CN108333583B - A Resource Allocation Method Based on Phased Array Radar Search and Tracking Dual Target Optimization - Google Patents

A Resource Allocation Method Based on Phased Array Radar Search and Tracking Dual Target Optimization Download PDF

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CN108333583B
CN108333583B CN201810057487.5A CN201810057487A CN108333583B CN 108333583 B CN108333583 B CN 108333583B CN 201810057487 A CN201810057487 A CN 201810057487A CN 108333583 B CN108333583 B CN 108333583B
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CN108333583A (en
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严俊坤
戴金辉
纠博
刘宏伟
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
    • G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
    • G01S13/726—Multiple target tracking
    • 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
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Abstract

本发明公开了一种基于相控阵雷达搜索和跟踪双目标优化的资源分配方法，属于雷达技术领域，其主要思路为：设定第k次分配时相控阵雷达的搜索区域存在Qk个目标，并且第k次分配时相控阵雷达的搜索区域被分割为Nk个不重叠的搜索扇区；令k为第k次分配，1≤k≤K，k的初始值为1，K为大于0的偶数；分别得到第1次分配期间相控阵雷达分配给N1个不重叠搜索扇区的最优搜索时间资源

Figure DDA0001554226170000011
至第K次分配期间相控阵雷达分配给NK个不重叠搜索扇区的最优搜索时间资源
Figure DDA0001554226170000012
以及第1次分配期间相控阵雷达分配给Q1个目标的跟踪时间资源列向量最优解
Figure DDA0001554226170000013
至第K次分配期间相控阵雷达分配给QK个目标的跟踪时间资源列向量最优解
Figure DDA0001554226170000014
并记为基于相控阵雷达搜索和跟踪双目标优化的资源分配结果。

Figure 201810057487

The invention discloses a resource allocation method based on phased array radar search and tracking dual target optimization, which belongs to the technical field of radar . target, and the search area of the phased array radar is divided into N k non-overlapping search sectors during the kth assignment; let k be the kth assignment, 1≤k≤K, the initial value of k is 1, K is an even number greater than 0; the optimal search time resources allocated by the phased array radar to N 1 non-overlapping search sectors during the first allocation period are obtained respectively

Figure DDA0001554226170000011
Optimal search time resources allocated by phased array radar to N K non-overlapping search sectors during the period up to the K-th allocation
Figure DDA0001554226170000012
and the optimal solution of the column vector of tracking time resources allocated by the phased array radar to Q 1 targets during the first allocation
Figure DDA0001554226170000013
Optimal solution of column vector of tracking time resources allocated by phased array radar to Q K targets during the period of Kth allocation
Figure DDA0001554226170000014
And denoted as the resource allocation result based on phased array radar search and tracking dual target optimization.

Figure 201810057487

Description

基于相控阵雷达搜索和跟踪双目标优化的资源分配方法A Resource Allocation Method Based on Phased Array Radar Search and Tracking Dual Target Optimization

技术领域technical field

本发明属于雷达技术领域，尤其涉及一种基于相控阵雷达搜索和跟踪双目标优化的资源分配方法，适用于有限时间资源预算条件下的资源分配，最大限度地提高相控阵雷达的搜索能力和目标的跟踪精度。The invention belongs to the technical field of radar, in particular to a resource allocation method based on phased array radar search and tracking dual target optimization, which is suitable for resource allocation under the condition of limited time resource budget and maximizes the search capability of phased array radar and target tracking accuracy.

背景技术Background technique

近来，技术的进步使敏捷、多任务相控阵雷达系统的开发得以实现；通常，相控阵雷达利用电子操纵阵列天线，因此具有极高的波束灵活性，这种特性使相控阵雷达能够执行多个任务；实际上，不同的雷达功能可能对系统资源有相互竞争的需求，因此需要根据雷达的能力和它们的目标采用自动化技术来分配资源；对于雷达搜索和跟踪(SAT)应用，如果一个相控阵雷达利用不充足的时间资源探测目标，那么多个低可探测目标可能仍然不会被发现；与此同时，如果一个相控阵雷达没有足够的时间资源来照亮之前的跟踪目标，可能产生不连续的轨迹。Recent advances in technology have enabled the development of agile, multi-mission phased array radar systems; typically, phased array radars utilize electronically steered array antennas and therefore have extremely high beam flexibility, a feature that enables phased array radars to Perform multiple missions; in fact, different radar functions may have competing demands on system resources, thus requiring the use of automated techniques to allocate resources based on the capabilities of the radars and their targets; for radar search and track (SAT) applications, if A phased array radar uses insufficient time resources to detect targets, then multiple low detectable targets may still go undetected; at the same time, if a phased array radar does not have sufficient time resources to illuminate previously tracked targets , which may produce discontinuous trajectories.

在此之前，许多方法已经应用于资源分配的问题，无论是搜索函数或是跟踪函数还是两个函数共同作用；对于雷达搜索应用来说，其挑战是扩大雷达监视区域和提高目标探测概率，同时尽可能少地使用资源；对于目标跟踪，可寻求通过优化跟踪-重新访问间隔、目标信号强度和检测阈值来使跟踪目标所需的总雷达资源最小化，现有的工作，即为SAT应用设计的资源分配方案，大致可分为两类:基于规则和基于优化；在基于规则的方案中，根据一些操作需要或雷达特征，制定了一系列规则，这些方法尽管非常有效，但在贝叶斯理论中并不是最优的，而且可能出现不可预测的行为；另一种方法是通过使用单一的成本函数来计算SAT任务；雷达资源分配问题可以作为一种数学优化方案来制定，通常，成本函数是与搜索能力和跟踪精度相对应的度量指标的加权和，例如，检测目标的概率、跟踪贝叶斯克拉美罗下界(BCRLB)和预期测量信号与噪声的比(SNR)；但是，这些方法的缺点是对权重的选择和非相应度量的无意义聚合。Prior to this, many methods have been applied to the problem of resource allocation, whether it is a search function or a tracking function or a combination of the two functions; for radar search applications, the challenge is to expand the radar surveillance area and improve the target detection probability, while at the same time Use as few resources as possible; for target tracking, one seeks to minimize the total radar resources required to track a target by optimizing the track-revisit interval, target signal strength, and detection thresholds, existing work, designed for SAT applications The resource allocation schemes can be roughly divided into two categories: rule-based and optimization-based; in the rule-based scheme, a series of rules are formulated according to some operational needs or radar characteristics. Although these methods are very effective, they are not effective in Bayesian is not optimal in theory and may exhibit unpredictable behavior; another approach is to compute SAT tasks by using a single cost function; the radar resource allocation problem can be formulated as a mathematical optimization scheme, usually, the cost function is a weighted sum of metrics corresponding to search capability and tracking accuracy, such as probability of detecting a target, tracking Bayesian Cramero lower bound (BCRLB), and expected measured signal-to-noise ratio (SNR); however, these methods The downside is the choice of weights and meaningless aggregation of non-corresponding metrics.

发明内容SUMMARY OF THE INVENTION

针对上述现有技术存在的问题，本发明的目的在于提出一种基于相控阵雷达搜索和跟踪双目标优化的资源分配方法，该种基于相控阵雷达搜索和跟踪双目标优化的资源分配方法能够解决在有限的照明时间预算内，同时最大限度地提高相控阵雷达的搜索能力和目标的跟踪精度的资源分配。In view of the problems existing in the above-mentioned prior art, the purpose of the present invention is to propose a resource allocation method based on phased array radar search and tracking dual target optimization, and this kind of resource allocation method based on phased array radar search and tracking dual target optimization Ability to address resource allocation within a limited lighting time budget while maximizing the phased array radar's search capability and target tracking accuracy.

针对上述现有技术存在的问题，本发明的目的在于本发明将SAT任务的资源分配方案设计成一个双目标约束优化问题，并利用帕累托理论来确定其著名的帕累托子集(BK-PS)。资源分配方案采用两个成本函数：(i)就多搜索扇区搜索最小信噪比(最坏情况下搜索信噪比(WCS-SNR))而言,强调目标搜索能力最大化；(ii)就最坏情况下的跟踪贝叶斯克拉美罗下界(WCT-BCRLB)而言，强调多目标跟踪均方差最小化；为了探讨这两个目标之间的多重权衡，需要找出双目标问题的帕累托最优解集；然而，对于许多双目标问题，因为解集中解的个数很多，故确定整个帕累托最优集实际上是不可能的；因此，对双目标优化的一种实用方法是计算BK-PS，并尽可能地用BK-PS表示帕累托最优集，有了这个BK-PS，就能够在SAT任务之间找到一个适当的折中，并相应地选择一个资源分配方案，以满足特定的应用需求。In view of the problems existing in the above-mentioned prior art, the purpose of the present invention is that the present invention designs the resource allocation scheme of the SAT task as a dual-objective constrained optimization problem, and uses Pareto theory to determine its famous Pareto subset (BK -PS). The resource allocation scheme employs two cost functions: (i) in terms of multiple search sectors searching for the minimum signal-to-noise ratio (Worst-case Search Signal-to-Noise Ratio (WCS-SNR)), the emphasis is on maximizing the target search capability; (ii) As far as the worst-case tracking Bayesian Cramero lower bound (WCT-BCRLB) is concerned, the multi-target tracking mean square error minimization is emphasized; in order to explore the multiple trade-offs between these two targets, it is necessary to find out the two-target problem. Pareto optimal solution set; however, for many dual-objective problems, because of the large number of solutions in the solution set, it is practically impossible to determine the entire Pareto-optimal set; therefore, a method for dual-objective optimization is A practical approach is to compute BK-PS and use BK-PS to represent the Pareto optimal set as much as possible, with this BK-PS one can find an appropriate compromise between SAT tasks and choose one accordingly Resource allocation schemes to meet specific application needs.

为达到上述技术目的，本发明采用如下技术方案予以实现。In order to achieve the above technical purpose, the present invention adopts the following technical solutions to achieve.

一种基于相控阵雷达搜索和跟踪双目标优化的资源分配方法，包括以下步骤：A resource allocation method based on phased array radar search and tracking dual target optimization, comprising the following steps:

步骤1，初始化：令

Figure GDA0003105725120000021
为第
Figure GDA0003105725120000022
次分配，
Figure GDA0003105725120000023
的初始值为1，
Figure GDA0003105725120000024
为大于0的偶数；设定第
Figure GDA0003105725120000025
次分配时相控阵雷达的搜索区域存在
Figure GDA0003105725120000026
个目标，并且第
Figure GDA0003105725120000027
次分配时相控阵雷达的搜索区域被分割为
Figure GDA0003105725120000028
个不重叠的搜索扇区；Step 1, initialization: let
Figure GDA0003105725120000021
for the first
Figure GDA0003105725120000022
sub-allocation,
Figure GDA0003105725120000023
The initial value of is 1,
Figure GDA0003105725120000024
is an even number greater than 0; set the first
Figure GDA0003105725120000025
The search area of the phased array radar exists when the sub-allocation
Figure GDA0003105725120000026
goal, and the
Figure GDA0003105725120000027
The search area of the phased array radar is divided into
Figure GDA0003105725120000028
non-overlapping search sectors;

步骤2，确定第

Figure GDA0003105725120000029
次分配时相控阵雷达在第
Figure GDA00031057251200000210
个搜索扇区的搜索模型和第
Figure GDA00031057251200000211
次分配期间第
Figure GDA00031057251200000212
个目标的跟踪模型；其中，
Figure GDA00031057251200000213
表示第
Figure GDA00031057251200000214
次分配时相控阵雷达的搜索区域存在的目标个数；
Figure GDA00031057251200000215
表示第
Figure GDA00031057251200000216
次分配时相控阵雷达搜索扇区总个数；Step 2, determine the
Figure GDA0003105725120000029
The phased array radar is in the first
Figure GDA00031057251200000210
The search model of the search sector and the
Figure GDA00031057251200000211
sub-allocation period
Figure GDA00031057251200000212
tracking model of a target; where,
Figure GDA00031057251200000213
means the first
Figure GDA00031057251200000214
The number of targets existing in the search area of the phased array radar at the time of sub-allocation;
Figure GDA00031057251200000215
means the first
Figure GDA00031057251200000216
The total number of search sectors of the phased array radar at the time of sub-allocation;

步骤3，根据第

Figure GDA00031057251200000217
次分配时相控阵雷达在第
Figure GDA00031057251200000218
个搜索扇区的搜索模型，得到第
Figure GDA00031057251200000219
次分配期间搜索资源分配方案的目标函数和第
Figure GDA00031057251200000220
次分配期间搜索资源分配方案的转换目标函数；Step 3, according to the
Figure GDA00031057251200000217
The phased array radar is in the first
Figure GDA00031057251200000218
The search model of the search sector, get the first
Figure GDA00031057251200000219
The objective function and the first
Figure GDA00031057251200000220
The transformation objective function of the search resource allocation scheme during the sub-allocation period;

步骤4，根据第

Figure GDA00031057251200000221
次分配期间第
Figure GDA00031057251200000222
个目标的跟踪模型，确定第
Figure GDA00031057251200000223
次分配期间跟踪资源分配方案的目标标准函数；Step 4, according to the
Figure GDA00031057251200000221
sub-allocation period
Figure GDA00031057251200000222
The tracking model of the target, determine the first
Figure GDA00031057251200000223
The objective standard function of tracking resource allocation scheme during sub-allocation period;

步骤5，根据第

Figure GDA00031057251200000224
次分配期间搜索资源分配方案的转换目标函数和第
Figure GDA00031057251200000225
次分配期间跟踪资源分配方案的目标标准函数，得到第
Figure GDA00031057251200000226
次分配期间双目标资源分配方案的数学优化模型；Step 5, according to the
Figure GDA00031057251200000224
The transformation objective function and the first
Figure GDA00031057251200000225
The objective standard function of tracking the resource allocation scheme during the sub-allocation period, obtains the first
Figure GDA00031057251200000226
Mathematical optimization model of dual-objective resource allocation scheme during secondary allocation;

步骤6，求解第

Figure GDA00031057251200000227
次分配期间双目标资源分配方案的数学优化模型，分别得到第
Figure GDA00031057251200000228
次分配期间相控阵雷达分配给
Figure GDA00031057251200000229
个不重叠搜索扇区的最优搜索时间资源
Figure GDA00031057251200000230
和第
Figure GDA00031057251200000231
次分配期间相控阵雷达分配给
Figure GDA0003105725120000031
个目标的跟踪时间资源列向量最优解
Figure GDA0003105725120000032
Step 6, solve the first
Figure GDA00031057251200000227
The mathematical optimization model of the dual-objective resource allocation scheme during the secondary allocation period, respectively,
Figure GDA00031057251200000228
Phased Array Radar is assigned to
Figure GDA00031057251200000229
optimal search time resources for non-overlapping search sectors
Figure GDA00031057251200000230
and
Figure GDA00031057251200000231
Phased Array Radar is assigned to
Figure GDA0003105725120000031
The optimal solution of tracking time resource column vector for each target
Figure GDA0003105725120000032

步骤7，令

Figure GDA0003105725120000033
的值加1，返回步骤2，直到得到第1次分配期间相控阵雷达分配给
Figure GDA0003105725120000034
个不重叠搜索扇区的最优搜索时间资源
Figure GDA0003105725120000035
至第
Figure GDA0003105725120000036
次分配期间相控阵雷达分配给
Figure GDA0003105725120000037
个不重叠搜索扇区的最优搜索时间资源
Figure GDA0003105725120000038
以及第1次分配期间相控阵雷达分配给
Figure GDA0003105725120000039
个目标的跟踪时间资源列向量最优解
Figure GDA00031057251200000310
至第
Figure GDA00031057251200000311
次分配期间相控阵雷达分配给
Figure GDA00031057251200000312
个目标的跟踪时间资源列向量最优解
Figure GDA00031057251200000313
记为基于相控阵雷达搜索和跟踪双目标优化的资源分配结果。Step 7, let
Figure GDA0003105725120000033
Add 1 to the value of , and return to step 2 until the phased array radar is assigned to
Figure GDA0003105725120000034
optimal search time resources for non-overlapping search sectors
Figure GDA0003105725120000035
to the
Figure GDA0003105725120000036
Phased array radar is assigned to
Figure GDA0003105725120000037
optimal search time resources for non-overlapping search sectors
Figure GDA0003105725120000038
and the phased array radar was assigned to
Figure GDA0003105725120000039
The optimal solution of the tracking time resource column vector for each target
Figure GDA00031057251200000310
to the
Figure GDA00031057251200000311
Phased array radar is assigned to
Figure GDA00031057251200000312
The optimal solution of the tracking time resource column vector for each target
Figure GDA00031057251200000313
Denoted as the resource allocation result based on phased array radar search and tracking dual target optimization.

本发明的有益效果：Beneficial effects of the present invention:

第一，本发明方法利用双目标约束优化问题的独特结构，能够通过并行求解凸极小极大优化(CMO)问题来获得帕累托子集BK-PS；在以往的研究中，为获得帕累托子集BK-PS，研究人员开发了许多方法，如加权和法、蚁群优化算法和遗传算法；本发明方法通过利用双目标优化问题的独特结构，开发了一种并行最小化方案来研究帕累托子集BK-PS，使得本发明方法作为获得BK-PS的一种替代方法，不同的帕累托解可以通过并行地解具有不同SAT需求的多个双目标问题来得到，每个复杂的双目标问题可以被划分为两个CMO问题，一个用于搜索任务，另一个用于跟踪任务，不同SAT需求对应的搜索资源分配(S-RA)问题的解是成比例的。First, the method of the present invention utilizes the unique structure of the dual-objective constrained optimization problem, and can obtain the Pareto subset BK-PS by solving the convex minimax optimization (CMO) problem in parallel; Reto subset BK-PS, researchers have developed many methods, such as weighted sum method, ant colony optimization algorithm and genetic algorithm; the method of the present invention develops a parallel minimization scheme by using the unique structure of the dual-objective optimization problem. The Pareto subset BK-PS is studied so that the method of the present invention can be used as an alternative to obtain BK-PS. Different Pareto solutions can be obtained by solving multiple dual-objective problems with different SAT requirements in parallel, each This complex dual-objective problem can be divided into two CMO problems, one for the search task and the other for the tracking task, and the solutions of the search resource allocation (S-RA) problem corresponding to different SAT requirements are proportional.

