CN111399395A - The Realization Method of F-M II State Space Model Based on Radar Target Prediction System - Google Patents

The Realization Method of F-M II State Space Model Based on Radar Target Prediction System Download PDF

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CN111399395A
CN111399395A CN202010206817.XA CN202010206817A CN111399395A CN 111399395 A CN111399395 A CN 111399395A CN 202010206817 A CN202010206817 A CN 202010206817A CN 111399395 A CN111399395 A CN 111399395A
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dimensional array
transfer function
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CN111399395B (en
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程骅
刘昶
曹中泳
陈君昊
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Wuhan University of Science and Engineering WUSE
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Abstract

The invention provides a method for realizing an F-M II state space model based on a radar target prediction system, which comprises the following steps: s1, constructing an F-M II model, and obtaining a transfer function from the F-M II model; s2, setting up a one-dimensional array
Figure DDA0002421406500000011
And according to the transfer function, each term of the characteristic polynomial is recorded as an array element
Figure DDA0002421406500000012
S3, rearranging the array elements from small to large, and then judging the array
Figure DDA0002421406500000013
Whether the ratio of the adjacent elements is equal to
Figure DDA0002421406500000014
Or
Figure DDA0002421406500000015
If yes, delete directly
Figure DDA0002421406500000016
An element of (1); s4, in the deletion
Figure DDA0002421406500000017
Then, two adjacent elements are judged
Figure DDA0002421406500000018
And
Figure DDA0002421406500000019
if it is
Figure DDA00024214065000000110
Or
Figure DDA00024214065000000111
Then
Figure DDA00024214065000000112
And
Figure DDA00024214065000000113
no new elements are inserted between the two; if it is
Figure DDA00024214065000000114
Then is at
Figure DDA00024214065000000115
And
Figure DDA00024214065000000116
is inserted between
Figure DDA00024214065000000117
To delete previously
Figure DDA00024214065000000118
Reinsertion; s5, mixing
Figure DDA00024214065000000119
For array elements in
Figure DDA00024214065000000120
Is expressed according to
Figure DDA00024214065000000121
Matrix A of model obtained from transfer function1,A2,B1,B2C and D. The invention effectively reduces the number of the realization possibility of various system matrixes generated by the description and conversion of the diagram in the existing algorithm and reduces the redundancy of the system by setting the one-dimensional array, thereby improving the calculation efficiency in the realization process of the system.

Description

基于雷达目标预测系统的F-M II状态空间模型的实现方法The Realization Method of F-M II State Space Model Based on Radar Target Prediction System

技术领域technical field

本发明涉及空间模型技术领域，具体为一种基于雷达目标预测系统的F-M II状态空间模型的实现方法。The invention relates to the technical field of space models, in particular to a method for realizing an F-M II state space model based on a radar target prediction system.

背景技术Background technique

随着计算机技术的发展与进步，计算机对数据的处理速度也越来越快，这些性能使得系统设计者想要考虑设计更加复杂的系统处理过程，得到更准确的系统实现，并且提高分析系统的效率，这些需求使得MIMO雷达成为目前研究的热点。MIMO雷达是在传统的相控阵雷达的基础上，将多输入多输出技术应用于雷达系统而发展起来的一种新型雷达。车载雷达是MIMO雷达的一个重要应用。从系统本身看，车载雷达系统要考虑多方面的信息，因此它是一个多输入多输出的控制系统。由于真实的路况复杂多变，要求车载雷达要有较高的性能，以提高道路安全性，减少交通事故的发生。With the development and progress of computer technology, the speed of computer processing of data is getting faster and faster. These performances make system designers want to consider designing more complex system processing procedures, obtain more accurate system implementation, and improve the analysis system. Efficiency, these requirements make MIMO radar a hot research topic. MIMO radar is a new type of radar developed by applying multiple input multiple output technology to radar system on the basis of traditional phased array radar. Vehicle radar is an important application of MIMO radar. From the point of view of the system itself, the vehicle radar system needs to consider many aspects of information, so it is a multi-input and multi-output control system. Because the real road conditions are complex and changeable, the on-board radar is required to have high performance to improve road safety and reduce the occurrence of traffic accidents.

在车载雷达相关技术中，目标预测技术能够通过对周围的行人、车辆等物体进行感知和识别，获取周围运动目标大小和速度等相关信息，从而预测出目标下一时刻的状态估计，让车辆能提前做出规避行为，达到减少事故发生率的目的。In vehicle-mounted radar-related technologies, target prediction technology can obtain relevant information such as the size and speed of surrounding moving targets by perceiving and identifying surrounding objects such as pedestrians and vehicles, so as to predict the state estimation of the target at the next moment, so that the vehicle can Make avoidance behaviors in advance to achieve the purpose of reducing the accident rate.

同样，随着控制对象的日趋复杂化，系统需要实现的控制功能日益多样化，这些都对多维系统的研究提出了新的要求。多维系统是多个信号共同作用从而实现控制的系统。因此，多维系统能全面、精确地描述多个系统参数，实时反映出各种影响因素的变化，从而能有效地提高系统的控制性能。虽然多维系统比一维系统的复杂度更高，但是也更能高效地描述控制系统的性能，因为多个变量在多个方向上描述多个系统参数能更加真实地还原系统。以多维系统理论作为基础，建立的典型模型中，Fornasini-Marchesini II模型(F-MII模型)利用与之关联的前一个状态和输入来控制当前状态，这种局部计算的性质不仅极大地简化了多维系统的数学表达式，而且便于系统的分析研究，对系统的设计有较大的贡献。F-M II模型当前的主要研究方向为改进已有的算法从而得到更低阶的实现矩阵。Similarly, with the increasingly complex control objects, the control functions that the system needs to achieve are increasingly diversified, which all put forward new requirements for the study of multi-dimensional systems. A multi-dimensional system is a system in which multiple signals work together to achieve control. Therefore, the multi-dimensional system can describe multiple system parameters comprehensively and accurately, and reflect the changes of various influencing factors in real time, thereby effectively improving the control performance of the system. Although a multi-dimensional system is more complex than a one-dimensional system, it can also describe the performance of the control system more efficiently, because multiple variables describing multiple system parameters in multiple directions can more realistically restore the system. Based on the theory of multi-dimensional systems, among the typical models established, the Fornasini-Marchesini II model (F-MII model) uses the previous state and input associated with it to control the current state. The nature of this local calculation not only greatly simplifies The mathematical expression of the multi-dimensional system is convenient for the analysis and research of the system, and it has a great contribution to the design of the system. The current main research direction of the F-M II model is to improve the existing algorithm to obtain a lower-order realization matrix.

