[go: up one dir, main page]

CN115561748A - Networked radar target search tracking resource allocation method based on radio frequency stealth - Google Patents

Networked radar target search tracking resource allocation method based on radio frequency stealth Download PDF

Info

Publication number
CN115561748A
CN115561748A CN202211225716.2A CN202211225716A CN115561748A CN 115561748 A CN115561748 A CN 115561748A CN 202211225716 A CN202211225716 A CN 202211225716A CN 115561748 A CN115561748 A CN 115561748A
Authority
CN
China
Prior art keywords
radar
target
tracking
search
radio frequency
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202211225716.2A
Other languages
Chinese (zh)
Other versions
CN115561748B (en
Inventor
时晨光
石兆
周建江
李海林
谭静
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing University of Aeronautics and Astronautics
Original Assignee
Nanjing University of Aeronautics and Astronautics
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing University of Aeronautics and Astronautics filed Critical Nanjing University of Aeronautics and Astronautics
Priority to CN202211225716.2A priority Critical patent/CN115561748B/en
Publication of CN115561748A publication Critical patent/CN115561748A/en
Application granted granted Critical
Publication of CN115561748B publication Critical patent/CN115561748B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • 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
    • 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
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
    • 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
    • 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
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

Landscapes

  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

本发明公开了基于射频隐身的网络化雷达目标搜索跟踪资源分配方法，包括：考虑由多部同步的相控阵雷达组成的网络化雷达，需要同时完成对多个圆形重点观测区域的搜索，以及对已知数量的运动目标的跟踪；构建网络化雷达对多个圆形重点观测区域搜索场景，并采用检测概率作为搜索性能的衡量指标；构建网络化雷达对多目标跟踪场景，并采用目标位置估计的预测贝叶斯克拉美‑罗下界作为多目标跟踪性能的衡量指标；建立基于射频隐身的网络化雷达搜索跟踪资源分配模型；采用内点法和循环最小法的两步求解算法对优化模型进行求解，实现资源优化分配。本发明提升了网络化雷达执行多空域搜索和多目标跟踪任务时的射频隐身性能。

Figure 202211225716

The invention discloses a radio frequency stealth-based networked radar target search and tracking resource allocation method, which includes: considering that a networked radar composed of multiple synchronized phased array radars needs to simultaneously complete the search for multiple circular key observation areas, And the tracking of a known number of moving targets; build a networked radar to search for multiple circular key observation areas, and use the detection probability as a measure of search performance; build a networked radar to track multiple targets, and use the target Prediction of Bayesian Cramer-Rao lower bound for position estimation as a measure of multi-target tracking performance; establishment of a networked radar search and tracking resource allocation model based on radio frequency stealth; two-step solution algorithms using interior point method and cyclic minimum method to optimize The model is solved to realize the optimal allocation of resources. The invention improves the radio frequency stealth performance when the networked radar performs multi-airspace search and multi-target tracking tasks.

Figure 202211225716

Description

基于射频隐身的网络化雷达目标搜索跟踪资源分配方法Resource allocation method for networked radar target search and tracking based on radio frequency stealth

技术领域technical field

本发明涉及雷达信号处理技术，具体涉及一种基于射频隐身的网络化雷达目标搜索跟踪资源分配方法。The invention relates to radar signal processing technology, in particular to a radio frequency stealth-based networked radar target search and track resource allocation method.

背景技术Background technique

雷达起初用于目标的检测与定位测量，而随着技术的不断进步以及对雷达能力需求的不断增加，雷达的功能也逐步多样化。其中，相控阵雷达由于波束无惯性扫描、抗干扰能力强等特点，在军事领域得到了广泛应用，尤其是针对目标的搜索与跟踪这两大重点任务。相较于传统单站雷达，网络化雷达能够从多个视角、多种维度来提取目标的特征信息，并通过信息融合达到提升分辨率、降低干扰误差等目的，进一步提高雷达目标搜索跟踪等性能。由此，便涉及到网络化雷达资源分配的技术。如何通过分配不同雷达的不同辐射资源以提升网络化雷达的性能，成为了众多学者的研究内容。Radar was originally used for target detection and positioning measurement. With the continuous advancement of technology and the increasing demand for radar capabilities, the functions of radar have gradually diversified. Among them, phased array radar has been widely used in the military field due to the characteristics of non-inertial beam scanning and strong anti-interference ability, especially for the two key tasks of target search and tracking. Compared with the traditional single-station radar, the networked radar can extract the characteristic information of the target from multiple perspectives and dimensions, and achieve the purpose of improving the resolution and reducing the interference error through information fusion, and further improving the radar target search and tracking performance. . Therefore, it involves the technology of networked radar resource allocation. How to improve the performance of networked radars by allocating different radiation resources of different radars has become the research content of many scholars.

然而，雷达在执行任务时向空间传输的信号若被敌方无源探测系统截获，雷达将面临着被打击的风险。因此，射频隐身性能的提升也成为了作战过程中的迫切需求。射频隐身技术是一种对抗敌方无源探测系统对射频设备主动辐射信号截获、分选和识别的技术，利用有限的射频辐射资源优化雷达性能的同时，还需要考虑其射频隐身性能，降低辐射资源消耗。However, if the signal transmitted by the radar to space during the mission is intercepted by the enemy's passive detection system, the radar will face the risk of being attacked. Therefore, the improvement of radio frequency stealth performance has become an urgent need in the combat process. Radio frequency stealth technology is a technology that counters the interception, sorting and identification of active radiation signals of radio frequency equipment by enemy passive detection systems. While optimizing radar performance with limited radio frequency radiation resources, it is also necessary to consider its radio frequency stealth performance and reduce radiation LF.

已有的大多研究成果虽然在雷达节点选择和资源分配方面进行了优化，在一定程度上实现了网络化雷达多目标跟踪精度的提升，或是射频隐身性能的提升。但是这些研究并未考虑多种任务并存时的雷达的节点选择以及资源分配问题，具有一定的局限性。Although most of the existing research results have been optimized in terms of radar node selection and resource allocation, to a certain extent, the improvement of networked radar multi-target tracking accuracy or the improvement of radio frequency stealth performance has been achieved. However, these studies have not considered the radar node selection and resource allocation when multiple tasks coexist, which has certain limitations.

目前尚未有基于射频隐身的网络化雷达目标搜索跟踪资源分配方面的公开报道。At present, there is no public report on resource allocation of networked radar target search and tracking based on radio frequency stealth.

发明内容Contents 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网络化雷达目标搜索跟踪资源分配方法，不仅考虑了网络化雷达多任务共同进行的场景，能够在满足一定的目标搜索性能和多目标跟踪性能的条件下，对雷达节点选择、各雷达的辐射功率和驻留时间等参数进行联合优化，有效降低总射频辐射资源消耗，提升网络化雷达的射频隐身性能。Purpose of the invention: The purpose of the present invention is to provide a networked radar target search and tracking resource allocation method based on radio frequency stealth, which not only considers the scene where networked radars are multi-tasked together, but also can satisfy certain target search performance and multi-target tracking. Under the condition of high performance, the joint optimization of parameters such as radar node selection, radiation power and dwell time of each radar can effectively reduce the consumption of total radio frequency radiation resources and improve the radio frequency stealth performance of networked radars.

技术方案：本发明的基于射频隐身的网络化雷达目标搜索跟踪资源分配方法，包括以下步骤：Technical solution: The networked radar target search and tracking resource allocation method based on radio frequency stealth of the present invention includes the following steps:

建立系统模型：考虑由多部同步的相控阵雷达组成的网络化雷达，需要同时完成对多个圆形重点观测区域的搜索，以及对已知数量的运动目标的跟踪；多目标跟踪任务的优先级高于目标搜索任务，每一部相控阵雷达每一时刻只能产生一个波束；Establish a system model: Considering a networked radar composed of multiple synchronized phased array radars, it is necessary to simultaneously complete the search for multiple circular key observation areas and track a known number of moving targets; the multi-target tracking task The priority is higher than the target search task, and each phased array radar can only generate one beam at a time;

构建网络化雷达对多个圆形重点观测区域搜索场景，并采用检测概率作为搜索性能的衡量指标；Construct a networked radar to search for multiple circular key observation areas, and use the detection probability as a measure of search performance;

构建网络化雷达对多目标跟踪场景，并采用目标位置估计的预测贝叶斯克拉美-罗下界作为多目标跟踪性能的衡量指标；Construct a multi-target tracking scenario of networked radar, and use the predictive Bayesian Cramer-Rao lower bound of target position estimation as a measure of multi-target tracking performance;

在满足预先设定的搜索和多目标跟踪性能以及射频资源约束的条件下，以最小化网络化雷达的总射频资源消耗为优化目标，以雷达节点选择方式、辐射功率和驻留时间为优化参数，建立基于射频隐身的网络化雷达搜索跟踪资源分配模型；Under the conditions of satisfying the pre-set search and multi-target tracking performance and radio frequency resource constraints, the optimization goal is to minimize the total radio frequency resource consumption of networked radars, and the radar node selection method, radiation power and dwell time are optimized parameters , establish a networked radar search and track resource allocation model based on radio frequency stealth;

将模型分解为两个子优化模型，并采用内点法和循环最小法的两步求解算法对两个子优化模型进行求解，在搜索跟踪性能和射频资源的约束下，联合优化网络化雷达搜索和多目标跟踪时的节点选择、辐射功率和驻留时间资源分配。The model is decomposed into two sub-optimization models, and the two-step solution algorithm of the interior point method and the circular minimum method are used to solve the two sub-optimization models. Under the constraints of search and tracking performance and radio frequency resources, the joint optimization of networked radar search and multiple Node selection, radiated power and dwell time resource allocation for target tracking.