第二，对于不同的SAT参数，最小搜索资源分配问题只需要解一次，由于目标跟踪资源分配的目标函数是非线性的，因此，本发明方法通过并行求解M+1个CMO问题，能够得到具有基数为M的帕累托子集BK-PS；结果表明，极小极大雷达搜索资源分配问题将产生一个线性规划模型，因此很容易地通过著名的线性规划方法来求解；对于目标跟踪资源分配方案，其产生的极小极大问题由一组可分离的单调递减凸函数组成，可使用极小极大解算法来解决T-RA问题。Second, for different SAT parameters, the minimum search resource allocation problem only needs to be solved once. Since the objective function of target tracking resource allocation is nonlinear, the method of the present invention solves M+1 CMO problems in parallel, and can obtain a base is the Pareto subset BK-PS of M; the results show that the minimax radar search resource allocation problem will produce a linear programming model, so it can be easily solved by the well-known linear programming method; for the target tracking resource allocation scheme , the resulting minimax problem consists of a set of separable monotonically decreasing convex functions, and the minimax solution algorithm can be used to solve the T-RA problem.

附图说明Description of drawings

下面结合附图和具体实施方式对本发明作进一步详细说明。The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

图1是本发明的一种基于相控阵雷达搜索和跟踪双目标优化的资源分配方法流程图；1 is a flow chart of a method for resource allocation based on phased array radar search and tracking dual target optimization of the present invention;

图2是将相控阵雷达的搜索区域量化为不重叠扇区示意图；2 is a schematic diagram of quantizing the search area of a phased array radar into non-overlapping sectors;

图3是相控阵雷达雷达检测范围内的目标部署示意图；Figure 3 is a schematic diagram of the target deployment within the detection range of the phased array radar radar;

图4(a)是第5次分配期间资源平均分配方案与基于帕累托的双目标优化资源分配方案的性能比较示意图；Figure 4 (a) is a schematic diagram of the performance comparison between the average resource allocation scheme and the Pareto-based dual-objective optimal resource allocation scheme during the fifth allocation;

图4(b)是第15次分配期间资源平均分配方案与基于帕累托的双目标优化资源分配方案的性能比较示意图。Fig. 4(b) is a schematic diagram showing the performance comparison between the average resource allocation scheme and the Pareto-based dual-objective optimal resource allocation scheme during the 15th allocation.

具体实施方式Detailed ways

参照图1，为本发明的一种基于相控阵雷达搜索和跟踪双目标优化的资源分配方法流程图；其中所述基于相控阵雷达搜索和跟踪双目标优化的资源分配方法，包括以下步骤：Referring to Fig. 1, it is a flow chart of a method for resource allocation based on phased array radar search and tracking dual target optimization of the present invention; wherein the resource allocation method based on phased array radar search and tracking dual target optimization includes the following steps :

步骤1，初始化：令

Figure GDA0003105725120000041
为第
Figure GDA0003105725120000042
次分配，
Figure GDA0003105725120000043
的初始值为1，
Figure GDA0003105725120000044
为大于0的偶数；设定第
Figure GDA0003105725120000045
次分配时相控阵雷达的搜索区域存在
Figure GDA0003105725120000046
个目标，并且第
Figure GDA0003105725120000047
次分配时相控阵雷达的搜索区域被分割为
Figure GDA0003105725120000048
个不重叠的搜索扇区。Step 1, initialization: let
Figure GDA0003105725120000041
for the first
Figure GDA0003105725120000042
sub-allocation,
Figure GDA0003105725120000043
The initial value of is 1,
Figure GDA0003105725120000044
is an even number greater than 0; set the first
Figure GDA0003105725120000045
The search area of the phased array radar exists when the sub-allocation
Figure GDA0003105725120000046
target, and
Figure GDA0003105725120000047
The search area of the phased array radar is divided into
Figure GDA0003105725120000048
non-overlapping search sectors.

具体地，确定相控阵雷达，并以相控阵雷达正南方向93km、正西方向45km作为原点

Figure GDA0003105725120000049
以正北方向为Y轴、正东方向为X轴建立平面直角坐标系。Specifically, the phased array radar is determined, and the origin is 93km due south and 45km due west of the phased array radar.
Figure GDA0003105725120000049
A plane rectangular coordinate system is established with the due north direction as the Y axis and the due east direction as the X axis.

如图2所示，令

Figure GDA00031057251200000410
为第
Figure GDA00031057251200000411
次分配，
Figure GDA00031057251200000412
的初始值为1，
Figure GDA00031057251200000413
为大于0的偶数，本实施例中
Figure GDA00031057251200000414
取值为20；设定第
Figure GDA00031057251200000415
次分配时相控阵雷达的搜索区域存在
Figure GDA00031057251200000416
个目标，本实施例中
Figure GDA00031057251200000417
取值为5；并且第
Figure GDA00031057251200000418
次分配时相控阵雷达的搜索区域被分割为
Figure GDA00031057251200000419
个不重叠的搜索扇区
Figure GDA00031057251200000420
前
Figure GDA00031057251200000421
次分配时相控阵雷达的搜索区域分别被分割为
Figure GDA00031057251200000422
个不重叠的搜索扇区，后
Figure GDA00031057251200000423
次分配时相控阵雷达的搜索区域分别被分割为
Figure GDA00031057251200000424
个不重叠的搜索扇区；本实施例中
Figure GDA00031057251200000425
As shown in Figure 2, let
Figure GDA00031057251200000410
for the first
Figure GDA00031057251200000411
sub-allocation,
Figure GDA00031057251200000412
The initial value of is 1,
Figure GDA00031057251200000413
is an even number greater than 0, in this embodiment
Figure GDA00031057251200000414
The value is 20; set the first
Figure GDA00031057251200000415
The search area of the phased array radar exists when the sub-allocation
Figure GDA00031057251200000416
target, in this example
Figure GDA00031057251200000417
takes the value 5; and
Figure GDA00031057251200000418
The search area of the phased array radar is divided into
Figure GDA00031057251200000419
non-overlapping search sectors
Figure GDA00031057251200000420
forward
Figure GDA00031057251200000421
The search area of the phased array radar is divided into
Figure GDA00031057251200000422
non-overlapping search sectors, after
Figure GDA00031057251200000423
The search area of the phased array radar is divided into
Figure GDA00031057251200000424
non-overlapping search sectors; in this embodiment
Figure GDA00031057251200000425

步骤2，确定第

Figure GDA00031057251200000426
次分配时相控阵雷达在第
Figure GDA00031057251200000427
个搜索扇区的搜索模型和第
Figure GDA00031057251200000428
次分配期间第
Figure GDA00031057251200000429
个目标的跟踪模型；其中，
Figure GDA00031057251200000430
表示第
Figure GDA00031057251200000431
次分配时相控阵雷达的搜索区域存在的目标个数；
Figure GDA00031057251200000432
表示第
Figure GDA00031057251200000433
次分配时相控阵雷达搜索扇区总个数。Step 2, determine the
Figure GDA00031057251200000426
The phased array radar is in the first
Figure GDA00031057251200000427
The search model of the search sector and the
Figure GDA00031057251200000428
sub-allocation period
Figure GDA00031057251200000429
tracking model of a target; where,
Figure GDA00031057251200000430
means the first
Figure GDA00031057251200000431
The number of targets existing in the search area of the phased array radar at the time of sub-allocation;
Figure GDA00031057251200000432
means the first
Figure GDA00031057251200000433
The total number of search sectors of the phased array radar during the sub-allocation.

具体地，为了寻找未被探测到的目标，相控阵雷达需要把它的时间资源分配给不同的搜索扇区；进而得到第

Figure GDA00031057251200000434
次分配时相控阵雷达在第
Figure GDA00031057251200000435
个搜索扇区
Figure GDA00031057251200000436
的搜索模型为：Specifically, in order to find undetected targets, the phased array radar needs to allocate its time resources to different search sectors; and then obtain the first
Figure GDA00031057251200000434
The phased array radar is in the first
Figure GDA00031057251200000435
search sectors
Figure GDA00031057251200000436
The search model is:

Figure GDA00031057251200000437
Figure GDA00031057251200000437

其中，

Figure GDA00031057251200000438
α表示中间变量，
Figure GDA00031057251200000439
表示第
Figure GDA00031057251200000440
次分配时相控阵雷达分配给第
Figure GDA0003105725120000051
个搜索扇区
Figure GDA0003105725120000052
的搜索时间资源，
Figure GDA0003105725120000053
表示第
Figure GDA0003105725120000054
次分配时相控阵雷达在第
Figure GDA0003105725120000055
个搜索扇区
Figure GDA0003105725120000056
的目标搜索信噪比，
Figure GDA0003105725120000057
表示相控阵雷达的平均发射功率，
Figure GDA0003105725120000058
表示设定的相控阵雷达天线有效接收孔径，
Figure GDA0003105725120000059
表示第
Figure GDA00031057251200000510
次分配时相控阵雷达在第
Figure GDA00031057251200000511
个搜索扇区
Figure GDA00031057251200000512
的目标散射截面积，
Figure GDA00031057251200000513
表示玻尔兹曼常数，
Figure GDA00031057251200000514
表示设定的相控阵雷达温度，
Figure GDA00031057251200000515
表示相控阵雷达损耗，
Figure GDA00031057251200000516
表示第
Figure GDA00031057251200000517
次分配时相控阵雷达所扫描的第
Figure GDA00031057251200000518
个搜索扇区
Figure GDA00031057251200000519
的角度，本实施例中
Figure GDA00031057251200000520
取经验值，
Figure GDA00031057251200000521
的经验值为6°、8°、12°、16°；
Figure GDA00031057251200000522
表示第
Figure GDA00031057251200000523
次分配时相控阵雷达在第
Figure GDA00031057251200000524
个搜索扇区
Figure GDA00031057251200000525
的目标距离搜索值，本实施例中
Figure GDA00031057251200000526
取经验值，
Figure GDA00031057251200000527
的经验值为200km、240km、295km、300km、310km；
Figure GDA00031057251200000528
可以根据先验信息直接测得。in,
Figure GDA00031057251200000438
α represents the intermediate variable,
Figure GDA00031057251200000439
means the first
Figure GDA00031057251200000440
When the phased array radar is assigned to the first
Figure GDA0003105725120000051
search sectors
Figure GDA0003105725120000052
search time resource,
Figure GDA0003105725120000053
means the first
Figure GDA0003105725120000054
The phased array radar is in the first
Figure GDA0003105725120000055
search sectors
Figure GDA0003105725120000056
The target search signal-to-noise ratio of ,
Figure GDA0003105725120000057
represents the average transmit power of the phased array radar,
Figure GDA0003105725120000058
Indicates the effective receiving aperture of the set phased array radar antenna,
Figure GDA0003105725120000059
means the first
Figure GDA00031057251200000510
The phased array radar is in the first
Figure GDA00031057251200000511
search sectors
Figure GDA00031057251200000512
the target scattering cross-sectional area,
Figure GDA00031057251200000513
is the Boltzmann constant,
Figure GDA00031057251200000514
represents the set phased array radar temperature,
Figure GDA00031057251200000515
represents the phased array radar loss,
Figure GDA00031057251200000516
means the first
Figure GDA00031057251200000517
The first time the phased array radar scans
Figure GDA00031057251200000518
search sectors
Figure GDA00031057251200000519
angle, in this example
Figure GDA00031057251200000520
Take the experience value,
Figure GDA00031057251200000521
The experience value of 6°, 8°, 12°, 16°;
Figure GDA00031057251200000522
means the first
Figure GDA00031057251200000523
The phased array radar is in the first
Figure GDA00031057251200000524
search sectors
Figure GDA00031057251200000525
The target distance search value of , in this example
Figure GDA00031057251200000526
Take the experience value,
Figure GDA00031057251200000527
The experience value of 200km, 240km, 295km, 300km, 310km;
Figure GDA00031057251200000528
It can be directly measured based on prior information.

设定第

Figure GDA00031057251200000529
次分配期间目标的数量
Figure GDA00031057251200000530
是已知的，本实施例中
Figure GDA00031057251200000531
将第
Figure GDA00031057251200000532
次分配期间第
Figure GDA00031057251200000533
个目标的状态矢量记为
Figure GDA00031057251200000534
表示行向量转置，
Figure GDA00031057251200000535
表示第
Figure GDA00031057251200000536
次分配期间第
Figure GDA00031057251200000537
个目标的X轴方向位置，
Figure GDA00031057251200000538
表示第
Figure GDA00031057251200000539
次分配期间第
Figure GDA00031057251200000540
个目标的Y轴方向位置，
Figure GDA00031057251200000541
表示第
Figure GDA00031057251200000542
次分配期间第
Figure GDA00031057251200000543
个目标沿X轴方向的速度，
Figure GDA00031057251200000544
表示第
Figure GDA00031057251200000545
次分配期间第
Figure GDA00031057251200000546
个目标沿Y轴方向的速度，约束条件为第
Figure GDA00031057251200000547
次分配期间第
Figure GDA00031057251200000548
个目标的状态矢量
Figure GDA00031057251200000549
的维数
Figure GDA00031057251200000550
本实施例中
Figure GDA00031057251200000551
表示第
Figure GDA00031057251200000552
次分配时相控阵雷达的搜索区域存在的目标个数。set the first
Figure GDA00031057251200000529
Number of targets during sub-allocation
Figure GDA00031057251200000530
is known, in this example
Figure GDA00031057251200000531
will
Figure GDA00031057251200000532
sub-allocation period
Figure GDA00031057251200000533
The state vector of each target is denoted as
Figure GDA00031057251200000534
represents the row vector transpose,
Figure GDA00031057251200000535
means the first
Figure GDA00031057251200000536
sub-allocation period
Figure GDA00031057251200000537
the X-axis position of the target,
Figure GDA00031057251200000538
means the first
Figure GDA00031057251200000539
sub-allocation period
Figure GDA00031057251200000540
the Y-axis position of the target,
Figure GDA00031057251200000541
means the first
Figure GDA00031057251200000542
sub-allocation period
Figure GDA00031057251200000543
The velocity of the target along the X-axis,
Figure GDA00031057251200000544
means the first
Figure GDA00031057251200000545
sub-allocation period
Figure GDA00031057251200000546
The velocity of the target along the Y-axis direction, the constraint condition is the first
Figure GDA00031057251200000547
sub-allocation period
Figure GDA00031057251200000548
target state vector
Figure GDA00031057251200000549
dimension
Figure GDA00031057251200000550
In this example
Figure GDA00031057251200000551
means the first
Figure GDA00031057251200000552
The number of targets that exist in the search area of the phased array radar during sub-allocation.

然后，第

Figure GDA00031057251200000553
次分配期间第
Figure GDA00031057251200000554
个目标的跟踪模型如下:Then, the first
Figure GDA00031057251200000553
sub-allocation period
Figure GDA00031057251200000554
The tracking model of each target is as follows:

Figure GDA00031057251200000555
Figure GDA00031057251200000555

其中，

Figure GDA00031057251200000556
表示第
Figure GDA00031057251200000557
次分配期间第
Figure GDA00031057251200000558
个目标的过程噪声，
Figure GDA00031057251200000559
表示第
Figure GDA00031057251200000560
次分配期间第
Figure GDA00031057251200000561
个目标的状态矢量，
Figure GDA00031057251200000562
为第
Figure GDA00031057251200000563
次分配期间第
Figure GDA00031057251200000564
个目标的转换矩阵，
Figure GDA00031057251200000565
表示克罗内克算符，
Figure GDA00031057251200000566
表示2×2维单位矩阵，假设该过程噪声
Figure GDA00031057251200000567
服从均值为零的高斯过程，该过程噪声
Figure GDA00031057251200000568
的协方差矩阵为
Figure GDA00031057251200000569
表示每次分配期间时长，本实施例中
Figure GDA00031057251200000570
当
Figure GDA00031057251200000571
取值为1时第0次分配期间第
Figure GDA00031057251200000572
个目标的状态矢量记为第
Figure GDA00031057251200000573
个目标的初始状态矢量
Figure GDA0003105725120000061
第
Figure GDA0003105725120000062
个目标的初始状态矢量的过程噪声
Figure GDA0003105725120000063
为第
Figure GDA0003105725120000064
个目标的过程噪声在初始分配期间的随机数。in,
Figure GDA00031057251200000556
means the first
Figure GDA00031057251200000557
sub-allocation period
Figure GDA00031057251200000558
the process noise of a target,
Figure GDA00031057251200000559
means the first
Figure GDA00031057251200000560
sub-allocation period
Figure GDA00031057251200000561
the state vector of a target,
Figure GDA00031057251200000562
for the first
Figure GDA00031057251200000563
sub-allocation period
Figure GDA00031057251200000564
transformation matrix of a target,
Figure GDA00031057251200000565
represents the Kronecker operator,
Figure GDA00031057251200000566
represents a 2 × 2 dimensional identity matrix, assuming the process is noisy
Figure GDA00031057251200000567
obeys a Gaussian process with zero mean, which is noisy
Figure GDA00031057251200000568
The covariance matrix of is
Figure GDA00031057251200000569
Indicates the duration of each allocation period, in this embodiment
Figure GDA00031057251200000570
when
Figure GDA00031057251200000571
When the value is 1, the 0th allocation period
Figure GDA00031057251200000572
The state vector of the target is denoted as the
Figure GDA00031057251200000573
initial state vector of a target
Figure GDA0003105725120000061
the first
Figure GDA0003105725120000062
process noise of the initial state vector of a target
Figure GDA0003105725120000063
for the first
Figure GDA0003105725120000064
The random number of the target's process noise during the initial assignment.

