CN111399395A - Implementation method of F-M II state space model based on radar target prediction system - Google Patents

Implementation 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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array
elements
dimensional array
transfer function
state space
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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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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B17/00—Systems involving the use of models or simulators of said systems
    • G05B17/02—Systems involving the use of models or simulators of said systems electric
    • G—PHYSICS
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    • 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
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/93—Radar or analogous systems specially adapted for specific applications for anti-collision purposes
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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

Implementation method of F-M II state space model based on radar target prediction system
Technical Field
The invention relates to the technical field of space models, in particular to an implementation method of an F-M II state space model based on a radar target prediction system.
Background
With the development and progress of computer technology, the data processing speed of a computer is also faster and faster, and these performances enable a system designer to consider designing a more complex system processing process, obtain a more accurate system implementation, and improve the efficiency of an analysis system, and these requirements make the MIMO radar a hot spot of current research. The MIMO radar is a novel radar developed by applying a multi-input multi-output technology to a radar system on the basis of the traditional phased array radar. Vehicle-mounted radar is an important application of MIMO radar. The vehicle-mounted radar system considers various information from the view of the system, so that the vehicle-mounted radar system is a multi-input multi-output control system. Because real road conditions are complex and changeable, the vehicle-mounted radar is required to have higher performance so as to improve the safety of roads and reduce traffic accidents.
In the related technology of vehicle-mounted radar, a target prediction technology can acquire related information such as the size and the speed of surrounding moving targets by sensing and identifying objects such as surrounding pedestrians and vehicles, so that the state estimation of the target at the next moment is predicted, the vehicle can make evasive behavior in advance, and the purpose of reducing the accident rate is achieved.
Also, as the control objects become more complex, the control functions that the system needs to implement become more diversified, which all put new demands on the research of multidimensional systems. A multi-dimensional system is a system in which a plurality of signals act together to achieve control. Therefore, the multidimensional system can comprehensively and accurately describe a plurality of system parameters and reflect the change of various influencing factors in real time, thereby effectively improving the control performance of the system. Although multidimensional systems are more complex than one-dimensional systems, they are also more efficient at describing the performance of the control system, since multiple variables describing multiple system parameters in multiple directions can more realistically restore the system. Based on the multi-dimensional system theory, in the established typical model, the Fornasini-Marchesini II model (F-MII model) utilizes the previous state and input associated with the Fornasini-Marchesini II model to control the current state, and the property of local calculation not only greatly simplifies the mathematical expression of the multi-dimensional system, but also is convenient for the analysis and research of the system and greatly contributes to the design of the system. The current main research direction of the F-M II model is to improve the existing algorithm so as to obtain a lower-order realization matrix.
The characteristics that an F-M II model can more truly restore a vehicle-mounted radar surrounding environment system and simplify a vehicle-mounted radar target prediction realization matrix are utilized, so that a radar target prediction network has distributed processing capacity of information, and a vehicle-mounted radar is enabled to predict a moving target to be detected in a complex environment under the condition of meeting real-time requirements and safety requirements. The research of the patent aims to provide a new research idea for the practical application of the F-M II state space model and the vehicle-mounted radar target prediction, not only is the detection algorithm of the vehicle-mounted radar target prediction on the dynamic target expanded, but also the application of the F-M II model in practice can be expanded.
Disclosure of Invention
The invention aims to provide an implementation method of an F-M II state space model based on a radar target prediction system, which aims to reduce the complexity of an image algorithm when a multi-dimensional transfer function characteristic polynomial is subjected to chart conversion operation.
