温度，B r为各雷达接收机匹配滤波器带宽，F r为各雷达接收机噪声系数，R i,k|k-1为第i部雷达k-1时刻预测k时刻与目标之间的距离，
Figure PCTCN2020111323-appb-000016
为目标的真实方位角与第i部雷达发射波束之间的角度差，θ 3dB为各雷达天线3dB波束宽度；
对目标的贝叶斯信息矩阵计算表达式求逆，即得到目标运动状态估计误差的预测 贝叶斯克拉美-罗下界矩阵，其数学表达式为：
Figure PCTCN2020111323-appb-000017
在此，采用预测贝叶斯克拉美-罗下界矩阵C k|k-1的迹来表征目标跟踪精度Q k|k-1，即：
Q k|k-1＝Tr(C k|k-1)   ；
其中，Tr(·)表示求矩阵的迹运算。
进一步的，步骤S3中优化目标函数F k的数学表达式为：
Figure PCTCN2020111323-appb-000018
其中，α和ξ分别为驻留时间和辐射功率的权重系数，T d,i,k和P i,k分别为k时刻第i部雷达照射目标的驻留时间和辐射功率，T d,min和T d,max分别为各雷达驻留时间的下限和上限，P min和P max分别为各雷达辐射功率的下限和上限，N rad表示单基地相控阵雷达的数量。
进一步的，步骤S4中以目标跟踪精度满足预先设定的目标跟踪误差阈值及组网雷达系统辐射资源为约束条件，以最小化各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标，建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型，如下所示：
Figure PCTCN2020111323-appb-000019
其中，F k为各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标，α 和ξ分别为驻留时间和辐射功率的权重系数，N rad表示单基地相控阵雷达的数量，T d,i,k和P i,k分别为k时刻第i部雷达照射目标的驻留时间和辐射功率，T d,min和T d,max分别为各雷达驻留时间的下限和上限，P min和P max分别为各雷达辐射功率的下限和上限，Q k|k-1为目标跟踪精度，Q max为预先设定的目标跟踪误差阈值。
进一步的，步骤S5中采用MATLAB软件中的fmincon函数对面向低截获的组网雷达驻留时间与辐射功率联合优化模型进行计算求解，所得即为k时刻第i部雷达的最优驻留时间
Figure PCTCN2020111323-appb-000020
与辐射功率
Figure PCTCN2020111323-appb-000021
其中，(·) *表示参数的最优值。
有益效果：与现有技术相比，本发明方法所完成的主要任务是考虑有多部单基地相控阵雷达构成的组网雷达系统对单目标进行跟踪，这些雷达分散部署于二维空间中并保持时间、空间、频率同步，且每部雷达只能接收并处理来自自身发射信号的目标回波。首先，以各雷达驻留时间和辐射功率为自变量，构造目标状态估计误差的预测贝叶斯克拉美-罗下界矩阵，取预测贝叶斯克拉美-罗下界矩阵的迹作为目标跟踪精度的衡量指标；其次，以各时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标函数；在此基础上，以目标跟踪精度满足预先设定的目标跟踪误差阈值及组网雷达系统辐射资源为约束条件，以最小化各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标，建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型，从而降低组网雷达系统的射频辐射资源消耗，有效提升其低截获性能。
该发明的优点是不仅能够满足预先设定的目标跟踪精度性能要求及组网雷达系统辐射资源，而且能够降低组网雷达系统的射频辐射资源消耗，从而提升其低截获性能。产生该优点的原因是本发明采用了面向低截获的组网雷达驻留时间与辐射功率联合优化方法。
附图说明
图1为面向低截获的组网雷达驻留时间与辐射功率联合优化方法流程图；
图2为目标运动轨迹与组网雷达几何位置关系图；
图3为组网雷达驻留时间与辐射功率分配图；
图4为不同方法下目标跟踪均方根误差对比曲线；
图5为不同方法下组网雷达总驻留时间与总辐射功率对比曲线；
图6为组网雷达总驻留时间节省率、总辐射功率节省率与优化目标函数减小率图。
具体实施方式
下面结合附图和具体实施例对本发明进行详细说明。
本发明从当今军事应用需求出发，提出了面向低截获的组网雷达驻留时间与辐射功率联合优化方法，以目标跟踪精度满足预先设定的目标跟踪误差阈值及组网雷达系统辐射资源为约束条件，以最小化各时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标，建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型，从而降低了组网雷达系统的射频辐射资源消耗，有效提升了其低截获性能。