第

Figure GDA0003105725120000065
次分配期间第
Figure GDA0003105725120000066
个目标的测量值为
Figure GDA0003105725120000067
其表达式为：the first
Figure GDA0003105725120000065
sub-allocation period
Figure GDA0003105725120000066
A target is measured as
Figure GDA0003105725120000067
Its expression is:

Figure GDA0003105725120000068
Figure GDA0003105725120000068

式(3)中In formula (3)

Figure GDA0003105725120000069
Figure GDA0003105725120000069

其中，

Figure GDA00031057251200000610
表示第
Figure GDA00031057251200000611
次分配期间第
Figure GDA00031057251200000612
个目标的状态矢量
Figure GDA00031057251200000613
的
Figure GDA00031057251200000614
维非线性距离和方位测量函数，
Figure GDA00031057251200000659
表示相控阵雷达在平面直角坐标系中的坐标，
Figure GDA00031057251200000661
表示相控阵雷达在平面直角坐标系中X轴方向位置，
Figure GDA00031057251200000660
表示相控阵雷达在平面直角坐标系中Y轴方向位置，
Figure GDA00031057251200000615
表示第
Figure GDA00031057251200000616
次分配期间第
Figure GDA00031057251200000617
个目标的方位信息，
Figure GDA00031057251200000618
表示第
Figure GDA00031057251200000619
次分配期间第
Figure GDA00031057251200000620
个目标与相控阵雷达的径向距离，
Figure GDA00031057251200000621
表示第
Figure GDA00031057251200000622
次分配期间第
Figure GDA00031057251200000623
个目标的X轴方向位置，
Figure GDA00031057251200000624
表示第
Figure GDA00031057251200000625
次分配期间第
Figure GDA00031057251200000626
个目标的Y轴方向位置，上标
Figure GDA00031057251200000627
表示转置，arctan表示反正切。in,
Figure GDA00031057251200000610
means the first
Figure GDA00031057251200000611
sub-allocation period
Figure GDA00031057251200000612
target state vector
Figure GDA00031057251200000613
of
Figure GDA00031057251200000614
dimensional nonlinear distance and bearing measurement functions,
Figure GDA00031057251200000659
Represents the coordinates of the phased array radar in the plane rectangular coordinate system,
Figure GDA00031057251200000661
Indicates the position of the phased array radar in the X-axis direction in the plane rectangular coordinate system,
Figure GDA00031057251200000660
Represents the position of the phased array radar in the Y-axis direction of the plane rectangular coordinate system,
Figure GDA00031057251200000615
means the first
Figure GDA00031057251200000616
sub-allocation period
Figure GDA00031057251200000617
location information of a target,
Figure GDA00031057251200000618
means the first
Figure GDA00031057251200000619
sub-allocation period
Figure GDA00031057251200000620
The radial distance between a target and the phased array radar,
Figure GDA00031057251200000621
means the first
Figure GDA00031057251200000622
sub-allocation period
Figure GDA00031057251200000623
the X-axis position of the target,
Figure GDA00031057251200000624
means the first
Figure GDA00031057251200000625
sub-allocation period
Figure GDA00031057251200000626
Y-axis position of each target, superscript
Figure GDA00031057251200000627
means transpose, arctan means arc tangent.

将第

Figure GDA00031057251200000628
次分配期间第
Figure GDA00031057251200000629
个目标的误差记为
Figure GDA00031057251200000630
设定误差
Figure GDA00031057251200000631
是均值为零的非耦合测量误差，第
Figure GDA00031057251200000632
次分配期间第
Figure GDA00031057251200000633
个目标的误差
Figure GDA00031057251200000634
的对角协方差矩阵为
Figure GDA00031057251200000635
will
Figure GDA00031057251200000628
sub-allocation period
Figure GDA00031057251200000629
The error of each target is recorded as
Figure GDA00031057251200000630
Setting error
Figure GDA00031057251200000631
is the uncoupled measurement error with zero mean, and
Figure GDA00031057251200000632
sub-allocation period
Figure GDA00031057251200000633
target error
Figure GDA00031057251200000634
The diagonal covariance matrix of is
Figure GDA00031057251200000635

Figure GDA00031057251200000636
Figure GDA00031057251200000636

其中，

Figure GDA00031057251200000637
表示第
Figure GDA00031057251200000638
次分配期间第
Figure GDA00031057251200000639
个目标的距离估计均方误差的克拉美罗界下界，
Figure GDA00031057251200000640
表示第
Figure GDA00031057251200000641
次分配期间第
Figure GDA00031057251200000642
个目标的方位信息估计均方误差的克拉美罗界下界，其值分别为：in,
Figure GDA00031057251200000637
means the first
Figure GDA00031057251200000638
sub-allocation period
Figure GDA00031057251200000639
The lower bound of the Cramero bound of the mean square error of the distance estimation for each target,
Figure GDA00031057251200000640
means the first
Figure GDA00031057251200000641
sub-allocation period
Figure GDA00031057251200000642
The lower bounds of the Cramero bound of the mean square error of the azimuth information estimation of each target are as follows:

Figure GDA00031057251200000643
Figure GDA00031057251200000643

其中，

Figure GDA00031057251200000644
表示光速，
Figure GDA00031057251200000645
表示设定常数，
Figure GDA00031057251200000646
表示第
Figure GDA00031057251200000647
次分配期间第
Figure GDA00031057251200000648
个目标的预期测量回波信号与噪声的比(信噪比)，
Figure GDA00031057251200000649
表示第
Figure GDA00031057251200000650
次分配期间第
Figure GDA00031057251200000651
个目标的反射率，
Figure GDA00031057251200000652
表示第
Figure GDA00031057251200000653
次分配期间相控阵雷达分配给第
Figure GDA00031057251200000654
个目标的跟踪时间资源，
Figure GDA00031057251200000655
表示第
Figure GDA00031057251200000656
次分配期间第
Figure GDA00031057251200000657
个目标到相控阵雷达的径向距离，
Figure GDA00031057251200000658
表示第
Figure GDA0003105725120000071
次分配期间相控阵雷达发射的电磁波信号-3dB带宽，上标-1表示求逆，
Figure GDA0003105725120000072
表示第
Figure GDA0003105725120000073
次分配期间相控阵雷达天线的-3dB波束宽度；本实施例中
Figure GDA0003105725120000074
in,
Figure GDA00031057251200000644
represents the speed of light,
Figure GDA00031057251200000645
represents the setting constant,
Figure GDA00031057251200000646
means the first
Figure GDA00031057251200000647
sub-allocation period
Figure GDA00031057251200000648
The expected measurement echo signal-to-noise ratio (signal-to-noise ratio) of each target,
Figure GDA00031057251200000649
means the first
Figure GDA00031057251200000650
sub-allocation period
Figure GDA00031057251200000651
the reflectivity of a target,
Figure GDA00031057251200000652
means the first
Figure GDA00031057251200000653
The phased array radar is assigned to the
Figure GDA00031057251200000654
tracking time resource for each target,
Figure GDA00031057251200000655
means the first
Figure GDA00031057251200000656
sub-allocation period
Figure GDA00031057251200000657
The radial distance from a target to the phased array radar,
Figure GDA00031057251200000658
means the first
Figure GDA0003105725120000071
The -3dB bandwidth of the electromagnetic wave signal emitted by the phased array radar during the sub-distribution period, the superscript -1 indicates the inversion,
Figure GDA0003105725120000072
means the first
Figure GDA0003105725120000073
-3dB beamwidth of the phased array radar antenna during the sub-allocation period; in this example
Figure GDA0003105725120000074

由于第

Figure GDA0003105725120000075
次分配期间第
Figure GDA0003105725120000076
个目标的距离估计均方误差的克拉美罗界下界
Figure GDA0003105725120000077
第
Figure GDA0003105725120000078
次分配期间第
Figure GDA0003105725120000079
个目标的方位信息估计均方误差的克拉美罗界下界
Figure GDA00031057251200000710
电磁波信号-3dB带宽
Figure GDA00031057251200000711
-3dB波束宽度
Figure GDA00031057251200000712
和信噪比
Figure GDA00031057251200000713
都与跟踪时间资源
Figure GDA00031057251200000714
成反比，因此将第
Figure GDA00031057251200000715
次分配期间第
Figure GDA00031057251200000716
个目标的误差
Figure GDA00031057251200000717
的对角协方差矩阵提取公因子
Figure GDA00031057251200000718
后重写为：Due to the
Figure GDA0003105725120000075
sub-allocation period
Figure GDA0003105725120000076
The lower bound of the Cramero bound of the mean square error of the distance estimation for each target
Figure GDA0003105725120000077
the first
Figure GDA0003105725120000078
sub-allocation period
Figure GDA0003105725120000079
The lower bound of the Cramero bound of the mean square error of the azimuth information estimation for each target
Figure GDA00031057251200000710
Electromagnetic wave signal -3dB bandwidth
Figure GDA00031057251200000711
-3dB beamwidth
Figure GDA00031057251200000712
and SNR
Figure GDA00031057251200000713
both with track time resources
Figure GDA00031057251200000714
is inversely proportional, so the
Figure GDA00031057251200000715
sub-allocation period
Figure GDA00031057251200000716
target error
Figure GDA00031057251200000717
Extract common factors from the diagonal covariance matrix of
Figure GDA00031057251200000718
Rewrite as:

Figure GDA00031057251200000719
Figure GDA00031057251200000719

其中，

Figure GDA00031057251200000720
表示第
Figure GDA00031057251200000721
次分配期间第
Figure GDA00031057251200000722
个目标的剩余矩阵，
Figure GDA00031057251200000723
in,
Figure GDA00031057251200000720
means the first
Figure GDA00031057251200000721
sub-allocation period
Figure GDA00031057251200000722
the residual matrix of the targets,
Figure GDA00031057251200000723

步骤3，根据第

Figure GDA00031057251200000724
次分配时相控阵雷达在第
Figure GDA00031057251200000725
个搜索扇区的搜索模型，得到第
Figure GDA00031057251200000726
次分配期间搜索资源分配方案的目标函数和第
Figure GDA00031057251200000727
次分配期间搜索资源分配方案的转换目标函数。Step 3, according to the
Figure GDA00031057251200000724
The phased array radar is in the first
Figure GDA00031057251200000725
The search model of the search sector, get the first
Figure GDA00031057251200000726
The objective function and the first
Figure GDA00031057251200000727
The transformation objective function to search for resource allocation schemes during secondary allocations.

具体地，对于第

Figure GDA00031057251200000728
次分配期间
Figure GDA00031057251200000729
个不重叠的搜索扇区，相控阵雷达搜索资源分配的目标是将搜索时间资源最优地分配给多个区域并使最坏情况下的搜索信噪比最大化；用
Figure GDA00031057251200000730
表示第
Figure GDA00031057251200000731
次分配期间相控阵雷达分配给
Figure GDA00031057251200000732
个不重叠的搜索扇区的搜索时间列向量，第
Figure GDA00031057251200000733
次分配期间搜索资源分配方案的目标函数为：Specifically, for the
Figure GDA00031057251200000728
sub-allocation period
Figure GDA00031057251200000729
A non-overlapping search sector, the goal of phased array radar search resource allocation is to optimally allocate search time resources to multiple areas and maximize the worst-case search signal-to-noise ratio; using
Figure GDA00031057251200000730
means the first
Figure GDA00031057251200000731
Phased Array Radar is assigned to
Figure GDA00031057251200000732
column vector of search times for non-overlapping search sectors, th
Figure GDA00031057251200000733
The objective function of searching for resource allocation schemes during the secondary allocation period is:

Figure GDA00031057251200000734
Figure GDA00031057251200000734

其中，

Figure GDA00031057251200000735
表示第
Figure GDA00031057251200000736
次分配期间
Figure GDA00031057251200000737
个不重叠的搜索扇区编号组成的集合，
Figure GDA00031057251200000738
Figure GDA00031057251200000739
表示约束条件，
Figure GDA00031057251200000740
表示第
Figure GDA00031057251200000741
次分配期间相控阵雷达分配给
Figure GDA00031057251200000742
个不重叠搜索扇区的总搜索时间资源，
Figure GDA00031057251200000743
表示第
Figure GDA00031057251200000744
次分配期间相控阵雷达分配给第
Figure GDA00031057251200000745
个搜索扇区的搜索时间资源；式(8)中第一个约束表明，第
Figure GDA00031057251200000746
次分配期间相控阵雷达分配给
Figure GDA00031057251200000747
个不重叠搜索扇区的总搜索时间资源为
Figure GDA00031057251200000748
第二个约束条件表明，第
Figure GDA00031057251200000749
次分配期间相控阵雷达分配给每个搜索扇区的搜索时间资源都要受到最小值的限制，即第
Figure GDA00031057251200000750
次分配期间相控阵雷达分配给每个搜索扇区的搜索时间资源都要大于或等于0。in,
Figure GDA00031057251200000735
means the first
Figure GDA00031057251200000736
sub-allocation period
Figure GDA00031057251200000737
A set of non-overlapping search sector numbers,
Figure GDA00031057251200000738
Figure GDA00031057251200000739
represents the constraints,
Figure GDA00031057251200000740
means the first
Figure GDA00031057251200000741
Phased Array Radar is assigned to
Figure GDA00031057251200000742
The total search time resources of non-overlapping search sectors,
Figure GDA00031057251200000743
means the first
Figure GDA00031057251200000744
The phased array radar is assigned to the
Figure GDA00031057251200000745
search time resources of each search sector; the first constraint in equation (8) indicates that the
Figure GDA00031057251200000746
Phased Array Radar is assigned to
Figure GDA00031057251200000747
The total search time resource of non-overlapping search sectors is
Figure GDA00031057251200000748
The second constraint states that the
Figure GDA00031057251200000749
During the sub-allocation period, the search time resources allocated by the phased array radar to each search sector are limited by the minimum value, that is, the first
Figure GDA00031057251200000750
During the secondary allocation period, the search time resources allocated by the phased array radar to each search sector must be greater than or equal to 0.

易知，一个最大化目标类型可以通过求逆转换为最小化目标类型；因此，式(8)的搜索资源分配问题可以重新制定为第

Figure GDA0003105725120000081
次分配期间搜索资源分配方案的转换目标函数：It is easy to know that a maximizing objective type can be transformed into a minimizing objective type by inversion; therefore, the search resource allocation problem of Eq. (8) can be reformulated as the first
Figure GDA0003105725120000081
The transformation objective function of searching resource allocation scheme during secondary allocation:

Figure GDA0003105725120000082
Figure GDA0003105725120000082

其中，

Figure GDA0003105725120000083
表示第
Figure GDA0003105725120000084
次分配期间的凸函数，
Figure GDA0003105725120000085
表示第
Figure GDA0003105725120000086
次分配期间第1个搜索扇区到第
Figure GDA0003105725120000087
个搜索扇区搜索时间资源的累加和，α表示中间变量，
Figure GDA0003105725120000088
表示计算
Figure GDA0003105725120000089
的最小值，
Figure GDA00031057251200000810
表示计算集合
Figure GDA00031057251200000811
中每个搜索扇区的比值
Figure GDA00031057251200000812
后得到
Figure GDA00031057251200000813
个比值,然后比较
Figure GDA00031057251200000814
个比值进而选出最大值操作。in,
Figure GDA0003105725120000083
means the first
Figure GDA0003105725120000084
Convex function during suballocation,
Figure GDA0003105725120000085
means the first
Figure GDA0003105725120000086
During the sub-allocation period, the first search sector to the first
Figure GDA0003105725120000087
The accumulated sum of the search time resources of the search sectors, α represents the intermediate variable,
Figure GDA0003105725120000088
means calculation
Figure GDA0003105725120000089
the minimum value of ,
Figure GDA00031057251200000810
Represents a collection of computations
Figure GDA00031057251200000811
The ratio of each search sector in
Figure GDA00031057251200000812
get after
Figure GDA00031057251200000813
ratios, and then compare
Figure GDA00031057251200000814
A ratio and then select the maximum operation.

步骤4，根据第

Figure GDA00031057251200000815
次分配期间第
Figure GDA00031057251200000816
个目标的跟踪模型，确定第
Figure GDA00031057251200000817
次分配期间跟踪资源分配方案的目标标准函数。Step 4, according to the
Figure GDA00031057251200000815
sub-allocation period
Figure GDA00031057251200000816
The tracking model of the target, determine the first
Figure GDA00031057251200000817
The objective criterion function for tracking resource allocation schemes during sub-allocations.

