CN112014789B - Composite weighted time-frequency direction-finding method based on quantum dot dog mechanism - Google Patents

Composite weighted time-frequency direction-finding method based on quantum dot dog mechanism Download PDF

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CN112014789B
CN112014789B CN202010816137.XA CN202010816137A CN112014789B CN 112014789 B CN112014789 B CN 112014789B CN 202010816137 A CN202010816137 A CN 202010816137A CN 112014789 B CN112014789 B CN 112014789B
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CN112014789A (en
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高洪元
孙贺麟
程建华
张世铂
臧国建
杜亚男
王世豪
张志伟
马静雅
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Harbin Engineering University
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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
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
    • 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
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • 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
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
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    • G01S3/10—Means for reducing or compensating for quadrantal, site, or like errors

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Abstract

The invention provides a composite weighting time-frequency direction finding method based on a quantum dot dog mechanism, which designs a composite weighting time-frequency direction finding method with higher robustness, realizes better suppression on impact noise by carrying out composite weighting on snapshot sampling data and a time-frequency distribution matrix, can also find direction in a Gaussian noise environment, improves the gain on an expected signal and can distinguish related information sources by utilizing the advantages of the time-frequency maximum likelihood direction finding method, can still obtain more accurate direction finding results when stronger interference such as atmospheric noise, ground clutter, radar scattering echoes, artificial noise and the like exists in the working environment of a receiver, and the designed scheme is more suitable for the actual engineering. The method does not need prior knowledge of noise and additional parameter selection, has robustness in a strong interference environment, designs a quantum dot dog mechanism for efficient solution, and breaks through the application limit of the existing direction finding method.

Description

Composite weighting time-frequency direction finding method based on quantum dot dog mechanism
Technical Field
The invention relates to a composite weighted time-frequency direction finding method in an impact noise environment, in particular to a composite weighted time-frequency direction finding method based on a quantum dot dog mechanism, and belongs to the field of array signal processing.
Background
The direction finding is a key technology in the field of array signal processing, and is widely applied to the fields of communication, navigation, electronic countermeasure and the like. In practical application, radar and wireless communication systems face more and more complex electromagnetic environments, which put higher requirements on the signal processing capability of receivers of the radar and wireless communication systems, so that the research on practical direction finding methods in the strong interference environment with low signal-to-noise ratio and impact noise has important significance and value.
The time-frequency direction finding method utilizes the specific characteristics of the signal energy density changing along with time and frequency to realize the suppression of noise, the direction finding precision is higher under the condition of low signal-to-noise ratio, but the performance of the traditional time-frequency direction finding method is seriously deteriorated under the impact noise environment, if the traditional impact resistance method and the time-frequency direction finding method are simply combined, the direction finding problem under the severe noise environment can not be really and effectively solved, and therefore, the direction finding method with robustness under the strong interference environment needs to be designed.
The time-frequency direction finding is carried out by using a maximum likelihood principle, the theoretical optimal performance can be obtained, coherent information sources can be distinguished, the global maximum value search needs to be carried out on a multi-dimensional nonlinear optimization problem, the bottleneck problem of how to quickly and accurately obtain the search result is the application of the maximum likelihood direction finding method, the solution of the method by using an intelligent optimization algorithm is a potential solution, but the existing intelligent optimization algorithm has defects of different degrees, such as low convergence speed, easiness in falling into local extreme values and the like, and therefore a new efficient solution method needs to be designed for specific problems.
Through the search of the prior art documents, Wanhai shores and the like carry out time-frequency direction finding by utilizing fractional low-order moment in ' space time-frequency DOA estimation under alpha stable distributed noise ' published in ' computer engineering ' (2012,38(02):284-287 '), and the method shows certain robustness under an impact noise environment but needs prior knowledge of noise and is greatly influenced by parameter selection; how much, the correlation matrix of the array signals is reconstructed in a DOA estimation algorithm under the impact noise environment based on the sequenced Ratio principle published in the journal of electronics and information (2006(05):875 and 878), and the direction finding is realized by using the MUSIC algorithm, so that the impact noise can be inhibited, but a coherent information source cannot be distinguished, and a quantization error exists in a direction finding result.