利用F-M II模型能更真实地还原车载雷达周围环境系统与化简车载雷达目标预测实现矩阵的特点，使得雷达目标预测网络具备信息的分布式处理能力，在满足实时性需求和安全性需求的情况下令车载雷达在复杂的环境中对移动的待测目标进行预测。本专利的研究旨在为F-M II状态空间模型的实际运用和车载雷达目标预测提供了一种新的研究思路，不仅扩展了车载雷达目标预测对动态目标的检测算法，也能扩展F-M II模型在实际中的应用。The use of the F-M II model can more truly restore the vehicle radar surrounding environment system and simplify the characteristics of the vehicle radar target prediction implementation matrix, so that the radar target prediction network has the ability to process information in a distributed manner. The on-board radar is ordered to predict the moving target under test in a complex environment. The research of this patent aims to provide a new research idea for the practical application of the F-M II state space model and vehicle radar target prediction, which not only expands the detection algorithm of vehicle radar target prediction for dynamic targets, but also extends the F-M II model in practical application.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于提供一种基于雷达目标预测系统的F-M II状态空间模型的实现方法，对多维传递函数特征多项式运用图表转换运算时，减少图像算法复杂度的目的，提出了一种新的低阶实现解决方法，通过直接获得分解结果，避开部分计算，并用这些结果实现系统模型，有效降低由图表描述转换而产生多种系统矩阵实现可能性的数量，并减少系统的冗余度，从而提高系统实现过程中的计算效率。The purpose of the present invention is to provide a realization method of the F-M II state space model based on the radar target prediction system. When using the graph transformation operation for the multi-dimensional transfer function characteristic polynomial, the purpose of reducing the complexity of the image algorithm is proposed. The first-order implementation solution, by directly obtaining the decomposition results, avoiding part of the calculation, and using these results to realize the system model, effectively reduces the number of realization possibilities of various system matrices generated by the transformation of the diagram description, and reduces the redundancy of the system, thereby Improve the computational efficiency in the system implementation process.

为实现上述目的，本发明实施例提供如下技术方案：一种基于雷达目标预测系统的F-M II状态空间模型的实现方法，包括如下步骤：To achieve the above purpose, the embodiments of the present invention provide the following technical solutions: a method for implementing an F-M II state space model based on a radar target prediction system, comprising the following steps:

S1，对不定系统进行分析，并构建F-M II模型，从所述F-M II模型获得传递函数；S1, analyzes the indeterminate system, and constructs the F-M II model, and obtains the transfer function from the F-M II model;

S2，设立一维数组

Figure BDA0002421406480000021
并根据所述传递函数，将其特征多项式的每项式记为数组元素
Figure BDA0002421406480000022
S2, set up a one-dimensional array
Figure BDA0002421406480000021
And according to the transfer function, each term of its characteristic polynomial is recorded as an array element
Figure BDA0002421406480000022

S3，将所述数组元素从小到大重新排列，然后判断数组

Figure BDA0002421406480000023
中相邻元素之比是否等于
Figure BDA0002421406480000031
或
Figure BDA0002421406480000032
若否则插入数组元素
Figure BDA0002421406480000033
使相邻元素之比符合条件，再删除
Figure BDA0002421406480000034
的元素，若是则直接删除
Figure BDA0002421406480000035
的元素；S3, rearrange the array elements from small to large, and then judge the array
Figure BDA0002421406480000023
Is the ratio of adjacent elements in
Figure BDA0002421406480000031
or
Figure BDA0002421406480000032
if else insert array element
Figure BDA0002421406480000033
Make the ratio of adjacent elements meet the conditions, and then delete
Figure BDA0002421406480000034
element, if it is, delete it directly
Figure BDA0002421406480000035
Elements;

S4，在删除

Figure BDA0002421406480000036
后，判断相邻两元素
Figure BDA0002421406480000037
和
Figure BDA0002421406480000038
若
Figure BDA0002421406480000039
或
Figure BDA00024214064800000310
则
Figure BDA00024214064800000311
与
Figure BDA00024214064800000312
之间不插入新元素；若
Figure BDA00024214064800000313
则在
Figure BDA00024214064800000314
与
Figure BDA00024214064800000315
之间插入
Figure BDA00024214064800000316
再将之前删除的
Figure BDA00024214064800000317
重新插入；S4, in delete
Figure BDA0002421406480000036
Then, judge the adjacent two elements
Figure BDA0002421406480000037
and
Figure BDA0002421406480000038
like
Figure BDA0002421406480000039
or
Figure BDA00024214064800000310
but
Figure BDA00024214064800000311
and
Figure BDA00024214064800000312
No new elements are inserted between; if
Figure BDA00024214064800000313
then in
Figure BDA00024214064800000314
and
Figure BDA00024214064800000315
insert between
Figure BDA00024214064800000316
delete the previously
Figure BDA00024214064800000317
reinsert;

S5，将

Figure BDA00024214064800000318
中的数组元素用
Figure BDA00024214064800000319
方式表达，根据
Figure BDA00024214064800000320
与所述传递函数求得模型的矩阵A1,A2,B1,B2,C,D。S5, will
Figure BDA00024214064800000318
array elements in
Figure BDA00024214064800000319
way of expression, according to
Figure BDA00024214064800000320
The matrixes A 1 , A 2 , B 1 , B 2 , C, D of the model are obtained with the transfer function.

进一步，在所述S1步骤中，构建的F-M II模型为：Further, in the step S1, the constructed F-M II model is:

x(i,j)＝A1x(i-1,j)+A2x(i,j-1)+B1u(i-1,j)+B2u(i,j-1)x(i,j)=A 1 x(i-1,j)+A 2 x(i,j-1)+B 1 u(i-1,j)+B 2 u(i,j-1)

y(i,j)＝Cx(i,j)+Du(i,j)y(i,j)=Cx(i,j)+Du(i,j)

其中x(i,j)表示状态向量，u(i,j)表示外部扰动输入，y(i,j)表示被控输出，A1,A2,B1,B2,C,D是实数矩阵；where x(i,j) represents the state vector, u(i,j) represents the external disturbance input, y(i,j) represents the controlled output, A 1 ,A 2 ,B 1 ,B 2 ,C,D are real numbers matrix;

传递函数为：The transfer function is:

Figure BDA00024214064800000321
Figure BDA00024214064800000321

其中

Figure BDA00024214064800000322
zi表示单位延迟运算，in
Figure BDA00024214064800000322
z i represents unit delay operation,

对给定的传递函数，系统矩阵D为：For a given transfer function, the system matrix D is:

Figure BDA00024214064800000323
Figure BDA00024214064800000323

进一步，在所述S2步骤中，将H(z1,z2)的特征多项式的每项顺序填充到一维数组

Figure BDA00024214064800000324
的每个数组元素
Figure BDA00024214064800000325
中，Further, in the step S2, each item of the characteristic polynomial of H(z 1 , z 2 ) is sequentially filled into a one-dimensional array
Figure BDA00024214064800000324
each array element of
Figure BDA00024214064800000325
middle,