具体地，针对多目标跟踪，可以根据之前的跟踪信息对其时间资源进行优化，以改善多个目标在最坏情况下的跟踪性能；这里，使用WCT-BCRLB作为标准函数，并将目标跟踪资源分配问题的目标函数制定为第

Figure GDA00031057251200000818
次分配期间跟踪资源分配方案的目标标准函数：Specifically, for multi-target tracking, its time resources can be optimized according to the previous tracking information to improve the tracking performance of multiple targets in the worst case; here, WCT-BCRLB is used as the standard function, and the target tracking resources The objective function of the assignment problem is formulated as
Figure GDA00031057251200000818
The objective standard function for tracking resource allocation schemes during sub-allocations:

Figure GDA00031057251200000819
Figure GDA00031057251200000819

其中，

Figure GDA00031057251200000820
表示第
Figure GDA00031057251200000821
次分配期间
Figure GDA00031057251200000822
个目标编号组成的集合，
Figure GDA00031057251200000823
表示第
Figure GDA00031057251200000824
次分配期间相控阵雷达分配给
Figure GDA00031057251200000825
个目标的跟踪时间资源列向量，
Figure GDA00031057251200000826
表示第
Figure GDA00031057251200000827
次分配期间相控阵雷达分配给第
Figure GDA00031057251200000828
个目标的跟踪时间资源，
Figure GDA00031057251200000829
表示第
Figure GDA00031057251200000830
次分配期间相控阵雷达分配给
Figure GDA00031057251200000831
个目标的总跟踪时间资源；
Figure GDA00031057251200000832
表示求
Figure GDA00031057251200000833
的最小值，
Figure GDA00031057251200000834
表示归一化最坏情况下第
Figure GDA00031057251200000835
次分配期间
Figure GDA00031057251200000836
个目标的跟踪贝叶斯克拉美罗下界凸函数；第一个约束条件表明第
Figure GDA00031057251200000837
次分配期间相控阵雷达分配给
Figure GDA00031057251200000838
个目标的总跟踪时间资源为
Figure GDA00031057251200000839
而第二个约束表示第
Figure GDA00031057251200000840
次分配期间相控阵雷达分配给每个目标的跟踪时间资源受到最小值的限制，即第
Figure GDA00031057251200000841
次分配期间相控阵雷达分配给每个目标的跟踪时间资源都要大于或等于0；所述归一化最坏情况下第
Figure GDA00031057251200000842
次分配期间
Figure GDA00031057251200000843
个目标的跟踪贝叶斯克拉美罗下界凸函数
Figure GDA0003105725120000091
其表达式为：in,
Figure GDA00031057251200000820
means the first
Figure GDA00031057251200000821
sub-allocation period
Figure GDA00031057251200000822
A set of target numbers,
Figure GDA00031057251200000823
means the first
Figure GDA00031057251200000824
Phased array radar is assigned to
Figure GDA00031057251200000825
A column vector of tracking time resources for each target,
Figure GDA00031057251200000826
means the first
Figure GDA00031057251200000827
The phased array radar is assigned to the
Figure GDA00031057251200000828
tracking time resource for each target,
Figure GDA00031057251200000829
means the first
Figure GDA00031057251200000830
Phased array radar is assigned to
Figure GDA00031057251200000831
total tracking time resources for each target;
Figure GDA00031057251200000832
express request
Figure GDA00031057251200000833
the minimum value of ,
Figure GDA00031057251200000834
represents the normalized worst-case
Figure GDA00031057251200000835
sub-allocation period
Figure GDA00031057251200000836
tracking Bayesian Cramero lower bound convex function for a target; the first constraint states that the first
Figure GDA00031057251200000837
Phased array radar is assigned to
Figure GDA00031057251200000838
The total tracking time resource for each target is
Figure GDA00031057251200000839
while the second constraint expresses the
Figure GDA00031057251200000840
The tracking time resource allocated by the phased array radar to each target during the sub-allocation period is limited by the minimum value, that is, the first
Figure GDA00031057251200000841
During the sub-allocation period, the tracking time resource allocated by the phased array radar to each target must be greater than or equal to 0; the normalized worst case
Figure GDA00031057251200000842
sub-allocation period
Figure GDA00031057251200000843
Tracking Bayesian Cramero Lower Bound Convex Function for a Target
Figure GDA0003105725120000091
Its expression is:

Figure GDA0003105725120000092
Figure GDA0003105725120000092

其中，

Figure GDA0003105725120000093
表示矩阵
Figure GDA0003105725120000094
的迹，Λ表示标准化矩阵，表明贝叶斯克拉美罗下界矩阵的元素在不同的尺度上，其表达式为：in,
Figure GDA0003105725120000093
representation matrix
Figure GDA0003105725120000094
The trace of , Λ represents the normalized matrix, indicating that the elements of the Bayesian Cramero lower bound matrix are at different scales, and its expression is:

Figure GDA0003105725120000096
Figure GDA0003105725120000096

Figure GDA0003105725120000097
表示每次分配期间时长，本实施例中
Figure GDA0003105725120000098
表示集合
Figure GDA0003105725120000099
中每个目标对应的
Figure GDA00031057251200000910
中最大值；
Figure GDA00031057251200000911
表示第
Figure GDA00031057251200000912
次分配期间相控阵雷达分配给第
Figure GDA00031057251200000913
个目标的跟踪时间资源
Figure GDA00031057251200000914
的贝叶斯克拉美罗下界矩阵，其表达式为：
Figure GDA0003105725120000097
Indicates the duration of each allocation period, in this embodiment
Figure GDA0003105725120000098
Represents a collection
Figure GDA0003105725120000099
for each target
Figure GDA00031057251200000910
medium and maximum;
Figure GDA00031057251200000911
means the first
Figure GDA00031057251200000912
The phased array radar is assigned to the
Figure GDA00031057251200000913
tracking time resource for a target
Figure GDA00031057251200000914
The Bayesian Cramero lower bound matrix of , whose expression is:

Figure GDA00031057251200000915
Figure GDA00031057251200000915

其中，

Figure GDA00031057251200000916
表示第
Figure GDA00031057251200000917
次分配期间第
Figure GDA00031057251200000918
个目标观测状态的预测贝叶斯信息矩阵，
Figure GDA00031057251200000919
通过下式得到：in,
Figure GDA00031057251200000916
means the first
Figure GDA00031057251200000917
sub-allocation period
Figure GDA00031057251200000918
The predicted Bayesian information matrix of a target observation state,
Figure GDA00031057251200000919
It is obtained by the following formula:

Figure GDA00031057251200000920
Figure GDA00031057251200000920

其中，

Figure GDA00031057251200000921
表示对第
Figure GDA00031057251200000922
次分配期间第
Figure GDA00031057251200000923
个目标的状态矢量
Figure GDA00031057251200000924
的
Figure GDA00031057251200000925
维非线性距离和方位测量函数
Figure GDA00031057251200000926
的转置
Figure GDA00031057251200000927
关于状态矢量
Figure GDA00031057251200000928
的变化量，△表示求变化量，
Figure GDA00031057251200000929
表示第
Figure GDA00031057251200000930
次分配期间第
Figure GDA00031057251200000931
个目标的状态矢量，
Figure GDA00031057251200000932
表示第
Figure GDA00031057251200000933
次分配期间第
Figure GDA00031057251200000934
个目标的
Figure GDA00031057251200000935
维雅克比矩阵，
Figure GDA00031057251200000936
表示设定常数，
Figure GDA00031057251200000937
表示将
Figure GDA00031057251200000938
的值带入
Figure GDA00031057251200000939
中，
Figure GDA00031057251200000940
表示
Figure GDA00031057251200000941
的值由
Figure GDA00031057251200000942
的值计算得到；当
Figure GDA00031057251200000943
时第0次分配期间第
Figure GDA00031057251200000944
个目标的状态矢量
Figure GDA00031057251200000945
表示第
Figure GDA00031057251200000946
次分配期间第
Figure GDA00031057251200000947
个目标的过程噪声
Figure GDA00031057251200000948
的协方差矩阵，
Figure GDA00031057251200000949
为第
Figure GDA00031057251200000950
次分配期间第
Figure GDA00031057251200000951
个目标的转换矩阵，
Figure GDA00031057251200000952
表示第
Figure GDA00031057251200000953
次分配期间相控阵雷达分配给
Figure GDA00031057251200000954
个目标的跟踪时间资源列向量，
Figure GDA00031057251200000955
表示第
Figure GDA00031057251200000956
次分配期间相控阵雷达分配给第
Figure GDA00031057251200000957
个目标的跟踪时间资源，
Figure GDA00031057251200000958
表示第
Figure GDA00031057251200000959
次分配期间第
Figure GDA00031057251200000960
个目标的剩余矩阵，上标-1表示求逆，
Figure GDA00031057251200000961
表示行向量转置。in,
Figure GDA00031057251200000921
express the
Figure GDA00031057251200000922
sub-allocation period
Figure GDA00031057251200000923
target state vector
Figure GDA00031057251200000924
of
Figure GDA00031057251200000925
Dimensional Nonlinear Distance and Bearing Measurement Functions
Figure GDA00031057251200000926
transpose of
Figure GDA00031057251200000927
About the state vector
Figure GDA00031057251200000928
The amount of change, △ represents the amount of change,
Figure GDA00031057251200000929
means the first
Figure GDA00031057251200000930
sub-allocation period
Figure GDA00031057251200000931
the state vector of a target,
Figure GDA00031057251200000932
means the first
Figure GDA00031057251200000933
sub-allocation period
Figure GDA00031057251200000934
target
Figure GDA00031057251200000935
Viacobi matrix,
Figure GDA00031057251200000936
represents the setting constant,
Figure GDA00031057251200000937
means to
Figure GDA00031057251200000938
bring the value of
Figure GDA00031057251200000939
middle,
Figure GDA00031057251200000940
express
Figure GDA00031057251200000941
The value of is given by
Figure GDA00031057251200000942
The value of is calculated; when
Figure GDA00031057251200000943
When the 0th allocation period
Figure GDA00031057251200000944
target state vector
Figure GDA00031057251200000945
means the first
Figure GDA00031057251200000946
sub-allocation period
Figure GDA00031057251200000947
target process noise
Figure GDA00031057251200000948
The covariance matrix of ,
Figure GDA00031057251200000949
for the first
Figure GDA00031057251200000950
sub-allocation period
Figure GDA00031057251200000951
transformation matrix of a target,
Figure GDA00031057251200000952
means the first
Figure GDA00031057251200000953
Phased array radar is assigned to
Figure GDA00031057251200000954
A column vector of tracking time resources for each target,
Figure GDA00031057251200000955
means the first
Figure GDA00031057251200000956
The phased array radar is assigned to the
Figure GDA00031057251200000957
tracking time resource for each target,
Figure GDA00031057251200000958
means the first
Figure GDA00031057251200000959
sub-allocation period
Figure GDA00031057251200000960
The residual matrix of the target, the superscript -1 indicates the inversion,
Figure GDA00031057251200000961
Represents row vector transpose.

步骤5，根据第

Figure GDA00031057251200000962
次分配期间搜索资源分配方案的转换目标函数和第
Figure GDA00031057251200000963
次分配期间跟踪资源分配方案的目标标准函数，得到第
Figure GDA00031057251200000964
次分配期间双目标资源分配方案的数学优化模型。Step 5, according to the
Figure GDA00031057251200000962
The transformation objective function and the first
Figure GDA00031057251200000963
The objective standard function of tracking the resource allocation scheme during the sub-allocation period, obtains the first
Figure GDA00031057251200000964
Mathematical optimization model for a dual-objective resource allocation scheme during secondary allocation.

具体地，相控阵雷达的能力对雷达资源管理器提出了重大挑战，管理器必须在每一次分配期间确定雷达是否应该搜索新的目标或跟踪已存在的目标；理想情况下，搜索能力的最大化和多目标跟踪精度是两个相互冲突的目标，必须同时考虑；因此，第

Figure GDA0003105725120000101
次分配期间相控阵雷达集成SAT应用的双目标资源分配方案的数学模型可以写成：Specifically, the capabilities of phased array radars present significant challenges to radar resource managers, who must determine during each assignment whether the radar should search for new targets or track existing targets; ideally, the maximum search capability Targeting and multi-target tracking accuracy are two conflicting goals that must be considered simultaneously; therefore, the first
Figure GDA0003105725120000101
The mathematical model of the dual-target resource allocation scheme for phased array radar integrated SAT applications during sub-allocation can be written as:

Figure GDA0003105725120000102
Figure GDA0003105725120000102

其中，

Figure GDA0003105725120000103
表示求得的
Figure GDA0003105725120000104
和
Figure GDA0003105725120000105
同时使
Figure GDA0003105725120000106
和
Figure GDA0003105725120000107
最小化，
Figure GDA0003105725120000108
表示第
Figure GDA0003105725120000109
次分配期间相控阵雷达分配给
Figure GDA00031057251200001010
个不重叠搜索扇区的总搜索时间资源，
Figure GDA00031057251200001011
表示第
Figure GDA00031057251200001012
次分配期间相控阵雷达分配给
Figure GDA00031057251200001013
个目标的总跟踪时间资源，
Figure GDA00031057251200001014
表示第
Figure GDA00031057251200001015
次分配期间集成相控阵雷达搜索和跟踪应用的总时间资源；最后一个约束条件表明在第
Figure GDA00031057251200001016
次分配期间集成相控阵雷达搜索和跟踪应用的总资源为
Figure GDA00031057251200001017
表示第
Figure GDA00031057251200001018
次分配期间占空比，
Figure GDA00031057251200001019
表示第
Figure GDA00031057251200001020
次分配期间相控阵雷达分配给第
Figure GDA00031057251200001021
个搜索扇区的搜索时间资源，
Figure GDA00031057251200001022
表示第
Figure GDA00031057251200001023
次分配期间相控阵雷达分配给第
Figure GDA00031057251200001024
个目标的跟踪时间资源，
Figure GDA00031057251200001025
表示第
Figure GDA00031057251200001026
次分配期间的凸函数，
Figure GDA00031057251200001027
表示归一化最坏情况下第
Figure GDA00031057251200001028
次分配期间
Figure GDA00031057251200001029
个目标的跟踪贝叶斯克拉美罗下界凸函数，
Figure GDA00031057251200001030
表示第
Figure GDA00031057251200001031
次分配期间相控阵雷达分配给
Figure GDA00031057251200001032
个不重叠的搜索扇区的搜索时间列向量，
Figure GDA00031057251200001033
表示第
Figure GDA00031057251200001034
次分配期间相控阵雷达分配给
Figure GDA00031057251200001035
个目标的跟踪时间资源列向量。in,
Figure GDA0003105725120000103
to express
Figure GDA0003105725120000104
and
Figure GDA0003105725120000105
at the same time make
Figure GDA0003105725120000106
and
Figure GDA0003105725120000107
minimize,
Figure GDA0003105725120000108
means the first
Figure GDA0003105725120000109
Phased array radar is assigned to
Figure GDA00031057251200001010
The total search time resources of non-overlapping search sectors,
Figure GDA00031057251200001011
means the first
Figure GDA00031057251200001012
Phased array radar is assigned to
Figure GDA00031057251200001013
total tracking time resource for each target,
Figure GDA00031057251200001014
means the first
Figure GDA00031057251200001015
The total time resources for the integrated phased array radar search and track application during the sub-allocation; the last constraint indicates that in the first
Figure GDA00031057251200001016
The total resources for the integrated phased array radar search and track application during the sub-allocation period are
Figure GDA00031057251200001017
means the first
Figure GDA00031057251200001018
duty cycle during sub-distribution,
Figure GDA00031057251200001019
means the first
Figure GDA00031057251200001020
The phased array radar is assigned to the
Figure GDA00031057251200001021
search time resources for each search sector,
Figure GDA00031057251200001022
means the first
Figure GDA00031057251200001023
The phased array radar is assigned to the
Figure GDA00031057251200001024
tracking time resource for each target,
Figure GDA00031057251200001025
means the first
Figure GDA00031057251200001026
Convex function during suballocation,
Figure GDA00031057251200001027
represents the normalized worst-case
Figure GDA00031057251200001028
sub-allocation period
Figure GDA00031057251200001029
The tracking Bayesian Cramero lower bound convex function of a target,
Figure GDA00031057251200001030
means the first
Figure GDA00031057251200001031
Phased array radar is assigned to
Figure GDA00031057251200001032
A column vector of search times for non-overlapping search sectors,
Figure GDA00031057251200001033
means the first
Figure GDA00031057251200001034
Phased array radar is assigned to
Figure GDA00031057251200001035
A column vector of tracking time resources for each target.