如图1所示，本发明的面向低截获的组网雷达驻留时间与辐射功率联合优化方法，包括以下步骤：
S1、确定组网雷达系统架构及其任务；
考虑有N rad部单基地相控阵雷达构成的组网雷达系统对单目标进行跟踪，这些雷达分散部署于二维空间中并保持时间、空间、频率同步，且每部雷达只能接收并处理来自自身发射信号的目标回波。
S2、以各雷达驻留时间和辐射功率为自变量，构造目标状态估计误差的预测贝叶斯克拉美-罗下界矩阵，取预测贝叶斯克拉美-罗下界矩阵的迹作为目标跟踪精度的衡量指标，如下所示：
目标的贝叶斯信息矩阵计算表达式为：
Figure PCTCN2020111323-appb-000022
其中，(·) -1表示矩阵的逆运算，J(X k|k-1)为目标的贝叶斯信息矩阵；
Figure PCTCN2020111323-appb-000023
为k-1时刻预测k时刻的目标状态向量，其中，(·) T表示矩阵或矢量的转置运算，(x k|k-1,y k|k-1)表示k-1时刻预测k时刻的目标位置，
Figure PCTCN2020111323-appb-000024
表示k-1时刻预测k时刻的目标运动速度；Q为过程噪声协方差矩阵，其数学表达式为：
Figure PCTCN2020111323-appb-000025
其中，ΔT 0为采样间隔，
Figure PCTCN2020111323-appb-000026
表示矩阵直积运算，I 2为2阶单位矩阵，r为过程噪声强度；F为目标状态转移矩阵，其数学表达式为：
Figure PCTCN2020111323-appb-000027
Figure PCTCN2020111323-appb-000028
为第i部雷达量测函数g i(X k|k-1)的雅克比矩阵，其中，
Figure PCTCN2020111323-appb-000029
表示对目标状态向量X k|k-1求一阶偏导，第i部雷达量测函数g i(X k|k-1)的数学表达式为：
Figure PCTCN2020111323-appb-000030
其中，(x i,y i)为第i部雷达在二维空间中的位置坐标；ψ i,k|k-1为第i部雷达的量测噪声协方差矩阵，其数学表达式为：
Figure PCTCN2020111323-appb-000031
其中，
Figure PCTCN2020111323-appb-000032
为k-1时刻预测k时刻的目标距离量测误差，
Figure PCTCN2020111323-appb-000033
为k-1时刻预测k时刻的目标方位角量测误差，其数学表达式分别为：
Figure PCTCN2020111323-appb-000034
Figure PCTCN2020111323-appb-000035
其中，c＝3×10 8m/s，β为雷达发射信号有效带宽，λ为雷达工作波长，γ为天线孔径，SNR i,k|k-1为第i部雷达k-1时刻预测k时刻的目标回波信噪比，其数学表达式为：
Figure PCTCN2020111323-appb-000036
其中，T d,i,k和P i,k分别为k时刻第i部雷达照射目标的驻留时间和辐射功率，T r为各雷达脉冲重复周期，G t和G r分别为各雷达发射天线增益和接收天线增益，σ i为目标相对第i部雷达的雷达散射截面，G RP为雷达接收机处理增益，k 0和T 0分别为玻尔兹曼常数和各雷达接收机噪声温度，B r为各雷达接收机匹配滤波器带宽，F r为各雷达接收机噪声系数，R i,k|k-1为第i部雷达k-1时刻预测k时刻与目标之间的距离，
Figure PCTCN2020111323-appb-000037
为目标的真实方位角与第i部雷达发射波束之间的角度差，θ 3dB为各雷达天线3dB波束宽度。
对式(1)求逆，即可得到目标运动状态估计误差的预测贝叶斯克拉美-罗下界矩阵，其数学表达式为：
Figure PCTCN2020111323-appb-000038
在此，采用预测贝叶斯克拉美-罗下界矩阵C k|k-1的迹来表征目标跟踪精度Q k|k-1，即：
Q k|k-1＝Tr(C k|k-1)    (10)；
其中，Tr(·)表示求矩阵的迹运算。
S3、以k时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和F k为优化目标函数，其数学表达式为：
Figure PCTCN2020111323-appb-000039
其中，α和ξ分别为驻留时间和辐射功率的权重系数，T d,min和T d,max分别为各雷达驻留时间的下限和上限，P min和P max分别为各雷达辐射功率的下限和上限。