进一步，所述S3步骤具体为：对一维数组

Figure BDA0002421406480000041
中的每个数组元素的数值
Figure BDA0002421406480000042
从大到小重新排列，将得到的新排列顺序数组元素下标按现有顺序依次替换成1,2,…,l，即新的一维数组
Figure BDA0002421406480000043
对传递函数H(z1,z2)进行判断，如果函数中含有
Figure BDA0002421406480000044
和
Figure BDA0002421406480000045
则从一维数组
Figure BDA0002421406480000046
的第三个元素开始；如果函数中含有
Figure BDA0002421406480000047
或
Figure BDA0002421406480000048
则从一维数组
Figure BDA0002421406480000049
的第二个元素开始；如果函数中不含有
Figure BDA00024214064800000410
和
Figure BDA00024214064800000411
则从一维数组
Figure BDA00024214064800000412
的第一个元素开始。当数组中第i元素对应数值与前i-1个元素对应值之比都不等于
Figure BDA00024214064800000413
或
Figure BDA00024214064800000414
时，在该一维数组
Figure BDA00024214064800000415
中第i元素之前添加n(n≥1)个
Figure BDA00024214064800000416
使得添加后的一维数组
Figure BDA00024214064800000417
中从第三个元素开始每个元素对应值与该元素之前所有元素对应值中的至少一个数值之比为
Figure BDA00024214064800000418
或
Figure BDA00024214064800000419
Further, the step S3 is specifically: for a one-dimensional array
Figure BDA0002421406480000041
the value of each array element in
Figure BDA0002421406480000042
Rearrange from large to small, and replace the subscripts of the array elements in the new arrangement order with 1, 2, ..., l in the existing order, that is, a new one-dimensional array
Figure BDA0002421406480000043
Judge the transfer function H(z 1 ,z 2 ), if the function contains
Figure BDA0002421406480000044
and
Figure BDA0002421406480000045
then from a one-dimensional array
Figure BDA0002421406480000046
starts with the third element of ; if the function contains
Figure BDA0002421406480000047
or
Figure BDA0002421406480000048
then from a one-dimensional array
Figure BDA0002421406480000049
starts with the second element of ; if the function does not contain
Figure BDA00024214064800000410
and
Figure BDA00024214064800000411
then from a one-dimensional array
Figure BDA00024214064800000412
starts with the first element of . When the ratio of the corresponding value of the i-th element in the array to the corresponding value of the first i-1 elements is not equal to
Figure BDA00024214064800000413
or
Figure BDA00024214064800000414
, in this one-dimensional array
Figure BDA00024214064800000415
Add n (n≥1) before the i-th element in
Figure BDA00024214064800000416
makes the added one-dimensional array
Figure BDA00024214064800000417
The ratio of the corresponding value of each element starting from the third element to at least one of the corresponding values of all the elements before the element is
Figure BDA00024214064800000418
or
Figure BDA00024214064800000419

进一步，所述S4步骤具体为：删除

Figure BDA00024214064800000420
的元素后，对数组
Figure BDA00024214064800000421
中的剩余元素判断，当相邻两元素
Figure BDA00024214064800000422
或
Figure BDA00024214064800000423
时，在
Figure BDA00024214064800000424
与
Figure BDA00024214064800000425
之间不添加任何元素，并将之前删除的元素
Figure BDA00024214064800000426
以删除前位置左侧插入
Figure BDA00024214064800000427
接着在添加后的一维数组
Figure BDA00024214064800000428
的新排列顺序数组元素下标按现有顺序依次替换成1,2,…,n，数组
Figure BDA00024214064800000429
为
Figure BDA00024214064800000430
用
Figure BDA00024214064800000431
的表达方法表示出来。Further, the step S4 is specifically: delete
Figure BDA00024214064800000420
After the elements of the array
Figure BDA00024214064800000421
The remaining elements in the judgment, when two adjacent elements
Figure BDA00024214064800000422
or
Figure BDA00024214064800000423
when, at
Figure BDA00024214064800000424
and
Figure BDA00024214064800000425
add no elements in between, and insert the previously removed elements
Figure BDA00024214064800000426
Insert left at position before deletion
Figure BDA00024214064800000427
Then after adding the one-dimensional array
Figure BDA00024214064800000428
The new arrangement order of the array element subscripts are replaced by 1, 2, ..., n in the existing order, and the array
Figure BDA00024214064800000429
for
Figure BDA00024214064800000430
use
Figure BDA00024214064800000431
expression method.

进一步，对

Figure BDA00024214064800000432
中
Figure BDA00024214064800000433
的
Figure BDA00024214064800000434
判断：further, yes
Figure BDA00024214064800000432
middle
Figure BDA00024214064800000433
of
Figure BDA00024214064800000434
judge:

当n＝1时，系统矩阵A1的第β行第α列的数值为1；When n=1, the value of the βth row and the αth column of the system matrix A1 is 1 ;

当n＝2时，系统矩阵A2的第β行第α列的数值为1。When n= 2 , the value of the βth row and the αth column of the system matrix A2 is 1.

进一步，结合传递函数中的

Figure BDA00024214064800000435
项所对应的
Figure BDA0002421406480000051
判断：Further, combining the transfer function with
Figure BDA00024214064800000435
item corresponding to
Figure BDA0002421406480000051
judge:

当

Figure BDA0002421406480000052
属于
Figure BDA0002421406480000053
时，系统矩阵A1的第i行第1列数值为
Figure BDA0002421406480000054
其中i＝τ1，τ1为一维数组
Figure BDA0002421406480000055
中元素数值为
Figure BDA0002421406480000056
的元素
Figure BDA0002421406480000057
的下标数值；when
Figure BDA0002421406480000052
belong
Figure BDA0002421406480000053
When , the value of the i-th row and the first column of the system matrix A 1 is
Figure BDA0002421406480000054
where i=τ 1 , τ 1 is a one-dimensional array
Figure BDA0002421406480000055
The value of the element is
Figure BDA0002421406480000056
Elements
Figure BDA0002421406480000057
The subscript value of ;

当

Figure BDA0002421406480000058
属于
Figure BDA0002421406480000059
时，系统矩阵A2的第i行第1列数值为
Figure BDA00024214064800000510
其中i＝τ2-1，τ2为一维数组
Figure BDA00024214064800000511
中元素数值为
Figure BDA00024214064800000512
的元素
Figure BDA00024214064800000513
的下标数值；则when
Figure BDA0002421406480000058
belong
Figure BDA0002421406480000059
When , the value of the i-th row and the first column of the system matrix A 2 is
Figure BDA00024214064800000510
Where i=τ 2 -1, τ 2 is a one-dimensional array
Figure BDA00024214064800000511
The value of the element is
Figure BDA00024214064800000512
Elements
Figure BDA00024214064800000513
The subscript value of ; then