将第

Figure GDA00031057251200001036
次分配期间相控阵雷达分配给
Figure GDA00031057251200001037
个不重叠的搜索扇区的搜索时间列向量
Figure GDA00031057251200001038
和第
Figure GDA00031057251200001039
次分配期间相控阵雷达分配给
Figure GDA00031057251200001040
个目标的跟踪时间资源列向量
Figure GDA00031057251200001041
整合为单个向量，记为
Figure GDA00031057251200001042
维向量
Figure GDA00031057251200001043
表示行向量转置；进而得到第
Figure GDA00031057251200001044
次分配期间双目标资源分配方案的数学优化模型为：will
Figure GDA00031057251200001036
Phased Array Radar is assigned to
Figure GDA00031057251200001037
column vector of search times for non-overlapping search sectors
Figure GDA00031057251200001038
and
Figure GDA00031057251200001039
Phased Array Radar is assigned to
Figure GDA00031057251200001040
a column vector of tracking time resources for each target
Figure GDA00031057251200001041
integrated into a single vector, denoted as
Figure GDA00031057251200001042
dimensional vector
Figure GDA00031057251200001043
represents the row vector transpose; and then we get the first
Figure GDA00031057251200001044
The mathematical optimization model of the dual-objective resource allocation scheme during the secondary allocation period is:

Figure GDA0003105725120000111
Figure GDA0003105725120000111

其中，

Figure GDA0003105725120000112
表示第
Figure GDA00031057251200001128
次分配期间的凸函数，
Figure GDA0003105725120000113
表示归一化最坏情况下第
Figure GDA00031057251200001127
次分配期间
Figure GDA00031057251200001126
个目标的跟踪贝叶斯克拉美罗下界凸函数，
Figure GDA0003105725120000114
表示长度为
Figure GDA00031057251200001129
且前
Figure GDA00031057251200001130
个元素为1、其余元素均为零的行向量，
Figure GDA0003105725120000115
表示长度为
Figure GDA00031057251200001131
且从第
Figure GDA00031057251200001132
个元素到第
Figure GDA00031057251200001133
个元素为1、其余元素均为0的行向量，
Figure GDA0003105725120000116
表示行向量
Figure GDA0003105725120000117
中第
Figure GDA00031057251200001134
个元素；第一个约束条件表明第
Figure GDA00031057251200001135
次分配期间相控阵雷达分配给
Figure GDA00031057251200001136
个不重叠搜索扇区的总搜索时间资源为
Figure GDA00031057251200001124
第
Figure GDA00031057251200001125
次分配期间相控阵雷达分配给
Figure GDA00031057251200001123
个目标的总跟踪时间资源为
Figure GDA00031057251200001122
第二个约束条件表明第
Figure GDA00031057251200001160
次分配期间每个搜索扇区的搜索时间及每个目标的跟踪时间均需大于或等于0；最后一个约束条件表明第
Figure GDA00031057251200001137
次分配期间相控阵雷达分配给
Figure GDA00031057251200001121
个不重叠搜索扇区的总搜索时间资源
Figure GDA00031057251200001117
与第
Figure GDA00031057251200001139
次分配期间相控阵雷达分配给
Figure GDA00031057251200001138
个目标的总跟踪时间资源
Figure GDA00031057251200001118
的和为第
Figure GDA00031057251200001119
次分配期间集成相控阵雷达搜索和跟踪应用的总时间资源为
Figure GDA00031057251200001120
in,
Figure GDA0003105725120000112
means the first
Figure GDA00031057251200001128
Convex function during suballocation,
Figure GDA0003105725120000113
represents the normalized worst-case
Figure GDA00031057251200001127
sub-allocation period
Figure GDA00031057251200001126
The tracking Bayesian Cramero lower bound convex function of a target,
Figure GDA0003105725120000114
represents the length of
Figure GDA00031057251200001129
and before
Figure GDA00031057251200001130
A row vector with 1 element and all other elements being zero,
Figure GDA0003105725120000115
represents the length of
Figure GDA00031057251200001131
and from the
Figure GDA00031057251200001132
element to
Figure GDA00031057251200001133
A row vector with 1 element and 0 elements,
Figure GDA0003105725120000116
represents a row vector
Figure GDA0003105725120000117
B
Figure GDA00031057251200001134
elements; the first constraint states that the first
Figure GDA00031057251200001135
Phased array radar is assigned to
Figure GDA00031057251200001136
The total search time resource of non-overlapping search sectors is
Figure GDA00031057251200001124
the first
Figure GDA00031057251200001125
Phased array radar is assigned to
Figure GDA00031057251200001123
The total tracking time resource for each target is
Figure GDA00031057251200001122
The second constraint states that the
Figure GDA00031057251200001160
The search time of each search sector and the tracking time of each target during the sub-allocation must be greater than or equal to 0; the last constraint indicates that the first
Figure GDA00031057251200001137
Phased array radar is assigned to
Figure GDA00031057251200001121
Total search time resources for non-overlapping search sectors
Figure GDA00031057251200001117
with the first
Figure GDA00031057251200001139
Phased array radar is assigned to
Figure GDA00031057251200001138
total tracking time resource for goals
Figure GDA00031057251200001118
The sum is the first
Figure GDA00031057251200001119
The total time resource for the integrated phased array radar search and track application during the sub-allocation period is
Figure GDA00031057251200001120

步骤6，求解第

Figure GDA00031057251200001140
次分配期间双目标资源分配方案的数学优化模型，分别得到第
Figure GDA00031057251200001142
次分配期间相控阵雷达分配给
Figure GDA00031057251200001141
个不重叠搜索扇区的最优搜索时间资源
Figure GDA0003105725120000118
和第
Figure GDA00031057251200001143
次分配期间相控阵雷达分配给
Figure GDA00031057251200001144
个目标的跟踪时间资源列向量最优解
Figure GDA0003105725120000119
Step 6, solve the first
Figure GDA00031057251200001140
The mathematical optimization model of the dual-objective resource allocation scheme during the secondary allocation period, respectively,
Figure GDA00031057251200001142
Phased array radar is assigned to
Figure GDA00031057251200001141
optimal search time resources for non-overlapping search sectors
Figure GDA0003105725120000118
and
Figure GDA00031057251200001143
Phased array radar is assigned to
Figure GDA00031057251200001144
The optimal solution of the tracking time resource column vector for each target
Figure GDA0003105725120000119

步骤6的子步骤为：The sub-steps of step 6 are:

6.1为了获得帕累托子集(不同的总搜索预算求解式(9)得到的解相互独立，不同的总跟踪预算求解问题(10)得到的解相互独立)；设定第

Figure GDA00031057251200001145
次分配期间有
Figure GDA00031057251200001146
个总搜索预算和
Figure GDA00031057251200001147
个总跟踪预算，本实施例中
Figure GDA00031057251200001148
从第1个总搜索预算到第
Figure GDA00031057251200001149
个总搜索预算满足：
Figure GDA00031057251200001110
其中
Figure GDA00031057251200001111
表示第
Figure GDA00031057251200001150
次分配期间第
Figure GDA00031057251200001151
个总搜索预算，将第
Figure GDA00031057251200001152
次分配期间第
Figure GDA00031057251200001153
个总跟踪预算记为
Figure GDA00031057251200001112
且第
Figure GDA00031057251200001154
次分配期间第
Figure GDA00031057251200001155
个总搜索预算
Figure GDA00031057251200001113
和第
Figure GDA00031057251200001156
次分配期间第
Figure GDA00031057251200001157
个总跟踪预算
Figure GDA00031057251200001114
满足：6.1 In order to obtain Pareto subsets (the solutions obtained by different total search budgets to solve Equation (9) are independent of each other, and the solutions obtained from different total tracking budgets to solve problem (10) are independent of each other); set the first
Figure GDA00031057251200001145
The allocation period has
Figure GDA00031057251200001146
total search budget and
Figure GDA00031057251200001147
total tracking budget, in this example
Figure GDA00031057251200001148
From the 1st total search budget to the 1st
Figure GDA00031057251200001149
total search budgets meet:
Figure GDA00031057251200001110
in
Figure GDA00031057251200001111
means the first
Figure GDA00031057251200001150
sub-allocation period
Figure GDA00031057251200001151
total search budget, will
Figure GDA00031057251200001152
sub-allocation period
Figure GDA00031057251200001153
The total tracking budget is recorded as
Figure GDA00031057251200001112
and the first
Figure GDA00031057251200001154
sub-allocation period
Figure GDA00031057251200001155
total search budget
Figure GDA00031057251200001113
and
Figure GDA00031057251200001156
sub-allocation period
Figure GDA00031057251200001157
total tracking budget
Figure GDA00031057251200001114
Satisfy:

Figure GDA00031057251200001115
其中
Figure GDA00031057251200001158
表示第
Figure GDA00031057251200001159
次分配期间集成相控阵雷达搜索和跟踪应用的总时间资源。
Figure GDA00031057251200001115
in
Figure GDA00031057251200001158
means the first
Figure GDA00031057251200001159
Total time resources for integrated phased array radar search and track applications during sub-allocations.

6.2根据第

Figure GDA00031057251200001230
次分配期间第
Figure GDA00031057251200001231
个总搜索预算
Figure GDA0003105725120000121
和线性规划法求解式(9)，即将第
Figure GDA00031057251200001232
次分配期间第
Figure GDA00031057251200001233
个总搜索预算
Figure GDA0003105725120000122
代入式(9)中第一个约束条件右边，根据线性规划法得到第
Figure GDA00031057251200001234
次分配期间相控阵雷达分配给
Figure GDA00031057251200001235
个不重叠的搜索扇区的搜索时间向量对第
Figure GDA00031057251200001236
个总搜索预算资源分配的最优解
Figure GDA0003105725120000123
根据第
Figure GDA00031057251200001237
次分配期间第
Figure GDA00031057251200001238
个总跟踪预算
Figure GDA0003105725120000124
和极大极小解算法求解式(10)，即将第
Figure GDA00031057251200001239
次分配期间第
Figure GDA00031057251200001240
个总跟踪预算
Figure GDA0003105725120000125
代入(10)中第一个约束条件右边，并根据极大极小解算法得到第
Figure GDA00031057251200001242
次分配期间相控阵雷达分配给
Figure GDA00031057251200001241
个目标的跟踪时间资源列向量对第
Figure GDA00031057251200001243
个总跟踪预算资源分配的最优解
Figure GDA0003105725120000126
下标
Figure GDA00031057251200001244
表示第
Figure GDA00031057251200001245
次分配期间，下标
Figure GDA00031057251200001275
表示搜索，下标
Figure GDA00031057251200001276
表示跟踪，下标
Figure GDA00031057251200001277
表示最优解；将所述第
Figure GDA00031057251200001246
个总搜索预算资源分配的最优解
Figure GDA0003105725120000127
和所述第
Figure GDA00031057251200001247
个总跟踪预算资源分配的最优解
Figure GDA0003105725120000128
组成双目标资源第
Figure GDA00031057251200001248
次分配(式(16))的第
Figure GDA00031057251200001249
个帕累托最优解
Figure GDA0003105725120000129
Figure GDA00031057251200001210
(并行最小化方案)，其中上标
Figure GDA00031057251200001250
表示转置，双目标资源分配的第
Figure GDA00031057251200001251
个帕累托最优解
Figure GDA00031057251200001211
包括
Figure GDA00031057251200001252
个元素。6.2 According to the
Figure GDA00031057251200001230
sub-allocation period
Figure GDA00031057251200001231
total search budget
Figure GDA0003105725120000121
and the linear programming method to solve equation (9), that is, the first
Figure GDA00031057251200001232
sub-allocation period
Figure GDA00031057251200001233
total search budget
Figure GDA0003105725120000122
Substitute into the right side of the first constraint in Eq. (9), according to the linear programming method, the first
Figure GDA00031057251200001234
Phased array radar is assigned to
Figure GDA00031057251200001235
search time vector pair of non-overlapping search sectors
Figure GDA00031057251200001236
The optimal solution for resource allocation of total search budget
Figure GDA0003105725120000123
According to the
Figure GDA00031057251200001237
sub-allocation period
Figure GDA00031057251200001238
total tracking budget
Figure GDA0003105725120000124
and the max-min solution algorithm to solve equation (10), that is, the first
Figure GDA00031057251200001239
sub-allocation period
Figure GDA00031057251200001240
total tracking budget
Figure GDA0003105725120000125
Substitute into the right side of the first constraint in (10), and obtain the first
Figure GDA00031057251200001242
Phased array radar is assigned to
Figure GDA00031057251200001241
tracking time resource column vector pair
Figure GDA00031057251200001243
The optimal solution for resource allocation of total tracking budget
Figure GDA0003105725120000126
subscript
Figure GDA00031057251200001244
means the first
Figure GDA00031057251200001245
sub-allocation period, subscript
Figure GDA00031057251200001275
Indicates search, subscript
Figure GDA00031057251200001276
Indicates trace, subscript
Figure GDA00031057251200001277
represents the optimal solution; the first
Figure GDA00031057251200001246
The optimal solution for resource allocation of total search budget
Figure GDA0003105725120000127
and the
Figure GDA00031057251200001247
The optimal solution for resource allocation of total tracking budget
Figure GDA0003105725120000128
Composition of dual-target resources
Figure GDA00031057251200001248
sub-allocation (equation (16))
Figure GDA00031057251200001249
Pareto optimal solutions
Figure GDA0003105725120000129
Figure GDA00031057251200001210
(parallel minimization scheme), where superscript
Figure GDA00031057251200001250
represents the transpose, the first
Figure GDA00031057251200001251
Pareto optimal solutions
Figure GDA00031057251200001211
include
Figure GDA00031057251200001252
elements.

6.3令

Figure GDA00031057251200001253
的值分别取1至
Figure GDA00031057251200001255
重复执行6.2，直到得到双目标资源第
Figure GDA00031057251200001254
次分配的第1个帕累托最优解
Figure GDA00031057251200001212
至双目标资源第
Figure GDA00031057251200001256
次分配的第
Figure GDA00031057251200001257
个帕累托最优解
Figure GDA00031057251200001213
记为基数为
Figure GDA00031057251200001258
的帕累托子集
Figure GDA00031057251200001259
6.3 Order
Figure GDA00031057251200001253
The values are taken from 1 to
Figure GDA00031057251200001255
Repeat 6.2 until you get the dual target resource No.
Figure GDA00031057251200001254
The first Pareto optimal solution of the sub-distribution
Figure GDA00031057251200001212
to double target resource
Figure GDA00031057251200001256
sub-allocated
Figure GDA00031057251200001257
Pareto optimal solutions
Figure GDA00031057251200001213
recorded as the base
Figure GDA00031057251200001258
Pareto subset of
Figure GDA00031057251200001259

由于对于第

Figure GDA00031057251200001260
次分配期间任意两个不同的总搜索预算
Figure GDA00031057251200001215
和
Figure GDA00031057251200001216
上标
Figure GDA00031057251200001270
表示第
Figure GDA00031057251200001271
个总搜索预算，上标
Figure GDA00031057251200001267
表示第
Figure GDA00031057251200001268
个总搜索预算，
Figure GDA00031057251200001266
表示第
Figure GDA00031057251200001261
次分配期间第
Figure GDA00031057251200001269
个总搜索预算，
Figure GDA00031057251200001218
表示第
Figure GDA00031057251200001262
次分配期间第
Figure GDA00031057251200001274
个总搜索预算，第
Figure GDA00031057251200001263
次分配期间第
Figure GDA00031057251200001272
个总搜索预算资源分配的最优解
Figure GDA00031057251200001219
和第
Figure GDA00031057251200001264
次分配期间第
Figure GDA00031057251200001273
个总搜索预算资源分配的最优解
Figure GDA00031057251200001220
具有如下关系
Figure GDA00031057251200001221
故由第
Figure GDA00031057251200001265
次分配期间其中一个总搜索预算和该搜索预算资源分配的最优解和
Figure GDA00031057251200001222
个总搜索预算间的比例关系，可以得到
Figure GDA00031057251200001223
个总搜索预算分别关于式(9)的解。Due to the
Figure GDA00031057251200001260
Any two different total search budgets during the allocation period
Figure GDA00031057251200001215
and
Figure GDA00031057251200001216
superscript
Figure GDA00031057251200001270
means the first
Figure GDA00031057251200001271
total search budget, superscript
Figure GDA00031057251200001267
means the first
Figure GDA00031057251200001268
total search budget,
Figure GDA00031057251200001266
means the first
Figure GDA00031057251200001261
sub-allocation period
Figure GDA00031057251200001269
total search budget,
Figure GDA00031057251200001218
means the first
Figure GDA00031057251200001262
sub-allocation period
Figure GDA00031057251200001274
total search budget, No.
Figure GDA00031057251200001263
sub-allocation period
Figure GDA00031057251200001272
The optimal solution for resource allocation of total search budget
Figure GDA00031057251200001219
and
Figure GDA00031057251200001264
sub-allocation period
Figure GDA00031057251200001273
The optimal solution for resource allocation of total search budget
Figure GDA00031057251200001220
has the following relationship
Figure GDA00031057251200001221
Therefore, the first
Figure GDA00031057251200001265
One of the total search budgets during the sub-allocation period and the optimal solution sum of the resource allocation for this search budget
Figure GDA00031057251200001222
The proportional relationship between the total search budgets, we can get
Figure GDA00031057251200001223
Each total search budget is about the solution of Eq. (9).