进一步的，构建网络化雷达对多个圆形重点观测区域搜索场景，并采用检测概率作为搜索性能的衡量指标，具体为：Further, a networked radar is constructed to search for multiple circular key observation areas, and the detection probability is used as a measure of search performance, specifically:

在由N部雷达组成的网络化雷达中，MS部雷达用于对A个圆形重点观测区域执行搜索任务；每一时刻单部雷达只能照射一片区域，每一片区域需要同时被LS部雷达搜索；k时刻雷达i对重点观测区域a扫描n次后得到的检测概率

Figure BDA0003879662280000021
为：In a networked radar composed of N radars, the M S radar is used to perform search tasks on A circular key observation areas; a single radar can only illuminate one area at a time, and each area needs to be covered by L S at the same time. The local radar search; the detection probability obtained after the radar i scans the key observation area a n times at time k
Figure BDA0003879662280000021
for:

Figure BDA0003879662280000022
Figure BDA0003879662280000022

其中，a＝1,2,…,A，Pfa为虚警概率，

Figure BDA0003879662280000023
为k时刻雷达i搜索重点观测区域a时照射到目标后可获得的回波信噪比；Among them, a=1,2,...,A, P fa is the false alarm probability,
Figure BDA0003879662280000023
is the echo signal-to-noise ratio that can be obtained after the radar i searches for the key observation area a at time k when it irradiates the target;

有LS部雷达用于对重点观测区域a的搜索，k时刻网络化雷达对圆形重点观测区域a中目标的检测概率表示为：There are L and S parts of the radar used to search for the key observation area a, and the detection probability of the target in the circular key observation area a by the networked radar at time k is expressed as:

Figure BDA0003879662280000024
Figure BDA0003879662280000024

进一步的，多目标跟踪性能的衡量指标为：Further, the metrics for multi-target tracking performance are:

Figure BDA0003879662280000025
Figure BDA0003879662280000025

其中，

Figure BDA0003879662280000031
为目标状态估计误差预测贝叶斯克拉美-罗下界矩阵，表达式为：in,
Figure BDA0003879662280000031
To predict the Bayesian Cramer-Rao lower bound matrix for the target state estimation error, the expression is:

Figure BDA0003879662280000032
Figure BDA0003879662280000032

其中，

Figure BDA0003879662280000033
表示k-1时刻目标状态的贝叶斯信息矩阵，
Figure BDA0003879662280000034
表示k时刻目标预测状态的贝叶斯信息矩阵；
Figure BDA0003879662280000035
表示k时刻目标预测状态的雅克比矩阵；
Figure BDA0003879662280000036
表示k时刻目标量测误差协方差矩阵；上标(·)-1表示矩阵的逆矩阵；上标(·)T表示矩阵的转置；Qq表示均值为零的高斯过程白噪声的协方差矩阵；F表示状态转移矩阵；N表示网络化雷达中雷达的数量；
Figure BDA0003879662280000037
表示k时刻雷达i是否对目标q进行照射。in,
Figure BDA0003879662280000033
Represents the Bayesian information matrix of the target state at time k-1,
Figure BDA0003879662280000034
Represents the Bayesian information matrix of the target prediction state at time k;
Figure BDA0003879662280000035
Represents the Jacobian matrix of the target prediction state at time k;
Figure BDA0003879662280000036
Indicates the target measurement error covariance matrix at time k; the superscript (·) -1 represents the inverse matrix of the matrix; the superscript (·) T represents the transpose of the matrix; Q q represents the covariance of Gaussian process white noise with a mean value of zero Matrix; F represents the state transition matrix; N represents the number of radars in the networked radar;
Figure BDA0003879662280000037
Indicates whether radar i illuminates target q at time k.

进一步的，基于射频隐身的网络化雷达搜索跟踪资源分配模型为：Further, the resource allocation model of networked radar search and tracking based on radio frequency stealth is:

Figure BDA0003879662280000038
Figure BDA0003879662280000038

其中，Etot,k表示总射频资源消耗；uk＝[uS,k,uT,k]T表示k时刻的网络化雷达节点选择方式，

Figure BDA0003879662280000039
表示搜索重点观测区域a的节点选择方式，
Figure BDA00038796622800000310
表示网络化雷达搜索节点选择方式，
Figure BDA00038796622800000311
表示跟踪目标q的节点选择方式，
Figure BDA00038796622800000312
表示网络化雷达跟踪节点选择方式；Pk＝[PS,k,PT,k]T和Tk＝[TS,k,TT,k]T分别表示k时刻的网络化雷达的辐射功率和驻留时间资源分配；
Figure BDA00038796622800000313
表示k时刻网络化雷达对重点观测区域a中目标的检测概率；
Figure BDA00038796622800000314
表示表征目标跟踪精度的衡量指标；pd,min和
Figure BDA00038796622800000315
分别为目标搜索性能和多目标跟踪精度要求；对于搜索任务，PS,max和PS,min分别表示搜索辐射功率的上下限，TS,max和TS,min分别表示搜索波束驻留时间的上下限；
Figure BDA00038796622800000316
表示雷达i搜索重点观测区域a时的辐射功率；
Figure BDA00038796622800000317
表示雷达i搜索重点观测区域a时波束的驻留时间；对于跟踪任务，PT,max和PT,min分别表示跟踪辐射功率的上下限，TT,max和TT,min分别表示跟踪波束驻留时间的上下限；
Figure BDA0003879662280000041
和
Figure BDA0003879662280000042
分别为k时刻雷达i单次照射目标q的辐射功率和驻留时间；LS表示同时搜索同一片圆形重点观测区域的雷达数量；A表示圆形重点观测区域的数量；MS表示用于对A个圆形重点观测区域执行搜索任务的雷达数量；
Figure BDA0003879662280000043
表示k时刻雷达i是否被选中对重点观测区域a进行搜索；
Figure BDA0003879662280000044
表示k时刻雷达i是否对目标q进行照射；LT表示同时照射同一个目标需要的雷达数量；Q表示运动目标的数量；MT表示用于执行对多个目标的跟踪任务的雷达的数量；1N×1表示N×1维的全1矩阵。Among them, E tot,k represents the total radio frequency resource consumption; u k =[u S,k ,u T,k ] T represents the networked radar node selection method at time k,
Figure BDA0003879662280000039
Indicates the node selection method for searching the key observation area a,
Figure BDA00038796622800000310
Indicates the networked radar search node selection method,
Figure BDA00038796622800000311
Indicates the node selection method for tracking target q,
Figure BDA00038796622800000312
Indicates the networked radar tracking node selection method; P k ＝[P S,k ,P T,k ] T and T k ＝[T S,k ,T T,k ] T respectively represent the radiation of the networked radar at time k Power and dwell time resource allocation;
Figure BDA00038796622800000313
Indicates the detection probability of the target in the key observation area a by the networked radar at time k;
Figure BDA00038796622800000314
Represents the measurement index that characterizes the target tracking accuracy; p d,min and
Figure BDA00038796622800000315
are target search performance and multi-target tracking accuracy requirements; for search tasks, PS ,max and PS ,min respectively represent the upper and lower limits of search radiation power, and T S,max and T S,min represent the dwell time of search beams respectively upper and lower limits;
Figure BDA00038796622800000316
Indicates the radiation power of radar i when searching key observation area a;
Figure BDA00038796622800000317
Indicates the dwell time of the beam when radar i searches the key observation area a; for the tracking task, PT ,max and PT ,min respectively represent the upper and lower limits of the tracking radiation power, and TT,max and TT,min respectively represent the tracking beam The upper and lower limits of the dwell time;
Figure BDA0003879662280000041
and
Figure BDA0003879662280000042
Respectively, the radiation power and dwell time of radar i’s single irradiation target q at time k; L S represents the number of radars searching the same circular key observation area at the same time; A represents the number of circular key observation areas; M S represents the The number of radars performing search tasks on A circular key observation area;
Figure BDA0003879662280000043
Indicates whether radar i is selected to search key observation area a at time k;
Figure BDA0003879662280000044
Indicates whether radar i illuminates target q at time k; L T indicates the number of radars required to illuminate the same target at the same time; Q indicates the number of moving targets; M T indicates the number of radars used to perform tracking tasks for multiple targets; 1 N×1 means an N×1-dimensional matrix of all 1s.

进一步的，总射频资源消耗Etot,k定义为搜索和跟踪射频资源消耗的总和，表示为：Further, the total radio frequency resource consumption E tot,k is defined as the sum of searching and tracking radio frequency resource consumption, expressed as:

Figure BDA0003879662280000045
Figure BDA0003879662280000045

其中，ES,k表示搜索射频资源消耗，ET,k表示跟踪射频资源消耗；α1和α2分别表示辐射功率和驻留时间的权重系数。Among them, E S,k represents the consumption of radio frequency resources in search, E T,k represents the consumption of radio frequency resources in tracking; α 1 and α 2 represent the weight coefficients of radiation power and dwell time, respectively.

进一步的，分解的两个子优化模型为：Further, the two sub-optimization models for decomposition are:

Figure BDA0003879662280000046
Figure BDA0003879662280000046

和and

Figure BDA0003879662280000051
Figure BDA0003879662280000051

其中，ES,k表示搜索射频资源消耗，ET,k表示跟踪射频资源消耗；

Figure BDA0003879662280000052
表示搜索重点观测区域a的节点选择方式，uS,k表示网络化雷达搜索节点选择方式，
Figure BDA0003879662280000053
表示跟踪目标q的节点选择方式，uT,k表示网络化雷达跟踪节点选择方式；
Figure BDA0003879662280000054
表示k时刻网络化雷达对重点观测区域a中目标的检测概率；
Figure BDA0003879662280000055
表示表征目标跟踪精度的衡量指标；pd,min和
Figure BDA0003879662280000056
分别为目标搜索性能和多目标跟踪精度要求；对于搜索任务，PS,max和PS,min分别表示搜索辐射功率的上下限，TS,max和TS,min分别表示搜索波束驻留时间的上下限；
Figure BDA0003879662280000057
表示雷达i搜索重点观测区域a时的辐射功率；
Figure BDA0003879662280000058
表示雷达i搜索重点观测区域a时波束的驻留时间；对于跟踪任务，PT,max和PT,min分别表示跟踪辐射功率的上下限，TT,max和TT,min分别表示跟踪波束驻留时间的上下限；
Figure BDA0003879662280000059
和
Figure BDA00038796622800000510
分别为k时刻雷达i单次照射目标q的辐射功率和驻留时间；LS表示同时搜索同一片圆形重点观测区域的雷达数量；A表示圆形重点观测区域的数量；MS表示用于对A个圆形重点观测区域执行搜索任务的雷达数量；
Figure BDA00038796622800000511
表示k时刻雷达i是否被选中对重点观测区域a进行搜索；
Figure BDA00038796622800000512
表示k时刻雷达i是否对目标q进行照射；LT表示同时照射同一个目标需要的雷达数量；Q表示运动目标的数量；MT表示用于执行对多个目标的跟踪任务的雷达的数量；1N×1表示N×1维的全1矩阵；Among them, E S,k represents the consumption of radio frequency resources for searching, and E T,k represents the consumption of radio frequency resources for tracking;
Figure BDA0003879662280000052
Indicates the node selection method for searching the key observation area a, u S,k indicates the node selection method for networked radar search,
Figure BDA0003879662280000053
Indicates the node selection method for tracking target q, uT ,k indicates the node selection method for networked radar tracking;
Figure BDA0003879662280000054
Indicates the detection probability of the target in the key observation area a by the networked radar at time k;
Figure BDA0003879662280000055
Represents the measurement index that characterizes the target tracking accuracy; p d,min and
Figure BDA0003879662280000056
are target search performance and multi-target tracking accuracy requirements; for search tasks, PS ,max and PS ,min respectively represent the upper and lower limits of search radiation power, and T S,max and T S,min represent the dwell time of search beams respectively upper and lower limits;
Figure BDA0003879662280000057
Indicates the radiation power of radar i when searching key observation area a;
Figure BDA0003879662280000058
Indicates the dwell time of the beam when radar i searches the key observation area a; for the tracking task, PT ,max and PT ,min respectively represent the upper and lower limits of the tracking radiation power, and TT,max and TT,min respectively represent the tracking beam The upper and lower limits of the dwell time;
Figure BDA0003879662280000059
and
Figure BDA00038796622800000510
Respectively, the radiation power and dwell time of radar i’s single irradiation target q at time k; L S represents the number of radars searching the same circular key observation area at the same time; A represents the number of circular key observation areas; M S represents the The number of radars performing search tasks on A circular key observation area;
Figure BDA00038796622800000511
Indicates whether radar i is selected to search key observation area a at time k;
Figure BDA00038796622800000512
Indicates whether radar i illuminates target q at time k; L T indicates the number of radars required to illuminate the same target at the same time; Q indicates the number of moving targets; M T indicates the number of radars used to perform tracking tasks for multiple targets; 1 N×1 means N×1-dimensional all-1 matrix;