The retrieval results of the existing documents show that the existing direction finding method has the advantages of narrow application range, high calculation complexity and poor robustness, and a method capable of quickly and accurately finding the direction under the strong interference environment with low signal to noise ratio and impulse noise is lacked, so that the direction finding method under the strong interference environment is provided, specifically, a composite weighted time-frequency direction finding method is used, the direction finding result is quickly obtained through a quantum dot dog mechanism, and the technical problems that the performance of the existing direction finding method is deteriorated under the background of strong impulse noise and low signal to noise ratio, and the accurate direction finding result cannot be quickly obtained are solved.
Disclosure of Invention
The invention aims to provide a composite weighted time-frequency direction finding method based on a quantum dot dog mechanism, aiming at the defects and shortcomings of the existing method, the composite weighted time-frequency direction finding method is designed, the snapshot sampling data and the time-frequency distribution matrix are subjected to composite weighted processing, the prior knowledge of noise and extra parameter selection are not needed, the robustness is realized in a strong interference environment, the quantum dot dog mechanism is designed for efficient solution, and the application limit of the existing direction finding method is broken through.
The purpose of the invention is realized by the following steps: the method comprises the following steps:
the method comprises the following steps: establishing a mathematical model of an array receiving signal under impact noise for composite weighting time-frequency direction finding;
step two: carrying out K times of snapshot sampling on signals received by the array;
step three: carrying out composite weighted time-frequency processing on snapshot sampling data, and the specific process is as follows:
(1) first take tkThe maximum value and the minimum value of the absolute values of the snapshot sampling values of the M array elements at the moment are respectively
Figure BDA0002632759860000021
K is 1,2, …, K, defining a weighting function of
Figure BDA0002632759860000022
k＝1,2,…,K，ω1Is constant, the output of the m-th array element after weighting is
Figure BDA0002632759860000023
M-1, 2, …, M, K-1, 2, …, K; writing the m-th array element weighted data into a vector form of ym＝[ym(t1),ym(t2),…,ym(tK)]，m＝1,2,…,M；
(2) Carrying out time-frequency transformation on the weighted data by using discrete pseudo Wigner-Ville distribution, and carrying out weighted data y on the u-th and v-th array elementsu、yvThe pseudo Wigner-Vile transformed values are:
Figure BDA0002632759860000024
u＝1,2,…,M，v＝1,2,…,M
wherein (t)k,fp(tk) Time-frequency points in the time-frequency domain, K is 1,2, …, K, P is 1,2, …, P, σ is a lag variable, η is a rectangular window length; arranging the pseudo Wigner-Ville distribution among all array elements into a time-frequency distribution matrix
Figure BDA0002632759860000025
(3) Carrying out smooth weighting processing on the time-frequency distribution matrix, and defining a smooth weighting matrix:
B(tk)＝diag{b1(tk),b2(tk),…,bM(tk)}，k＝1,2,…,K，
the smoothed weighting matrix is { b }1(tk),b2(tk),…,bM(tk) Is a diagonal matrix of diagonal elements, where
Figure BDA0002632759860000031
m＝1,2,…,M，ω2Is constant, the time-frequency distribution matrix after smooth weighting processing is
Figure BDA0002632759860000032
p＝1,2,…,P，k＝1,2,…,K；
(4) Selecting a plurality of corresponding time frequency points on a time frequency domain according to the information of each signal frequency changing along with the time, and obtaining a time frequency distribution matrix of the average time frequency as
Figure BDA0002632759860000033
Step four: constructing a maximum likelihood direction-finding equation by utilizing the time-frequency distribution matrix;
step five: initializing a quantum position of the quantum spot dog and setting parameters;
step six: defining and calculating the distance between the quantum dot dog and the prey;
step seven: sequencing all the quantum dot dogs according to the distance between the quantum dot dogs and prey;
step eight: the optimizing search process of the quantum dot dog surrounding prey is realized by using the analog quantum revolving door;
step nine: determining the quantum position of the next generation of quantum dot dog by applying a truncation selection strategy;
step ten: judging whether the maximum iteration number G is reached, if not, making G equal to G +1, and returning to the seventh step; and if so, stopping the iterative cycle, and outputting the mapping state of the optimal quantum position in the last generation as a direction finding result.