根据基数为

Figure GDA00031057251200001224
的帕累托子集
Figure GDA00031057251200001225
计算基数为
Figure GDA00031057251200001226
的帕累托子集
Figure GDA00031057251200001227
中每个最优解的函数值，将基数为
Figure GDA00031057251200001228
的帕累托子集
Figure GDA00031057251200001229
中每个最优解的函数值分别记为帕累托点，进而得到第
Figure GDA00031057251200001351
次分配时相控阵雷达的帕累托点集
Figure GDA0003105725120000131
Figure GDA0003105725120000132
Figure GDA0003105725120000133
Figure GDA0003105725120000134
(只计算前
Figure GDA00031057251200001336
个元素)，α表示中间变量，
Figure GDA00031057251200001337
表示第
Figure GDA00031057251200001352
次分配时相控阵雷达在第
Figure GDA00031057251200001373
个搜索扇区
Figure GDA00031057251200001339
的目标距离搜索值，
Figure GDA00031057251200001338
表示第
Figure GDA00031057251200001353
次分配时相控阵雷达所扫描的第
Figure GDA00031057251200001371
个搜索扇区
Figure GDA00031057251200001340
的角度，
Figure GDA00031057251200001341
表示第
Figure GDA00031057251200001354
次分配期间
Figure GDA00031057251200001342
个不重叠的搜索扇区编号组成的集合，
Figure GDA00031057251200001343
表示第
Figure GDA00031057251200001355
次分配时相控阵雷达的第1个帕累托最优解
Figure GDA0003105725120000136
的函数值，
Figure GDA0003105725120000137
表示第
Figure GDA00031057251200001356
次分配时相控阵雷达的第
Figure GDA00031057251200001370
个帕累托最优解
Figure GDA0003105725120000138
的函数值，
Figure GDA0003105725120000139
表示第
Figure GDA00031057251200001357
次分配时相控阵雷达的第
Figure GDA00031057251200001372
个帕累托最优解
Figure GDA00031057251200001310
的函数值。According to the base
Figure GDA00031057251200001224
Pareto subset of
Figure GDA00031057251200001225
The calculation base is
Figure GDA00031057251200001226
Pareto subset of
Figure GDA00031057251200001227
The function value of each optimal solution in , the base is
Figure GDA00031057251200001228
Pareto subset of
Figure GDA00031057251200001229
The function value of each optimal solution is recorded as the Pareto point, and then the first
Figure GDA00031057251200001351
Pareto Point Sets of Phased Array Radars in Subdistribution
Figure GDA0003105725120000131
Figure GDA0003105725120000132
Figure GDA0003105725120000133
Figure GDA0003105725120000134
(only before counting
Figure GDA00031057251200001336
elements), α represents the intermediate variable,
Figure GDA00031057251200001337
means the first
Figure GDA00031057251200001352
The phased array radar is in the first
Figure GDA00031057251200001373
search sectors
Figure GDA00031057251200001339
The target distance search value of ,
Figure GDA00031057251200001338
means the first
Figure GDA00031057251200001353
The first time the phased array radar scans
Figure GDA00031057251200001371
search sectors
Figure GDA00031057251200001340
Angle,
Figure GDA00031057251200001341
means the first
Figure GDA00031057251200001354
sub-allocation period
Figure GDA00031057251200001342
A set of non-overlapping search sector numbers,
Figure GDA00031057251200001343
means the first
Figure GDA00031057251200001355
The 1st Pareto Optimal Solution of Phased Array Radar in Subdistribution
Figure GDA0003105725120000136
the function value of ,
Figure GDA0003105725120000137
means the first
Figure GDA00031057251200001356
Phased Array Radar
Figure GDA00031057251200001370
Pareto optimal solution
Figure GDA0003105725120000138
the function value of ,
Figure GDA0003105725120000139
means the first
Figure GDA00031057251200001357
Phased Array Radar
Figure GDA00031057251200001372
Pareto optimal solution
Figure GDA00031057251200001310
the function value.

利用第

Figure GDA00031057251200001358
次分配期间的凸函数
Figure GDA00031057251200001311
的单调性，即
Figure GDA00031057251200001312
Figure GDA00031057251200001313
表示双目标资源第
Figure GDA00031057251200001359
次分配的第γ个帕累托最优解
Figure GDA00031057251200001314
的函数值，
Figure GDA00031057251200001315
表示双目标资源第
Figure GDA00031057251200001360
次分配的第β个帕累托最优解
Figure GDA00031057251200001316
的函数值，
Figure GDA00031057251200001317
Figure GDA00031057251200001318
表示第
Figure GDA00031057251200001361
次分配期间第β个总搜索预算资源分配的最优解，
Figure GDA00031057251200001319
表示第β个总跟踪预算资源分配的最优解，
Figure GDA00031057251200001320
表示第
Figure GDA00031057251200001362
次分配期间第γ个总搜索预算资源分配的最优解，
Figure GDA00031057251200001321
表示第γ个总跟踪预算资源分配的最优解；上标Τ表示转置，
Figure GDA00031057251200001344
表示第
Figure GDA00031057251200001346
次分配期间
Figure GDA00031057251200001345
个不重叠搜索扇区中最坏情况下的搜索信噪比，
Figure GDA00031057251200001347
和
Figure GDA00031057251200001323
是两个相邻的帕累托最优解的函数值。Use the
Figure GDA00031057251200001358
Convex function during suballocation
Figure GDA00031057251200001311
the monotonicity of
Figure GDA00031057251200001312
Figure GDA00031057251200001313
Represents a dual target resource
Figure GDA00031057251200001359
The γth Pareto optimal solution of the subdistribution
Figure GDA00031057251200001314
the function value of ,
Figure GDA00031057251200001315
Represents a dual target resource
Figure GDA00031057251200001360
The βth Pareto optimal solution of the subdistribution
Figure GDA00031057251200001316
the function value of ,
Figure GDA00031057251200001317
Figure GDA00031057251200001318
means the first
Figure GDA00031057251200001361
The optimal solution of resource allocation for the βth total search budget during the sub-allocation period,
Figure GDA00031057251200001319
represents the optimal solution of the βth total tracking budget resource allocation,
Figure GDA00031057251200001320
means the first
Figure GDA00031057251200001362
the optimal solution of resource allocation for the γth total search budget during the sub-allocation period,
Figure GDA00031057251200001321
represents the optimal solution of the γth total tracking budget resource allocation; the superscript Τ represents the transposition,
Figure GDA00031057251200001344
means the first
Figure GDA00031057251200001346
sub-allocation period
Figure GDA00031057251200001345
Worst-case search SNR in non-overlapping search sectors,
Figure GDA00031057251200001347
and
Figure GDA00031057251200001323
is the function value of two adjacent Pareto optimal solutions.

由两个帕累托最优解

Figure GDA00031057251200001324
和
Figure GDA00031057251200001325
可以得到两个总搜索预算
Figure GDA00031057251200001326
和
Figure GDA00031057251200001327
Figure GDA00031057251200001328
表示第
Figure GDA00031057251200001363
次分配期间第β个总搜索预算，是双目标资源第
Figure GDA00031057251200001364
次分配的第β个帕累托最优解
Figure GDA00031057251200001329
中前
Figure GDA00031057251200001365
个元素的累加和；
Figure GDA00031057251200001330
表示第
Figure GDA00031057251200001366
次分配期间第γ个总搜索预算，是双目标资源第
Figure GDA00031057251200001367
次分配的第γ个帕累托最优解
Figure GDA00031057251200001331
中前
Figure GDA00031057251200001348
个元素的累加和；对两个总搜索预算
Figure GDA00031057251200001332
和
Figure GDA00031057251200001333
使用二分法得到第
Figure GDA00031057251200001368
次分配期间相控阵雷达分配给
Figure GDA00031057251200001349
个不重叠搜索扇区的最优总搜索时间资源
Figure GDA00031057251200001334
和第
Figure GDA00031057251200001369
次分配期间相控阵雷达分配给
Figure GDA00031057251200001350
个目标的最优总跟踪时间资源
Figure GDA00031057251200001335
by two Pareto optimal solutions
Figure GDA00031057251200001324
and
Figure GDA00031057251200001325
You can get two total search budgets
Figure GDA00031057251200001326
and
Figure GDA00031057251200001327
Figure GDA00031057251200001328
means the first
Figure GDA00031057251200001363
The βth total search budget during the sub-allocation period is the first
Figure GDA00031057251200001364
The βth Pareto optimal solution of the subdistribution
Figure GDA00031057251200001329
middle front
Figure GDA00031057251200001365
cumulative sum of elements;
Figure GDA00031057251200001330
means the first
Figure GDA00031057251200001366
The γth total search budget during the sub-allocation period is the second
Figure GDA00031057251200001367
The γth Pareto optimal solution of the subdistribution
Figure GDA00031057251200001331
middle front
Figure GDA00031057251200001348
Cumulative sum of elements; for two total search budgets
Figure GDA00031057251200001332
and
Figure GDA00031057251200001333
Use dichotomy to get the
Figure GDA00031057251200001368
Phased array radar is assigned to
Figure GDA00031057251200001349
optimal total search time resource for non-overlapping search sectors
Figure GDA00031057251200001334
and
Figure GDA00031057251200001369
Phased array radar is assigned to
Figure GDA00031057251200001350
optimal total tracking time resource for each target
Figure GDA00031057251200001335

将所述最优总搜索时间资源

Figure GDA0003105725120000141
代入第
Figure GDA00031057251200001428
次分配期间搜索资源分配方案的转换目标函数中，并利用线性规划法求解得到第
Figure GDA00031057251200001429
次分配期间相控阵雷达分配给
Figure GDA00031057251200001418
个不重叠搜索扇区的最优搜索时间资源
Figure GDA0003105725120000142
将所述最优总跟踪时间资源
Figure GDA0003105725120000143
代入第
Figure GDA00031057251200001430
次分配期间跟踪资源分配方案的目标标准函数中，并利用极小极大解算法得到第
Figure GDA00031057251200001431
次分配期间相控阵雷达分配给
Figure GDA00031057251200001419
个目标的跟踪时间资源列向量最优解
Figure GDA0003105725120000144
The optimal total search time resource
Figure GDA0003105725120000141
Substitute the first
Figure GDA00031057251200001428
During the sub-allocation period, the conversion objective function of the resource allocation scheme is searched, and the linear programming method is used to obtain the first
Figure GDA00031057251200001429
Phased Array Radar is assigned to
Figure GDA00031057251200001418
optimal search time resources for non-overlapping search sectors
Figure GDA0003105725120000142
The optimal total tracking time resource
Figure GDA0003105725120000143
Substitute the first
Figure GDA00031057251200001430
In the objective standard function of tracking the resource allocation scheme during the sub-allocation period, and using the minimax solution algorithm to obtain the first
Figure GDA00031057251200001431
Phased Array Radar is assigned to
Figure GDA00031057251200001419
The optimal solution of tracking time resource column vector for each target
Figure GDA0003105725120000144

其中，

Figure GDA0003105725120000145
是第
Figure GDA00031057251200001432
次分配期间最优搜索资源分配结果，
Figure GDA0003105725120000146
是第
Figure GDA00031057251200001433
次分配期间最优目标跟踪资源分配结果，所述第
Figure GDA00031057251200001434
次分配期间相控阵雷达分配给
Figure GDA00031057251200001420
个不重叠搜索扇区的最优总搜索时间资源
Figure GDA0003105725120000147
和所述第
Figure GDA00031057251200001435
次分配期间相控阵雷达分配给
Figure GDA00031057251200001421
个目标的最优总跟踪时间资源
Figure GDA0003105725120000148
的和作为第
Figure GDA00031057251200001436
次分配期间集成相控阵雷达搜索和跟踪应用的总时间资源
Figure GDA00031057251200001422
in,
Figure GDA0003105725120000145
is the first
Figure GDA00031057251200001432
The optimal search resource allocation results during the secondary allocation period,
Figure GDA0003105725120000146
is the first
Figure GDA00031057251200001433
The optimal target tracking resource allocation results during the secondary allocation, the
Figure GDA00031057251200001434
Phased array radar is assigned to
Figure GDA00031057251200001420
optimal total search time resource for non-overlapping search sectors
Figure GDA0003105725120000147
and the
Figure GDA00031057251200001435
Phased array radar is assigned to
Figure GDA00031057251200001421
optimal total tracking time resource for each target
Figure GDA0003105725120000148
the sum as the first
Figure GDA00031057251200001436
Total time resources for integrated phased array radar search and track applications during sub-allocations
Figure GDA00031057251200001422

具体步骤为：The specific steps are:

6a)分别设置迭代索引

Figure GDA00031057251200001449
和停止阈值ε＝10-3，以及设置第
Figure GDA00031057251200001437
次分配期间搜索资源下界
Figure GDA0003105725120000149
和第
Figure GDA00031057251200001438
次分配期间搜索资源上界
Figure GDA00031057251200001410
Figure GDA00031057251200001411
表示第
Figure GDA00031057251200001439
次分配期间第β个总搜索预算，
Figure GDA00031057251200001412
表示第
Figure GDA00031057251200001440
次分配期间第γ个总搜索预算；其中，γ＝β+1，
Figure GDA00031057251200001448
表示第
Figure GDA00031057251200001441
次分配期间设定的总搜索预算个数或总跟踪预算个数。6a) Set the iteration index separately
Figure GDA00031057251200001449
and stop threshold ε=10 -3 , and set the first
Figure GDA00031057251200001437
Search resource lower bound during sub-allocation
Figure GDA0003105725120000149
and
Figure GDA00031057251200001438
Search resource upper bound during sub-allocation
Figure GDA00031057251200001410
Figure GDA00031057251200001411
means the first
Figure GDA00031057251200001439
the βth total search budget during the sub-allocation period,
Figure GDA00031057251200001412
means the first
Figure GDA00031057251200001440
The γth total search budget during the sub-allocation period; where γ=β+1,
Figure GDA00031057251200001448
means the first
Figure GDA00031057251200001441
The total search budget or total tracking budget set during the allocation period.

6b)根据第

Figure GDA00031057251200001442
次分配期间搜索资源下界
Figure GDA00031057251200001455
和第
Figure GDA00031057251200001443
次分配期间搜索资源上界
Figure GDA00031057251200001456
计算第
Figure GDA00031057251200001453
次迭代后第
Figure GDA00031057251200001444
次分配期间相控阵雷达的总搜索资源
Figure GDA00031057251200001423
然后利用第
Figure GDA00031057251200001454
次迭代后第
Figure GDA00031057251200001445
次分配期间相控阵雷达的总搜索资源
Figure GDA00031057251200001424
和线性规划法求解第
Figure GDA00031057251200001446
次分配期间搜索资源分配方案的转换目标函数，得到第
Figure GDA00031057251200001450
次迭代后第
Figure GDA00031057251200001447
次分配期间相控阵雷达分配给
Figure GDA00031057251200001425
个不重叠的搜索扇区的搜索时间列向量最优解
Figure GDA00031057251200001413
6b) According to the
Figure GDA00031057251200001442
Search resource lower bound during sub-allocation
Figure GDA00031057251200001455
and
Figure GDA00031057251200001443
Search resource upper bound during sub-allocation
Figure GDA00031057251200001456
Calculate the first
Figure GDA00031057251200001453
after the iteration
Figure GDA00031057251200001444
Total search resources of phased array radar during sub-allocation
Figure GDA00031057251200001423
Then use the
Figure GDA00031057251200001454
after the iteration
Figure GDA00031057251200001445
Total search resources of phased array radar during sub-allocation
Figure GDA00031057251200001424
and linear programming to solve the first
Figure GDA00031057251200001446
During the sub-allocation period, the transformation objective function of the resource allocation scheme is searched to obtain the first
Figure GDA00031057251200001450
after the iteration
Figure GDA00031057251200001447
Phased Array Radar is assigned to
Figure GDA00031057251200001425
search time column vector optimal solution for non-overlapping search sectors
Figure GDA00031057251200001413

6c)如果

Figure GDA00031057251200001414
更新
Figure GDA00031057251200001426
令
Figure GDA00031057251200001451
的值加1,执行6b)；否则执行6d)。6c) If
Figure GDA00031057251200001414
renew
Figure GDA00031057251200001426
make
Figure GDA00031057251200001451
Add 1 to the value of , and execute 6b); otherwise, execute 6d).

6d)如果

Figure GDA00031057251200001415
更新
Figure GDA00031057251200001427
令
Figure GDA00031057251200001452
的值加1,执行6b)；否则执行6e)。6d) If
Figure GDA00031057251200001415
renew
Figure GDA00031057251200001427
make
Figure GDA00031057251200001452
Add 1 to the value of , and execute 6b); otherwise, execute 6e).

6e)如果

Figure GDA00031057251200001416
取
Figure GDA00031057251200001417
搜索资源分配最优解为
Figure GDA00031057251200001520
表示第
Figure GDA00031057251200001530
次分配期间相控阵雷达分配给
Figure GDA00031057251200001531
个不重叠搜索扇区的最优搜索时间资源，
Figure GDA0003105725120000153
表示第
Figure GDA00031057251200001543
次迭代后第
Figure GDA00031057251200001532
次分配期间相控阵雷达分配给
Figure GDA00031057251200001521
个不重叠的搜索扇区的搜索时间向量最优解。6e) If
Figure GDA00031057251200001416
Pick
Figure GDA00031057251200001417
The optimal solution of search resource allocation is
Figure GDA00031057251200001520
means the first
Figure GDA00031057251200001530
Phased Array Radar is assigned to
Figure GDA00031057251200001531
optimal search time resources for non-overlapping search sectors,
Figure GDA0003105725120000153
means the first
Figure GDA00031057251200001543
after the iteration
Figure GDA00031057251200001532
Phased Array Radar is assigned to
Figure GDA00031057251200001521
The optimal solution of the search time vector for the non-overlapping search sectors.