In order to achieve the above purpose, the embodiments of the present invention provide the following technical solutions: an implementation method of an F-M II state space model based on a radar target prediction system comprises 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 BDA0002421406480000021
And according to the transfer function, each term of the characteristic polynomial is recorded as an array element
Figure BDA0002421406480000022
S3, rearranging the array elements from small to large, and then judging the array
Figure BDA0002421406480000023
Whether the ratio of the adjacent elements is equal to
Figure BDA0002421406480000031
Or
Figure BDA0002421406480000032
If not, inserting array elements
Figure BDA0002421406480000033
Making the ratio of adjacent elements meet the condition, and then deleting
Figure BDA0002421406480000034
If yes, directly deleting the element(s)
Figure BDA0002421406480000035
An element of (1);
s4, in the deletion
Figure BDA0002421406480000036
Then, two adjacent elements are judged
Figure BDA0002421406480000037
And
Figure BDA0002421406480000038
if it is
Figure BDA0002421406480000039
Or
Figure BDA00024214064800000310
Then
Figure BDA00024214064800000311
And
Figure BDA00024214064800000312
no new elements are inserted between the two; if it is
Figure BDA00024214064800000313
Then is at
Figure BDA00024214064800000314
And
Figure BDA00024214064800000315
is inserted between
Figure BDA00024214064800000316
To delete previously
Figure BDA00024214064800000317
Reinsertion;
s5, mixing
Figure BDA00024214064800000318
For array elements in
Figure BDA00024214064800000319
Is expressed according to
Figure BDA00024214064800000320
Solving a matrix A of a model with the transfer function1,A2,B1,B2,C,D。
Further, 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 BDA00024214064800000321
wherein
Figure BDA00024214064800000322
ziIt is expressed as a unit delay operation,
for a given transfer function, the system matrix D is:
Figure BDA00024214064800000323
further, in the step S2, H (z)1,z2) Each term of the characteristic polynomial is sequentially filled into a one-dimensional array
Figure BDA00024214064800000324
Each array element of
Figure BDA00024214064800000325
In (1),
further, the step S3 specifically includes: for a one-dimensional array
Figure BDA0002421406480000041
The value of each array element in (1)
Figure BDA0002421406480000042
Rearranging from large to small, and arranging the obtained new arrangement sequence array elements underThe labels are sequentially replaced by 1,2, …, l according to the existing sequence, namely a new one-dimensional array
Figure BDA0002421406480000043
For transfer function H (z)1,z2) Making a judgment if the function contains
Figure BDA0002421406480000044
And
Figure BDA0002421406480000045
then from the one-dimensional array
Figure BDA0002421406480000046
The third element of (a); if the function contains
Figure BDA0002421406480000047
Or
Figure BDA0002421406480000048
Then from the one-dimensional array
Figure BDA0002421406480000049
The second element of (a); if the function does not contain
Figure BDA00024214064800000410
And
Figure BDA00024214064800000411
then from the one-dimensional array
Figure BDA00024214064800000412
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 BDA00024214064800000413
Or
Figure BDA00024214064800000414
Then, in the one-dimensional array
Figure BDA00024214064800000415
N (n is more than or equal to 1) elements are added before the ith element
Figure BDA00024214064800000416
So that the added one-dimensional array
Figure BDA00024214064800000417
Wherein the ratio of the corresponding value of each element starting from the third element to at least one of the corresponding values of all elements preceding the element is
Figure BDA00024214064800000418
Or
Figure BDA00024214064800000419
Further, the step S4 specifically includes: deleting
Figure BDA00024214064800000420
After the elements of (2), logarithmic series
Figure BDA00024214064800000421
Judging when two adjacent elements are adjacent
Figure BDA00024214064800000422
Or
Figure BDA00024214064800000423
When is at
Figure BDA00024214064800000424
And
Figure BDA00024214064800000425
does not add any element in between and delete the previously deleted elements
Figure BDA00024214064800000426
Left side insert with pre-delete position
Figure BDA00024214064800000427
Then one-dimensional array after addition
Figure BDA00024214064800000428
The new permutation order array element subscripts are sequentially replaced by 1,2, …, n, arrays according to the existing order
Figure BDA00024214064800000429
Is composed of
Figure BDA00024214064800000430
By using
Figure BDA00024214064800000431
The expression method of (2) is shown.