The invention also comprises the following structural features:
1. the first step is specifically as follows: assuming that P far-field signals are incident on a uniform linear array consisting of M array elements, and the included angle between the incoming wave direction of the signals and the normal line of the array is [ theta ]1,θ2,…,θP]At time t, the p-th signal may be denoted as sp(t), P is 1,2, …, P with instantaneous frequency fp(t), P ═ 1,2, …, P; under the assumption that the signal is a narrowband signal, the pth signal received by the mth array element is:
Figure BDA0002632759860000034
m＝1,2,…,M，p＝1,2,…,P
wherein: a ismp(θp,fp(t)) may be abbreviated as ampThe response of the mth array element to the pth signal is shown, if the array element interval is d and the first array element is used as the phase reference point, the response is shown
Figure BDA0002632759860000035
The time difference of the p-th incident signal reaching the m-th array element relative to the arrival time of the signal at the reference array element is shown, wherein c is the propagation speed of the electromagnetic wave; obtaining the array element output signal of P incident signals after the m array element is superposed
Figure BDA0002632759860000041
M is 1,2, …, M, wherein nm(t) additive noise at the mth array element, considering additive noise nm(t) is the complex impulse noise which follows a symmetrical alpha stationary distribution whose characteristic function has the form ψ (t) ═ exp (j μ t- γ | t |, yα) Wherein alpha is a characteristic index, and alpha is more than 0 and less than or equal to 2; gamma is a dispersion coefficient, and gamma is more than 0; mu is a position parameter, - ∞ < mu < <infinity.
2. The second step is specifically as follows: at the sampling time t of the kth snapshotkThe sampling value of the mth array element signal is xm(tk) M1, 2, …, M, K1, 2, …, K, s is satisfied because the digital system sampling interval is much longer than the time the signal sweeps across the arrayp(tk-τmp)≈sp(tk) When P is 1,2, …, P, M is 1,2, …, M, K is 1,2, …, K, the array snapshot data vector is
Figure BDA0002632759860000042
K is 1,2, …, K, all K snapshot sampling values are combined into a snapshot data matrix
Figure BDA0002632759860000043
Figure BDA0002632759860000044
Can also be expressed as
Figure BDA0002632759860000045
Where A is an array flow pattern matrix of size M P, S is a signal matrix of size P K, and N is a noise matrix of size M K.
3. The fourth step is specifically: defining search array flow pattern matrix
Figure BDA0002632759860000046
The structure of the direction-finding matrix is the same as the array flow pattern matrix, and the maximum likelihood direction-finding equation is represented by
Figure BDA0002632759860000047
tr represents matrix tracking operation to minimize the value of the likelihood function
Figure BDA0002632759860000048
I.e. the optimal estimate of the direction of arrival of the signal, wherein
Figure BDA0002632759860000049
And I is a unit array for searching a projection complement operator of the array flow pattern matrix.
4. The fifth step is specifically: setting the number of quantum spot dogs in the population as L, the maximum iteration times as G, the iteration number label as G, and G belonging to [1, G ]](ii) a In the g iteration, the quantum position of the first quantum blob dog in the P-dimensional search space is
Figure BDA00026327598600000410
When g is 1, each dimension of the quantum position of the primary quantum dot dog is initialized to [0, 1%]A uniform random number in between.
5. The sixth step is specifically: in the g iteration, each dimension of quantum positions of all the quantum spot dogs is mapped into an angle solution space range to obtain the mapping state of the quantum spot dogs
Figure BDA00026327598600000411
Figure BDA00026327598600000411
Figure BDA00026327598600000411
1,2, …, L, which searches for the projected complement of the array flow pattern matrix as
Figure BDA00026327598600000412
Substituting likelihood function to obtain corresponding objective function value
Figure BDA00026327598600000413
l＝1,2,....L。
6. The seventh step is specifically: arranging all the quantum spot dogs in a sequence from near to far from the prey, and setting the quantum position closest to the prey as the optimal quantum position
Figure BDA0002632759860000051
The corresponding minimum objective function value is
Figure BDA0002632759860000052
The quantum position farthest from the prey is the worst quantum position
Figure BDA0002632759860000053
The corresponding maximum objective function value is
Figure BDA0002632759860000054
7. The eighth step is specifically:
(1) defining threshold values
Figure BDA0002632759860000055
And calculating the target function values of all the quantum spot dogs, wherein the target function values are less than or equal to xigOfNumber of
Figure BDA0002632759860000056
Each quantum dot dog considers the top Q closest to the prey in the populationgThe motion is carried out only by the quantum position information of the quantum dot dog;
(2) the movement of the first quantum dot dog to the q quantum dot dog in the population corresponds to a quantum rotation angle vector of
Figure BDA0002632759860000057
l＝1,2,…,L，q＝1,2,…,QgWherein the p-th dimension of the quantum rotation angle is calculated by
Figure BDA0002632759860000058
P is 1,2, …, P, wherein
Figure BDA0002632759860000059
Is [0,1 ]]A uniform random number therebetween; if it is calculated to obtain
Figure BDA00026327598600000510
Then order
Figure BDA00026327598600000511
ω3Sign is a symbol decision function;
(3) calculating the displacement component of the motion of the first quantum dot dog to the q-th quantum dot dog by using an analog quantum rotating gate as
Figure BDA00026327598600000512
l＝1,2,…,L，q＝1,2,…,QgWherein the p-th dimension of the displacement component is calculated by
Figure BDA00026327598600000513
p＝1,2,…,P；
(4) The first quantum spot dog determines the quantum position after movement according to the current quantum position and the displacement component
Figure BDA00026327598600000514
And L is 1,2, … and L, wherein all L quantum speckle dogs in the population move in the P-dimensional search space according to the rule, so that the prey is surrounded.