6f)计算第

Figure GDA00031057251200001533
次分配期间相控阵雷达分配给
Figure GDA00031057251200001522
个目标的最优总跟踪时间资源
Figure GDA0003105725120000154
Figure GDA0003105725120000155
其中，
Figure GDA00031057251200001523
表示第
Figure GDA00031057251200001534
次分配期间集成相控阵雷达搜索和跟踪应用的总资源，
Figure GDA00031057251200001524
表示第
Figure GDA00031057251200001535
次分配期间占空比，
Figure GDA00031057251200001525
表示每次分配期间时长，本实施例中
Figure GDA00031057251200001526
6f) Calculate the first
Figure GDA00031057251200001533
Phased array radar is assigned to
Figure GDA00031057251200001522
optimal total tracking time resource for each target
Figure GDA0003105725120000154
Figure GDA0003105725120000155
in,
Figure GDA00031057251200001523
means the first
Figure GDA00031057251200001534
total resources for integrated phased array radar search and track applications during the sub-allocation,
Figure GDA00031057251200001524
means the first
Figure GDA00031057251200001535
duty cycle during sub-distribution,
Figure GDA00031057251200001525
Indicates the duration of each allocation period, in this embodiment
Figure GDA00031057251200001526

6g)将所述最优总跟踪时间资源

Figure GDA0003105725120000156
代入第
Figure GDA00031057251200001536
次分配期间跟踪资源分配方案的目标标准函数中，并利用极小极大解算法得到第
Figure GDA00031057251200001537
次分配期间相控阵雷达分配给
Figure GDA00031057251200001527
个目标的跟踪时间资源列向量最优解
Figure GDA0003105725120000157
6g) The optimal total tracking time resource
Figure GDA0003105725120000156
Substitute the first
Figure GDA00031057251200001536
In the objective standard function of tracking the resource allocation scheme during the sub-allocation period, and using the minimax solution algorithm to obtain the first
Figure GDA00031057251200001537
Phased array radar is assigned to
Figure GDA00031057251200001527
The optimal solution of the tracking time resource column vector for each target
Figure GDA0003105725120000157

步骤7，令

Figure GDA00031057251200001538
的值加1，返回步骤2，直到得到第1次分配期间相控阵雷达分配给
Figure GDA00031057251200001539
个不重叠搜索扇区的最优搜索时间资源
Figure GDA0003105725120000158
至第
Figure GDA00031057251200001540
次分配期间相控阵雷达分配给
Figure GDA00031057251200001528
个不重叠搜索扇区的最优搜索时间资源
Figure GDA0003105725120000159
以及第1次分配期间相控阵雷达分配给
Figure GDA00031057251200001541
个目标的跟踪时间资源列向量最优解
Figure GDA00031057251200001510
至第
Figure GDA00031057251200001542
次分配期间相控阵雷达分配给
Figure GDA00031057251200001529
个目标的跟踪时间资源列向量最优解
Figure GDA00031057251200001511
记为基于相控阵雷达搜索和跟踪双目标优化的资源分配结果；本实施例取
Figure GDA00031057251200001512
Step 7, let
Figure GDA00031057251200001538
Add 1 to the value of , and return to step 2 until the phased array radar is assigned to
Figure GDA00031057251200001539
optimal search time resources for non-overlapping search sectors
Figure GDA0003105725120000158
to the
Figure GDA00031057251200001540
Phased array radar is assigned to
Figure GDA00031057251200001528
optimal search time resources for non-overlapping search sectors
Figure GDA0003105725120000159
and the phased array radar was assigned to
Figure GDA00031057251200001541
The optimal solution of the tracking time resource column vector for each target
Figure GDA00031057251200001510
to the
Figure GDA00031057251200001542
Phased array radar is assigned to
Figure GDA00031057251200001529
The optimal solution of the tracking time resource column vector for each target
Figure GDA00031057251200001511
It is recorded as the resource allocation result based on phased array radar search and tracking dual target optimization; this embodiment takes
Figure GDA00031057251200001512

本发明将资源分配方案制定为一个双目标优化框架，根据并行最小化方案得到基数为

Figure GDA00031057251200001513
的帕累托子集；然后利用线性规划法和极小极大解算法，有效地解决了双目标资源分配问题。The invention formulates the resource allocation scheme as a dual-objective optimization framework, and obtains the cardinal number according to the parallel minimization scheme as
Figure GDA00031057251200001513
The Pareto subset of , and then use the linear programming method and the minimax solution algorithm to effectively solve the dual-objective resource allocation problem.

通过以下仿真对本发明效果进行进一步验证说明。The effect of the present invention is further verified and explained by the following simulation.

1.仿真参数：1. Simulation parameters:

相控阵雷达固定的位置为(93,45)km，其信号有效带宽和半功率波束宽度分别设置为

Figure GDA00031057251200001514
和
Figure GDA00031057251200001515
总的时间资源为
Figure GDA00031057251200001516
使用20次分配期间来进行模拟，每次分配的时长被设置为
Figure GDA00031057251200001517
实际上，相控阵雷达可能有不同的搜索需求。因此，考虑两种类型的搜索模型
Figure GDA00031057251200001518
和
Figure GDA00031057251200001519
来描述两种不同的搜索需求，详细请参阅表I和表II，表I为模型
Figure GDA00031057251200001618
中的每个扇区的搜索参数，表II为模型
Figure GDA00031057251200001619
中的每个扇区的搜索参数。The fixed position of the phased array radar is (93, 45) km, and its signal effective bandwidth and half-power beamwidth are respectively set as
Figure GDA00031057251200001514
and
Figure GDA00031057251200001515
The total time resource is
Figure GDA00031057251200001516
The simulation is run using 20 allocation periods, each allocation duration is set to
Figure GDA00031057251200001517
In practice, phased array radars may have different search needs. Therefore, consider two types of search models
Figure GDA00031057251200001518
and
Figure GDA00031057251200001519
To describe two different search requirements, please refer to Table I and Table II for details, Table I is the model
Figure GDA00031057251200001618
search parameters for each sector in Table II for the model
Figure GDA00031057251200001619
search parameters for each sector in .

前10次分配期间

Figure GDA00031057251200001612
相控阵雷达采用第一个搜索模型
Figure GDA00031057251200001620
其中扇区的数量被设置为
Figure GDA0003105725120000168
在后10个分配期间
Figure GDA0003105725120000169
相控阵雷达采用第二种搜索模型
Figure GDA00031057251200001621
扇区的数量为
Figure GDA00031057251200001610
During the first 10 allocations
Figure GDA00031057251200001612
Phased Array Radar Adopts First Search Model
Figure GDA00031057251200001620
where the number of sectors is set to
Figure GDA0003105725120000168
During the last 10 allocation periods
Figure GDA0003105725120000169
Phased array radar uses a second search model
Figure GDA00031057251200001621
The number of sectors is
Figure GDA00031057251200001610

表ITable I

扇区号sector number 11 22 33 44 55 66 77 88 R<sub>i,k</sub>(km)R<sub>i,k</sub>(km) 240240 240240 240240 300300 200200 300300 310310 295295 θ<sub>i,k</sub>(<sup>○</sup>)θ<sub>i,k</sub>(<sup>○</sup>) 88 88 88 88 88 66 88 1212

表IITable II

扇区号sector number 11 22 33 44 55 66 R<sub>i,k</sub>(km)R<sub>i,k</sub>(km) 240240 240240 240240 300300 200200 300300 θ<sub>i,k</sub>(<sup>○</sup>)θ<sub>i,k</sub>(<sup>○</sup>) 88 88 1616 88 88 88

在模拟中，将需要跟踪的目标数量设置为

Figure GDA00031057251200001613
表III中给出每个目标状态参数。In the simulation, set the number of targets that need to be tracked to
Figure GDA00031057251200001613
Each target state parameter is given in Table III.

表IIITable III

目标号target number 11 22 33 44 55 位置(km)Location (km) (3,55)(3,55) (-23,85)(-23,85) (233,60)(233,60) (300,30)(300,30) (52,80)(52,80) 速度(m/s)Speed (m/s) (300,0)(300,0) (100,-150)(100,-150) (200,-200)(200,-200) (10,-200)(10,-200) (200,100)(200,100) 初始范围(m)Initial range (m) 127.28127.28 126.32126.32 169.19169.19 86.4586.45 122.09122.09 目标反射率target reflectivity 22 0.80.8 1.51.5 11 11

参照图3，为相控阵雷达雷达检测范围内的目标部署示意图；图3给出了这些目标相对雷达系统的角分布。Referring to FIG. 3 , it is a schematic diagram of the deployment of targets within the detection range of the phased array radar radar; FIG. 3 shows the angular distribution of these targets relative to the radar system.

为了得到基数为

Figure GDA00031057251200001616
的帕累托子集,
Figure GDA00031057251200001617
个搜索时间预算设置为
Figure GDA0003105725120000161
对于给定的
Figure GDA0003105725120000162
Figure GDA0003105725120000163
表示基准解(资源平均分配方案的解)，其中
Figure GDA0003105725120000164
Figure GDA0003105725120000165
表示具有
Figure GDA00031057251200001611
个元素的全1列向量，
Figure GDA0003105725120000166
表示第
Figure GDA00031057251200001614
次分配期间第
Figure GDA00031057251200001615
个总资源预算采用资源平均分配方案的解，
Figure GDA0003105725120000167
表示第
Figure GDA0003105725120000174
次分配期间第
Figure GDA0003105725120000176
个总搜索资源预算采用搜索资源平均分配方案的解，
Figure GDA0003105725120000171
表示第
Figure GDA0003105725120000175
次分配期间第
Figure GDA0003105725120000177
个总跟踪资源预算采用跟踪资源平均分配方案的解，基准集为
Figure GDA0003105725120000172
各基准解的目标函数值称为基准结果，由基准结果构成的曲线称为基准曲线，同样帕累托子集
Figure GDA0003105725120000173
中各帕累托解的目标函数值称为帕累托结果，由帕累托结果构成的曲线称为帕累托曲线。In order to get the base as
Figure GDA00031057251200001616
Pareto subset of ,
Figure GDA00031057251200001617
search time budgets are set to
Figure GDA0003105725120000161
for a given
Figure GDA0003105725120000162
Figure GDA0003105725120000163
represents the benchmark solution (the solution of the resource average allocation scheme), where
Figure GDA0003105725120000164
Figure GDA0003105725120000165
means to have
Figure GDA00031057251200001611
an all-one-column vector of elements,
Figure GDA0003105725120000166
means the first
Figure GDA00031057251200001614
sub-allocation period
Figure GDA00031057251200001615
A total resource budget adopts the solution of the resource average allocation scheme,
Figure GDA0003105725120000167
means the first
Figure GDA0003105725120000174
sub-allocation period
Figure GDA0003105725120000176
The total search resource budget adopts the solution of the search resource average allocation scheme,
Figure GDA0003105725120000171
means the first
Figure GDA0003105725120000175
sub-allocation period
Figure GDA0003105725120000177
The total tracking resource budget adopts the solution of the tracking resource average allocation scheme, and the benchmark set is
Figure GDA0003105725120000172
The objective function value of each benchmark solution is called the benchmark result, and the curve formed by the benchmark result is called the benchmark curve, and the same Pareto subset
Figure GDA0003105725120000173
The objective function value of each Pareto solution in is called the Pareto result, and the curve formed by the Pareto result is called the Pareto curve.

2.仿真内容：2. Simulation content:

本发明针对资源平均分配方案和基于帕累托理论的双目标优化资源分配方案的分配结果作对比仿真实验。The present invention conducts a comparative simulation experiment for the allocation results of the resource average allocation scheme and the dual-objective optimal resource allocation scheme based on Pareto theory.

3.仿真结果分析：3. Analysis of simulation results:

图4(a)的结果显示，搜索需求模型

Figure GDA0003105725120000178
就最坏情况下的搜索信噪比和最坏情况下的跟踪贝叶斯克拉美罗界下界而言，帕累托曲线明显优于基准曲线；图4(b)的结果显示，搜索需求模型
Figure GDA0003105725120000179
就最坏情况下的搜索信噪比和最坏情况下的跟踪贝叶斯克拉美罗界下界而言，帕累托曲线明显优于基准曲线；因此有了帕累托曲线，对于任意的任务需求，使用二分法可以轻松地获得最佳搜索和跟踪性能。The results in Figure 4(a) show that the search demand model
Figure GDA0003105725120000178
In terms of worst-case search SNR and worst-case tracking Bayesian Cramero lower bound, the Pareto curve is significantly better than the benchmark curve; the results in Figure 4(b) show that the search demand model
Figure GDA0003105725120000179
In terms of worst-case search SNR and worst-case tracking Bayesian Cramero lower bound, the Pareto curve is significantly better than the benchmark curve; therefore, with the Pareto curve, for arbitrary tasks requirements, optimal search and tracking performance can be easily obtained using the dichotomy method.

综上所述，仿真实验验证了本发明的正确性，有效性和可靠性。To sum up, the simulation experiment verifies the correctness, effectiveness and reliability of the present invention.

显然，本领域的技术人员可以对本发明进行各种改动和变型而不脱离本发明的精神和范围。这样，倘若本发明的这些修改和变型属于本发明权利要求及其等同技术的范围之内，则本发明也意图包含这些改动和变型在内。It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit and scope of the invention. Thus, provided that these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims (7)