Further, it is to
Figure BDA00024214064800000432
In
Figure BDA00024214064800000433
Is/are as follows
Figure BDA00024214064800000434
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.
Further, in combination with transfer functions
Figure BDA00024214064800000435
The items correspond to
Figure BDA0002421406480000051
And (3) judging:
when in use
Figure BDA0002421406480000052
Belong to
Figure BDA0002421406480000053
Time, system matrix A1Is the ith row and 1 st column values of
Figure BDA0002421406480000054
Where i ═ τ1，τ1Is a one-dimensional array
Figure BDA0002421406480000055
The numerical value of the middle element is
Figure BDA0002421406480000056
Of (2) element(s)
Figure BDA0002421406480000057
Subscript value of (d);
when in use
Figure BDA0002421406480000058
Belong to
Figure BDA0002421406480000059
Time, system matrix A2Is the ith row and 1 st column values of
Figure BDA00024214064800000510
Where i ═ τ2-1，τ2Is a one-dimensional array
Figure BDA00024214064800000511
The numerical value of the middle element is
Figure BDA00024214064800000512
Of (2) element(s)
Figure BDA00024214064800000513
Subscript value of (d); then
System matrix A1,A2Comprises the following steps:
Figure BDA00024214064800000514
further, in combination with transfer functions
Figure BDA00024214064800000515
The items correspond to
Figure BDA00024214064800000516
Each is judged
Figure BDA00024214064800000517
Corresponding to
Figure BDA00024214064800000518
Belong to
Figure BDA00024214064800000519
Or also
Figure BDA00024214064800000520
When in use
Figure BDA00024214064800000521
Belong to
Figure BDA00024214064800000522
Time, system matrix B1Is the ith row and 1 st column values of
Figure BDA00024214064800000523
Wherein i is each
Figure BDA00024214064800000524
Corresponding to
Figure BDA00024214064800000525
In a one-dimensional array
Figure BDA00024214064800000526
The element subscripts of (a);
when in use
Figure BDA00024214064800000527
Belong to
Figure BDA00024214064800000528
Time, system matrix B2Is the ith row and 1 st column values of
Figure BDA00024214064800000529
Wherein i is each
Figure BDA00024214064800000530
Corresponding to
Figure BDA00024214064800000531
In a one-dimensional array
Figure BDA00024214064800000532
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。
Further, the matrix A is obtained1,A2,B1,B2C and D are respectively:
Figure BDA0002421406480000061
B1＝[bm-1,n0… 0 b00]Τ,B2＝[bm,n-10 … 0 b10]Τ
C＝[1,0,0,...,0],D＝[bm]
further, Matlab software is used for verification, specifically: a is to be1,A2,B1,B2Substituting C and D into F-M II state space model
Figure BDA0002421406480000062
The obtained transfer function is consistent with the original transfer function.
Compared with the prior art, the invention has the beneficial effects that: a method for realizing an F-M II state space model based on a radar target prediction system aims at the problems existing in the F-M II state space model realization method based on a block diagram, such as complexity increase caused by applying chart conversion operation to a multi-dimensional transfer function characteristic polynomial in the low-order realization process of the system state space model and increase of system matrix realization possibility quantity caused by the existence of an invalid coefficient in the conversion process.