8. The ninth step is specifically: calculating the objective function value corresponding to the vector mapping state of the moved quantum dot dog position, and calculating the objective function value from the original quantum position
Figure BDA00026327598600000515
And post-exercise quantum position
Figure BDA00026327598600000516
In 2L quantum positions in total, selecting the L quantum positions closest to the prey as the quantum positions of the quantum spot dog of the new generation
Figure BDA00026327598600000517
l＝1,2,…,L。
Compared with the prior art, the invention has the beneficial effects that: aiming at the problem that the performance of the existing direction finding method is deteriorated in a strong interference environment, the invention designs a composite weighting time-frequency direction finding method with higher robustness, realizes better suppression on impact noise by carrying out composite weighting on snapshot sampling data and a time-frequency distribution matrix, can also carry out direction finding in a Gaussian noise environment, utilizes the advantages of the time-frequency maximum likelihood direction finding method, improves the gain on an expected signal, can distinguish related information sources, can still obtain more accurate direction finding results when stronger interference such as atmospheric noise, ground clutter, radar scattering echoes, artificial noise and the like exists in the working environment of a receiver, and is more suitable for the actual engineering.
The quantum dot dog mechanism designed by the invention can quickly obtain a composite weighting time-frequency direction finding result, and has no quantization error. The effectiveness of the composite weighting time-frequency direction-finding method based on the quantum dot dog mechanism is proved through true simulation verification, and compared with a traditional solving method, the method is high in speed and high in precision.
Drawings
FIG. 1 is a schematic diagram of a quantum dot dog mechanism-based composite weighted time-frequency direction finding method.
The root mean square error of the direction-finding angle and the generalized signal-to-noise ratio are plotted in the graph of fig. 2 alpha being 1.0.
Fig. 3 a is a curve of the direction finding success probability and the generalized signal-to-noise ratio when the α is 1.0.
The root mean square error of the direction-finding angle is related to the generalized signal-to-noise ratio when the alpha is 1.6 in figure 4.
The relation curve of the direction finding success probability and the generalized signal-to-noise ratio is shown in the graph 5 alpha-1.6.
In fig. 2,3, 4 and 5, the composite weighted time-frequency direction finding method based on the quantum dot dog mechanism designed by the invention is denoted as QSHO-CW-TFML; recording an infinite norm normalization preprocessing maximum likelihood direction finding method based on a quantum dot dog mechanism as QSHO-INF-ML; a fraction low-order covariance maximum likelihood direction finding method based on a quantum dot dog mechanism is recorded as QSHO-FLOC-ML.
In a simulation experiment, two signals are incident on the uniform linear arrays with the spacing of half of the carrier wavelength from-10 degrees and 20 degrees, and simulation experiment parameters are set as follows: m6, K512, λ 1, μ 0, ω1＝0.25，ω2＝0.001，ω 35, 101, 60, 200, 100 Monte Carlo experiments, and setting the sum of the difference between the estimated angle and the actual angle to be less than 2 degrees as the estimation success. Under two impact noises with different intensities of alpha-1.0 and alpha-1.6, the curve of the variation of the root mean square error of the direction-finding angle along with the generalized signal-to-noise ratio and the curve of the variation of the success probability of direction-finding along with the generalized signal-to-noise ratio are compared, so that the advantages of the method designed by the invention in comparison with two traditional direction-finding methods under the environment of the impact noises are reflected.