将

Figure BDA00038796622800000513
和
Figure BDA00038796622800000514
分别松弛为
Figure BDA00038796622800000515
和
Figure BDA00038796622800000516
Will
Figure BDA00038796622800000513
and
Figure BDA00038796622800000514
respectively relax to
Figure BDA00038796622800000515
and
Figure BDA00038796622800000516

进一步的，采用内点法和循环最小法的两步求解算法对两个子优化模型进行求解的方法为：Furthermore, the method of solving the two sub-optimization models using the two-step solution algorithm of the interior point method and the circular minimum method is as follows:

(1)跟踪节点选择及资源分配；(1) Track node selection and resource allocation;

(a)初始化k时刻对目标q的预测贝叶斯信息矩阵

Figure BDA0003879662280000061
(a) Initialize the predicted Bayesian information matrix for target q at time k
Figure BDA0003879662280000061

(b)为各个雷达节点分配初始跟踪辐射功率和跟踪驻留时间；(b) Assign initial tracking radiation power and tracking dwell time to each radar node;

(c)将经过松弛后得到的连续变量

Figure BDA0003879662280000062
看作k时刻雷达i跟踪目标q的贡献度；在当前资源分配情况下，通过优化变量uT,k，最小化对目标q的跟踪误差；采用内点法求解子优化模型：(c) The continuous variable obtained after relaxation
Figure BDA0003879662280000062
It is regarded as the contribution degree of radar i tracking target q at time k; in the current resource allocation situation, by optimizing the variable u T,k , the tracking error of target q is minimized; the sub-optimization model is solved by interior point method:

Figure BDA0003879662280000063
Figure BDA0003879662280000063

得出各雷达在当前资源分配下跟踪目标q的贡献度

Figure BDA0003879662280000064
选择其中最大的LT个元素对应的雷达照射目标q，即选择对跟踪目标q贡献最大的LT部雷达；Obtain the contribution of each radar to track the target q under the current resource allocation
Figure BDA0003879662280000064
Select the radar irradiation target q corresponding to the largest L T elements, that is, select the L T radar that contributes the most to the tracking target q;

(d)在步骤(c)所得节点选择

Figure BDA0003879662280000065
的基础上，在目标跟踪精度和射频资源的约束下，联合优化相应雷达的辐射功率和驻留时间，以最小化总射频资源消耗；采用内点法求解子优化模型：(d) Node selection obtained in step (c)
Figure BDA0003879662280000065
On the basis of , under the constraints of target tracking accuracy and radio frequency resources, jointly optimize the radiation power and dwell time of the corresponding radar to minimize the total radio frequency resource consumption; use the interior point method to solve the sub-optimization model:

Figure BDA0003879662280000066
Figure BDA0003879662280000066

得出跟踪资源分配结果PT,k,0和TT,k,0，将该结果作为新的资源分配方案代入步骤(b)中并跳转步骤(b)，直到相邻两次计算出的总跟踪射频资源消耗之间的差值小于预设值；将最终被指定跟踪目标q的雷达对应的

Figure BDA0003879662280000067
置1，其余置0，即得出k时刻跟踪节点选择与资源分配结果；Obtain the tracking resource allocation results P T,k,0 and T T,k,0 , substitute the results into step (b) as a new resource allocation scheme and skip to step (b) until two consecutive calculations The difference between the total tracking radio frequency resource consumption of is less than the preset value; the radar corresponding to the designated tracking target q will eventually be
Figure BDA0003879662280000067
Set it to 1, and set the rest to 0, that is, the results of node selection and resource allocation at time k are obtained;

(2)搜索节点选择及资源分配；(2) Search node selection and resource allocation;

(a)确定跟踪节点选择之后，将在剩余雷达节点中进行对于多空域搜索任务的节点选择，先为剩余的雷达分配初始的搜索资源；(a) After determining the selection of tracking nodes, the node selection for the multi-airspace search task will be carried out among the remaining radar nodes, and the initial search resources will be allocated for the remaining radars;

(b)将经过松弛后得到的连续变量

Figure BDA0003879662280000068
看作k时刻雷达i对搜索重点观测区域a效果的贡献度；在当前资源分配下，优化搜索节点选择变量uS,k，最大化目标检测概率；求解子优化模型：(b) The continuous variable obtained after relaxation
Figure BDA0003879662280000068
Consider it as the contribution of radar i to the effect of searching the key observation area a at time k; under the current resource allocation, optimize the search node selection variable u S,k to maximize the target detection probability; solve the sub-optimization model:

Figure BDA0003879662280000071
Figure BDA0003879662280000071

得出各雷达在当前资源分配下对重点观测区域a中目标检测概率的贡献度，选择对应贡献最大的LS部雷达搜索重点观测区域a；Obtain the contribution degree of each radar to the target detection probability in the key observation area a under the current resource allocation, and select the L S part radar with the largest corresponding contribution to search the key observation area a;

(c)在当前节点选择下，联合优化相应雷达的辐射功率和驻留时间，以最小化总射频资源消耗为优化目标；求解子优化模型：(c) Under the current node selection, jointly optimize the radiation power and dwell time of the corresponding radar, and minimize the total radio frequency resource consumption as the optimization goal; solve the sub-optimization model:

Figure BDA0003879662280000072
Figure BDA0003879662280000072

得出搜索资源分配结果后，跳转步骤(a)，更新初始的搜索资源分配方案，直到相邻两次所得的总搜索射频资源消耗之间的差值小于预设值；将最终被指定搜索重点观测区域a的雷达对应的

Figure BDA0003879662280000073
置1，其余置0，即得出k时刻搜索节点选择与资源分配结果。After the search resource allocation result is obtained, jump to step (a) and update the initial search resource allocation plan until the difference between the total search radio frequency resource consumption obtained between two adjacent times is less than the preset value; it will be finally designated as the search resource The radar corresponding to the key observation area a
Figure BDA0003879662280000073
Set it to 1, and set the rest to 0, that is, the result of search node selection and resource allocation at time k is obtained.

本发明的基于射频隐身的网络化雷达目标搜索跟踪资源分配系统，包括：The networked radar target search and track resource allocation system based on radio frequency stealth of the present invention includes:

系统建模模块，用于建立由多部同步的相控阵雷达组成的网络化雷达，该网络化雷达需要同时完成对多个圆形重点观测区域的搜索，以及对已知数量的运动目标的跟踪；The system modeling module is used to establish a networked radar composed of multiple synchronized phased array radars. The networked radar needs to simultaneously complete the search for multiple circular key observation areas and the detection of a known number of moving targets. track;

衡量指标计算模块，用于基于网络化雷达对多个圆形重点观测区域搜索场景，计算网络化雷达对圆形重点观测区域中目标的检测概率作为搜索性能的衡量指标；并基于网络化雷达对多目标跟踪场景，计算目标位置估计的预测贝叶斯克拉美-罗下界作为多目标跟踪性能的衡量指标；The measurement index calculation module is used to search scenarios based on the networked radar for multiple circular key observation areas, and calculates the detection probability of the target in the circular key observation area by the networked radar as a measure of search performance; and based on the networked radar For multi-target tracking scenarios, compute a predictive Bayesian Cramer-Rao lower bound for target position estimates as a measure of multi-target tracking performance;

优化模型构建模块，用于在满足预先设定的搜索和多目标跟踪性能以及射频资源约束的条件下，以最小化网络化雷达的总射频资源消耗为优化目标，以雷达节点选择方式、辐射功率和驻留时间为优化参数，建立基于射频隐身的网络化雷达搜索跟踪资源分配模型；The optimization model building block is used to minimize the total radio frequency resource consumption of networked radar under the condition of satisfying the pre-set search and multi-target tracking performance and radio frequency resource constraints. and dwell time as optimization parameters, a networked radar search and tracking resource allocation model based on radio frequency stealth is established;

优化模型求解模块，用于将基于射频隐身的网络化雷达搜索跟踪资源分配模型分解为两个子优化模型，并采用内点法和循环最小法的两步求解算法对两个子优化模型进行求解。The optimization model solving module is used to decompose the networked radar search and tracking resource allocation model based on radio frequency stealth into two sub-optimization models, and solve the two sub-optimization models by using the two-step solution algorithm of interior point method and circular minimum method.

本发明的一种装置设备，包括存储器和处理器，其中：An apparatus of the present invention, comprising a memory and a processor, wherein:

存储器，用于存储能够在处理器上运行的计算机程序；memory for storing computer programs capable of running on the processor;

处理器，用于在运行所述计算机程序时，执行如上述基于射频隐身的网络化雷达目标搜索跟踪资源分配方法的步骤。The processor is configured to execute the steps of the radio frequency stealth-based networked radar target search and track resource allocation method when running the computer program.

本发明的一种存储介质，所述存储介质上存储有计算机程序，所述计算机程序被至少一个处理器执行时实现如上述基于射频隐身的网络化雷达目标搜索跟踪资源分配方法的步骤。A storage medium of the present invention stores a computer program on the storage medium, and when the computer program is executed by at least one processor, the steps of the above method for allocating networked radar target search and tracking resources based on radio frequency stealth are realized.

