CN111399395B - 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 PDFInfo
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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 arrayAnd according to the transfer function, each term of the characteristic polynomial is recorded as an array elementS3, rearranging the array elements from small to large, and then judging the arrayWhether the ratio of the adjacent elements is equal toOrIf yes, delete directlyAn element of (1); s4, in the deletionThen, two adjacent elements are judgedAndif it isOrThenAndno new elements are inserted between the two; if it isThen is inAndis inserted betweenTo delete previouslyReinsertion; s5, mixingFor array elements inIs expressed according toMatrix A of model obtained from transfer function 1 ,A 2 ,B 1 ,B 2 C, 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
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 make a system designer want 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 puts new demands on the research of multidimensional systems. A multidimensional system is a system in which a plurality of signals work 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. While multi-dimensional systems are more complex than one-dimensional systems, they are also more efficient at describing the performance of the control system because multiple variables describe multiple system parameters in multiple directions to more realistically restore the system. The method is characterized in that a multidimensional system theory is taken as a basis, in an established typical model, a Fornasini-Marchesini II model (F-M II model) utilizes a previous state and input associated with the Fornasini-Marchesini II model to control a current state, and the property of local calculation not only greatly simplifies the mathematical expression of the multidimensional 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.
By utilizing the characteristics that the F-M II model can more truly restore the surrounding environment system of the vehicle-mounted radar and simplify the target prediction realization matrix of the vehicle-mounted radar, the radar target prediction network has distributed processing capacity of information, and the vehicle-mounted radar can predict a moving target to be detected in a complex environment under the condition of meeting the real-time requirement and the safety requirement. 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 an 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 arrayAnd recording each term of the characteristic polynomial as array element according to the transfer function
S3, rearranging the array elements from small to large, and then judging the arrayWhether the ratio of the adjacent elements is equal toOrIf not, inserting array elementsMaking the ratio of adjacent elements meet the condition, and then deletingIf yes, directly deleting the element(s)An element of (1);
s4, in the deletionThen, two adjacent elements are judgedAndif it isOrThenAndno new elements are inserted between the two; if it isThen is atAndis inserted betweenTo delete previouslyReinserting;
s5, mixingFor array elements inIs expressed according toSolving a matrix A of a model with the transfer function 1 ,A 2 ,B 1 ,B 2 ,C,D。
Further, in the step S1, the constructed F-M II model is:
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)
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 is a real number matrix;
the transfer function is:
for a given transfer function, the system matrix D is:
further, in the S2 step, H (z) is added 1 ,z 2 ) Each term of the characteristic polynomial is sequentially filled into a one-dimensional arrayEach array element ofIn (1),
further, the step S3 specifically includes: for a one-dimensional arrayThe value of each array element in (1)Rearranging from large to small, sequentially replacing the subscripts of the array elements in the new arrangement order by 1,2, \ 8230:, i.e. new one-dimensional arrayFor transfer function H (z) 1 ,z 2 ) Making a judgment if the function containsAndthen from the one-dimensional arrayThe third element of (a); if the function containsOrThen from the one-dimensional arrayThe second element of (a); if the function does not containAndthen from the one-dimensional arrayBegins 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 toOrThen, in the one-dimensional arrayN (n is more than or equal to 1) elements are added before the ith elementSo that the added one-dimensional arrayWherein 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 isOr
Further, the step S4 specifically includes: deletingAfter the elements of (2), logarithmic seriesJudging when two adjacent elements are adjacentOrWhen is atAnddoes not add any element in between, and deletes the previously deleted elementsLeft side insert with pre-delete positionThen one-dimensional array after additionThe subscripts of the elements of the array in the new arrangement sequence are sequentially replaced by 1,2, \8230, n, array in the existing sequenceIs composed ofBy usingExpression of (2)The method is shown.
when n =1, the system matrix a 1 The value of the beta row and the alpha column of (1);
when n =2, the system matrix a 2 Is 1, and the value of the beta row and alpha column of (b) is 1.