系统矩阵A1,A2为：The system matrix A 1 , A 2 is:

Figure BDA00024214064800000514
Figure BDA00024214064800000514

进一步，结合传递函数中的

Figure BDA00024214064800000515
项所对应的
Figure BDA00024214064800000516
判断每个
Figure BDA00024214064800000517
所对应的
Figure BDA00024214064800000518
属于
Figure BDA00024214064800000519
还是
Figure BDA00024214064800000520
Further, combining the transfer function with
Figure BDA00024214064800000515
item corresponding to
Figure BDA00024214064800000516
judge each
Figure BDA00024214064800000517
corresponding to
Figure BDA00024214064800000518
belong
Figure BDA00024214064800000519
still
Figure BDA00024214064800000520

当

Figure BDA00024214064800000521
属于
Figure BDA00024214064800000522
时，系统矩阵B1的第i行第1列数值为
Figure BDA00024214064800000523
其中i为每个
Figure BDA00024214064800000524
所对应的
Figure BDA00024214064800000525
在一维数组
Figure BDA00024214064800000526
的元素下标；when
Figure BDA00024214064800000521
belong
Figure BDA00024214064800000522
When , the value of the i-th row and the first column of the system matrix B 1 is
Figure BDA00024214064800000523
where i is each
Figure BDA00024214064800000524
corresponding to
Figure BDA00024214064800000525
one-dimensional array
Figure BDA00024214064800000526
The element subscript of ;

当

Figure BDA00024214064800000527
属于
Figure BDA00024214064800000528
时，系统矩阵B2的第i行第1列数值为
Figure BDA00024214064800000529
其中i为每个
Figure BDA00024214064800000530
所对应的
Figure BDA00024214064800000531
在一维数组
Figure BDA00024214064800000532
的元素下标减1；when
Figure BDA00024214064800000527
belong
Figure BDA00024214064800000528
When , the value of the i-th row and the first column of the system matrix B 2 is
Figure BDA00024214064800000529
where i is each
Figure BDA00024214064800000530
corresponding to
Figure BDA00024214064800000531
one-dimensional array
Figure BDA00024214064800000532
The element subscript of is minus 1;

可得系统矩阵B1,B2：The system matrix B 1 , B 2 can be obtained:

B1＝[bm-1,n 0 … 0 b00]Τ B2＝[bm,n-1 0 … 0 b10]Τ。B 1 =[b m-1,n 0 . . . 0 b 00 ] Τ B 2 =[b m,n-1 0 . . . 0 b 10 ] Τ .

进一步，求得的矩阵A1,A2,B1,B2,C,D分别为：Further, the obtained matrices A 1 , A 2 , B 1 , B 2 , C and D are respectively:

Figure BDA0002421406480000061
Figure BDA0002421406480000061

B1＝[bm-1,n 0… 0 b00]Τ,B2＝[bm,n-1 0 … 0 b10]Τ B 1 =[b m-1,n 0... 0 b 00 ] Τ ,B 2 =[b m,n-1 0... 0 b 10 ] Τ

C＝[1,0,0,...,0],D＝[bm]C=[1,0,0,...,0], D=[b m ]

进一步，运用Matlab软件进行验证，具体的：将A1,A2,B1,B2,C,D代入F-M II状态空间模型

Figure BDA0002421406480000062
中，得到的传递函数与原传递函数一致。Further, use Matlab software to verify, specifically: Substitute A 1 , A 2 , B 1 , B 2 , C, D into the FM II state space model
Figure BDA0002421406480000062
, the obtained transfer function is consistent with the original transfer function.

与现有技术相比，本发明的有益效果是：一种基于雷达目标预测系统的F-M II状态空间模型的实现方法，针对基于方框图的F-M II状态空间模型实现方法中存在的一些问题，比如系统状态空间模型低阶实现过程中因对多维传递函数特征多项式运用图表转换运算而导致的复杂度增加，以及转换过程中无效系数的存在而导致的系统矩阵实现可能性数量的增加等问题，通过对一维数组的设立，有效降低现有算法中由图表描述转换而产生多种系统矩阵实现可能性的数量，并减少系统的冗余度，从而提高系统实现过程中的计算效率。Compared with the prior art, the beneficial effects of the present invention are: an implementation method of the F-M II state space model based on the radar target prediction system, aiming at some problems existing in the implementation method of the F-M II state space model based on the block diagram, such as the system In the low-order implementation of the state space model, the complexity increases due to the use of graph transformation operations on the multi-dimensional transfer function characteristic polynomial, and the number of system matrix realization possibilities caused by the existence of invalid coefficients in the transformation process increases. The establishment of a one-dimensional array effectively reduces the number of realization possibilities of various system matrices generated by the conversion of graph descriptions in the existing algorithm, and reduces the redundancy of the system, thereby improving the computational efficiency in the process of system realization.

附图说明Description of drawings

图1为本发明实施例提供的一种基于雷达目标预测系统的F-M II状态空间模型的实现方法的逻辑图。FIG. 1 is a logic diagram of a method for implementing an F-M II state space model based on a radar target prediction system according to an embodiment of the present invention.

具体实施方式Detailed ways

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其它实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

请参阅图1，本发明实施例提供一种基于雷达目标预测系统的F-M II状态空间模型的实现方法，包括如下步骤：S1，对不定系统进行分析，并构建F-M II模型，从所述F-M II模型获得传递函数；S2，设立一维数组