有益效果：与现有技术相比，本发明显著的技术效果为：通过对多空域搜索和多目标跟踪任务并存时的雷达节点选择、辐射功率和驻留时间等参数进行联合优化，在同时满足预先设定的目标搜索和多目标跟踪性能需求的条件下，最大限度地降低了网络化雷达的总射频资源消耗，提升了网络化雷达的射频隐身性能。产生该优点的原因是本发明推导了以雷达节点选择二元变量、各雷达辐射功率和驻留时间为自变量的目标检测概率以及预测贝叶斯克拉美-罗下界，并分别作为衡量目标搜索性能和多目标跟踪性能的指标；在此基础上，以网络化雷达有限的射频辐射资源、预先设定的各空域内目标的检测概率和对各运动目标的跟踪精度需求为约束条件，以最小化网络化雷达总射频辐射消耗为优化目标，联合优化雷达节点选择、各雷达辐射功率和驻留时间等参数。该方法可在同时满足搜索与跟踪性能需求的条件下，有效提升了网络化雷达多目标跟踪时的射频隐身性能。Beneficial effects: Compared with the prior art, the obvious technical effect of the present invention is: through the joint optimization of parameters such as radar node selection, radiation power and dwell time when multi-airspace search and multi-target tracking tasks coexist, while satisfying Under the condition of preset target search and multi-target tracking performance requirements, the total radio frequency resource consumption of the networked radar is minimized, and the radio frequency stealth performance of the networked radar is improved. The reason for this advantage is that the present invention derives the target detection probability and predicts the Bayesian Cramer-Rao lower bound with the radar node selection binary variable, each radar radiation power and dwell time as independent variables, and uses them respectively as a measure of target search Performance and multi-target tracking performance indicators; on this basis, with the limited radio frequency radiation resources of networked radars, the pre-set detection probability of targets in each airspace and the tracking accuracy requirements for each moving target as constraints, the minimum The total radio frequency radiation consumption of the networked radar is the optimization goal, and the parameters such as radar node selection, radar radiation power and dwell time are jointly optimized. This method can effectively improve the radio frequency stealth performance of networked radar multi-target tracking under the condition of meeting the performance requirements of search and tracking at the same time.

附图说明Description of drawings

图1为本发明方法流程图。Fig. 1 is a flow chart of the method of the present invention.

具体实施方式detailed description

下面结合附图对本发明做进一步说明。The present invention will be further described below in conjunction with the accompanying drawings.

本发明针对由多部时间同步的相控阵雷达组成的、需要同时完成多区域搜索和多目标跟踪任务的网络化雷达，在满足预先设定的目标检测概率和多目标预测跟踪精度以及网络化雷达发射资源约束的条件下，自适应地联合优化雷达节点选择、辐射功率和驻留时间等参数，最小化网络化雷达的总射频资源消耗，分别构建搜索和跟踪模型，推导以雷达节点选择二元变量、各雷达辐射功率和驻留时间为自变量的目标检测概率以及预测贝叶斯克拉美-罗下界，并分别作为衡量目标搜索性能和多目标跟踪性能的指标。以预先设定的目标搜索性能、多目标跟踪性能以及有限的射频资源为约束条件，以雷达节点选择方案uk、各雷达辐射功率Pk和驻留时间Tk为优化变量，以最小化网络化雷达的总射频资源消耗为优化目标，建立基于射频隐身的网络化雷达目标搜索跟踪资源分配数学模型。提出基于内点法和循环最小法的两步求解算法对该优化模型进行求解，在保证预先设定的搜索和跟踪性能的条件下，提升网络化雷达在搜索和跟踪任务并存时的射频隐身性能。The present invention is aimed at the networked radar which is composed of multiple time-synchronized phased array radars and needs to simultaneously complete multi-area search and multi-target tracking tasks. Under the constraints of radar transmission resources, adaptively jointly optimize parameters such as radar node selection, radiation power and dwell time, minimize the total radio frequency resource consumption of networked radar, build search and tracking models respectively, and derive the radar node selection The meta-variables, the radar radiation power and the dwell time are the independent variables of the target detection probability and the predicted Bayesian Cramer-Root lower bound, which are used as indicators to measure the target search performance and multi-target tracking performance. With the pre-set target search performance, multi-target tracking performance and limited radio frequency resources as constraints, the radar node selection scheme u k , each radar radiation power P k and dwell time T k are optimized variables to minimize the network Taking the total radio frequency resource consumption of radar as the optimization goal, a mathematical model of networked radar target search and tracking resource allocation based on radio frequency stealth is established. A two-step solution algorithm based on the interior point method and the circular minimum method is proposed to solve the optimization model. Under the condition of ensuring the preset search and tracking performance, the radio frequency stealth performance of the networked radar when the search and tracking tasks coexist is improved. .

本发明从实际工程应用需求出发，提出了基于射频隐身的网络化雷达目标搜索跟踪资源分配方法，以有限的射频辐射资源和预先设定的目标搜索性能和多目标跟踪性能为约束，以最小化网络化雷达的总射频资源消耗为优化目标，通过联合优化雷达选择、雷达辐射功率和驻留时间等参数，提升网络化雷达执行目标搜索和跟踪任务时的射频隐身性能。Starting from the actual engineering application requirements, the present invention proposes a networked radar target search and tracking resource allocation method based on radio frequency stealth, constrained by limited radio frequency radiation resources and preset target search performance and multi-target tracking performance, to minimize The total radio frequency resource consumption of networked radars is the optimization goal. By jointly optimizing parameters such as radar selection, radar radiation power, and dwell time, the radio frequency stealth performance of networked radars when performing target search and tracking tasks is improved.

如图1所示，本发明的基于射频隐身的网络化雷达目标搜索跟踪资源分配方法，包括以下步骤：As shown in Figure 1, the networked radar target search and track resource allocation method based on radio frequency stealth of the present invention comprises the following steps:

1、建立系统模型：1. Establish a system model:

考虑由多部同步的相控阵雷达组成的网络化雷达，需要同时完成对多个圆形重点观测区域的搜索，以及对已知数量的运动目标的跟踪。假设多目标跟踪任务的优先级高于目标搜索任务，每一部相控阵雷达每一时刻只能产生一个波束，即单部雷达每一时刻只能搜索一片空域或照射一个目标，并且每部雷达只能接收并处理自身发射信号的回波。Considering a networked radar composed of multiple synchronized phased array radars, it is necessary to simultaneously complete the search of multiple circular key observation areas and the tracking of a known number of moving targets. Assuming that the priority of the multi-target tracking task is higher than that of the target search task, each phased array radar can only generate one beam at a time, that is, a single radar can only search an airspace or illuminate one target at a time, and each Radar can only receive and process the echoes of its own transmitted signal.

2、构建网络化雷达对多个圆形重点观测区域搜索场景，并采用检测概率作为搜索性能的衡量指标：2. Build a networked radar to search for multiple circular key observation areas, and use the detection probability as a measure of search performance:

在由N部雷达组成的网络化雷达中，MS部雷达用于对S个圆形重点观测区域执行搜索任务。假设每一时刻单部雷达只能照射一片区域，每一片区域需要同时被LS部雷达搜索。k时刻雷达i对重点观测区域a(a＝1,2,…,A)扫描n次后得到的检测概率

Figure BDA0003879662280000091
为：In the networked radar composed of N radars, M S radars are used to perform search tasks on S circular key observation areas. Assume that a single radar can only illuminate one area at a time, and each area needs to be searched by the L S radar at the same time. The detection probability obtained by radar i scanning the key observation area a (a=1,2,…,A) n times at time k
Figure BDA0003879662280000091
for:

Figure BDA0003879662280000092
Figure BDA0003879662280000092

其中，Pfa为虚警概率，

Figure BDA0003879662280000093
为k时刻雷达i搜索重点观测区域a时照射到目标后可获得的回波信噪比，表示为：Among them, Pfa is the false alarm probability,
Figure BDA0003879662280000093
is the echo signal-to-noise ratio that can be obtained after the radar i searches for the key observation area a at time k and irradiates the target, expressed as:

Figure BDA0003879662280000101
Figure BDA0003879662280000101

其中，二元变量

Figure BDA0003879662280000102
表示k时刻雷达i是否被选中对重点观测区域a进行搜索；
Figure BDA0003879662280000103
表示雷达i搜索重点观测区域a时的辐射功率；Ae和σ分别表示天线有效面积和目标的雷达散射截面；
Figure BDA0003879662280000104
表示雷达i搜索重点观测区域a时波束的驻留时间；kB、Te和L分别表示玻尔兹曼常数、雷达系统温度和系统损耗；搜索距离范围
Figure BDA0003879662280000105
为雷达i与重点观测区域a边界之间最远的距离，搜索角度范围
Figure BDA0003879662280000106
为雷达i覆盖重点观测区域a的角度值。where the binary variable
Figure BDA0003879662280000102
Indicates whether radar i is selected to search key observation area a at time k;
Figure BDA0003879662280000103
Indicates the radiation power when radar i searches key observation area a; A e and σ denote the effective area of the antenna and the radar cross section of the target, respectively;
Figure BDA0003879662280000104
Indicates the residence time of the beam when radar i searches for the key observation area a; k B , Te and L represent the Boltzmann constant, radar system temperature and system loss respectively; the search distance range
Figure BDA0003879662280000105
is the farthest distance between radar i and the boundary of key observation area a, search angle range
Figure BDA0003879662280000106
is the angle value of the key observation area a covered by radar i.

如前所述，有LS部雷达用于对重点观测区域a的搜索，于是，k时刻网络化雷达对圆形重点观测区域a中目标的检测概率可以表示为：As mentioned above, there are L and S radars used to search the key observation area a, so the detection probability of the target in the circular key observation area a by the networked radar at time k can be expressed as:

Figure BDA0003879662280000107
Figure BDA0003879662280000107

3、构建网络化雷达对多目标跟踪场景，并采用目标位置估计的预测贝叶斯克拉美-罗下界作为多目标跟踪性能的衡量指标：3. Construct a multi-target tracking scenario of networked radar, and use the predicted Bayesian Cramer-Rao lower bound of target position estimation as a measure of multi-target tracking performance:

在由N部雷达组成的网络化雷达中，共有MT部雷达执行对多个目标的跟踪任务。k时刻运动目标q(q＝1,2,…,Q)的状态向量可以表示为

Figure BDA0003879662280000108
其中，
Figure BDA0003879662280000109
和
Figure BDA00038796622800001010
分别表示在k时刻第q个目标的位置和速度。假设目标做匀速直线运动，则运动目标的状态方程可以表示为：In the networked radar composed of N radars, there are M T radars to perform tracking tasks for multiple targets. The state vector of moving target q (q=1,2,...,Q) at time k can be expressed as
Figure BDA0003879662280000108
in,
Figure BDA0003879662280000109
and
Figure BDA00038796622800001010
represent the position and velocity of the qth target at time k, respectively. Assuming that the target moves in a straight line at a uniform speed, the state equation of the moving target can be expressed as:

Figure BDA00038796622800001011
Figure BDA00038796622800001011

其中，

Figure BDA00038796622800001012
表示状态转移矩阵，T表示采样间隔，
Figure BDA00038796622800001013
表示克罗内克积，I2为2阶单位矩阵。
Figure BDA00038796622800001014
表示k+1时刻运动目标q的状态向量；Wq表示均值为零的高斯过程白噪声，其协方差矩阵Qq可以表示为：in,
Figure BDA00038796622800001012
Represents the state transition matrix, T represents the sampling interval,
Figure BDA00038796622800001013
Represents the Kronecker product, and I 2 is a 2nd-order identity matrix.
Figure BDA00038796622800001014
Represents the state vector of the moving target q at time k+1; W q represents Gaussian process white noise with a mean value of zero, and its covariance matrix Q q can be expressed as:

Figure BDA00038796622800001015
Figure BDA00038796622800001015

其中，rq表示过程噪声强度。Among them, r q represents the process noise intensity.