when the temperature is higher than the set temperatureBelong toTime, system matrix A 1 Is the ith row and 1 st column values ofWhere i = τ 1 ,τ 1 Is a one-dimensional arrayThe numerical value of the middle element isElement (b) ofSubscripts of (2)A numerical value;
when in useBelong toTime, system matrix A 2 Is row i, column 1, having a value ofWhere i = τ 2 -1,τ 2 Is a one-dimensional arrayThe numerical value of the middle element isOf (2) element(s)Subscript value of (d); then
System matrix A 1 ,A 2 Comprises the following steps:
further, in combination with transfer functionsThe item corresponds toDetermine each ofCorresponding toBelong toOr
When in useBelong toTime, system matrix B 1 Is the ith row and 1 st column values ofWherein i is eachCorresponding toIn a one-dimensional arrayThe element subscripts of (a);
when the temperature is higher than the set temperatureBelong toTime, system matrix B 2 Is row i, column 1, having a value ofWherein i is eachCorresponding toIn a one-dimensional arrayThe subscript of the element(s) of (a) minus 1;
the system matrix B can be obtained 1 ,B 2 :
B 1 =[b m-1,n 0 … 0 b 00 ] Τ B 2 =[b m,n-1 0 … 0 b 10 ] Τ 。
Further, the matrix A is obtained 1 ,A 2 ,B 1 ,B 2 And C and D are respectively:
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=[b m ]
further, matlab software is used for verification, specifically: a is to be 1 ,A 2 ,B 1 ,B 2 Substituting C and D into F-M II state space modelIn (3), 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 an 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 arrayAnd recording each term of the characteristic polynomial as array element according to the transfer functionS3, rearranging the array elements from small to large, and then judging the arrayWhether the ratio of the adjacent elements is equal toOrIf not, inserting array elementsMaking the ratio of adjacent elements meet the condition, and then deletingIf yes, directly deleting the element(s)The element (b); s4, in the deletionThen, two adjacent elements are judgedAndif it isOrThenAndno new elements are inserted between the two; if it isThen is atAndis inserted betweenTo delete previouslyReinserting; s5, mixingFor array elements inIs expressed according toSolving a matrix A of a model with the transfer function 1 ,A 2 ,B 1 ,B 2 C, 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 realization possibilities of various system matrixes generated by graph 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 realization process is improved.
The following are specific examples:
optimizing the scheme, wherein in the step S1, the constructed F-M II model is as follows:
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)
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 number matrixes;
the transfer function is:
for a given transfer function, the system matrix D is:
in this embodiment, the targeted indeterminate system may be a two-dimensional radar system, and after modeling, a system transfer function may be obtained:
as an optimization scheme of the embodiment of the invention, in the step S2, H (z) is added 1 ,z 2 ) Each term of the characteristic polynomial is sequentially filled into a one-dimensional arrayEach array element ofIn (1),
for H (z) 1 ,z 2 ) Judging, it is known that 1 Not equal to 0 and a 2 Not equal to 0, thenNo new array elements are inserted on the left.
As an optimization scheme of the embodiment of the present invention, the step S3 specifically includes: for a one-dimensional arrayValue of each array element in (1)Rearranging from large to small, the subscripts of elements in array in new arrangement order are sequentially replaced by 1,2, \ 8230, i.e. new one-dimensional array
As an optimization scheme of the embodiment of the present invention, the step S4 specifically includes: to pairArray element judgment ofThen theAnddo not insert array elements betweenAdding the added one-dimensional arrayDeletion ofElement of (1) pairArray of elementsJudging when two adjacent elements are adjacentOrWhen is atAnd withDoes not add any element in between, and deletes the previously deleted elementsInsert to the left with the pre-delete position:combining a one-dimensional arrayThe subscripts of the array elements in the new arrangement order are replaced by 1,2, \ 8230;, n, array in turn according to the existing orderIs composed ofBy usingThe expression method (2) is shown. .
Further optimizing the above scheme, the slave arrayStarting with the third element ofThe expression method of (2) is to form an arrayEach element of (1) represents, toIn (1)Is/are as followsAnd (3) judging:
when n =1, the system matrix a 1 The value of row betath and column alphath of (1);
when n =2, the system matrix a 2 Is 1 and alpha column of the beta row,
then the system matrix A 2 Row 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 of the embodiment of the invention, in combination with the transfer functionThe item corresponds toAnd (3) judging:
when the temperature is higher than the set temperatureBelong toTime, system matrix A 1 Is the ith row and 1 st column values ofWhere i = τ 1 ,τ 1 Is a one-dimensional arrayThe numerical value of the middle element isOf (2) element(s)Subscript value of (d);
when in useBelong toTime, system matrix A 2 Is row i, column 1, having a value ofWhere i = τ 2 -1,τ 2 Is a one-dimensional arrayThe numerical value of the middle element isElement (b) ofSubscript value of (d);
then the system matrix A 1 Is a at row 1 and column 1 1 The value of row 3, column 1 is a 4 The value of row 5, column 1 is a 5 (ii) a System matrix A 2 Is a at row 1 and column 1 2 The value of row 3, column 1 is a 3 The system matrix A is obtained 1 ,A 2 。