From the simulation graph, the composite weighted time-frequency direction-finding method based on the quantum dot dog mechanism shows direction-finding performance superior to that of the traditional method under the impact noises with different intensities, and particularly has higher direction-finding precision under the condition of low signal-to-noise ratio.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
Step one, establishing a mathematical model for combining weighted time-frequency direction finding of array receiving signals under impact noise according to alpha stable distribution.
Suppose that P far-field signals are incident on a uniform linear array consisting of M array elements, and the included angle between the incoming wave direction of the signals and the array normal is [ theta ═ theta1,θ2,…,θP]. At time t, the p-th signal may be denoted as sp(t), P is 1,2, …, P with instantaneous frequency fp(t), P is 1,2, …, P. Under the assumption that the signal is a narrowband signal, the p-th signal received by the m-th array element is
Figure BDA0002632759860000071
M-1, 2, …, M, P-1, 2, …, P, wherein amp(θp,fp(t)) may be abbreviated as ampThe response of the mth array element to the pth signal is shown, if the array element interval is d and the first array element is used as the phase reference point, the response is shown
Figure BDA0002632759860000072
The time difference of the p-th incident signal reaching the m-th array element relative to the arrival of the signal at the reference array element, wherein c is the propagation speed of the electromagnetic wave. Under the condition that a propagation medium and a receiving system are linear, multiple signals received by the array meet the superposition principle, and thus array element output signals obtained after P incident signals are superposed at the m-th array element are obtained
Figure BDA0002632759860000073
M is 1,2, …, M, wherein nm(t) additive noise at the mth array element, considering additive noise nm(t) is the complex impulsive noise subject to a symmetrical alpha stationary distribution. The characteristic function of the symmetrical α stable distribution has the form ψ (t) ═ exp (j μ t- γ | t! luminanceα) Wherein alpha is a characteristic index, and alpha is more than 0 and less than or equal to 2; gamma is a dispersion coefficient, and gamma is more than 0; mu is a position parameter, - ∞ < mu < <infinity.
And step two, carrying out K times of snapshot sampling on the received signals to obtain a snapshot sampling data matrix.
At the sampling time t of the kth snapshotkThe sample value of the m-th array element signal is
Figure BDA0002632759860000074
M1, 2, …, M, K1, 2, …, K, s is satisfied because the digital system sampling interval is much longer than the time the signal sweeps across the arrayp(tk-τmp)≈sp(tk) When P is 1,2, …, P, M is 1,2, …, M, K is 1,2, …, K, the array snapshot data vector is
Figure BDA0002632759860000081
K is 1,2, …, K, and all K snapshot sampling values are combined into a snapshot data matrix
Figure BDA0002632759860000082
Figure BDA0002632759860000083
Can also be expressed as
Figure BDA0002632759860000084
Where A is an array flow pattern matrix of size M P, S is a signal matrix of size P K, and N is a noise matrix of size M K.
Thirdly, carrying out composite weighted time-frequency processing on the snapshot sampling data to obtain a time-frequency distribution matrix, wherein the concrete process is as follows:
(1) first get tkThe maximum value and the minimum value of the absolute values of the snapshot sampling values of M array elements at the moment are respectively
Figure BDA0002632759860000085
K is 1,2, …, K, thereby defining a weighting function of
Figure BDA0002632759860000086
k＝1,2,…,K，ω1Is constant, the output of the m-th array element after weighting is
Figure BDA0002632759860000087
M-1, 2, …, M, K-1, 2, …, K. Writing the m-th array element weighted data into a vector form of ym＝[ym(t1),ym(t2),…,ym(tK)]，m＝1,2,…,M。
(2) And performing time-frequency transformation on the weighted data by using discrete pseudo Wigner-Ville distribution (DT-PWVD). U and v array element weighted data yu、yvThe pseudo Wigner-Vile transformed value is
Figure BDA0002632759860000088
u-1, 2, …, M, v-1, 2, …, M, wherein (t) isk,fp(tk) K is 1,2, …, K, P is 1,2, …, P, σ is a lag variable, and η is a rectangular window length. Arranging the pseudo Wigner-Ville distribution among all array elements into a time-frequency distribution matrix
Figure BDA0002632759860000089
The time-frequency distribution matrix is a self-conjugate matrix, only the main diagonal and the elements above the main diagonal need to be calculated in actual calculation, and other elements can be obtained through conjugate transformation.