本发明假设网络化雷达在执行多目标跟踪任务时，每个时刻单部雷达只能照射一个目标，每个目标需要同时被LT部雷达照射。二元变量

Figure BDA00038796622800001016
表示k时刻雷达i是否对目标q进行照射。因此，k时刻雷达i对目标q的量测模型可以表示为：The present invention assumes that when the networked radar performs multi-target tracking tasks, a single radar can only illuminate one target at each moment, and each target needs to be illuminated by the L T radar at the same time. binary variable
Figure BDA00038796622800001016
Indicates whether radar i illuminates target q at time k. Therefore, the measurement model of radar i to target q at time k can be expressed as:

Figure BDA0003879662280000111
Figure BDA0003879662280000111

其中，

Figure BDA0003879662280000112
表示在k时刻雷达i跟踪目标q时对应的量测矢量，
Figure BDA0003879662280000113
表示包含目标距离和方位角信息的非线性观测函数，可以表示为：in,
Figure BDA0003879662280000112
Indicates the corresponding measurement vector when radar i tracks target q at time k,
Figure BDA0003879662280000113
Represents a nonlinear observation function containing target distance and azimuth information, which can be expressed as:

Figure BDA0003879662280000114
Figure BDA0003879662280000114

其中，(xi,yi)表示雷达i的位置坐标，

Figure BDA0003879662280000115
表示服从零均值高斯分布的量测噪声矢量，其协方差矩阵
Figure BDA0003879662280000116
Figure BDA0003879662280000117
和
Figure BDA0003879662280000118
分别为距离和方位角信息估计均方误差的下限：Among them, (x i , y i ) represent the position coordinates of radar i,
Figure BDA0003879662280000115
Represents a measurement noise vector subject to a zero-mean Gaussian distribution, and its covariance matrix
Figure BDA0003879662280000116
Figure BDA0003879662280000117
and
Figure BDA0003879662280000118
The lower bounds of the mean square error are estimated for range and azimuth information respectively:

Figure BDA0003879662280000119
Figure BDA0003879662280000119

其中，c为光速；β为发射信号的有效带宽；λ和γ分别为信号波长和天线孔径。假设

Figure BDA00038796622800001110
和
Figure BDA00038796622800001111
分别为k时刻雷达i单次照射目标q的辐射功率和驻留时间，Tr为脉冲重复周期，则k时刻雷达可进行
Figure BDA00038796622800001112
个脉冲的相干积累，便可得到相干积累后雷达i对目标q照射的回波信噪比
Figure BDA00038796622800001113
该信噪比是关于
Figure BDA00038796622800001114
和
Figure BDA00038796622800001115
的函数。Among them, c is the speed of light; β is the effective bandwidth of the transmitted signal; λ and γ are the signal wavelength and antenna aperture, respectively. suppose
Figure BDA00038796622800001110
and
Figure BDA00038796622800001111
are respectively the radiation power and dwell time of radar i irradiating target q once at time k, and T r is the pulse repetition period, then the radar at time k can perform
Figure BDA00038796622800001112
The coherent accumulation of pulses can obtain the echo signal-to-noise ratio of radar i irradiating target q after coherent accumulation
Figure BDA00038796622800001113
The signal-to-noise ratio is about
Figure BDA00038796622800001114
and
Figure BDA00038796622800001115
The function.

将k时刻预测贝叶斯克拉美-罗下界矩阵的对角线元素中表示目标位置估计均方误差下界的元素提取出来，作为表征目标跟踪精度的衡量指标：Extract the elements representing the lower bound of the target position estimation mean square error from the diagonal elements of the predicted Bayesian Cramer-Roo lower bound matrix at k time, as a measure of the target tracking accuracy:

Figure BDA00038796622800001116
Figure BDA00038796622800001116

其中，结合k时刻目标预测状态的贝叶斯信息矩阵

Figure BDA00038796622800001117
和雅克比矩阵
Figure BDA00038796622800001118
目标状态估计误差预测贝叶斯克拉美-罗下界矩阵
Figure BDA00038796622800001119
的表达式为：Among them, combined with the Bayesian information matrix of the target prediction state at time k
Figure BDA00038796622800001117
and the Jacobian matrix
Figure BDA00038796622800001118
Target State Estimation Error Prediction Bayesian Cramer-Rao Lower Bound Matrix
Figure BDA00038796622800001119
The expression is:

Figure BDA00038796622800001120
Figure BDA00038796622800001120

其中，

Figure BDA00038796622800001121
表示k-1时刻目标状态的贝叶斯信息矩阵，
Figure BDA00038796622800001122
表示k时刻目标预测状态的贝叶斯信息矩阵；
Figure BDA0003879662280000121
表示k时刻目标预测状态的雅克比矩阵；
Figure BDA0003879662280000122
表示k时刻目标量测误差协方差矩阵；上标(·)-1表示矩阵的逆矩阵；上标(·)T表示矩阵的转置。in,
Figure BDA00038796622800001121
Represents the Bayesian information matrix of the target state at time k-1,
Figure BDA00038796622800001122
Represents the Bayesian information matrix of the target prediction state at time k;
Figure BDA0003879662280000121
Represents the Jacobian matrix of the target prediction state at time k;
Figure BDA0003879662280000122
Represents the target measurement error covariance matrix at time k; the superscript (·) -1 represents the inverse matrix of the matrix; the superscript (·) T represents the transpose of the matrix.

4、在满足预先设定的搜索和多目标跟踪性能以及射频资源约束的条件下，以最小化网络化雷达的总射频资源消耗为优化目标，以雷达节点选择方式、辐射功率和驻留时间为优化参数，建立基于射频隐身的网络化雷达搜索跟踪资源分配模型：4. Under the conditions of satisfying the pre-set search and multi-target tracking performance and radio frequency resource constraints, the optimization goal is to minimize the total radio frequency resource consumption of networked radar, and the radar node selection method, radiation power and dwell time are Optimize parameters and establish a networked radar search and tracking resource allocation model based on radio frequency stealth:

Figure BDA0003879662280000123
Figure BDA0003879662280000123

其中，Etot,k表示总射频资源消耗；

Figure BDA0003879662280000124
表示k时刻的网络化雷达节点选择方式，
Figure BDA0003879662280000125
表示搜索重点观测区域a的节点选择方式，
Figure BDA0003879662280000126
表示网络化雷达搜索节点选择方式，
Figure BDA0003879662280000127
表示跟踪目标q的节点选择方式，
Figure BDA0003879662280000128
表示网络化雷达跟踪节点选择方式；类似地，Pk＝[PS,k,PT,k]T和Tk＝[TS,k,TT,k]T分别表示k时刻的网络化雷达的辐射功率和驻留时间资源分配；1N×1表示N×1维的全1矩阵；pd,min和
Figure BDA0003879662280000129
分别为目标搜索性能和多目标跟踪精度要求；对于搜索任务，PS,max和PS,min分别表示搜索辐射功率的上下限，TS,max和TS,min分别表示搜索波束驻留时间的上下限；对于跟踪任务，PT,max和PT,min分别表示跟踪辐射功率的上下限，TT,max和TT,min分别表示跟踪波束驻留时间的上下限。Wherein, E tot,k represents the total radio frequency resource consumption;
Figure BDA0003879662280000124
Indicates the networked radar node selection method at time k,
Figure BDA0003879662280000125
Indicates the node selection method for searching the key observation area a,
Figure BDA0003879662280000126
Indicates the networked radar search node selection method,
Figure BDA0003879662280000127
Indicates the node selection method for tracking target q,
Figure BDA0003879662280000128
Indicates the networked radar tracking node selection method; similarly, P k ＝[P S,k ,P T,k ] T and T k ＝[T S,k ,T T,k ] T respectively represent the networked Radar radiated power and dwell time resource allocation; 1 N×1 represents an N×1-dimensional all-ones matrix; p d,min and
Figure BDA0003879662280000129
are target search performance and multi-target tracking accuracy requirements; for search tasks, PS ,max and PS ,min respectively represent the upper and lower limits of search radiation power, and T S,max and T S,min represent the dwell time of search beams respectively For the tracking task, PT ,max and PT ,min represent the upper and lower limits of the tracking radiation power, and TT,max and TT ,min respectively represent the upper and lower limits of the tracking beam dwell time.

总射频资源消耗Etot,k定义为搜索和跟踪射频资源消耗的总和，可以表示为：The total radio frequency resource consumption E tot,k is defined as the sum of search and track radio resource consumption, which can be expressed as:

Figure BDA0003879662280000131
Figure BDA0003879662280000131

其中，ES,k表示搜索射频资源消耗，ET,k表示跟踪射频资源消耗；α1和α2分别表示辐射功率和驻留时间的权重系数；pd,min和

Figure BDA0003879662280000134
分别为目标搜索性能和多目标跟踪精度要求；对于搜索任务，PS,max和PS,min表示搜索辐射功率的上下限，TS,max和TS,min表示搜索波束驻留时间的上下限；类似地，对于多目标跟踪任务，辐射功率介于PT,min与PT,max之间，驻留时间介于TT,min和TT,max之间。Among them, E S,k represents the search radio frequency resource consumption, E T,k represents the tracking radio frequency resource consumption; α 1 and α 2 represent the weight coefficients of radiation power and dwell time respectively; p d,min and
Figure BDA0003879662280000134
are target search performance and multi-target tracking accuracy requirements; for search tasks, PS ,max and PS ,min represent the upper and lower limits of the search radiation power, and T S,max and T S,min represent the upper and lower limits of the search beam dwell time Lower bound; similarly, for the multi-target tracking task, the radiation power is between PT ,min and PT ,max , and the dwell time is between TT,min and TT,max .