Figure BDA0002421406480000071
并根据所述传递函数，将其特征多项式的每项式记为数组元素
Figure BDA0002421406480000072
S3，将所述数组元素从小到大重新排列，然后判断数组
Figure BDA0002421406480000073
中相邻元素之比是否等于
Figure BDA0002421406480000074
或
Figure BDA0002421406480000075
若否则插入数组元素
Figure BDA0002421406480000076
使相邻元素之比符合条件，再删除
Figure BDA0002421406480000077
的元素，若是则直接删除
Figure BDA0002421406480000078
的元素；S4，在删除
Figure BDA0002421406480000079
后，判断相邻两元素
Figure BDA00024214064800000710
和
Figure BDA00024214064800000711
若
Figure BDA00024214064800000712
或
Figure BDA00024214064800000713
则
Figure BDA00024214064800000714
与
Figure BDA00024214064800000715
之间不插入新元素；若
Figure BDA00024214064800000716
则在
Figure BDA00024214064800000717
与
Figure BDA00024214064800000718
之间插入
Figure BDA00024214064800000719
再将之前删除的
Figure BDA00024214064800000720
重新插入；S5，将
Figure BDA00024214064800000721
中的数组元素用
Figure BDA00024214064800000722
方式表达，根据
Figure BDA00024214064800000723
与所述传递函数求得模型的矩阵A1,A2,B1,B2,C,D。现有技术中，在方框图的F-M II状态空间模型实现方法中存在着一些问题，比如系统状态空间模型低阶实现过程中因对多维传递函数特征多项式运用图表转换运算而导致的复杂度增加，以及转换过程中无效系数的存在而导致的系统矩阵实现可能性数量的增加等问题。因此在本实施例中，通过对一维数组的设立，有效降低现有算法中由图表描述转换而产生多种系统矩阵实现可能性的数量，并减少系统的冗余度，从而提高系统实现过程中的计算效率。Referring to FIG. 1, an embodiment of the present invention provides a method for implementing an FM II state space model based on a radar target prediction system, including the following steps: S1, analyzing an indeterminate system, and constructing an FM II model, from the FM II The model obtains the transfer function; S2, sets up a one-dimensional array
Figure BDA0002421406480000071
And according to the transfer function, each term of its characteristic polynomial is recorded as an array element
Figure BDA0002421406480000072
S3, rearrange the array elements from small to large, and then judge the array
Figure BDA0002421406480000073
Is the ratio of adjacent elements in
Figure BDA0002421406480000074
or
Figure BDA0002421406480000075
if else insert array element
Figure BDA0002421406480000076
Make the ratio of adjacent elements meet the conditions, and then delete
Figure BDA0002421406480000077
element, if it is, delete it directly
Figure BDA0002421406480000078
element of ; S4, after deleting
Figure BDA0002421406480000079
Then, judge the adjacent two elements
Figure BDA00024214064800000710
and
Figure BDA00024214064800000711
like
Figure BDA00024214064800000712
or
Figure BDA00024214064800000713
but
Figure BDA00024214064800000714
and
Figure BDA00024214064800000715
No new elements are inserted between; if
Figure BDA00024214064800000716
then in
Figure BDA00024214064800000717
and
Figure BDA00024214064800000718
insert between
Figure BDA00024214064800000719
delete the previously
Figure BDA00024214064800000720
reinsert; S5, will
Figure BDA00024214064800000721
array elements in
Figure BDA00024214064800000722
way of expression, according to
Figure BDA00024214064800000723
The matrixes A 1 , A 2 , B 1 , B 2 , C, D of the model are obtained with the transfer function. In the prior art, there are some problems in the implementation method of the FM II state space model of the block diagram, such as the increase in complexity caused by the use of graph transformation operations on the multi-dimensional transfer function characteristic polynomial during the low-order implementation of the system state space model, and The existence of invalid coefficients in the conversion process leads to the increase of the number of system matrix realization possibilities. Therefore, in this embodiment, through the establishment of a one-dimensional array, the number of realization possibilities of various system matrices generated by the conversion of graph description in the existing algorithm is effectively reduced, and the redundancy of the system is reduced, thereby improving the system realization process. computational efficiency in .

以下为具体实施例：The following are specific examples:

优化上述方案，在所述S1步骤中，构建的F-M II模型为：To optimize the above scheme, in the step S1, the constructed F-M II model is:

x(i,j)＝A1x(i-1,j)+A2x(i,j-1)+B1u(i-1,j)+B2u(i,j-1)x(i,j)=A 1 x(i-1,j)+A 2 x(i,j-1)+B 1 u(i-1,j)+B 2 u(i,j-1)

y(i,j)＝Cx(i,j)+Du(i,j)y(i,j)=Cx(i,j)+Du(i,j)

其中x(i,j)表示状态向量，u(i,j)表示外部扰动输入，y(i,j)表示被控输出，A1,A2,B1,B2,C,D是实数矩阵；where x(i,j) represents the state vector, u(i,j) represents the external disturbance input, y(i,j) represents the controlled output, A 1 ,A 2 ,B 1 ,B 2 ,C,D are real numbers matrix;

传递函数为：The transfer function is:

Figure BDA0002421406480000081
Figure BDA0002421406480000081

其中

Figure BDA00024214064800000811
zi表示单位延迟运算，in
Figure BDA00024214064800000811
z i represents unit delay operation,

对给定的传递函数，系统矩阵D为：For a given transfer function, the system matrix D is:

Figure BDA0002421406480000082
Figure BDA0002421406480000082

在本实施例中，针对的不定系统可以是一个二维雷达系统，对其进行建模后，可得到系统传递函数：

Figure BDA0002421406480000083
In this embodiment, the target indefinite system can be a two-dimensional radar system, and after modeling it, the system transfer function can be obtained:
Figure BDA0002421406480000083

作为本发明实施例的优化方案，在所述S2步骤中，将H(z1,z2)的特征多项式的每项顺序填充到一维数组

Figure BDA0002421406480000084
的每个数组元素
Figure BDA0002421406480000085
中，As an optimization solution of the embodiment of the present invention, in the step S2, each item of the characteristic polynomial of H(z 1 , z 2 ) is sequentially filled into a one-dimensional array
Figure BDA0002421406480000084
each array element of
Figure BDA0002421406480000085
middle,

Figure BDA0002421406480000086
Figure BDA0002421406480000086

Figure BDA0002421406480000087
Figure BDA0002421406480000087

数组

Figure BDA0002421406480000088
的数组元素值：array
Figure BDA0002421406480000088
Array element values:

Figure BDA0002421406480000089
Figure BDA0002421406480000089

对H(z1,z2)判断，可知a1≠0和a2≠0，则

Figure BDA00024214064800000810
左侧不插入新的数组元素。Judging H(z 1 , z 2 ), we know that a 1 ≠0 and a 2 ≠0, then
Figure BDA00024214064800000810
No new array elements are inserted on the left.