S4、建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型，如下所示：
以目标跟踪精度满足预先设定的目标跟踪误差阈值及组网雷达系统辐射资源为约束条件，以最小化各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目 标，建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型，如下所示：
Figure PCTCN2020111323-appb-000040
其中，Q max为预先设定的目标跟踪误差阈值。
S5、利用内点法对优化模型(12)进行求解：
对于优化模型(12)，可采用MATLAB软件中的fmincon函数进行计算求解，所得即为k时刻第i部雷达的最优驻留时间
Figure PCTCN2020111323-appb-000041
与辐射功率
Figure PCTCN2020111323-appb-000042
其中，(·) *表示参数的最优值。
仿真结果：
考虑由N rad＝4部雷达组成的组网雷达系统跟踪单目标的场景，系统中每部雷达的发射参数均相同，有效带宽为β＝1MHz，工作波长为λ＝0.03m，采样间隔为ΔT 0＝3s。目标相对各雷达的雷达散射截面均设为1m 2。雷达照射目标的驻留时间上、下限分别为T d,max＝0.1s和T d,min＝0.0005s，雷达辐射功率上、下限分别为P max＝2800W和P min＝50W。目标跟踪误差阈值设为Q max＝1000m 2。假设目标跟踪过程持续时间为150s，两个目标的过程噪声强度均为15。
图2示出了目标运动轨迹与组网雷达几何位置关系图。从图2中可以看出，本发明所提方法能够较好地对目标进行跟踪。
图3示出了组网雷达驻留时间与辐射功率分配图。从图3(a)和(b)中可以看出，组网雷达将优先选择与目标距离较近且相对位置较好的雷达对该目标进行照射；同时，更多的驻留时间资源和辐射功率资源会分配给距离目标较远且相对位置较差的雷达，从而保证组网雷达系统的射频总辐射资源消耗最少。
定义目标跟踪均方根误差(Root Mean Square Error,RMSE)的数学表达式为：
Figure PCTCN2020111323-appb-000043
式中，N MC为蒙特卡洛实验次数，(x k,y k)为k时刻目标的真实位置，
Figure PCTCN2020111323-appb-000044
为第n次蒙特卡洛实验时得到的k时刻目标估计位置，在此，设N MC＝500。本发明以驻留时间和辐射功率均匀分配算法(以下简称“均匀分配算法”)为对比算法来验证本发明所提方法的优势。图4示出了不同方法下目标跟踪均方根误差对比曲线。从图4中可以看出，本发明所提方法能够较好地满足目标跟踪精度要求。
图5示出了不同方法下组网雷达总驻留时间与总辐射功率对比曲线，其中，图5(a)示出了不同方法下组网雷达总驻留时间对比曲线，图5(b)示出了不同方法下组网雷达总辐射功率对比曲线。从图5中可以看出，与均匀分配算法相比，本发明所提方法能够在满足目标跟踪精度相近的条件下，显著减少组网雷达的总驻留时间资源和总辐射功率资源消耗，提升系统的低截获性能。
定义k时刻组网雷达系统的总驻留时间节省率
Figure PCTCN2020111323-appb-000045
总辐射功率节省率
Figure PCTCN2020111323-appb-000046
与优化目标函数值的减小率ρ k分别为：
Figure PCTCN2020111323-appb-000047
式中，
Figure PCTCN2020111323-appb-000048
和
Figure PCTCN2020111323-appb-000049
分别为本发明所提方法在k时刻第i部雷达对目标照射的驻留时间和辐射功率；
Figure PCTCN2020111323-appb-000050
和
Figure PCTCN2020111323-appb-000051
分别为均匀分配算法在k时刻第i部雷达对目标照射的驻留时间和辐射功率；
Figure PCTCN2020111323-appb-000052
表示本发明所提方法在k时刻的目标函数值，
Figure PCTCN2020111323-appb-000053
表示均匀分配算法在k时刻的目标函数值。图6示出了组网雷达总驻留时间节省率、总辐射功率节省率与优化目标函数减小率图，其中，图6(a)示出了组网雷达总驻留时间节省率图，图6(b)示出了组网雷达总辐射功率节省率图，图6(c)示出了组网雷达优化目标函数减小率图。从图6中可以看出，相比于均匀分配算法，本发明所提方法不仅有效减少了组网雷达系统的射频辐射资源消耗，而且降低了优化目标函数值，从而提升了组网雷达系统的低截 获性能。
本发明创造的工作原理及工作过程：