5、提出基于内点法和循环最小法的两步求解算法对上述优化模型进行求解，在搜索跟踪性能和射频资源的约束下，联合优化网络化雷达搜索和多目标跟踪时的节点选择、辐射功率和驻留时间资源分配。考虑到搜索资源与跟踪资源的分配并不存在耦合关系，所以可以将基于射频隐身的网络化雷达搜索跟踪资源分配模型(11)分解为如下两个子优化模型：5. A two-step solution algorithm based on the interior point method and the circular minimum method is proposed to solve the above optimization model, and under the constraints of search and tracking performance and radio frequency resources, jointly optimize node selection and radiation during networked radar search and multi-target tracking Power and dwell time resource allocation. Considering that there is no coupling relationship between the allocation of search resources and tracking resources, the networked radar search and tracking resource allocation model (11) based on radio frequency stealth can be decomposed into the following two sub-optimization models:

Figure BDA0003879662280000132
Figure BDA0003879662280000132

和and

Figure BDA0003879662280000133
Figure BDA0003879662280000133

由于优化变量

Figure BDA0003879662280000141
和
Figure BDA0003879662280000142
是离散的整数变量，以上优化模型都是难以求解的非凸、非线性的混合整数规划模型。于是，为简化求解，将
Figure BDA0003879662280000143
和
Figure BDA0003879662280000144
分别松弛为
Figure BDA0003879662280000145
和
Figure BDA0003879662280000146
考虑到多目标跟踪任务的优先级较高，提出基于内点法和循环最小法的两步求解算法，具体求解步骤如下：Due to optimization variables
Figure BDA0003879662280000141
and
Figure BDA0003879662280000142
is a discrete integer variable, and the above optimization models are non-convex, nonlinear mixed integer programming models that are difficult to solve. Therefore, to simplify the solution, the
Figure BDA0003879662280000143
and
Figure BDA0003879662280000144
respectively relax to
Figure BDA0003879662280000145
and
Figure BDA0003879662280000146
Considering the high priority of multi-target tracking tasks, a two-step solution algorithm based on interior point method and circular minimum method is proposed. The specific solution steps are as follows:

(1)跟踪节点选择及资源分配；(1) Track node selection and resource allocation;

(a)初始化k时刻对目标q的预测贝叶斯信息矩阵

Figure BDA0003879662280000147
(a) Initialize the predicted Bayesian information matrix for target q at time k
Figure BDA0003879662280000147

(b)为各个雷达节点分配初始跟踪辐射功率和跟踪驻留时间；(b) Assign initial tracking radiation power and tracking dwell time to each radar node;

(c)将经过松弛后得到的连续变量

Figure BDA0003879662280000148
看作k时刻雷达i跟踪目标q的贡献度。在当前资源分配情况下，通过优化变量uT,k，最小化对目标q的跟踪误差。采用内点法求解子优化模型：(c) The continuous variable obtained after relaxation
Figure BDA0003879662280000148
It is regarded as the contribution degree of radar i tracking target q at time k. In the current resource allocation situation, the tracking error of the target q is minimized by optimizing the variable u T,k . Solve the sub-optimization model using the interior point method:

Figure BDA0003879662280000149
Figure BDA0003879662280000149

可得出各雷达在当前资源分配下跟踪目标q的贡献度

Figure BDA00038796622800001410
选择其中最大的LT个元素对应的雷达照射目标q，即选择对跟踪目标q贡献最大的LT部雷达。The contribution of each radar to track target q under the current resource allocation can be obtained
Figure BDA00038796622800001410
Select the radar irradiation target q corresponding to the largest L T elements, that is, select the L T radar that contributes the most to the tracking target q.

(d)在步骤(c)所得节点选择

Figure BDA00038796622800001411
的基础上，在目标跟踪精度和射频资源的约束下，联合优化相应雷达的辐射功率和驻留时间，以最小化总射频资源消耗。采用内点法求解子优化模型：(d) Node selection obtained in step (c)
Figure BDA00038796622800001411
On the basis of , under the constraints of target tracking accuracy and radio frequency resources, the radiation power and dwell time of the corresponding radar are jointly optimized to minimize the total radio frequency resource consumption. Solve the sub-optimization model using the interior point method:

Figure BDA00038796622800001412
Figure BDA00038796622800001412

可得出跟踪资源分配结果PT,k,0和TT,k,0，将该结果作为新的资源分配方案代入步骤(b)中并跳转步骤(b)，直到相邻两次计算出的总跟踪射频资源消耗之间的差值小于一个预设值。将最终被指定跟踪目标q的雷达对应的

Figure BDA00038796622800001413
置1，其余置0，即可得出k时刻跟踪节点选择与资源分配结果。The tracking resource allocation results P T,k,0 and T T,k,0 can be obtained, and the results are substituted into step (b) as a new resource allocation scheme and skip to step (b) until two adjacent calculations The difference between the total traced radio frequency resource consumption is smaller than a preset value. will eventually be designated to track the target q radar corresponding to
Figure BDA00038796622800001413
Set it to 1, and set the rest to 0 to get the result of node selection and resource allocation at time k.

(2)搜索节点选择及资源分配；(2) Search node selection and resource allocation;

(a)确定跟踪节点选择之后，将在剩余雷达节点中进行对于多空域搜索任务的节点选择，与跟踪节点选择类似，先为剩余的雷达分配初始的搜索资源；(a) After determining the selection of tracking nodes, the node selection for the multi-airspace search task will be carried out among the remaining radar nodes. Similar to the selection of tracking nodes, the initial search resources will be allocated to the remaining radars;

(b)将经过松弛后得到的连续变量

Figure BDA0003879662280000151
看作k时刻雷达i对搜索重点观测区域a效果的贡献度。在当前资源分配下，优化搜索节点选择变量uS,k，最大化目标检测概率。求解子优化模型：(b) The continuous variable obtained after relaxation
Figure BDA0003879662280000151
It is regarded as the contribution of radar i to the effect of searching key observation area a at time k. Under the current resource allocation, optimize the search node selection variable u S,k to maximize the target detection probability. Solve a suboptimization model:

Figure BDA0003879662280000152
Figure BDA0003879662280000152

可得出各雷达在当前资源分配下对重点观测区域a中目标检测概率的贡献度，选择对应贡献最大的LS部雷达搜索重点观测区域a。The contribution degree of each radar to the target detection probability in the key observation area a can be obtained under the current resource allocation, and the corresponding L S radar with the largest contribution is selected to search the key observation area a.

(c)在当前节点选择下，联合优化相应雷达的辐射功率和驻留时间，以最小化总射频资源消耗为优化目标。求解子优化模型：(c) Under the current node selection, jointly optimize the radiation power and dwell time of the corresponding radar, with the optimization goal of minimizing the total radio frequency resource consumption. Solve a suboptimization model:

Figure BDA0003879662280000153
Figure BDA0003879662280000153

得出搜索资源分配结果后，跳转步骤(a)，更新初始的搜索资源分配方案，直到相邻两次所得的总搜索射频资源消耗之间的差值小于一个预设值。将最终被指定搜索空域s的雷达对应的

Figure BDA0003879662280000154
置1，其余置0，即可得出k时刻搜索节点选择与资源分配结果。After the search resource allocation result is obtained, jump to step (a) and update the initial search resource allocation scheme until the difference between the total search radio frequency resource consumption obtained twice adjacently is less than a preset value. will eventually be designated to search the airspace s for the radar corresponding to
Figure BDA0003879662280000154
Set it to 1, and set the rest to 0 to get the result of search node selection and resource allocation at time k.

本发明的基于射频隐身的网络化雷达目标搜索跟踪资源分配系统，包括：The networked radar target search and track resource allocation system based on radio frequency stealth of the present invention includes:

系统建模模块，用于建立由多部同步的相控阵雷达组成的网络化雷达，该网络化雷达需要同时完成对多个圆形重点观测区域的搜索，以及对已知数量的运动目标的跟踪；The system modeling module is used to establish a networked radar composed of multiple synchronized phased array radars. The networked radar needs to simultaneously complete the search for multiple circular key observation areas and the detection of a known number of moving targets. track;

衡量指标计算模块，用于基于网络化雷达对多个圆形重点观测区域搜索场景，计算网络化雷达对圆形重点观测区域中目标的检测概率作为搜索性能的衡量指标；并基于网络化雷达对多目标跟踪场景，计算目标位置估计的预测贝叶斯克拉美-罗下界作为多目标跟踪性能的衡量指标；The measurement index calculation module is used to search scenarios based on the networked radar for multiple circular key observation areas, and calculates the detection probability of the target in the circular key observation area by the networked radar as a measure of search performance; and based on the networked radar For multi-target tracking scenarios, compute a predictive Bayesian Cramer-Rao lower bound for target position estimates as a measure of multi-target tracking performance;

优化模型构建模块，用于在满足预先设定的搜索和多目标跟踪性能以及射频资源约束的条件下，以最小化网络化雷达的总射频资源消耗为优化目标，以雷达节点选择方式、辐射功率和驻留时间为优化参数，建立基于射频隐身的网络化雷达搜索跟踪资源分配模型；The optimization model building block is used to minimize the total radio frequency resource consumption of networked radar under the condition of satisfying the pre-set search and multi-target tracking performance and radio frequency resource constraints. and dwell time as optimization parameters, a networked radar search and tracking resource allocation model based on radio frequency stealth is established;

优化模型求解模块，用于将基于射频隐身的网络化雷达搜索跟踪资源分配模型分解为两个子优化模型，并采用内点法和循环最小法的两步求解算法对两个子优化模型进行求解。The optimization model solving module is used to decompose the networked radar search and tracking resource allocation model based on radio frequency stealth into two sub-optimization models, and solve the two sub-optimization models by using the two-step solution algorithm of interior point method and circular minimum method.

本发明的一种装置设备，包括存储器和处理器，其中：An apparatus of the present invention, comprising a memory and a processor, wherein:

存储器，用于存储能够在处理器上运行的计算机程序；memory for storing computer programs capable of running on the processor;

处理器，用于在运行所述计算机程序时，执行如上述基于射频隐身的网络化雷达目标搜索跟踪资源分配方法的步骤，并达到如上述方法一致的技术效果。The processor is configured to execute the steps of the radio frequency stealth-based networked radar target search and tracking resource allocation method described above when running the computer program, and achieve the same technical effect as the above method.

本发明的一种存储介质，所述存储介质上存储有计算机程序，所述计算机程序被至少一个处理器执行时实现如上述基于射频隐身的网络化雷达目标搜索跟踪资源分配方法的步骤，并达到如上述方法一致的技术效果。In a storage medium of the present invention, a computer program is stored on the storage medium, and when the computer program is executed by at least one processor, the steps of the above method for allocating networked radar target search and tracking resources based on radio frequency stealth are realized, and achieve Same technical effect as above method.