作为本发明实施例的优化方案，所述S3步骤具体为：对一维数组

Figure BDA0002421406480000091
中的每个数组元素的数值
Figure BDA0002421406480000092
从大到小重新排列，将得到的新排列顺序数组元素下标按现有顺序依次替换成1,2,…,l，即新的一维数组
Figure BDA0002421406480000093
Figure BDA0002421406480000094
As an optimization solution of the embodiment of the present invention, the step S3 is specifically: for a one-dimensional array
Figure BDA0002421406480000091
the value of each array element in
Figure BDA0002421406480000092
Rearrange from large to small, and replace the subscripts of the array elements in the new arrangement order with 1, 2, ..., l in the existing order, that is, a new one-dimensional array
Figure BDA0002421406480000093
Figure BDA0002421406480000094

作为本发明实施例的优化方案，所述S4步骤具体为：对

Figure BDA0002421406480000095
的数组元素判断
Figure BDA0002421406480000096
则
Figure BDA0002421406480000097
与
Figure BDA0002421406480000098
之间不插入数组元素
Figure BDA0002421406480000099
将添加后的一维数组
Figure BDA00024214064800000910
删除
Figure BDA00024214064800000911
的元素，对数组
Figure BDA00024214064800000912
中的剩余元素判断，当相邻两元素
Figure BDA00024214064800000913
或
Figure BDA00024214064800000914
时，在
Figure BDA00024214064800000915
与
Figure BDA00024214064800000916
之间不添加任何元素，并将之前删除的元素
Figure BDA00024214064800000917
以删除前位置左侧插入：
Figure BDA00024214064800000918
将一维数组
Figure BDA00024214064800000919
的新排列顺序数组元素下标按现有顺序依次替换成1,2,…,n，数组
Figure BDA00024214064800000920
为
Figure BDA00024214064800000921
用
Figure BDA00024214064800000922
的表达方法表示出来。。As an optimization solution of the embodiment of the present invention, the step S4 is specifically:
Figure BDA0002421406480000095
Array element judgment of
Figure BDA0002421406480000096
but
Figure BDA0002421406480000097
and
Figure BDA0002421406480000098
Do not insert array elements between
Figure BDA0002421406480000099
1D array after adding
Figure BDA00024214064800000910
delete
Figure BDA00024214064800000911
elements of an array of pairs
Figure BDA00024214064800000912
The remaining elements in the judgment, when two adjacent elements
Figure BDA00024214064800000913
or
Figure BDA00024214064800000914
when, at
Figure BDA00024214064800000915
and
Figure BDA00024214064800000916
add no elements in between, and insert the previously removed elements
Figure BDA00024214064800000917
Insert to the left of the position before deletion:
Figure BDA00024214064800000918
one-dimensional array
Figure BDA00024214064800000919
The new arrangement order of the array element subscripts are replaced by 1, 2, ..., n in the existing order, and the array
Figure BDA00024214064800000920
for
Figure BDA00024214064800000921
use
Figure BDA00024214064800000922
expression method. .

进一步优化上述方案，从数组

Figure BDA00024214064800000923
的第三个元素开始，用
Figure BDA00024214064800000924
的表示方法将数组
Figure BDA00024214064800000925
的每个元素表示出来，对
Figure BDA00024214064800000926
中
Figure BDA00024214064800000927
的
Figure BDA00024214064800000928
判断：Further optimize the above scheme, from the array
Figure BDA00024214064800000923
starting with the third element of
Figure BDA00024214064800000924
The representation method converts the array
Figure BDA00024214064800000925
to represent each element of , for
Figure BDA00024214064800000926
middle
Figure BDA00024214064800000927
of
Figure BDA00024214064800000928
judge:

当n＝1时，系统矩阵A1的第β行第α列的数值为1；When n=1, the value of the βth row and the αth column of the system matrix A1 is 1 ;

当n＝2时，系统矩阵A2的第β行第α列的数值为1，When n= 2 , the value of the βth row and the αth column of the system matrix A2 is 1,

则系统矩阵A2的第1行第3列的数值为1，第2行第4列的数值为1，第3行第4列的数值为1。Then the value of the 1st row and the 3rd column of the system matrix A2 is 1 , the value of the 2nd row and the 4th column is 1, and the value of the 3rd row and the 4th column is 1.

作为本发明实施例的优化方案，结合传递函数中的

Figure BDA0002421406480000101
项所对应的
Figure BDA0002421406480000102
判断：As an optimization solution of the embodiment of the present invention, combined with the transfer function
Figure BDA0002421406480000101
item corresponding to
Figure BDA0002421406480000102
judge:

当

Figure BDA0002421406480000103
属于
Figure BDA0002421406480000104
时，系统矩阵A1的第i行第1列数值为
Figure BDA0002421406480000105
其中i＝τ1，τ1为一维数组
Figure BDA0002421406480000106
中元素数值为
Figure BDA0002421406480000107
的元素
Figure BDA0002421406480000108
的下标数值；when
Figure BDA0002421406480000103
belong
Figure BDA0002421406480000104
When , the value of the i-th row and the first column of the system matrix A 1 is
Figure BDA0002421406480000105
where i=τ 1 , τ 1 is a one-dimensional array
Figure BDA0002421406480000106
The value of the element is
Figure BDA0002421406480000107
Elements
Figure BDA0002421406480000108
The subscript value of ;

当

Figure BDA0002421406480000109
属于
Figure BDA00024214064800001010
时，系统矩阵A2的第i行第1列数值为
Figure BDA00024214064800001011
其中i＝τ2-1，τ2为一维数组
Figure BDA00024214064800001012
中元素数值为
Figure BDA00024214064800001013
的元素
Figure BDA00024214064800001014
的下标数值；when
Figure BDA0002421406480000109
belong
Figure BDA00024214064800001010
When , the value of the i-th row and the first column of the system matrix A 2 is
Figure BDA00024214064800001011
Where i=τ 2 -1, τ 2 is a one-dimensional array
Figure BDA00024214064800001012
The value of the element is
Figure BDA00024214064800001013
Elements
Figure BDA00024214064800001014
The subscript value of ;

则系统矩阵A1的第1行第1列的数值为a1，第3行第1列的数值为a4，第5行第1列的数值为a5；系统矩阵A2的第1行第1列的数值为a2，第3行第1列的数值为a3，可得系统矩阵A1,A2。Then the value of the first row and the first column of the system matrix A 1 is a 1 , the value of the third row and the first column is a 4 , and the value of the fifth row and the first column is a 5 ; the first row of the system matrix A 2 The value of the first column is a 2 , the value of the third row and the first column is a 3 , and the system matrix A 1 , A 2 can be obtained.