Drawings
Fig. 1 is a logic diagram of an implementation method of an F-M II state space model based on a radar target prediction system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, an embodiment of the present invention provides a method for implementing an F-M II state space model based on a radar target prediction system, including 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 BDA0002421406480000071
And according to the transfer function, each term of the characteristic polynomial is recorded as an array element
Figure BDA0002421406480000072
S3, rearranging the array elements from small to large, and then judging the array
Figure BDA0002421406480000073
Whether the ratio of the adjacent elements is equal to
Figure BDA0002421406480000074
Or
Figure BDA0002421406480000075
If not, inserting array elements
Figure BDA0002421406480000076
Making the ratio of adjacent elements meet the condition, and then deleting
Figure BDA0002421406480000077
If yes, directly deleting the element(s)
Figure BDA0002421406480000078
An element of (1); s4, in the deletion
Figure BDA0002421406480000079
Then, two adjacent elements are judged
Figure BDA00024214064800000710
And
Figure BDA00024214064800000711
if it is
Figure BDA00024214064800000712
Or
Figure BDA00024214064800000713
Then
Figure BDA00024214064800000714
And
Figure BDA00024214064800000715
no new elements are inserted between the two; if it is
Figure BDA00024214064800000716
Then is at
Figure BDA00024214064800000717
And
Figure BDA00024214064800000718
is inserted between
Figure BDA00024214064800000719
To delete previously
Figure BDA00024214064800000720
Reinsertion; s5, mixing
Figure BDA00024214064800000721
For array elements in
Figure BDA00024214064800000722
Is expressed according to
Figure BDA00024214064800000723
Solving a matrix A of a model with the transfer function1,A2,B1,B2C and D. In the prior art, there are some problems in the F-M II state space model implementation method of the block diagram, such as complexity increase caused by applying graph transformation operation to the multidimensional transfer function characteristic polynomial in the system state space model low-order implementation process, and increase of the number of implementation possibilities of the system matrix caused by the existence of an invalid coefficient in the transformation process. Therefore, in the embodiment, by setting the one-dimensional array, the number of implementation possibilities of various system matrixes generated by chart description conversion in the existing algorithm is effectively reduced, and the redundancy of the system is reduced, so that the calculation efficiency in the system implementation process is improved.
The following are specific examples:
optimizing the 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)
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 BDA0002421406480000081
wherein
Figure BDA00024214064800000811
ziIt is expressed as a unit delay operation,
for a given transfer function, the system matrix D is:
Figure BDA0002421406480000082
in this embodiment, the targeted indefinite system may be a two-dimensional radar system, and after modeling, a system transfer function may be obtained:
Figure BDA0002421406480000083
as an optimization scheme of the embodiment of the present invention, in the step S2, H (z) is added1,z2) Each term of the characteristic polynomial is sequentially filled into a one-dimensional array
Figure BDA0002421406480000084
Each array element of
Figure BDA0002421406480000085
In (1),
Figure BDA0002421406480000086
Figure BDA0002421406480000087
array of elements
Figure BDA0002421406480000088
Array element value of (1):
Figure BDA0002421406480000089
for H (z)1,z2) Judging that a is known1Not equal to 0 and a2Not equal to 0, then
Figure BDA00024214064800000810
No new array elements are inserted to the left.
As an optimization scheme of the embodiment of the present invention, the step S3 specifically includes: for a one-dimensional array
Figure BDA0002421406480000091
The value of each array element in (1)
Figure BDA0002421406480000092
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 BDA0002421406480000093
Figure BDA0002421406480000094
As an optimization scheme of the embodiment of the present invention, the step S4 specifically includes: to pair
Figure BDA0002421406480000095
Array element judgment of
Figure BDA0002421406480000096
Then
Figure BDA0002421406480000097
And
Figure BDA0002421406480000098
do not insert array elements between
Figure BDA0002421406480000099
Adding the added one-dimensional array
Figure BDA00024214064800000910
Deleting
Figure BDA00024214064800000911
Element of (2), logarithmic group
Figure BDA00024214064800000912
Judging when two adjacent elements are adjacent
Figure BDA00024214064800000913
Or
Figure BDA00024214064800000914
When is at
Figure BDA00024214064800000915
And
Figure BDA00024214064800000916
does not add any element in between and delete the previously deleted elements
Figure BDA00024214064800000917
Insert to the left with the pre-delete position:
Figure BDA00024214064800000918
combining a one-dimensional array
Figure BDA00024214064800000919
The new permutation order array element subscripts are sequentially replaced by 1,2, …, n, arrays according to the existing order
Figure BDA00024214064800000920
Is composed of
Figure BDA00024214064800000921
By using
Figure BDA00024214064800000922
The expression method of (2) is shown. .