本发明创造的工作原理及工作过程：Working principle and working process of the present invention:

本发明考虑由多部同步的相控阵雷达组成的网络化雷达，需要同时完成对多个圆形重点观测区域的搜索，以及对已知数量的运动目标的跟踪。假设多目标跟踪任务的优先级高于目标搜索任务，每一部相控阵雷达每一时刻只能产生一个波束，即单部雷达每一时刻只能搜索一片空域或照射一个目标，并且每部雷达只能接收并处理自身发射信号的回波。首先，建立了网络化雷达对多个重点观测区域搜索场景，并推导了检测概率作为各区域内目标搜索性能衡量指标；同时，构建了网络化雷达对多目标跟踪场景，并推导了预测贝叶斯克拉美-罗下界作为目标跟踪性能衡量指标。然后，以最小化网络化雷达的射频资源消耗为优化目标，以雷达节点选择方式、各雷达发射功率和驻留时间作为优化参数，以预先设定的目标搜索性能和多目标跟踪性能以及有限的射频资源为约束条件，建立了基于射频隐身的网络化雷达搜索跟踪资源分配模型。最后，采用基于内点法和循环最小法的两步求解算法对上述优化模型进行了求解。求解该优化模型后，将所得的雷达节点选择方案uk、各雷达辐射功率Pk和驻留时间Tk代入式(11)，即可得到符合约束条件的基于射频隐身的网络化雷达搜索跟踪资源分配结果。The invention considers that the networked radar composed of multiple synchronous phased array radars needs to simultaneously complete the search of multiple circular key observation areas and the tracking of a known number of moving targets. Assuming that the priority of the multi-target tracking task is higher than that of the target search task, each phased array radar can only generate one beam at a time, that is, a single radar can only search an airspace or illuminate one target at a time, and each Radar can only receive and process the echoes of its own transmitted signal. First, a networked radar search scenario for multiple key observation areas is established, and the detection probability is derived as a target search performance indicator in each area; at the same time, a networked radar tracking scene for multiple targets is constructed, and the prediction Bayesian model is derived The Scramer-Roo lower bound is used as an object tracking performance measure. Then, with the optimization goal of minimizing the radio frequency resource consumption of networked radars, the radar node selection method, the transmit power and dwell time of each radar are used as optimization parameters, and the preset target search performance and multi-target tracking performance and limited With radio frequency resources as constraints, a networked radar search and tracking resource allocation model based on radio frequency stealth is established. Finally, a two-step solution algorithm based on the interior point method and the circular minimum method is used to solve the above optimization model. After solving the optimization model, substituting the obtained radar node selection scheme u k , each radar radiation power P k and dwell time T k into equation (11), the networked radar search and tracking based on radio frequency stealth that meets the constraints can be obtained Resource allocation results.

Claims (10)

1. The networked radar target searching and tracking resource allocation method based on radio frequency stealth is characterized by comprising the following steps of:
establishing a system model: considering a networked radar consisting of a plurality of synchronous phased array radars, searching a plurality of circular key observation areas and tracking a known number of moving targets need to be completed simultaneously; the priority of the multi-target tracking task is higher than that of the target searching task, and each phased array radar can only generate one wave beam at each moment;
constructing a search scene of a networked radar for a plurality of circular key observation areas, and adopting detection probability as a measurement index of search performance;
constructing a multi-target tracking scene of the networked radar, and adopting a predicted Bayesian-Lame lower bound of target position estimation as a measurement index of multi-target tracking performance;
under the condition of meeting preset searching and multi-target tracking performance and radio frequency resource constraint, taking the total radio frequency resource consumption of the minimized networked radar as an optimization target, and taking a radar node selection mode, radiation power and residence time as optimization parameters, and establishing a radio frequency stealth-based networked radar searching and tracking resource allocation model;
the model is decomposed into two sub-optimization models, the two sub-optimization models are solved by adopting a two-step solving algorithm of an inner point method and a cyclic minimum method, and node selection, radiation power and residence time resource allocation during networked radar search and multi-target tracking are jointly optimized under the constraints of search tracking performance and radio frequency resources.
2. The method for allocating the radio frequency stealth-based networked radar target search tracking resources according to claim 1, wherein a search scene of the networked radar for a plurality of circular key observation areas is constructed, and detection probability is used as a measure index of search performance, and specifically the method comprises the following steps:
in a networked radar consisting of N radars, M S The partial radar is used for executing a search task on A circular key observation areas; a single radar can only illuminate one area at a time, and each area needs to be simultaneously L S Searching by a radar; the detection probability obtained after the radar i scans the observation area a of the counterweight n times at the moment k
Figure FDA0003879662270000011
Comprises the following steps:
Figure FDA0003879662270000012
wherein, a =1,2, …, A, P fa In order to be the probability of a false alarm,
Figure FDA0003879662270000013
the echo signal-to-noise ratio which can be obtained after the radar i irradiates the target when searching the key observation area a at the moment k;
has L S The partial radar is used for searching the key observation area a, and the detection probability of the networked radar at the moment k on the target in the circular key observation area a is represented as follows:
Figure FDA0003879662270000021
3. the method for allocating the resources for searching and tracking the networked radar target based on the radio frequency stealth according to claim 1, wherein the measurement indexes of the multi-target tracking performance are as follows:
Figure FDA0003879662270000022
wherein,
Figure FDA0003879662270000023
predicting a Bayesian Classmei-Rou lower bound matrix for the target state estimation error, wherein the expression is as follows:
Figure FDA0003879662270000024
wherein,
Figure FDA0003879662270000025
a Bayesian information matrix representing the state of the target at time k-1,
Figure FDA0003879662270000026
a Bayesian information matrix representing a target prediction state at the moment k;
Figure FDA0003879662270000027
a Jacobian matrix representing the target prediction state at the time k;
Figure FDA0003879662270000028
representing a covariance matrix of target measurement errors at the moment k; superscript (·) -1 An inverse matrix representing a matrix; superscript (·) T Represents a transpose of a matrix; q q A covariance matrix representing white gaussian process noise with a mean of zero; f represents a state transition matrix; n meterIndicating the number of radars in the networked radar;
Figure FDA0003879662270000029
indicating whether the radar i is irradiating the target q at the time k.
4. The method for allocating the resources for searching and tracking the networked radar target based on the radio frequency stealth as claimed in claim 1, wherein the model for allocating the resources for searching and tracking the networked radar based on the radio frequency stealth is as follows:
Figure FDA00038796622700000210
Figure FDA00038796622700000211
wherein, E tot,k Representing the total radio frequency resource consumption; u. of k ＝[u S,k ,u T,k ] T Representing the networked radar node selection mode at the time k,
Figure FDA00038796622700000212
the node selection mode of searching the key observation area a is shown,
Figure FDA00038796622700000213
indicating a networked radar search node selection mode,
Figure FDA00038796622700000214
represents a node selection manner of the tracking target q,
Figure FDA0003879662270000031
representing a networked radar tracking node selection mode; p k ＝[P S,k ,P T,k ] T And T k ＝[T S,k ,T T,k ] T Respectively representDistributing the radiation power and residence time resources of the networked radar at the moment k;
Figure FDA0003879662270000032
the detection probability of the networked radar to the target in the key observation area a at the moment k is shown;
Figure FDA0003879662270000033
representing a measurement index representing the tracking precision of the target; p is a radical of d,min And
Figure FDA0003879662270000034
respectively meeting the requirements of target searching performance and multi-target tracking precision; for search tasks, P S,max And P S,min Respectively representing the upper and lower limits of the search radiation power, T S,max And T S,min Respectively representing the upper limit and the lower limit of the search beam residence time;
Figure FDA0003879662270000035
representing the radiation power when the radar i searches for the key observation area a;
Figure FDA0003879662270000036
representing the beam residence time when the radar i searches for the key observation area a; for trace tasks, P T,max And P T,min Respectively representing the upper and lower limits of the tracking radiation power, T T,max And T T,min Respectively representing the upper limit and the lower limit of the residence time of the tracking wave beam;
Figure FDA0003879662270000037
and
Figure FDA0003879662270000038
respectively determining the radiation power and the residence time of the radar i at the moment k for irradiating the target q once; l is S Representing the number of radars searching the same circular key observation area at the same time; a represents the number of circular key observation areas; m S Showing for A circular key observation regionsThe number of radars performing the search task;
Figure FDA0003879662270000039
whether the radar i at the moment k is selected or not is shown, and a key observation area a is searched;
Figure FDA00038796622700000310
indicating whether the radar i irradiates the target q at the moment k; l is T Representing the number of radars required to illuminate the same target simultaneously; q represents the number of moving objects; m is a group of T Representing a number of radars for performing tracking tasks on a plurality of targets; 1 N×1 Representing an N x 1 dimensional full 1 matrix.
5. The method for allocating the target search and tracking resources of the networked radar based on the radio frequency stealth as claimed in claim 4, wherein the total radio frequency resource consumption E tot,k Defined as the sum of the search and tracking radio frequency resource consumption, expressed as:
Figure FDA00038796622700000311
wherein E is S,k Indicating search radio frequency resource consumption, E T,k Representing tracking radio frequency resource consumption; alpha (alpha) ("alpha") 1 And alpha 2 Weight coefficients representing radiation power and dwell time, respectively.
6. The method for allocating the radio frequency stealth-based networked radar target search and tracking resources according to claim 1, wherein the two decomposed sub-optimization models are as follows:
Figure FDA0003879662270000041
Figure FDA0003879662270000042
and
Figure FDA0003879662270000043
Figure FDA0003879662270000044
wherein E is S,k Indicating search radio frequency resource consumption, E T,k Representing tracking radio frequency resource consumption;
Figure FDA0003879662270000045
node selection means u representing search area a S,k Represents a networked radar search node selection mode,
Figure FDA0003879662270000046
means for indicating the node selection of the tracking target q, u T,k Representing a networked radar tracking node selection mode;
Figure FDA0003879662270000047
representing the detection probability of the networked radar at the moment k to the target in the key observation area a;
Figure FDA0003879662270000048
representing a measurement index representing the tracking precision of the target; p is a radical of d,min And
Figure FDA0003879662270000049
respectively meeting the requirements of target searching performance and multi-target tracking precision; for search tasks, P S,max And P S,min Respectively representing the upper and lower limits of the search radiation power, T S,max And T S,min Respectively representing the upper limit and the lower limit of the residence time of the search wave beam;
Figure FDA00038796622700000410
representing the radiation power when the radar i searches for the key observation area a;
Figure FDA00038796622700000411
representing the residence time of the wave beam when the radar i searches for the key observation area a; for trace tasks, P T,max And P T,min Respectively representing the upper and lower limits of the tracking radiation power, T T,max And T T,min Respectively representing the upper limit and the lower limit of the residence time of the tracking wave beam;
Figure FDA00038796622700000412
and
Figure FDA00038796622700000413
respectively determining the radiation power and the residence time of the radar i at the moment k for irradiating the target q once; l is S Representing the number of radars searching the same circular key observation area at the same time; a represents the number of circular key observation areas; m S Representing the number of radars for performing a search task on a circular key observation regions;
Figure FDA00038796622700000414
whether the radar i at the moment k is selected or not is shown, and a key observation area a is searched;
Figure FDA00038796622700000415
indicating whether the radar i irradiates the target q at the moment k; l is T Representing the number of radars required to illuminate the same target simultaneously; q represents the number of moving objects; m T Representing a number of radars for performing tracking tasks on a plurality of targets; 1 N×1 An all-1 matrix representing N × 1 dimensions;
will be provided with
Figure FDA0003879662270000051
And
Figure FDA0003879662270000052
are respectively relaxed to
Figure FDA0003879662270000053
And
Figure FDA0003879662270000054
7. the method for allocating the radio frequency stealth-based networked radar target search and tracking resources according to claim 6, wherein the two-step solving algorithm adopting the interior point method and the cyclic minimum method is used for solving the two sub-optimization models:
(1) Tracking node selection and resource allocation;
(a) Initializing a prediction Bayesian information matrix of k time to a target q
Figure FDA0003879662270000055
(b) Allocating initial tracking radiation power and tracking residence time for each radar node;
(c) Continuous variable obtained after relaxation
Figure FDA0003879662270000056
The contribution degree of the radar i tracking target q at the moment k is regarded as the contribution degree; by optimizing the variable u in the case of current resource allocation T,k Minimizing the tracking error to the target q; solving the sub-optimization model by adopting an interior point method:
Figure FDA0003879662270000057
Figure FDA0003879662270000058
obtaining the contribution degree of each radar tracking target q under the current resource allocation
Figure FDA0003879662270000059
Selecting the largest L T The radar corresponding to each element irradiates a target q, namely, the L which has the maximum contribution to a tracking target q is selected T A radar;
(d) Selection of nodes obtained in step (c)
Figure FDA00038796622700000510
On the basis, under the constraints of target tracking precision and radio frequency resources, the radiation power and the residence time of the corresponding radar are optimized in a combined mode so as to minimize the total consumption of the radio frequency resources; solving the sub-optimization model by adopting an interior point method:
Figure FDA00038796622700000511
Figure FDA00038796622700000512
deriving trace resource allocation result P T,k,0 And T T,k,0 Substituting the result into the step (b) as a new resource allocation scheme and skipping to the step (b) until the difference between the total tracking radio frequency resource consumption calculated in two adjacent times is smaller than a preset value; corresponding to the radar to which the tracking target q is finally assigned
Figure FDA00038796622700000513
Setting 1, and setting 0 for the rest to obtain a k moment tracking node selection and resource allocation result;
(2) Searching node selection and resource allocation;
(a) After the selection of the tracking nodes is determined, the nodes for multi-airspace search tasks are selected from the rest radar nodes, and initial search resources are distributed to the rest radars;
(b) Continuous variable obtained after relaxation
Figure FDA0003879662270000061
The contribution degree of the radar i at the moment k to the effect of the search key observation area a is regarded as; optimizing search node selection variable u under current resource allocation S,k Maximizing the target detection probability; solving the sub-optimization model:
Figure FDA0003879662270000062
Figure FDA0003879662270000063
obtaining the contribution degree of each radar to the target detection probability in the gravity observation area a under the current resource allocation, and selecting the L with the maximum corresponding contribution S Searching a key observation area a by the partial radar;
(c) Under the current node selection, the radiation power and the residence time of the corresponding radar are optimized in a combined mode, and the aim of minimizing the total radio frequency resource consumption is taken as an optimization target; solving the sub-optimization model:
Figure FDA0003879662270000064
Figure FDA0003879662270000065
after obtaining a search resource allocation result, skipping to the step (a) to update an initial search resource allocation scheme until the difference value between the total search radio frequency resource consumption obtained in two adjacent times is smaller than a preset value; corresponding to the radar finally designated to search the key observation area a
Figure FDA0003879662270000066
Setting 1 and setting 0 for the rest, namely obtaining the search node selection and resource distribution result at the moment k.
8. A networked radar target searching and tracking resource distribution system based on radio frequency stealth is characterized by comprising:
the system modeling module is used for establishing a networked radar consisting of a plurality of synchronous phased array radars, and the networked radar needs to complete the search of a plurality of circular key observation areas and the tracking of a known number of moving targets at the same time;
the measurement index calculation module is used for searching scenes for a plurality of circular key observation areas based on the networked radar and calculating the detection probability of the networked radar on targets in the circular key observation areas as a measurement index of the search performance; calculating a predicted Bayesian-Lame lower bound of target position estimation as a measurement index of multi-target tracking performance based on a networked radar to a multi-target tracking scene;
the optimization model building module is used for building a networked radar search and tracking resource distribution model based on radio frequency stealth by taking the total radio frequency resource consumption of the minimized networked radar as an optimization target and taking a radar node selection mode, radiation power and residence time as optimization parameters under the condition of meeting preset search and multi-target tracking performance and radio frequency resource constraint;
and the optimization model solving module is used for decomposing the networked radar search and tracking resource allocation model based on radio frequency stealth into two sub-optimization models and solving the two sub-optimization models by adopting a two-step solving algorithm of an interior point method and a cyclic minimum method.
9. An apparatus, comprising a memory and a processor, wherein:
a memory for storing a computer program capable of running on the processor;
a processor for executing the steps of the method for allocating radio frequency stealth based networked radar target search tracking resources according to any one of claims 1 to 7 when running the computer program.
10. A storage medium, characterized in that the storage medium has a computer program stored thereon, and the computer program when executed by at least one processor implements the steps of the method for allocating resources for searching and tracking a target of a networked radar based on radio frequency stealth according to any one of claims 1 to 7.
CN202211225716.2A 2022-10-09 2022-10-09 Resource allocation method for target search and tracking in networked radar based on radio frequency stealth Active CN115561748B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202211225716.2A CN115561748B (en) 2022-10-09 2022-10-09 Resource allocation method for target search and tracking in networked radar based on radio frequency stealth