(3) To further suppress the influence of impulse noise, the time-frequency distribution matrix is subjected to smooth weighting processing to define a smooth weighting matrix B (t)k)＝diag{b1(tk),b2(tk),…,bM(tk) 1,2, …, K is { b }1(tk),b2(tk),…,bM(tk) Is a diagonal matrix of diagonal elements, where
Figure BDA0002632759860000091
m＝1,2,…,M，ω2Is constant, the time-frequency distribution matrix after smooth weighting processing is
Figure BDA0002632759860000092
P-1, 2, …, P, K-1, 2, …, K. The snapshot sampling data and the time-frequency distribution matrix are subjected to composite weighting, so that strong impact noise can be effectively inhibited, and the robustness of time-frequency direction finding is improved.
(4) The time-frequency average can improve the gain of the expected signal, and the frequency of each signal changes along with the timeSelecting a plurality of corresponding time frequency points on a time frequency domain to obtain a time frequency distribution matrix of which the time frequency is average
Figure BDA0002632759860000093
And fourthly, constructing a maximum likelihood direction-finding equation by using the time-frequency distribution matrix.
Defining search array flow pattern matrix
Figure BDA0002632759860000094
The structure of the direction-finding matrix is the same as the array flow pattern matrix, and the maximum likelihood direction-finding equation is represented by
Figure BDA0002632759860000095
tr represents matrix tracking operation to minimize the value of the likelihood function
Figure BDA0002632759860000096
I.e. the optimal estimate of the direction of arrival of the signal, wherein
Figure BDA0002632759860000097
And I is a unit array for searching a projection complement operator of the array flow pattern matrix.
And step five, initializing the quantum position of the quantum spot dog and setting parameters.
Firstly, setting the number of quantum spot dogs in a population as L, the maximum iteration number as G, the iteration number label as G, and G belonging to [1, G ]]. In the g iteration, the quantum position of the first quantum speckle dog in the P-dimensional search space is set as
Figure BDA0002632759860000098
When g is 1, each dimension of the quantum position of the primary quantum dot dog is initialized to [0, 1%]A uniform random number in between.
And step six, defining and calculating the distance between the quantum dot dog and the prey by utilizing a maximum likelihood direction finding equation.
In the g iteration, each dimension of all quantum positions of the quantum spot dog is mapped into an angle solution space range to obtainMapping states of Quantum dot dogs
Figure BDA0002632759860000099
L is 1,2, …, L, which searches the projection complement of the array flow pattern matrix as
Figure BDA00026327598600000910
Substituting likelihood function to obtain corresponding objective function value
Figure BDA00026327598600000911
L is 1, 2. The smaller the objective function value corresponding to the mapping state of the quantum dot dog is specified to be, the closer the quantum dot dog is to the prey.
And seventhly, sorting all the quantum dot dogs according to the distance between the quantum dot dogs and the prey.
Arranging all the quantum spot dogs in a sequence from near to far from the prey, and setting the quantum position closest to the prey as the optimal quantum position
Figure BDA0002632759860000101
The corresponding minimum objective function value is
Figure BDA0002632759860000102
The quantum position farthest from the prey is the worst quantum position
Figure BDA0002632759860000103
The corresponding maximum objective function value is
Figure BDA0002632759860000104
Step eight, evolving quantum positions of the quantum spot dog by using the simulated quantum revolving gate to realize the optimizing search process of surrounding prey of the quantum spot dog, and specifically comprising the following steps:
(1) defining threshold values
Figure BDA0002632759860000105
And calculating the target function value less than or equal to xi in all the quantum spot dogsgOfNumber of
Figure BDA0002632759860000106
Each quantum dot dog considers the top Q closest to the prey in the populationgThe quantum position information of the quantum dot dog only performs the exercise.
(2) The movement of the first quantum dot dog to the q quantum dot dog in the population corresponds to a quantum rotation angle vector of
Figure BDA0002632759860000107
l＝1,2,…,L，q＝1,2,…,QgWherein the p-th dimension of the quantum rotation angle is calculated by
Figure BDA0002632759860000108
P is 1,2, …, P wherein
Figure BDA0002632759860000109
Is [0,1 ]]A uniform random number in between; further specified, if calculated according to the above formula
Figure BDA00026327598600001010
Then order
Figure BDA00026327598600001011
ω3Sign is a symbol decision function.