As an optimization scheme of the embodiment of the invention, in combination with the transfer functionThe items correspond toEach is judgedCorresponding toBelong toOrWhen in useTime of day, system matrix B 1 Is the ith row and 1 st column values ofWhere i = τ 3 ,τ 3 Is a one-dimensional arrayThe numerical value of the middle element isOf (2) element(s)Subscript value of (d); (ii) a When in useBelong toThe value of the ith row and the 1 st column of the system matrix B2 isWhere i = τ 4 -1,τ 4 Is a one-dimensional arrayThe numerical value of the middle element isOf (2) element(s)The subscript value of (2) can obtain a system matrix B 1 ,B 2 。
Matrix A obtained as an optimization scheme of the embodiment of the invention 1 ,A 2 ,B 1 ,B 2 And C and D are respectively:
B 1 =[b 1 0 0 0 b 4 ] Τ
B 2 =[b 2 0 b 3 0 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 be 1 ,A 2 ,B 1 ,B 2 Substituting C and D into F-M II state space model
The obtained transfer function and the transfer function given in the exampleAnd (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-MII state space model based on a radar target prediction system is characterized by comprising the following steps:
s1, analyzing an indefinite system, constructing an F-MII model, and obtaining a transfer function from the F-MII model;
s2, setting up a one-dimensional arrayAnd according to the transfer function, each term of the characteristic polynomial is recorded as an array element
S3, rearranging the array elements from small to large, and then judging the arrayWhether the ratio of elements in (A) is equal toOrIf not, inserting array elementsMake the ratio of adjacent elements meet the condition, and delete itIf yes, directly deleting the element(s)An element of (1);
s4, in the deletionThen, two adjacent elements are judgedAndif it isOrThen theAndno new elements are inserted between the two; if it isThen is inAndis inserted betweenTo delete previouslyReinsertion;
2. The method for implementing the F-MII state space model based on the radar target prediction system as claimed in claim 1, wherein in the step S1, the constructed F-MII model is:
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)
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 number matrixes;
the transfer function is:
for a given transfer function, the system matrix D is:
3. the radar-target-based radar target according to claim 1The method for realizing the F-M II state space model of the measuring system is characterized by comprising the following steps of: in the S2 step, H (z) 1 ,z 2 ) Each term of the characteristic polynomial of (1) is sequentially filled into a one-dimensional arrayEach array element of (a)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 specifically comprises: for a one-dimensional arrayThe value of each array element in (1)Rearranging from large to small, sequentially replacing the subscripts of the array elements in the new arrangement order by 1,2, \ 8230:, i.e. new one-dimensional arrayFor transfer function H (z) 1 ,z 2 ) Making a judgment if the function containsAndthen from the one-dimensional arrayThe third element of (a); if the function containsOrThen from the one-dimensional arrayThe second element of (a); if the function does not containAndthen from the one-dimensional arrayWhen the ratio of the value corresponding to the ith element in the array to the value corresponding to the first i-1 elements is not equal toOrWhen in the one-dimensional arrayN (n is more than or equal to 1) elements are added before the ith elementSo that the added one-dimensional arrayWherein 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 isOr
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: deletion ofAfter the elements of (2), logarithmic seriesJudging when two adjacent elements are adjacentWhen is atAndadding an element in betweenMake the elementAnd deleting the previously deleted elementsLeft side insert with pre-delete positionThen one-dimensional array after additionIn the new arrangementThe subscripts of the elements of the ordinal number group are sequentially replaced by 1,2, \ 8230;, n, arrayIs composed ofBy usingExpression method of (2) will be arrayEach element of (a) is shown.
6. The method of claim 5 for implementing an F-MII state space model based on a radar target prediction system, whereinInIs/are as followsAnd (3) judging:
when n =1, the system matrix a 1 The value of the beta row and the alpha column of (1);
when n =2, the system matrix a 2 Is 1, and the value of the beta row and alpha column of (b) is 1.
7. The method of claim 2, in combination with a transfer functionThe items correspond toAnd (3) judging:
when in useBelong toTime, system matrix A 1 Is the ith row and 1 st column values ofWhere i = τ 1 ,τ 1 Is a one-dimensional arrayThe numerical value of the middle element isOf (2) element(s)Subscript value of (d);
when in useBelong toTime, system matrix A 2 Is the ith row and 1 st column values ofWhere i = τ 2 -1,τ 2 Is a one-dimensional arrayThe numerical value of the middle element isOf (2) element(s)Subscript value of (d);
then the system matrix A 1 ,A 2 Comprises the following steps:
8. the method of claim 2, wherein the F-MII state space model is implemented based on a radar target prediction system, and wherein: in combination with transfer functionsThe items correspond toEach is judgedCorresponding toBelong toOr also
When in useBelong toSystem matrix B 1 Is the ith row and 1 st column values ofWherein i is eachCorresponding toIn a one-dimensional arrayThe element subscripts of (a);
when in useBelong toSystem matrix B 2 Is row i, column 1, having a value ofWherein i is eachCorresponding toIn a one-dimensional arrayThe subscript of the element(s) of (a) minus 1;
the system matrix B can be obtained 1 ,B 2 :
B 1 =[b m-1,n 0…0 b 00 ] T B 2 =[b m,n-1 0…0 b 10 ] T 。
10. the method for implementing the F-MII state space model based on the radar target prediction system of claim 9, wherein verification is performed by Matlab software, specifically: a is to be 1 ,A 2 ,B 1 ,B 2 Substituting C and D into F-MII state space modelThe obtained transfer function is consistent with the original transfer function.
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