本发明考虑有多部单基地相控阵雷达构成的组网雷达系统对单目标进行跟踪，这些雷达分散部署于二维空间中并保持时间、空间、频率同步，且每部雷达只能接收并处理来自自身发射信号的目标回波。首先，以各雷达驻留时间和辐射功率为自变量，构造目标状态估计误差的预测贝叶斯克拉美-罗下界矩阵，取预测贝叶斯克拉美-罗下界矩阵的迹作为目标跟踪精度的衡量指标；其次，以各时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标函数；在此基础上，以目标跟踪精度满足预先设定的目标跟踪误差阈值及组网雷达系统辐射资源为约束条件，以最小化各时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标，建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型；从而降低组网雷达系统的射频辐射资源消耗，有效提升其低截获性能；最后，采用内点法对上述优化模型进行求解，即可得到符合约束条件的组网雷达驻留时间与辐射功率联合优化分配结果。
本发明创造的发明点：
1、针对由多部单基地相控阵雷达构成的组网雷达系统对单目标进行跟踪，这些雷达分散部署于二维空间中并保持时间、空间、频率同步，且每部雷达只能接收并处理来自自身发射信号的目标回波；以各雷达驻留时间和辐射功率为自变量，构造目标状态估计误差的预测贝叶斯克拉美-罗下界矩阵，取预测贝叶斯克拉美-罗下界矩阵的迹作为目标跟踪精度的衡量指标；以各时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标函数；
2、以各时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标函数；在此基础上，以目标跟踪精度满足预先设定的目标跟踪误差阈值及组网雷达系统辐射资源为约束条件，以最小化各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标，建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型，并采用内点法对该优化模型进行求解，确定使得组网雷达系统目标函数最小的驻留时间和辐射功率作为最优解。

Claims (6)

  1. 面向低截获的组网雷达驻留时间与辐射功率联合优化方法，其特征在于，包括以下步骤：
    S1、确定组网雷达系统架构及其任务；
    S2、以各雷达驻留时间和辐射功率为自变量，构造目标状态估计误差的预测贝叶斯克拉美-罗下界矩阵，取预测贝叶斯克拉美-罗下界矩阵的迹作为目标跟踪精度的衡量指标；
    S3、以k时刻各雷达照射目标的驻留时间资源和辐射功率资源加权和F k为优化目标函数；
    S4、建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型；
    S5、利用内点法对面向低截获的组网雷达驻留时间与辐射功率联合优化模型进行求解。
  2. 根据权利要求1所述的面向低截获的组网雷达驻留时间与辐射功率联合优化方法，其特征在于，步骤S1中考虑有N rad部单基地相控阵雷达构成的组网雷达系统对单目标进行跟踪，这些雷达分散部署于二维空间中并保持时间、空间、频率同步，且每部雷达只能接收并处理来自自身发射信号的目标回波。
  3. 根据权利要求1所述的面向低截获的组网雷达驻留时间与辐射功率联合优化方法，其特征在于，步骤S2具体为：
    目标的贝叶斯信息矩阵计算表达式为：
    Figure PCTCN2020111323-appb-100001
    其中，(·) -1表示矩阵的逆运算，J(X k|k-1)为目标的贝叶斯信息矩阵；
    Figure PCTCN2020111323-appb-100002
    为k-1时刻预测k时刻的目标状态向量，其中，(·) T表示矩阵或矢量的转置运算，(x k|k-1,y k|k-1)表示k-1时刻预测k时刻的目标位置，
    Figure PCTCN2020111323-appb-100003
    表示k-1时刻预测k时刻的目标运动速度，N rad表示单基地相控阵雷达的数量；Q为过程噪声协方差矩阵，其数学表达式为：
    Figure PCTCN2020111323-appb-100004
    其中，△T0为采样间隔，
    Figure PCTCN2020111323-appb-100005
    表示矩阵直积运算，I 2为2阶单位矩阵，r为过程噪声强度；F为目标状态转移矩阵，其数学表达式为：
    Figure PCTCN2020111323-appb-100006
    Figure PCTCN2020111323-appb-100007
    为第i部雷达量测函数g i(X k|k-1)的雅克比矩阵，其中，