作为本发明实施例的优化方案，结合传递函数中的

Figure BDA00024214064800001015
项所对应的
Figure BDA00024214064800001016
判断每个
Figure BDA00024214064800001017
所对应的
Figure BDA00024214064800001018
属于
Figure BDA00024214064800001019
还是
Figure BDA00024214064800001020
当
Figure BDA00024214064800001021
属于时，系统矩阵B1的第i行第1列数值为
Figure BDA00024214064800001022
其中i＝τ3，τ3为一维数组
Figure BDA00024214064800001023
中元素数值为
Figure BDA00024214064800001024
的元素
Figure BDA00024214064800001025
的下标数值；；当
Figure BDA00024214064800001026
属于
Figure BDA00024214064800001027
时，系统矩阵B2的第i行第1列数值为
Figure BDA00024214064800001028
其中i＝τ4-1，τ4为一维数组
Figure BDA00024214064800001029
中元素数值为
Figure BDA00024214064800001030
的元素
Figure BDA00024214064800001031
的下标数值，可得系统矩阵B1,B2。As an optimization solution of the embodiment of the present invention, combined with the transfer function
Figure BDA00024214064800001015
item corresponding to
Figure BDA00024214064800001016
judge each
Figure BDA00024214064800001017
corresponding to
Figure BDA00024214064800001018
belong
Figure BDA00024214064800001019
still
Figure BDA00024214064800001020
when
Figure BDA00024214064800001021
When belongs to, the value of the i-th row and the 1st column of the system matrix B 1 is
Figure BDA00024214064800001022
where i=τ 3 , τ 3 is a one-dimensional array
Figure BDA00024214064800001023
The value of the element is
Figure BDA00024214064800001024
Elements
Figure BDA00024214064800001025
The subscript value of ;; when
Figure BDA00024214064800001026
belong
Figure BDA00024214064800001027
When , the value of the i-th row and the first column of the system matrix B2 is
Figure BDA00024214064800001028
Where i=τ 4 -1, τ 4 is a one-dimensional array
Figure BDA00024214064800001029
The value of the element is
Figure BDA00024214064800001030
Elements
Figure BDA00024214064800001031
The subscript value of , the system matrix B 1 , B 2 can be obtained.

作为本发明实施例的优化方案，求得的矩阵A1,A2,B1,B2,C,D分别为：As an optimization scheme of the embodiment of the present invention, the obtained matrices A 1 , A 2 , B 1 , B 2 , C, and D are respectively:

Figure BDA00024214064800001032
Figure BDA00024214064800001032

Figure BDA00024214064800001033
Figure BDA00024214064800001033

B1＝[b1 0 0 0 b4]Τ B 1 =[b 1 0 0 0 b 4 ] Τ

B2＝[b2 0 b3 0 0]Τ B 2 =[b 2 0 b 3 0 0] Τ

C＝[1 0 0 0 0]C=[1 0 0 0 0]

D＝0。D=0.

作为本发明实施例的优化方案，运用Matlab软件进行验证，具体的：将A1,A2,B1,B2,C,D代入F-M II状态空间模型As the optimization scheme of the embodiment of the present invention, use Matlab software to verify, specifically: Substitute A 1 , A 2 , B 1 , B 2 , C, D into the FM II state space model

Figure BDA0002421406480000111
中，得到的传递函数与实例给出的传递函数
Figure BDA0002421406480000112
一致。
Figure BDA0002421406480000111
, the resulting transfer function is the same as the transfer function given by the example
Figure BDA0002421406480000112
Consistent.

尽管已经示出和描述了本发明的实施例，对于本领域的普通技术人员而言，可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由所附权利要求及其等同物限定。Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, and substitutions can be made in these embodiments without departing from the principle and spirit of the invention and modifications, the scope of the present invention is defined by the appended claims and their equivalents.

Claims (10)