1. A resource allocation method based on phased array radar searching and tracking dual-target optimization is characterized by comprising the following steps:
step 1, initialization: order to
Figure FDA0003105725110000011
Is as follows
Figure FDA0003105725110000012
The number of the sub-distribution is equal to the number of the sub-distribution,
Figure FDA0003105725110000013
is set to an initial value of 1,
Figure FDA0003105725110000014
an even number greater than 0; is set to
Figure FDA0003105725110000015
Search area existence of time-controlled array radar in sub-distribution
Figure FDA00031057251100000147
An object, and
Figure FDA0003105725110000016
time control of sub-distributionThe search area of the array radar is divided into
Figure FDA0003105725110000017
A plurality of non-overlapping search sectors;
step 2, determining
Figure FDA0003105725110000018
Time phased array radar in sub-distribution
Figure FDA0003105725110000019
Search model and method for searching sector
Figure FDA00031057251100000110
During the sub-distribution period
Figure FDA00031057251100000111
A tracking model of the individual target; wherein,
Figure FDA00031057251100000112
is shown as
Figure FDA00031057251100000113
Distributing the number of targets in a search area of the time-controlled array radar in a secondary mode;
Figure FDA00031057251100000114
is shown as
Figure FDA00031057251100000115
The time-controlled array radar searches the total number of sectors in the time distribution;
step 3, according to
Figure FDA00031057251100000116
Time phased array radar in sub-distribution
Figure FDA00031057251100000117
A search model of the search sector, get
Figure FDA00031057251100000118
Searching for objective function and second order of resource allocation scheme during secondary allocation
Figure FDA00031057251100000119
Searching a conversion objective function of the resource allocation scheme during the secondary allocation period;
step 4, according to
Figure FDA00031057251100000120
During the sub-distribution period
Figure FDA00031057251100000121
A tracking model of the object, determining
Figure FDA00031057251100000122
Tracking a target standard function of a resource allocation scheme during the secondary allocation;
step 5, according to
Figure FDA00031057251100000123
Search for transfer objective function and the second of resource allocation scheme during sub-allocation
Figure FDA00031057251100000124
Tracking a target criteria function of the resource allocation scheme during the sub-allocation period to obtain a second
Figure FDA00031057251100000125
A mathematical optimization model of a dual target resource allocation scheme during secondary allocation;
step 6, solving
Figure FDA00031057251100000126
The mathematical optimization model of the double-target resource allocation scheme in the secondary allocation period respectively obtains
Figure FDA00031057251100000127
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000128
Optimal search time resources for non-overlapping search sectors
Figure FDA00031057251100000129
And a first
Figure FDA00031057251100000130
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000131
Tracking time resource column vector optimal solution of each target
Figure FDA00031057251100000132
Step 7, let
Figure FDA00031057251100000133
Adds 1 to the value of (1), returns to step 2 until the phased array radar assignment during the 1 st assignment is obtained
Figure FDA00031057251100000134
Optimal search time resources for non-overlapping search sectors
Figure FDA00031057251100000135
To the first
Figure FDA00031057251100000136
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000137
Optimal search time for non-overlapping search sectors(Resource)
Figure FDA00031057251100000138
And phased array radar assignment during the 1 st assignment
Figure FDA00031057251100000139
Tracking time resource column vector optimal solution of each target
Figure FDA00031057251100000140
To the first
Figure FDA00031057251100000141
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000142
Tracking time resource column vector optimal solution of each target
Figure FDA00031057251100000143
And recording the resource allocation result as a resource allocation result based on dual target searching and tracking of the phased array radar.
2. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 2, the first step
Figure FDA00031057251100000144
Time phased array radar in sub-distribution
Figure FDA00031057251100000145
The search model for each search sector is:
Figure FDA00031057251100000146
wherein, alpha represents an intermediate variable,
Figure FDA0003105725110000021
is shown as
Figure FDA0003105725110000022
Time-controlled array radar allocation to the second
Figure FDA0003105725110000023
Search sector
Figure FDA0003105725110000024
The time resources of the search of (2),
Figure FDA0003105725110000025
is shown as
Figure FDA0003105725110000026
Time phased array radar in sub-distribution
Figure FDA0003105725110000027
Search sector
Figure FDA0003105725110000028
The target search signal-to-noise ratio of (c),
Figure FDA0003105725110000029
represents the average transmit power of the phased array radar,
Figure FDA00031057251100000210
indicating the set effective receive aperture of the phased array radar antenna,
Figure FDA00031057251100000211
is shown as
Figure FDA00031057251100000212
Time phased array radar in sub-distribution
Figure FDA00031057251100000213
Search sector
Figure FDA00031057251100000214
The cross-sectional area of scattering of the target,
Figure FDA00031057251100000215
which represents the boltzmann constant, represents,
Figure FDA00031057251100000216
indicating the set phased array radar temperature,
Figure FDA00031057251100000217
the loss of the phased array radar is shown,
Figure FDA00031057251100000218
is shown as
Figure FDA00031057251100000219
Time-controlled array radar scanned by sub-distribution
Figure FDA00031057251100000220
Search sector
Figure FDA00031057251100000221
The angle of (a) is determined,
Figure FDA00031057251100000222
is shown as
Figure FDA00031057251100000223
Time phased array radar in sub-distribution
Figure FDA00031057251100000224
Search sector
Figure FDA00031057251100000225
The target distance search value of (1);
the first mentioned
Figure FDA00031057251100000226
During the sub-distribution period
Figure FDA00031057251100000227
The tracking model of each target is as follows:
Figure FDA00031057251100000228
wherein,
Figure FDA00031057251100000229
is shown as
Figure FDA00031057251100000230
During the sub-distribution period
Figure FDA00031057251100000231
The process noise of the individual target is,
Figure FDA00031057251100000232
is shown as
Figure FDA00031057251100000233
During the sub-distribution period
Figure FDA00031057251100000234
The state vector of the individual objects is,
Figure FDA00031057251100000235
is as follows
Figure FDA00031057251100000236
During the sub-distribution period
Figure FDA00031057251100000237
The transformation matrix of the individual objects is,
Figure FDA00031057251100000238
the expression of the kronecker operator,
Figure FDA00031057251100000239
representing a 2 x 2 dimensional identity matrix,
Figure FDA00031057251100000240
indicating the duration of each dispense.
3. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 3, the first step
Figure FDA00031057251100000241
The objective function of searching the resource allocation scheme during the secondary allocation is:
Figure FDA00031057251100000242
wherein,
Figure FDA00031057251100000243
is shown as
Figure FDA00031057251100000244
During the sub-distribution period
Figure FDA00031057251100000245
A set of non-overlapping search sector numbers,
Figure FDA00031057251100000246
Figure FDA00031057251100000247
a constraint condition is expressed in terms of the number of the elements,
Figure FDA00031057251100000248
is shown as
Figure FDA00031057251100000249
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000250
The total search time resources of the non-overlapping search sectors,
Figure FDA00031057251100000251
is shown as
Figure FDA00031057251100000252
During the second allocation period phased array radar is allocated to the second
Figure FDA00031057251100000253
The search time resources of each search sector,
Figure FDA00031057251100000254
is shown as
Figure FDA00031057251100000255
Time phased array radar in sub-distribution
Figure FDA00031057251100000256
Search sector
Figure FDA00031057251100000257
The target search signal-to-noise ratio of (c),
Figure FDA00031057251100000258
is shown as
Figure FDA00031057251100000259
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000260
A search time column vector of non-overlapping search sectors,
Figure FDA00031057251100000261
upper label
Figure FDA00031057251100000262
The transpose is represented by,
Figure FDA00031057251100000263
the first mentioned
Figure FDA00031057251100000264
The transfer objective function for searching the resource allocation scheme during the secondary allocation is:
Figure FDA0003105725110000031
wherein,
Figure FDA0003105725110000032
is shown as
Figure FDA0003105725110000033
The convex function during the sub-allocation period,
Figure FDA0003105725110000034
is shown as
Figure FDA0003105725110000035
Search sector 1 to search sector 1 during sub-allocation
Figure FDA0003105725110000036
The accumulated sum of the search time resources of each search sector, wherein alpha represents an intermediate variable;
Figure FDA0003105725110000037
is shown as
Figure FDA0003105725110000038
Time phased array radar in sub-distribution
Figure FDA0003105725110000039
Search sector
Figure FDA00031057251100000310
Is calculated from the target distance of (a) to the target distance search value,
Figure FDA00031057251100000311
is shown as
Figure FDA00031057251100000312
Time-controlled array radar scanned by sub-distribution
Figure FDA00031057251100000313
Search sector
Figure FDA00031057251100000314
The angle of (d);
Figure FDA00031057251100000315
representation calculation
Figure FDA00031057251100000316
The minimum value of (a) is determined,
Figure FDA00031057251100000317
representing a set of computations
Figure FDA00031057251100000318
Ratio of each search sector in the search
Figure FDA00031057251100000319
Then obtain
Figure FDA00031057251100000320
A ratio is then compared
Figure FDA00031057251100000321
The ratio value is then used to select the maximum value operation.
4. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 4, the first step
Figure FDA00031057251100000322
The objective criteria function for tracking the resource allocation scheme during the secondary allocation is:
Figure FDA00031057251100000323
wherein,
Figure FDA00031057251100000324
is shown as
Figure FDA00031057251100000325
During the sub-distribution period
Figure FDA00031057251100000326
A set of object numbers, each object number being,
Figure FDA00031057251100000327
is shown as
Figure FDA00031057251100000328
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000329
A tracking time resource column vector for each target,
Figure FDA00031057251100000330
upper label
Figure FDA00031057251100000331
The transpose is represented by,
Figure FDA00031057251100000332
is shown as
Figure FDA00031057251100000333
During the second allocation period phased array radar is allocated to the second
Figure FDA00031057251100000334
The tracking time resources of the individual targets,
Figure FDA00031057251100000335
is shown as
Figure FDA00031057251100000336
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000337
Total tracking time resources of the individual targets;
Figure FDA00031057251100000338
expression solution
Figure FDA00031057251100000339
The minimum value of (a) is determined,
Figure FDA00031057251100000340
representing normalized worst case
Figure FDA00031057251100000341
During the sub-distribution period
Figure FDA00031057251100000342
And tracking a Bayesian Claritrol Laurve lower bound convex function of each target.
5. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 5, the first step
Figure FDA00031057251100000343
The mathematical optimization model of the double-target resource allocation scheme during the secondary allocation period comprises the following processes:
firstly, first, the
Figure FDA00031057251100000344
The mathematical model of the dual target resource allocation scheme during the secondary allocation is represented as:
Figure FDA00031057251100000345
wherein,
Figure FDA0003105725110000041
showing obtained
Figure FDA0003105725110000042
And
Figure FDA0003105725110000043
at the same time make
Figure FDA0003105725110000044
And
Figure FDA0003105725110000045
the size of the particles is minimized and,
Figure FDA0003105725110000046
is shown as
Figure FDA0003105725110000047
Phased array radar allocation during sub-allocation
Figure FDA0003105725110000048
The total search time resources of the non-overlapping search sectors,
Figure FDA0003105725110000049
is shown as
Figure FDA00031057251100000410
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000411
The total tracking time resources of the individual targets,
Figure FDA00031057251100000412
is shown as
Figure FDA00031057251100000413
The total time resources of the integrated phased array radar search and tracking application during the sub-allocation,
Figure FDA00031057251100000414
is shown as
Figure FDA00031057251100000415
The duty cycle during the sub-dispensing period,
Figure FDA00031057251100000416
is shown as
Figure FDA00031057251100000417
During the second allocation period phased array radar is allocated to the second
Figure FDA00031057251100000418
The search time resources of each search sector,
Figure FDA00031057251100000419
is shown as
Figure FDA00031057251100000420
During the second allocation period phased array radar is allocated to the second
Figure FDA00031057251100000421
The tracking time resources of the individual targets,
Figure FDA00031057251100000422
is shown as
Figure FDA00031057251100000423
The convex function during the sub-allocation period,
Figure FDA00031057251100000424
representing normalized worst case
Figure FDA00031057251100000425
During the sub-distribution period
Figure FDA00031057251100000426
The tracked Bayesian Clarithrome lower bound convex function of each target,
Figure FDA00031057251100000427
is shown as
Figure FDA00031057251100000428
Is divided into sub-divisionsAllocation of phased array radar to allocation periods
Figure FDA00031057251100000429
A search time column vector of non-overlapping search sectors,
Figure FDA00031057251100000430
is shown as
Figure FDA00031057251100000431
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000432
A tracking time resource column vector for each target;
then it will be
Figure FDA00031057251100000433
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000434
Search time vector of non-overlapping search sectors
Figure FDA00031057251100000435
And a first
Figure FDA00031057251100000436
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000437
Tracking time resource column vector of individual targets
Figure FDA00031057251100000438
Integrated into a single vector, denoted
Figure FDA00031057251100000439
Dimension vector
Figure FDA00031057251100000440
Representing a row vector transpose; thereby obtaining the first
Figure FDA00031057251100000441
The mathematical optimization model of the dual-target resource allocation scheme during the secondary allocation period is as follows:
Figure FDA00031057251100000442
wherein,
Figure FDA00031057251100000443
is shown as
Figure FDA00031057251100000444
The convex function during the sub-allocation period,
Figure FDA00031057251100000445
representing normalized worst case
Figure FDA00031057251100000446
During the sub-distribution period
Figure FDA00031057251100000447
The tracked Bayesian Clarithrome lower bound convex function of each target,
Figure FDA00031057251100000448
is expressed as length of
Figure FDA00031057251100000449
And before
Figure FDA00031057251100000450
A row vector with 1 element and zero elements,
Figure FDA00031057251100000451
is expressed as length of
Figure FDA00031057251100000452
And from the second
Figure FDA00031057251100000453
Element to element
Figure FDA00031057251100000454
A row vector with 1 element and 0 elements,
Figure FDA00031057251100000455
representing row vectors
Figure FDA00031057251100000456
To middle
Figure FDA00031057251100000457
The number of the elements is one,
Figure FDA00031057251100000458
is shown as
Figure FDA00031057251100000459
The total time resources of the phased array radar search and tracking application are integrated during the secondary allocation.
6. The method for resource allocation based on dual target optimization for phased array radar search and tracking as claimed in claim 1, wherein in step 6, the first step
Figure FDA00031057251100000460
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000461
Optimal search time resources for non-overlapping search sectors
Figure FDA0003105725110000051
And a first
Figure FDA0003105725110000052
Phased array radar allocation during sub-allocation
Figure FDA0003105725110000053
Tracking time resource column vector optimal solution of each target
Figure FDA0003105725110000054
The obtaining process comprises the following steps:
6a) separately setting iteration indexes
Figure FDA0003105725110000055
And a stop threshold epsilon, and setting
Figure FDA0003105725110000056
Searching for lower bounds of resources during secondary allocation
Figure FDA0003105725110000057
And a first
Figure FDA0003105725110000058
Searching for upper bounds of resources during secondary allocation
Figure FDA0003105725110000059
Is shown as
Figure FDA00031057251100000510
The beta total search budget during the secondary allocation,
Figure FDA00031057251100000511
is shown as
Figure FDA00031057251100000512
A gamma total search budget during the secondary allocation; wherein, gamma is beta +1,
Figure FDA00031057251100000513
is shown as
Figure FDA00031057251100000514
The total search budget number or the total tracking budget number set in the secondary allocation period;
6b) according to the first
Figure FDA00031057251100000515
Searching for lower bounds of resources during secondary allocation
Figure FDA00031057251100000516
And a first
Figure FDA00031057251100000517
Searching for upper bounds of resources during secondary allocation
Figure FDA00031057251100000518
Calculate the first
Figure FDA00031057251100000519
After the second iteration
Figure FDA00031057251100000520
Total search resources for phased array radar during secondary allocation
Figure FDA00031057251100000521
Then use the first
Figure FDA00031057251100000522
After the second iteration
Figure FDA00031057251100000523
Total search resources for phased array radar during secondary allocation
Figure FDA00031057251100000524
And linear programming method to solve
Figure FDA00031057251100000525
Searching a conversion objective function of the resource allocation scheme during the sub-allocation period to obtain a first step
Figure FDA00031057251100000526
After the second iteration
Figure FDA00031057251100000527
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000528
Search time column vector optimal solution for non-overlapping search sectors
Figure FDA00031057251100000529
6c) If it is not
Figure FDA00031057251100000530
Updating
Figure FDA00031057251100000531
Order to
Figure FDA00031057251100000532
Add 1 to the value of (6 b); otherwise 6d) is executed,
Figure FDA00031057251100000533
is shown as
Figure FDA00031057251100000534
After the second iteration
Figure FDA00031057251100000535
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000536
Function values of the search time vector optimal solution of the non-overlapping search sectors;
Figure FDA00031057251100000537
is shown as
Figure FDA00031057251100000538
During the sub-distribution period
Figure FDA00031057251100000539
Worst case search signal-to-noise ratios in non-overlapping search sectors; a represents an intermediate variable which is,
Figure FDA00031057251100000540
is shown as
Figure FDA00031057251100000541
Time phased array radar in sub-distribution
Figure FDA00031057251100000542
Search sector
Figure FDA00031057251100000543
Is calculated from the target distance of (a) to the target distance search value,
Figure FDA00031057251100000544
is shown as
Figure FDA00031057251100000545
Time-controlled array radar scanned by sub-distribution
Figure FDA00031057251100000546
Search sector
Figure FDA00031057251100000547
The angle of (d);
6d) if it is not
Figure FDA00031057251100000548
Updating
Figure FDA00031057251100000549
Order to
Figure FDA00031057251100000550
Add 1 to the value of (6 b); otherwise 6e) is executed;
6e) if it is not
Figure FDA00031057251100000551
Get
Figure FDA00031057251100000552
Search for the optimal solution for resource allocation as
Figure FDA00031057251100000553
Is shown as
Figure FDA00031057251100000554
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000555
The optimal search time resources of the non-overlapping search sectors,
Figure FDA00031057251100000556
is shown as
Figure FDA00031057251100000557
After the second iteration
Figure FDA00031057251100000558
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000559
Search time vector optimal solutions of non-overlapping search sectors;
6f) calculate the first
Figure FDA00031057251100000560
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000561
Optimal total tracking time resource of each target
Figure FDA00031057251100000562
Figure FDA00031057251100000563
Wherein,
Figure FDA00031057251100000564
is shown as
Figure FDA00031057251100000565
The total resources of the integrated phased array radar search and tracking application during the sub-allocation,
Figure FDA0003105725110000061
is shown as
Figure FDA0003105725110000062
The duty cycle during the sub-dispensing period,
Figure FDA0003105725110000063
indicating the duration of each dispensing period;
6g) tracking time resources according to the optimal total tracking time resources
Figure FDA0003105725110000064
And minimum maximum solution method
Figure FDA0003105725110000065
Tracking a target criteria function of the resource allocation scheme during the sub-allocation period to obtain a second
Figure FDA0003105725110000066
Phased array radar allocation during sub-allocation
Figure FDA0003105725110000067
Tracking time resource column vector optimal solution of each target
Figure FDA0003105725110000068
7. The method for resource allocation based on dual target optimization for phased array radar search and tracking according to claim 6, wherein in 6(a), the method comprises
Figure FDA0003105725110000069
Is shown as
Figure FDA00031057251100000610
Beta total search budget during secondary allocation and the
Figure FDA00031057251100000611
Is shown as
Figure FDA00031057251100000612
A γ th total search budget during the secondary allocation, further comprising:
Figure FDA00031057251100000613
is shown as
Figure FDA00031057251100000614
The beta total search budget during the secondary allocation period is the second of the dual target resources
Figure FDA00031057251100000615
Pareto optimal solution of the beta of the sub-distribution
Figure FDA00031057251100000616
Middle front
Figure FDA00031057251100000617
A cumulative sum of the elements;
Figure FDA00031057251100000618
represents the gamma total search budget during the kth allocation, is the second target resource
Figure FDA00031057251100000619
Sub-assigned [ gamma ] pareto optimal solution
Figure FDA00031057251100000620
Middle front
Figure FDA00031057251100000662
A cumulative sum of the elements;
the two target resources are treated as
Figure FDA00031057251100000621
Second of the sub distribution
Figure FDA00031057251100000622
The pareto optimal solution is recorded as
Figure FDA00031057251100000623
The obtaining process comprises the following steps:
6.1 setting of
Figure FDA00031057251100000624
Sub-distribution periodThere is a
Figure FDA00031057251100000625
Total search budget and
Figure FDA00031057251100000626
total tracking budget from 1 st total search budget to
Figure FDA00031057251100000627
The total search budget satisfies:
Figure FDA00031057251100000628
wherein
Figure FDA00031057251100000629
Is shown as
Figure FDA00031057251100000630
During the sub-distribution period
Figure FDA00031057251100000631
Total search budget, will
Figure FDA00031057251100000632
During the sub-distribution period
Figure FDA00031057251100000633
Total tracking budget as
Figure FDA00031057251100000634
And the first
Figure FDA00031057251100000635
During the sub-distribution period
Figure FDA00031057251100000636
Total search budget
Figure FDA00031057251100000637
And a first
Figure FDA00031057251100000638
During the sub-distribution period
Figure FDA00031057251100000639
Total tracking budget
Figure FDA00031057251100000640
Satisfies the following conditions:
Figure FDA00031057251100000641
wherein
Figure FDA00031057251100000642
Is shown as
Figure FDA00031057251100000643
Integrating the total time resources of phased array radar search and tracking applications during the secondary allocation;
6.2 according to the first
Figure FDA00031057251100000644
During the sub-distribution period
Figure FDA00031057251100000645
Total search budget
Figure FDA00031057251100000646
And linear programming method to solve
Figure FDA00031057251100000647
Searching a conversion objective function of the resource allocation scheme during the sub-allocation period to obtain a first step
Figure FDA00031057251100000648
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000649
Search time vector pair of non-overlapping search sectors
Figure FDA00031057251100000650
Optimal solution for individual search budget resource allocation
Figure FDA00031057251100000651
According to the first
Figure FDA00031057251100000652
During the sub-distribution period
Figure FDA00031057251100000653
Total tracking budget
Figure FDA00031057251100000654
And maximum and minimum solution algorithm solving
Figure FDA00031057251100000655
Tracking a target criteria function of the resource allocation scheme during the sub-allocation period to obtain a second
Figure FDA00031057251100000656
Phased array radar allocation during sub-allocation
Figure FDA00031057251100000657
Tracking time resource column vector pair of individual targets
Figure FDA00031057251100000658
Optimal solution for individual total tracking budget resource allocation
Figure FDA00031057251100000659
Will be the first
Figure FDA00031057251100000660
Optimal solution for individual search budget resource allocation
Figure FDA00031057251100000661
And the said first
Figure FDA0003105725110000071
Optimal solution for individual total tracking budget resource allocation
Figure FDA0003105725110000072
Form two target resources
Figure FDA0003105725110000073
Second of the sub distribution
Figure FDA0003105725110000074
Pareto optimal solution
Figure FDA0003105725110000075
Upper label
Figure FDA0003105725110000076
Second to indicate transposed, dual target resource allocation
Figure FDA0003105725110000077
Pareto optimal solution
Figure FDA0003105725110000078
Included
Figure FDA0003105725110000079
And (4) each element.
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