    Figure PCTCN2020111323-appb-100008
    表示对目标状态向量X k|k-1求一阶偏导，第i部雷达量测函数g i(X k|k-1)的数学表达式为：
    Figure PCTCN2020111323-appb-100009
    其中，(x i,y i)为第i部雷达在二维空间中的位置坐标；ψ i,k|k-1为第i部雷达的量测噪声协方差矩阵，其数学表达式为：
    Figure PCTCN2020111323-appb-100010
    其中，
    Figure PCTCN2020111323-appb-100011
    为k-1时刻预测k时刻的目标距离量测误差，
    Figure PCTCN2020111323-appb-100012
    为k-1时刻预测k时刻的目标方位角量测误差，其数学表达式分别为：
    Figure PCTCN2020111323-appb-100013
    Figure PCTCN2020111323-appb-100014
    其中，c＝3×10 8m/s，β为雷达发射信号有效带宽，λ为雷达工作波长，γ为天线孔径，SNR i,k|k-1为第i部雷达k-1时刻预测k时刻的目标回波信噪比，其数学表达式 为：
    Figure PCTCN2020111323-appb-100015
    其中，T d,i,k和P i,k分别为k时刻第i部雷达照射目标的驻留时间和辐射功率，T r为各雷达脉冲重复周期，G t和G r分别为各雷达发射天线增益和接收天线增益，σ i为目标相对第i部雷达的雷达散射截面，G RP为雷达接收机处理增益，k 0和T 0分别为玻尔兹曼常数和各雷达接收机噪声温度，B r为各雷达接收机匹配滤波器带宽，F r为各雷达接收机噪声系数，R i,k|k-1为第i部雷达k-1时刻预测k时刻与目标之间的距离，
    Figure PCTCN2020111323-appb-100016
    为目标的真实方位角与第i部雷达发射波束之间的角度差，θ 3dB为各雷达天线3dB波束宽度；
    对目标的贝叶斯信息矩阵计算表达式求逆，即得到目标运动状态估计误差的预测贝叶斯克拉美-罗下界矩阵，其数学表达式为：
    Figure PCTCN2020111323-appb-100017
    在此，采用预测贝叶斯克拉美-罗下界矩阵C k|k-1的迹来表征目标跟踪精度Q k|k-1，即：
    Q k|k-1＝Tr(C k|k-1)；
    其中，Tr(·)表示求矩阵的迹运算。
  4. 根据权利要求1所述的面向低截获的组网雷达驻留时间与辐射功率联合优化方法，其特征在于，步骤S3中优化目标函数F k的数学表达式为：
    Figure PCTCN2020111323-appb-100018
    其中，α和ξ分别为驻留时间和辐射功率的权重系数，T d,i,k和P i,k分别为k时刻第i部雷达照射目标的驻留时间和辐射功率，T d,min和T d,max分别为各雷达驻留时间的下限和 上限，P min和P max分别为各雷达辐射功率的下限和上限，N rad表示单基地相控阵雷达的数量。
  5. 根据权利要求1所述的面向低截获的组网雷达驻留时间与辐射功率联合优化方法，其特征在于，步骤S4中以目标跟踪精度满足预先设定的目标跟踪误差阈值及组网雷达系统辐射资源为约束条件，以最小化各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标，建立面向低截获的组网雷达驻留时间与辐射功率联合优化模型，如下所示：
    Figure PCTCN2020111323-appb-100019
    其中，F k为各雷达照射目标的驻留时间资源和辐射功率资源加权和为优化目标，α和ξ分别为驻留时间和辐射功率的权重系数，N rad表示单基地相控阵雷达的数量，T d,i,k和P i,k分别为k时刻第i部雷达照射目标的驻留时间和辐射功率，T d,min和T d,max分别为各雷达驻留时间的下限和上限，P min和P max分别为各雷达辐射功率的下限和上限，Q k|k-1为目标跟踪精度，Q max为预先设定的目标跟踪误差阈值。
  6. 根据权利要求1所述的面向低截获的组网雷达驻留时间与辐射功率联合优化方法，其特征在于，步骤S5中采用MATLAB软件中的fmincon函数对面向低截获的组网雷达驻留时间与辐射功率联合优化模型进行计算求解，所得即为k时刻第i部雷达的最优驻留时间
    Figure PCTCN2020111323-appb-100020
    与辐射功率
    Figure PCTCN2020111323-appb-100021
    其中，(·) *表示参数的最优值。
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