1. A method for realizing an F-M II state space model based on a radar target prediction system is characterized by comprising the following steps:
s1, analyzing the indefinite system, constructing an F-M II model, and obtaining a transfer function from the F-M II model;
s2, setting up a one-dimensional array
Figure FDA0002421406470000011
And according to the transfer function, each term of the characteristic polynomial is recorded as an array element
Figure FDA0002421406470000012
S3, rearranging the array elements from small to large, and then judging the array
Figure FDA0002421406470000013
Whether the ratio of elements in (A) is equal to
Figure FDA0002421406470000014
Or
Figure FDA0002421406470000015
If not, inserting array elements
Figure FDA0002421406470000016
Make the ratio of adjacent elements conform toConditional, then delete
Figure FDA0002421406470000017
If yes, directly deleting the element(s)
Figure FDA0002421406470000018
An element of (1);
s4, in the deletion
Figure FDA0002421406470000019
Then, two adjacent elements are judged
Figure FDA00024214064700000110
And
Figure FDA00024214064700000111
if it is
Figure FDA00024214064700000112
Or
Figure FDA00024214064700000113
Then
Figure FDA00024214064700000114
And
Figure FDA00024214064700000115
no new elements are inserted between the two; if it is
Figure FDA00024214064700000116
Then is at
Figure FDA00024214064700000117
And
Figure FDA00024214064700000118
is inserted between
Figure FDA00024214064700000119
To delete previously
Figure FDA00024214064700000120
Reinsertion;
s5, mixing
Figure FDA00024214064700000121
For array elements in
Figure FDA00024214064700000122
Is expressed according to
Figure FDA00024214064700000123
Solving a matrix A of a model with the transfer function1,A2,B1,B2,C,D。
2. The method of claim 1, wherein in the step S1, the F-M II model is constructed as follows:
x(i,j)＝A1x(i-1,j)+A2x(i,j-1)+B1u(i-1,j)+B2u(i,j-1)
y(i,j)＝Cx(i,j)+Du(i,j)
where x (i, j) represents the state vector, u (i, j) represents the external disturbance input, y (i, j) represents the controlled output, A1,A2,B1,B2C, D are real number matrixes;
the transfer function is:
Figure FDA0002421406470000021
wherein
Figure FDA00024214064700000224
ziIt is expressed as a unit delay operation,
for a given transfer function, the system matrix D is:
Figure FDA0002421406470000022
3. the method of claim 1, wherein the F-M II state space model based radar target prediction system is implemented as: in the step S2, H (z)1,z2) Each term of the characteristic polynomial is sequentially filled into a one-dimensional array
Figure FDA0002421406470000023
Each array element of
Figure FDA0002421406470000024
In (1).
4. The method for implementing the F-M II state space model based on the radar target prediction system as claimed in claim 1, wherein the step S3 is specifically as follows: for a one-dimensional array
Figure FDA0002421406470000025
The value of each array element in (1)
Figure FDA0002421406470000026
Rearranging from large to small, and sequentially replacing the subscripts of the array elements in the obtained new arrangement sequence by 1,2, …, l according to the existing sequence, namely, a new one-dimensional array
Figure FDA0002421406470000027
Judging the transfer function H (z1, z2), if the function contains
Figure FDA0002421406470000028
And
Figure FDA0002421406470000029
then from the one-dimensional array
Figure FDA00024214064700000210
The third element of (a); if the function contains
Figure FDA00024214064700000211
Or
Figure FDA00024214064700000212
Then from the one-dimensional array
Figure FDA00024214064700000213
The second element of (a); if the function does not contain
Figure FDA00024214064700000214
And
Figure FDA00024214064700000215
then from the one-dimensional array
Figure FDA00024214064700000216
Begins with the first element of (a). When the ratio of the corresponding value of the ith element to the corresponding value of the first i-1 elements in the array is not equal to
Figure FDA00024214064700000217
Or
Figure FDA00024214064700000218
Then, in the one-dimensional array
Figure FDA00024214064700000219
N (n is more than or equal to 1) elements are added before the ith element
Figure FDA00024214064700000220
So that the added one-dimensional array
Figure FDA00024214064700000221
From the third element eachThe ratio of the corresponding value of an element to at least one of the corresponding values of all elements preceding the element is
Figure FDA00024214064700000222
Or
Figure FDA00024214064700000223
5. The method for implementing the F-M II state space model based on the radar target prediction system as claimed in claim 1, wherein the step S4 is specifically as follows: deleting
Figure FDA0002421406470000031
After the elements of (2), logarithmic series
Figure FDA0002421406470000032
Judging when two adjacent elements are adjacent
Figure FDA0002421406470000033
When is at
Figure FDA0002421406470000034
And
Figure FDA0002421406470000035
adding an element in between
Figure FDA0002421406470000036
Make the element
Figure FDA0002421406470000037
And deleting the previously deleted elements
Figure FDA0002421406470000038
Left side insert with pre-delete position
Figure FDA0002421406470000039
Then one-dimensional array after addition
Figure FDA00024214064700000310
The new permutation order array element subscripts are sequentially replaced by 1,2, …, n, arrays according to the existing order
Figure FDA00024214064700000311
Is composed of
Figure FDA00024214064700000312
By using
Figure FDA00024214064700000313
Expression method of (2) will be array
Figure FDA00024214064700000314
Each element of (a) is shown.
6. The method of claim 5, wherein the F-M II state space model is implemented for a radar target prediction system
Figure FDA00024214064700000315
In
Figure FDA00024214064700000316
Is/are as follows
Figure FDA00024214064700000317
And (3) judging:
when n is 1, the system matrix A1Row β, column α has a value of 1;
when n is 2, the system matrix A2Line β, column α has a value of 1.
7. The method of claim 2, in combination with a transfer function
Figure FDA00024214064700000318
The items correspond to
Figure FDA00024214064700000319
And (3) judging:
when in use
Figure FDA00024214064700000320
Belong to
Figure FDA00024214064700000321
Time, system matrix A1Is the ith row and 1 st column values of
Figure FDA00024214064700000322
Where i ═ τ1，τ1Is a one-dimensional array
Figure FDA00024214064700000323
The numerical value of the middle element is
Figure FDA00024214064700000324
Of (2) element(s)
Figure FDA00024214064700000325
Subscript value of (d);
when in use
Figure FDA00024214064700000326
Belong to
Figure FDA00024214064700000327
Time, system matrix A2Is the ith row and 1 st column values of
Figure FDA00024214064700000328
Where i ═ τ2-1，τ2Is a one-dimensional array
Figure FDA00024214064700000329
The numerical value of the middle element is
Figure FDA00024214064700000330
Of (2) element(s)
Figure FDA00024214064700000331
Subscript value of (d);
then the system matrix A1,A2Comprises the following steps:
Figure FDA0002421406470000041
8. the method of claim 2, wherein the F-M II state space model is implemented based on a radar target prediction system, and wherein: in combination with transfer functions
Figure FDA0002421406470000042
The items correspond to
Figure FDA0002421406470000043
Each is judged
Figure FDA0002421406470000044
Corresponding to
Figure FDA0002421406470000045
Belong to
Figure FDA0002421406470000046
Or also
Figure FDA0002421406470000047
When in use
Figure FDA0002421406470000048
Belong to
Figure FDA0002421406470000049
System matrix B1Is the ith row and 1 st column values of
Figure FDA00024214064700000410
Wherein i is each
Figure FDA00024214064700000411
Corresponding to
Figure FDA00024214064700000412
In a one-dimensional array
Figure FDA00024214064700000413
The element subscripts of (a);
when in use
Figure FDA00024214064700000414
Belong to
Figure FDA00024214064700000415
System matrix B2Is the ith row and 1 st column values of
Figure FDA00024214064700000416
Wherein i is each
Figure FDA00024214064700000417
Corresponding to
Figure FDA00024214064700000418
In a one-dimensional array
Figure FDA00024214064700000419
The subscript of the element(s) of (a) minus 1;
the system matrix B can be obtained1,B2：
B1＝[bm-1,n0…0 b00]ΤB2＝[bm,n-10…0 b10]Τ。
9. The method of claim 1, wherein the derived matrix A is a matrix of F-M II state space model1,A2,B1,B2C and D are respectively:
Figure FDA00024214064700000420
B1＝[bm-1,n0…0 b00]Τ,B2＝[bm,n-10…0 b10]Τ
C＝[1,0,0,...,0],D＝[bm]。
10. the method for implementing the F-M II state space model based on the radar target prediction system of claim 9, wherein verification is performed by using Matlab software, specifically: a is to be1,A2,B1,B2Substituting C and D into F-M II state space model
Figure FDA0002421406470000051
The obtained transfer function is consistent with the original transfer function.
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2006053720A (en) * 2004-08-11 2006-02-23 Fuji Electric Holdings Co Ltd Transfer function setting device
CN104808190A (en) * 2015-04-09 2015-07-29 周口师范学院 Steady waveform design method for improving worst parameter estimation performance of MIMO (multiple-input and multiple-output) radar
CN106844828A (en) * 2016-12-02 2017-06-13 武汉科技大学 Two dimension H is realized based on digraph opinion∞The method of wave filter FM II state-space models
CN107728139A (en) * 2017-09-12 2018-02-23 电子科技大学 A kind of phased-array radar group network system method for managing resource based on multiple target tracking
CN109856637A (en) * 2017-11-30 2019-06-07 比亚迪股份有限公司 Automobile and car radar object detection method and device based on constant false alarm
CN110261841A (en) * 2019-07-26 2019-09-20 南京信息工程大学 MIMO radar list based on iteration weighting proximal end projection measures vector DOA estimation method

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2006053720A (en) * 2004-08-11 2006-02-23 Fuji Electric Holdings Co Ltd Transfer function setting device
CN104808190A (en) * 2015-04-09 2015-07-29 周口师范学院 Steady waveform design method for improving worst parameter estimation performance of MIMO (multiple-input and multiple-output) radar
CN106844828A (en) * 2016-12-02 2017-06-13 武汉科技大学 Two dimension H is realized based on digraph opinion∞The method of wave filter FM II state-space models
CN107728139A (en) * 2017-09-12 2018-02-23 电子科技大学 A kind of phased-array radar group network system method for managing resource based on multiple target tracking
CN109856637A (en) * 2017-11-30 2019-06-07 比亚迪股份有限公司 Automobile and car radar object detection method and device based on constant false alarm
CN110261841A (en) * 2019-07-26 2019-09-20 南京信息工程大学 MIMO radar list based on iteration weighting proximal end projection measures vector DOA estimation method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
郭修燕等: "离散区间2-D时滞系统的二次稳定与镇定", 《电机与控制学报》 *

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