Further optimizing the above scheme, the slave array
Figure BDA00024214064800000923
Starting with the third element of
Figure BDA00024214064800000924
The expression method of (2) is to form an array
Figure BDA00024214064800000925
Each element of (1) represents, to
Figure BDA00024214064800000926
In
Figure BDA00024214064800000927
Is/are as follows
Figure BDA00024214064800000928
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,
then the system matrix A2Row 1, column 3, has a value of 1, row 2, column 4, has a value of 1, and row 3, column 4 has a value of 1.
As an optimization scheme for embodiments of the invention, in combination with transfer functions
Figure BDA0002421406480000101
The items correspond to
Figure BDA0002421406480000102
And (3) judging:
when in use
Figure BDA0002421406480000103
Belong to
Figure BDA0002421406480000104
Time, system matrix A1Is the ith row and 1 st column values of
Figure BDA0002421406480000105
Where i ═ τ1，τ1Is a one-dimensional array
Figure BDA0002421406480000106
The numerical value of the middle element is
Figure BDA0002421406480000107
Of (2) element(s)
Figure BDA0002421406480000108
Subscript value of (d);
when in use
Figure BDA0002421406480000109
Belong to
Figure BDA00024214064800001010
Time, system matrix A2Is the ith row and 1 st column values of
Figure BDA00024214064800001011
Where i ═ τ2-1，τ2Is a one-dimensional array
Figure BDA00024214064800001012
The numerical value of the middle element is
Figure BDA00024214064800001013
Of (2) element(s)
Figure BDA00024214064800001014
Subscript value of (d);
then the system matrix A1Is a at row 1 and column 11The value of row 3, column 1 is a4The value of row 5, column 1 is a5(ii) a System matrix A2Is a at row 1 and column 12The value of row 3, column 1 is a3The system matrix A is obtained1,A2。
As an optimization scheme for embodiments of the invention, in combination with transfer functions
Figure BDA00024214064800001015
The items correspond to
Figure BDA00024214064800001016
Each is judged
Figure BDA00024214064800001017
Corresponding to
Figure BDA00024214064800001018
Belong to
Figure BDA00024214064800001019
Or also
Figure BDA00024214064800001020
When in use
Figure BDA00024214064800001021
Time of day, system matrix B1Is the ith row and 1 st column values of
Figure BDA00024214064800001022
Where i ═ τ3，τ3Is a one-dimensional array
Figure BDA00024214064800001023
The numerical value of the middle element is
Figure BDA00024214064800001024
Of (2) element(s)
Figure BDA00024214064800001025
Subscript value of (d); (ii) a When in use
Figure BDA00024214064800001026
Belong to
Figure BDA00024214064800001027
The value of the ith row and the 1 st column of the system matrix B2 is
Figure BDA00024214064800001028
Where i ═ τ4-1，τ4Is a one-dimensional array
Figure BDA00024214064800001029
The numerical value of the middle element is
Figure BDA00024214064800001030
Of (2) element(s)
Figure BDA00024214064800001031
The subscript value of (a) can obtain a system matrix B1,B2。
Matrix A obtained as an optimization scheme of the embodiment of the invention1,A2,B1,B2C and D are respectively:
Figure BDA00024214064800001032
Figure BDA00024214064800001033
B1＝[b10 0 0 b4]Τ
B2＝[b20 b30 0]Τ
C＝[1 0 0 0 0]
D＝0。
as an optimization scheme of the embodiment of the invention, Matlab software is used for verification, and specifically: a is to be1,A2,B1,B2Substituting C and D into F-M II state space model
Figure BDA0002421406480000111
In, obtained transmissionTransfer function and transfer function given in example
Figure BDA0002421406480000112
And (5) the consistency is achieved.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in 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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