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202211225716.2A CN115561748B (en) 2022-10-09 2022-10-09 Resource allocation method for target search and tracking in networked radar based on radio frequency stealth

Publications (2)

Publication Number Publication Date
CN115561748A true CN115561748A (en) 2023-01-03
CN115561748B CN115561748B (en) 2025-09-23

Family

ID=84744580

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202211225716.2A Active CN115561748B (en) 2022-10-09 2022-10-09 Resource allocation method for target search and tracking in networked radar based on radio frequency stealth

Country Status (1)

Country Link
CN (1) CN115561748B (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115219993A (en) * 2022-05-31 2022-10-21 中国人民解放军63892部队 Signal-level cooperative multi-radar networking search resource allocation method
CN115993596A (en) * 2023-03-27 2023-04-21 中国人民解放军63921部队 Characteristic parameter measurement radar resource allocation method and device and computer storage medium
CN116184387A (en) * 2023-02-21 2023-05-30 南京航空航天大学 Heterogeneous multi-radar network multi-domain resource joint optimization allocation method under non-ideal detection
CN117875000A (en) * 2023-11-17 2024-04-12 南京航空航天大学 Networking radar node selection and power time collaborative optimization method under multi-target search tracking

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105182317A (en) * 2015-08-20 2015-12-23 电子科技大学 Resource management method based on search pattern of centralized MIMO radar
CN108732543A (en) * 2018-04-24 2018-11-02 南京航空航天大学 A kind of airborne radar network radiation parameter combined optimization method stealthy based on radio frequency
CN108896985A (en) * 2018-06-11 2018-11-27 南京航空航天大学 Based on the stealthy radar network multiple target tracking sampling interval control method of radio frequency
CN112213718A (en) * 2020-09-25 2021-01-12 南京航空航天大学 Networking radar node selection and radiation resource joint optimization method under multi-target tracking

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105182317A (en) * 2015-08-20 2015-12-23 电子科技大学 Resource management method based on search pattern of centralized MIMO radar
CN108732543A (en) * 2018-04-24 2018-11-02 南京航空航天大学 A kind of airborne radar network radiation parameter combined optimization method stealthy based on radio frequency
CN108896985A (en) * 2018-06-11 2018-11-27 南京航空航天大学 Based on the stealthy radar network multiple target tracking sampling interval control method of radio frequency
CN112213718A (en) * 2020-09-25 2021-01-12 南京航空航天大学 Networking radar node selection and radiation resource joint optimization method under multi-target tracking

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115219993A (en) * 2022-05-31 2022-10-21 中国人民解放军63892部队 Signal-level cooperative multi-radar networking search resource allocation method
CN115219993B (en) * 2022-05-31 2025-09-05 中国人民解放军63892部队 Signal-level cooperative multi-radar network search resource allocation method
CN116184387A (en) * 2023-02-21 2023-05-30 南京航空航天大学 Heterogeneous multi-radar network multi-domain resource joint optimization allocation method under non-ideal detection
CN116184387B (en) * 2023-02-21 2025-09-23 南京航空航天大学 Joint optimization allocation method of multi-domain resources in heterogeneous multi-radar networks under non-ideal detection
CN115993596A (en) * 2023-03-27 2023-04-21 中国人民解放军63921部队 Characteristic parameter measurement radar resource allocation method and device and computer storage medium
CN115993596B (en) * 2023-03-27 2023-06-20 中国人民解放军63921部队 Characteristic parameter measurement radar resource allocation method and device and computer storage medium
CN117875000A (en) * 2023-11-17 2024-04-12 南京航空航天大学 Networking radar node selection and power time collaborative optimization method under multi-target search tracking

Also Published As

Publication number Publication date
CN115561748B (en) 2025-09-23

Similar Documents

Publication Publication Date Title
CN115561748A (en) Networked radar target search tracking resource allocation method based on radio frequency stealth
Romero et al. Cognitive radar network: Cooperative adaptive beamsteering for integrated search-and-track application
Yan et al. Prior knowledge-based simultaneous multibeam power allocation algorithm for cognitive multiple targets tracking in clutter
Yan et al. Power allocation algorithm for target tracking in unmodulated continuous wave radar network
CN107656264B (en) Power resource management method for multi-target tracking of opportunistic array radar in clutter environment
KR20220023749A (en) Co-optimization method of integrated network radar dwell time and radiated power for low detection
CN111025275B (en) Multi-objective joint optimization method of multi-base radar radiation parameters based on radio frequency stealth
CN111323773A (en) A joint optimal allocation method of networked radar power and bandwidth based on radio frequency stealth
Narykov et al. Algorithm for resource management of multiple phased array radars for target tracking
CN114662271B (en) Joint beam-power-bandwidth allocation method for centralized MIMO radar multi-target tracking
CN114666219B (en) Multi-radar network power and bandwidth joint optimization allocation method and system under non-ideal detection
Zhu et al. Cognitive radar target tracking using intelligent waveforms based on reinforcement learning
CN111190176A (en) Adaptive resource management method for co-located MIMO radar networking system
Sun et al. JPBA of ARN for target tracking in clutter
Pulkkinen et al. Time budget management in multifunction radars using reinforcement learning
Huang et al. Deep-Reinforcement-Learning-Based Radar Parameter Adaptation for Multiple-Target Tracking
Xiong et al. Hierarchical task and power coalition game of radars for maneuvering target tracking in self-defensive suppressive jamming
Nadjiasngar et al. A performance model for target tracking with a radar network
Gan et al. Cognitive Jammer Time Resource Scheduling With Imperfect Information Via Fuzzy Q-Learning
Müller et al. Quality of service based radar resource management for navigation and positioning
CN118859116A (en) Joint optimization method and system for phased array radar network node selection and power allocation
Lu et al. Learning-Based Cognitive Radar Resource Management for Scanning and Multi-Target Tracking
Wintenby Resource allocation in airborne surveillance radar
CN114662272B (en) An Optimal Allocation Method for Co-sited MIMO Radar Arrays for Multi-target Tracking
Zheng et al. A log-normal complex-amplitude likelihood ratio-based TBD method with soft orbit-information constraints for tracking space targets with space-based radar

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant