CN107290732A - A kind of single base MIMO radar direction-finding method of quantum huge explosion - Google Patents
A kind of single base MIMO radar direction-finding method of quantum huge explosion Download PDFInfo
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- CN107290732A CN107290732A CN201710562238.7A CN201710562238A CN107290732A CN 107290732 A CN107290732 A CN 107290732A CN 201710562238 A CN201710562238 A CN 201710562238A CN 107290732 A CN107290732 A CN 107290732A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/42—Diversity systems specially adapted for radar
Abstract
The invention provides a kind of single base MIMO radar direction-finding method of quantum huge explosion.(1) the arrowband list base MIMO radar system direction finding model that transmitting-receiving is put altogether is set up；(2) all quantum fragments in quantum huge explosion algorithm are determined, quantum fragment is evenly distributed to two subclass；(3) fitness of each quantum fragment is calculated, the initial optimal quantum position of the 1st quantum set of patches, the initial optimal solution quantum barycenter of the 2nd quantum set of patches and uniform solution quantum barycenter is determined；(4) the quantum position of each quantum fragment is updated；(5) the quantum position of each quantum fragment is mapped to the position of interval of definition, and calculates fitness value；(6) global optimum's quantum position is updated；(7) output global optimum's quantum position, and it is mapped as position, the direction of arrival to be estimated of position correspondence.The present invention can realize the direction finding of quick high accuracy under the complex environments such as impact noise, and Measure direction performance is outstanding.
Description
Technical field
The present invention relates to a kind of single base MIMO radar direction-finding method.
Background technology
Multiple-input and multiple-output (Multi-Input Multi-Output, MIMO) radar is a kind of new system radar, MIMO
The radar low gain broad beam mutually orthogonal by launching in space, can be substantially improved the antijamming capability of radar system.
Another important advantage of MIMO radar is, because its launching beam is fixed, and space need not be scanned, because
The same target illuminated time greatly increases in this beam area, and this provides time enough for long-time phase-coherent accumulation and protected
Barrier.MIMO radars have used for reference the MIMO technique in communication system, have many advantages, such as, it has also become current one
Study hotspot.Single base MIMO radar can obtain the virtual aperture bigger than traditional phased-array radar because of its virtual extended ability
Footpath, performance advantage is obvious in terms of direction finding.
By the retrieval discovery to prior art literature, Dang Xiaofang etc. exist《2016 11th
International Symposium on Antennas,Propagation and EM Theory(ISAPE)》(2016,
Pp.607-611 " the Direction of Arrival Estimation for Monostatic MIMO Radar delivered on)
Using Reduced-Dimension RISR Algorithm " propose a kind of single base MIMO based on dimensionality reduction RISR algorithms
Radar direction finding method, can preferably be estimated direction of arrival, but its direction finding precision is not high and computation complexity is larger.
Liang Hao etc. exists《Electronics and information journal》Delivered on (2016, Vol.38, No.1, pp. 80-89) " based on ESPRIT algorithms
Cross array MIMO radar dimensionality reduction DOA estimations " propose a kind of dimensionality reduction DOA algorithm for estimating based on ESPRIT algorithms, this method
Converted by the design of dimensionality reduction matrix and the dimensionality reduction of echo data, higher-dimension echo data is changed to low-dimensional signal space, it is maximum
All redundant datas are eliminated to degree, Measure direction performance is good under Gaussian noise background, but in complexity such as impact noises
Measure direction performance deteriorates serious under background.Existing document shows research at present on single base MIMO radar direction-finding method, direction finding
Precision is not high, and computation complexity is larger, and is applied to survey under Gaussian noise background existing single base MIMO radar direction finding methods more
To direction-finding method penalty is serious under the complex environments such as impact noise.
The content of the invention
It is an object of the invention to provide a kind of amount of calculation is small, direction finding precision is high and can guarantee that and is made an uproar in complexity such as impact noises
Single base MIMO radar direction-finding method of the quantum huge explosion of Measure direction performance under sound background.
The object of the present invention is achieved like this：
Step one, the transmitting antenna for the arrowband list base MIMO radar system that transmitting-receiving is put altogether is to be made up of M omnidirectional's array element
Even linear array, reception antenna is the even linear array that is made up of N number of omnidirectional's array element；Assuming that transmitting terminal transmits M kind carrier frequency simultaneously
With bandwidth all identical orthogonal waveforms, the processing for the matched filter group that radar return passes through each receiving channel, by M kind waveforms
Separate, while it is located at identical distance provided with P signal source, and the distance of information source is more than transmitting and the hole of reception antenna
Footpath, after the processing by matched filter group, is output as in m-th of matched filter of n-th of reception array element of l snap
ynm(l), n=1,2 ..., N, m=1,2 ..., M, then the echo that whole receiving antenna array is received is written as form： y
(l)=A (θ) s (l)+n (l), wherein, y (l)=[y1(l),y2(l),...,yNM(l)]T, A (θ)=[a (θ1),a(θ2),...,
a(θP)] it is the guiding matrix that MN × P is tieed up,For p-th of steering vector,It is Kronecker products,
ar(θp) it is to receive steering vector, at(θp) it is transmitting steering vector, θpFor the direction of arrival of p-th of target, s (l)=[s1(l),
s2(l),...,sP(l)]TTo receive the complex magnitude that exports after the matched filtering of signal, n (l) be the dimension of MN × 1 impact noise to
Amount；The data of reception are normalized to using Infinite Norm
Max is represented and is taken max function, and the covariance matrix of multiple snap sampled datas isE is represented and is asked the mathematics phase
The function of prestige, subscript H represents conjugate transposition, and carrying out feature decomposition to covariance matrix obtains signal subspace and noise subspace
Respectively UsAnd Un, ΛsAnd ΛnRespectively big eigenvalue cluster into diagonal matrix and small eigenvalue cluster into diagonal matrix, then plus
Weighing signal subspace fitting direction finding equation is It is corresponding when maximum is taken to function
Variable θ value,For optimal estimation value, PA(θ)=A (θ) (AH(θ)A(θ))-1AH(θ) is mapping matrix, θ=[θ1,
θ2,...,θP] it is the direction vector that direction of arrival is constituted, W represents weighting matrix, and trace [] representing matrix asks mark computing；
Step 2, produces all initial quantum fragments in quantum huge explosion method,
The quantum solution space being made up of 2H quantum fragment, 2H quantum fragment is evenly distributed to two subclass, each
Quantum fragment is moved in P dimensions search space, and the position of quantum fragment represents single base MIMO radar direction finding problem and potentially solved,
The t times iteration, the quantum position of k-th of quantum set of patches, i-th of quantum fragment is defined as follows:
Wherein i=1,2 ..., H；K=1,2；Represent the pth dimension quantum bit of the quantum position of i-th of quantum fragment, p
=1,2 ..., P；The quantum position of i-th of quantum fragment is mapped to interval of definition, is exactly the position of the quantum fragmentMapping relations areP=1,2 ..., P, upWith
lpRespectively pth ties up the interval upper and lower bound value of angle searching, the corresponding rotation step of i-th of quantum fragment of the 1st set
It is a length ofRepresent the pth dimension rotation step of i-th of quantum fragment
Long, quantum position is in quantum domain [0,1] random initializtion of definition, and rotary step is in [- 0.2,0.2] random initializtion, initially
Seasonal t=0；
Step 3, calculates the fitness of each quantum fragment,
Determine the initial optimal quantum position of the 1st quantum set of patches, the initial optimal solution of the 2nd quantum set of patches
Quantum barycenter and uniform solution quantum barycenter, i-th of quantum crumb positionInfinite model
The fitness value of number weighted signal subspace fitting direction finding equations is1st
Gather the local optimum quantum that the optimal quantum position that i-th of quantum fragment undergone till now is defined as the quantum fragment
Position, is denoted as It is to the t times iteration for i-th of quantum fragment of the 1st set
Only undergone pth ties up optimal quantum bit, p=1,2 ..., P, the optimal quantum position that all quantum fragments are undergone till now
Global optimum's quantum position, that is, the maximum quantum position of fitness value are denoted as, is denoted as For institute
The pth for having quantum fragment to be undergone untill the t times iteration is tieed up optimal in optimal quantum bit, 2 quantum set of patches of selection
Quantum bit is set to optimal solution quantum barycenterThe uniform solution of 2nd quantum set of patches
Quantum barycenter isWherein
Step 4, updates the quantum position of each quantum fragment, and each quantum set of patches is carried out more according to Different Rule
Newly,
For the 1st quantum set of patches, the pth dimension rotary step of i-th of quantum fragment is updated toWeight wtWith iterations increase and gradually successively decrease, i=1,2 ...,
H, p=1,2 ..., P；r1And r2All it is the uniform random number between [0,1], c1And c2For weighting constant；ForIf super
Go out boundary value, be limited in border, the new quantum bit of i-th of quantum fragment is set to
I=1,2 ..., H, whereinP=1,2 ...,
P, abs () represent the function that takes absolute value,
For the 2nd quantum set of patches, during huge explosion is realized, the pth dimension blast step-length of i-th of quantum fragment
ForI=1,2 ..., H, p=1,2 ..., P, ρ be contraction factor,To be uniform between [- 1,1]
Random number, produces the uniform random number γ between [0,1], when all quantum positions of 2 quantum set of patches of γ≤0.5, the
Updating rule isWhereinTo be optimal
Solve quantum barycenterPth dimension, p=1,2 ..., P；Otherwise, the 2nd quantum fragment collection
Close all quantum location updating rules be
Wherein,For uniform solution quantum barycenterPth dimension；
Step 5, by the quantum position of i-th of quantum fragment of k-th of quantum set of patchesIt is mapped to definition
Between positionK=1,2, the fitness value of all quantum fragments is calculated, fitness function isi
=1,2 ..., H；
Step 6, updates global optimum's quantum position, updates the part of each quantum fragment in the 1st quantum set of patches
Optimal quantum position, updates the optimal solution quantum barycenter and uniform solution quantum barycenter of the 2nd quantum set of patches,The global optimum's quantum bit undergone up to now by all quantum fragments in two quantum set of patches
Put, for i-th of quantum fragment of the 1st quantum set of patches, i=1,2 ..., H, ifThen make It is quantum positionMapping position；Otherwise,2nd quantum set of patches
Each dimension of uniform solution quantum barycenter be updated toThe quantum of p=1,2 ..., P, the 2nd
The optimal solution quantum barycenter of set of patchesUse current global optimum's quantum bit
Put replacement；
Step 7, judges whether to reach maximum iteration, if so, terminate iteration, output global optimum's quantum position, and
It is mapped as position, the direction of arrival to be estimated of position correspondence；Otherwise, t=t+1, return to step four are made.
In order to solve the above problems, the present invention devises a kind of quantum huge explosion method first, is then carried on the back in impact noise
A kind of single base MIMO based on quantum huge explosion searching method and Infinite Norm weighted signal subspace fitting is devised under scape
Radar direction finding method.
The invention provides single base MIMO radar direction-finding method under a kind of impulsive noise environment, specifically consider in punching
Hit under noise circumstance and single base MIMO radar is realized using quantum huge explosion and Infinite Norm Weighted Sub-Space Fitting Direction method
Direction finding.
The present invention is for existing single base MIMO radar direction-finding method is computationally intensive, direction finding precision is not high and in impact noise
The shortcoming and defect even failed Deng Measure direction performance severe exacerbation under Complex Noise background, it is proposed that one kind is in impact noise background
Down can quickly, single base MIMO radar direction-finding method of high-precision direction finding.This method devises one kind first can quick high accuracy
The quantum huge explosion method of solution, one kind is then devised under impact noise background and uses quantum huge explosion searching method and nothing
Single base MIMO radar direction-finding method of poor norm weighted signal subspace fitting.
The present invention considers a kind of quantum huge explosion list base MIMO radar direction-finding method under impact noise background, can
Direction finding speed and direction finding precision are considered simultaneously, and solving Infinite Norm weighted signal subspace fitting using quantum huge explosion method surveys
To equation, optimal Measure direction performance is obtained.
Compared with prior art, the present invention has taken into full account and met in the impulsive noise environment base MIMO radar direction finding that places an order
The requirement of the convergence rate, direction finding precision and the Measure direction performance that arrive, with advantages below：
(1) the suitable impulsive noise environment of the present invention, while being also adapted to Gaussian noise and thump noise circumstance, application
Extensively.
(2) single base MIMO radar direction-finding method, preferably resolves the coherent reception under impulsive noise environment designed by
The robust high-precision direction finding problem of information source and incoherent reception information source, with excellent Measure direction performance.
(3) can quick pair plus Infinite Norm power signal subspace fitting direction finding side using designed quantum huge explosion method
Cheng Jinhang is solved in high precision.
Brief description of the drawings
Fig. 1 is designed to be based on quantum huge explosion list base MIMO radar direction-finding method schematic diagram.
The direction of arrival of Fig. 2 independence incoming waves.
The Mutual coupling of the relevant incoming waves of Fig. 3.
Fig. 4 estimates the probability of success with characteristic index change curve.
Embodiment
The invention will be further described for citing below in conjunction with the accompanying drawings.
With reference to Fig. 1, the invention mainly includes steps：
Step one, it is considered to the arrowband list base MIMO radar system that a transmitting-receiving is put altogether, its transmitting antenna is by M omnidirectional's battle array
The even linear array of member composition, reception antenna is the even linear array being made up of N number of omnidirectional's array element.Assuming that transmitting terminal transmits M simultaneously
Plant carrier frequency and bandwidth all identical orthogonal waveforms, the processing for the matched filter group that radar return passes through each receiving channel, by M
Waveform is planted to separate.Assume there is P signal source to be located at identical distance simultaneously, and the distance of information source is far longer than transmitting and connect
Receive the aperture of antenna.After processing by matched filter group, in m-th of matched filtering of n-th of reception array element of l snap
The output (signal of m-th of transmitting antenna of correspondence) of device is ynm(l), n=1,2 ..., N, m=1,2 ..., M, then it is whole to receive
The echo that aerial array is received can be written as form：Y (l)=A (θ) s (l)+n (l).Wherein, y (l)=[y1(l),y2
(l),...,yNM(l)]T, A (θ)=[a (θ1),a(θ2),...,a(θP)] it is the guiding matrix that MN × P is tieed up,For p-th of steering vector,It is Kronecker products, ar(θp) it is to receive steering vector, at(θp)
For transmitting steering vector, θpFor the direction of arrival of p-th of target, s (l)=[s1(l),s2(l),...,sP(l)]TTo receive signal
The complex magnitude exported after matched filtering, n (l) is the impact noise vector that MN × 1 is tieed up.Infinite Norm can be used in the data of reception
It is normalized toMax is represented and is taken max function.It is multiple
The covariance matrix of snap sampled data isE represents the function for seeking mathematic expectaion, and subscript H represents conjugation and turned
Put.Feature decomposition is carried out to covariance matrix and obtains signal subspace and noise subspace respectively UsAnd Un, ΛsAnd ΛnRespectively
For big eigenvalue cluster into diagonal matrix and small eigenvalue cluster into diagonal matrix.Then weighted signal subspace fitting direction finding equation
For It is variable θ corresponding when maximum is taken to function value,Estimate to be optimal
Evaluation, PA(θ)=A (θ) (AH(θ)A(θ))-1AH(θ) is mapping matrix, θ=[θ1,θ2,...,θP] it is the side that direction of arrival is constituted
To vector, W represents weighting matrix, and trace [] representing matrix asks mark computing.
Step 2, produces all initial quantum fragments in quantum huge explosion method.Consider what is be made up of 2H quantum fragment
Quantum solution space, 2H quantum fragment is evenly distributed to two subclass, and each quantum fragment is moved in P dimensions search space,
The position of quantum fragment represents single base MIMO radar direction finding problem and potentially solved.In the t times iteration, k-th of quantum fragment collection
The quantum position for closing i-th of quantum fragment is defined as follows:Wherein i=1,2 ..., H； k
=1,2；Represent the pth dimension quantum bit of the quantum position of i-th of quantum fragment, p=1,2 ..., P；I-th of amount
The quantum position of sub- fragment is mapped to interval of definition, is exactly the position of the quantum fragmentMapping
Relation isP=1,2 ..., P, upAnd lpThe respectively interval upper limit of pth dimension angle searching is with
Limit value.1st set the corresponding rotary step of i-th of quantum fragment beTable
Show the pth dimension rotary step of i-th of quantum fragment.In order that initial position has certain dispersed and uniform property, quantum bit
Quantum domain [0,1] random initializtion in definition is put, rotary step is in [- 0.2,0.2] random initializtion, initial season t=0.
Step 3, calculates the fitness of each quantum fragment, determines the initial optimal quantum bit of the 1st quantum set of patches
Put, the initial optimal solution quantum barycenter of the 2nd quantum set of patches and uniform solution quantum barycenter.I-th of quantum crumb positionThe fitness value of Infinite Norm weighted signal subspace fitting direction finding equation beFitness value is bigger, and quantum fragment quantum position and position are more outstanding, estimation
Angle it is more accurate.The optimal quantum position that 1st set, i-th of quantum fragment is undergone till now is defined as the quantum
The local optimum quantum position of fragment, is denoted as It is broken for i-th of quantum of the 1st set
Piece undergoes pth untill the t times iteration and ties up optimal quantum bit, p=1,2 ..., P.All quantum fragments are undergone till now
Optimal quantum position be denoted as global optimum's quantum position, that is, the maximum quantum position of fitness value, be denoted as The optimal quantum bit of pth dimension undergone by all quantum fragments untill the t times iteration, p=1,
2,...,P.It is optimal solution quantum barycenter to select the optimal quantum position in 2 quantum set of patches
The uniform solution quantum barycenter of 2nd quantum set of patches isWhereinP=1,2 ..., P.
Step 4, updates the quantum position of each quantum fragment.Each quantum set of patches is updated according to Different Rule.
For the 1st quantum set of patches, the pth dimension rotary step of i-th of quantum fragment is updated toWeight wtIncrease with iterations and gradually successively decrease,
I=1,2 ..., H, p=1,2 ..., P；r1And r2All it is the uniform random number between [0,1], c1And c2For weighting constant；It is right
InIf beyond boundary value, being limited in border.The new quantum bit of i-th of quantum fragment is set toI=1,2 ..., H, wherein
P=1,2 ..., P, abs () represent and take absolute value function.
For the 2nd quantum set of patches, during huge explosion is realized, the pth dimension blast step-length of i-th of quantum fragment
ForI=1,2 ..., H, p=1,2 ..., P, ρ be contraction factor,To be uniform between [- 1,1]
Random number.The uniform random number γ between [0,1] is produced, when all quantum positions of 2 quantum set of patches of γ≤0.5, the
Updating rule isWhereinTo be optimal
Solve quantum barycenterPth dimension, p=1,2 ..., P；Otherwise, the 2nd quantum set of patches
All quantum location updating rules be
Wherein,For uniform solution quantum barycenterPth dimension.
Step 5, by the quantum position of i-th of quantum fragment of k-th of quantum set of patchesIt is mapped to definition
Between positionK=1,2.The fitness value of all quantum fragments is calculated, fitness function is
I=1,2 ..., H.
Step 6, updates global optimum's quantum position, updates the part of each quantum fragment in the 1st quantum set of patches
Optimal quantum position, updates the optimal solution quantum barycenter and uniform solution quantum barycenter of the 2nd quantum set of patches.The global optimum's quantum bit undergone up to now by all quantum fragments in two quantum set of patches
Put.For i-th of quantum fragment of the 1st quantum set of patches, i=1,2 ..., H, ifThen
Order It is quantum positionMapping position；Otherwise,2nd quantum fragment collection
Each dimension of the uniform solution quantum barycenter closed is updated toP=1,2 ..., P.2nd amount
The optimal solution quantum barycenter of sub- set of patchesUse current global optimum's quantum
Position is substituted.
Step 7, judges whether to reach maximum iteration, if so, terminate iteration, output global optimum's quantum position, and
It is mapped as position, the direction of arrival to be estimated of position correspondence；Otherwise, t=t+1, return to step four are made.
Consider that impulsive noise environment places an order base MIMO radar system, transmitting and to receive element number of array be all 5, and transmitting
It is the even linear array that array element spacing is half-wavelength with receiving array, fast umber of beats is 200.It is big based on quantum designed by the present invention
The direction-finding method note of single base MIMO radar of Infinite Norm (IN) the weighted signal subspace fitting (WSSF) of blast (QBB)
QBB-IN-WSSF is, its major parameter is set to：wtBy 0.9 monotone decreasing to 0.1, c1=c2=2, ρ=the 1, the 1st quantum are broken
The boundary of rotary step is [- 0.2,0.2] in piece set.Method for comparing has the MUSIC methods based on Fractional Lower Order Moments
(FLOM-MUSIC) the Fractional Lower Order Moments maximum likelihood method (PSO-FLOM-ML) and based on particle cluster algorithm, particle cluster algorithm
Some simulation parameters set and process refers to document " dynamic DOA tracking " under impact noise background, FLOM-MUSIC side
Method refers to the document of most original.The population of quantum fragment number and particle cluster algorithm in quantum huge explosion is all set to 100, eventually
Only iterations is all 100.
Fig. 2 is characterized index for α=1.30, and broad sense signal to noise ratio is 10dB, and 3 separate narrowbands receive the direction of arrival of signal
When respectively 5 °, 15 ° and 25 °, the relation between the arrival direction estimate and actual value of 50 test simulations, it can be seen that
Designed QBB-IN-WSSF methods are much better than FLOM-MUSIC, and close to actual value, FLOM-MUSIC number of values is all estimated
It has failed.
Fig. 3 is characterized index for α=1.30, and broad sense signal to noise ratio is 5dB, the direction of arrival of 3 relevant narrow band received signals
When respectively 5 °, 15 ° and 25 °, the pass between the arrival direction estimate and actual value of 50 test simulations, 50 test simulations
System, it can be seen that designed QBB-IN-WSSF methods are much better than PSO-FLOM-ML, and close to actual value, FLOM-MUSIC
Number of values all estimate have failed.FLOM-MUSIC does not estimate the ability of coherent, does not emulate in this figure.
From Fig. 2 and Fig. 3, under impulsive noise environment, single base MIMO radar of designed quantum huge explosion
The Measure direction performance of direction-finding method will be much better than FLOM-MUSIC and PSO-FLOM-ML, and designed method has very strong shock resistance
Noise immune.Characteristic index is smaller, and impact noise hangover is more serious, influences more serious to Measure direction performance.When characteristic index is 1
When, the estimation probability of success is 0.985, and other two kinds of algorithms are less than 0.2；When characteristic index is 1.2, designed method
During more than 1.2, the estimation probability of success is 1, and the probability of success just reaches other two methods in the case of 1.8 and 1.9 respectively
1。
Fig. 4 is that the direction of arrival that 2 separate narrowbands receive echo signal is respectively 10 ° and 18 °, and broad sense signal to noise ratio is set to
10dB, it is assumed that estimated bias is to estimate successfully within once, the estimation probability of success of 3 kinds of single base MIMO radar direction-finding methods
Relation between characteristic index.Simulation result shows, single base MIMO radar proposed by the present invention based on quantum huge explosion
Direction-finding method, can carry out effective direction finding, in different impulsive noise environments under impulsive noise environment to independence and coherent source
Under all have excellent performance.
Claims (1)
1. single base MIMO radar direction-finding method of a kind of quantum huge explosion, it is characterized in that comprising the following steps：
Step one, the transmitting antenna of arrowband list base MIMO radar system that transmitting-receiving is put altogether be by M omnidirectional's array element constitute it is equal
Even linear array, reception antenna is the even linear array being made up of N number of omnidirectional's array element；Assuming that transmitting terminal transmits M kinds carrier frequency and band simultaneously
Wide all identical orthogonal waveforms, the processing for the matched filter group that radar return passes through each receiving channel separates M kinds waveform
Come, while it is located at identical distance provided with P signal source, and the distance of information source is more than transmitting and the aperture of reception antenna, warp
After the processing of overmatching wave filter group, y is output as in m-th of matched filter of n-th of reception array element of l snapnm
(l), n=1,2 ..., N, m=1,2 ..., M, then the echo that whole receiving antenna array is received is written as form：Y (l)=
A (θ) s (l)+n (l), wherein, y (l)=[y1(l),y2(l),...,yNM(l)]T, A (θ)=[a (θ1),a(θ2),...,a(θP)]
The guiding matrix tieed up for MN × P,For p-th of steering vector,It is Kronecker products, ar(θp) be
Receive steering vector, at(θp) it is transmitting steering vector, θpFor the direction of arrival of p-th of target, s (l)=[s1(l),s2
(l),...,sP(l)]TTo receive the complex magnitude exported after the matched filtering of signal, n (l) is the impact noise vector that MN × 1 is tieed up；
The data of reception are normalized to using Infinite Normmax
Representative takes max function, and the covariance matrix of multiple snap sampled datas isE is represented and is sought mathematic expectaion
Function, subscript H represents conjugate transposition, and carrying out feature decomposition to covariance matrix obtains signal subspace and noise subspace point
Wei not UsAnd Un, ΛsAnd ΛnRespectively big eigenvalue cluster into diagonal matrix and small eigenvalue cluster into diagonal matrix, then weight
Signal subspace fitting direction finding equation is It is corresponding when maximum is taken to function
Variable θ value,For optimal estimation value, PA(θ)=A (θ) (AH(θ)A(θ))-1AH(θ) is mapping matrix, θ=[θ1,θ2,...,
θP] it is the direction vector that direction of arrival is constituted, W represents weighting matrix, and trace [] representing matrix asks mark computing；
Step 2, produces all initial quantum fragments in quantum huge explosion method,
The quantum solution space being made up of 2H quantum fragment, 2H quantum fragment is evenly distributed to two subclass, and each quantum is broken
Piece is moved in P dimensions search space, and the position of quantum fragment represents single base MIMO radar direction finding problem and potentially solved, at the t times
Iteration, the quantum position of k-th of quantum set of patches, i-th of quantum fragment is defined as follows:
Wherein i=1,2 ..., H；K=1,2；Represent the pth dimension quantum bit of the quantum position of i-th of quantum fragment, p
=1,2 ..., P；The quantum position of i-th of quantum fragment is mapped to interval of definition, is exactly the position of the quantum fragmentMapping relations areupAnd lpRespectively pth dimension angle is searched
The interval upper and lower bound value of rope, the corresponding rotary step of i-th of quantum fragment of the 1st set is Represent the pth dimension rotary step of i-th quantum fragment, quantum position the quantum domain [0,1] of definition with
Machine is initialized, and rotary step is in [- 0.2,0.2] random initializtion, initial season t=0；
Step 3, calculates the fitness of each quantum fragment,
Determine the initial optimal quantum position of the 1st quantum set of patches, the initial optimal solution quantum of the 2nd quantum set of patches
Barycenter and uniform solution quantum barycenter, i-th of quantum crumb positionInfinite Norm add
Power signal subspace fitting direction finding equation fitness value be1st set
The optimal quantum position that i-th of quantum fragment is undergone till now is defined as the local optimum quantum bit of the quantum fragment
Put, be denoted as It is the 1st and gathers i-th of quantum fragment untill the t times iteration
Undergone pth ties up optimal quantum bit, and the optimal quantum position that all quantum fragments are undergone till now is denoted as global optimum's quantum
Position, that is, the maximum quantum position of fitness value, are denoted as For all quantum fragments to t
The optimal quantum position that the pth undergone untill secondary iteration is tieed up in optimal quantum bit, 2 quantum set of patches of selection is optimal solution
Quantum barycenterThe uniform solution quantum barycenter of 2nd quantum set of patches isWherein
Step 4, updates the quantum position of each quantum fragment, and each quantum set of patches is updated according to Different Rule,
For the 1st quantum set of patches, the pth dimension rotary step of i-th of quantum fragment is updated to
Weight wtIncrease with iterations and gradually pass
Subtract；r1And r2All it is the uniform random number between [0,1], c1And c2For weighting constant；ForIf, will beyond boundary value
It is limited in border, and the new quantum bit of i-th of quantum fragment is set toWhereinAbs () represents the function that takes absolute value,
For the 2nd quantum set of patches, during huge explosion is realized, the pth dimension blast step-length of i-th of quantum fragment isρ is contraction factor,For the uniform random number between [- 1,1], produce between [0,1] it is uniform with
Machine number γ, when all quantum location updating rules of 2 quantum set of patches of γ≤0.5, the are
WhereinFor optimal solution quantum
BarycenterPth dimension；Otherwise, all quantum positions of the 2nd quantum set of patches are more
Newly rule isWherein,To be uniform
Solve quantum barycenterPth dimension；
Step 5, by the quantum position of i-th of quantum fragment of k-th of quantum set of patchesIt is mapped to interval of definition
PositionThe fitness value of all quantum fragments is calculated, fitness function is
Step 6, updates global optimum's quantum position, updates the local optimum of each quantum fragment in the 1st quantum set of patches
Quantum position, updates the optimal solution quantum barycenter and uniform solution quantum barycenter of the 2nd quantum set of patches,
The global optimum's quantum position undergone up to now by all quantum fragments in two quantum set of patches, for the 1st amount
I-th of quantum fragment of sub- set of patches, ifThen make It is quantum
PositionMapping position；Otherwise,Each dimension of the uniform solution quantum barycenter of 2nd quantum set of patches is more
It is newlyThe optimal solution quantum barycenter of 2nd quantum set of patchesMake
Substituted with current global optimum's quantum position；
Step 7, judges whether to reach maximum iteration, if so, terminate iteration, output global optimum's quantum position, and by its
It is mapped as position, the direction of arrival to be estimated of position correspondence；Otherwise, t=t+1, return to step four are made.
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