(3) Calculating the displacement component of the motion of the first quantum dot dog to the q-th quantum dot dog by using an analog quantum rotating gate as
Figure BDA00026327598600001012
l＝1,2,…,L，q＝1,2,…,QgWherein the p-th dimension of the displacement component is calculated as
Figure BDA00026327598600001013
p＝1,2,…,P。
(4) The quantum spot dog determines the quantum position after movement as
Figure BDA00026327598600001014
And L is 1,2, … and L, wherein all L quantum spotted dogs in the population move in the P-dimensional search space according to the rule, so that the prey is surrounded.
And step nine, calculating the distance between the quantum dot dog and the prey after the exercise, and generating the quantum position of the next generation of quantum dot dog by applying a truncation selection strategy.
Calculating the objective function value corresponding to the vector mapping state of the moved quantum dot dog position, and calculating the objective function value from the original quantum position
Figure BDA00026327598600001015
And post-exercise quantum position
Figure BDA00026327598600001016
Selecting the L quantum positions closest to the prey from the total 2L quantum positions as the quantum positions of the new generation of quantum dot dog
Figure BDA0002632759860000111
l＝1,2,…,L。
Step ten, judging whether the maximum iteration times G is reached, if not, making G equal to G +1, and returning to the step seven; if so, stopping the iterative loop, and outputting the mapping state of the optimal quantum position in the last generation as a direction finding result.

Claims (3)

1. A composite weighting time-frequency direction finding method based on a quantum dot dog mechanism is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: establishing a mathematical model of the array receiving signals under the impact noise for composite weighting time frequency direction finding;
step two: carrying out K times of snapshot sampling on signals received by the array;
step three: carrying out composite weighted time-frequency processing on snapshot sampling data, and the specific process is as follows:
(1) first get tkThe maximum value and the minimum value of the absolute values of the snapshot sampling values of the M array elements at the moment are respectively
Figure FDA0003626294900000011
Figure FDA0003626294900000012
Defining a weighting function as
Figure FDA0003626294900000013
ω1Is constant, the output of the m-th array element after weighting is
Figure FDA0003626294900000014
Writing the m-th array element weighted data into a vector form of ym＝[ym(t1),ym(t2),…,ym(tK)]，m＝1,2,…,M；
(2) Carrying out time-frequency transformation on the weighted data by using discrete pseudo Wigner-Ville distribution, and weighting the u-th and v-th array elements to obtain the data yu、yvThe pseudo-Wigner-Vile transformed values are:
Figure FDA0003626294900000015
wherein (t)k,fp(tk) Time-frequency points in the time-frequency domain, K is 1,2, …, K, P is 1,2, …, P, σ is a lag variable, η is a rectangular window length; arranging the pseudo Wigner-Ville distribution among all array elements into a time-frequency distribution matrix
Figure FDA0003626294900000016
(3) Carrying out smooth weighting processing on the time-frequency distribution matrix, and defining a smooth weighting matrix:
B(tk)＝diag{b1(tk),b2(tk),…,bM(tk)}，k＝1,2,…,K，
the smoothed weighting matrix is { b }1(tk),b2(tk),…,bM(tk) Of diagonal elementsA diagonal matrix of which
Figure FDA0003626294900000017
ω2Is a constant, the time-frequency distribution matrix after smooth weighting processing is
Figure FDA0003626294900000018
(4) Selecting a plurality of corresponding time frequency points on a time frequency domain according to the information of each signal frequency changing along with the time, and obtaining a time frequency distribution matrix of the average time frequency as
Figure FDA0003626294900000021
Step four: constructing a maximum likelihood direction-finding equation by using the time-frequency distribution matrix;
defining search array flow pattern matrix
Figure FDA0003626294900000022
The structure of the direction-finding matrix is the same as the array flow pattern matrix, and the maximum likelihood direction-finding equation is represented by
Figure FDA0003626294900000023
tr represents a matrix tracking operation to minimize the value of the likelihood function
Figure FDA0003626294900000024
I.e. an optimal estimate of the direction of arrival of the signal, wherein
Figure FDA0003626294900000025
I is a unit array for searching a projection complement operator of the array flow pattern matrix;
step five: initializing a quantum position of the quantum spot dog and setting parameters;
setting the number of quantum spot dogs in the population as L, the maximum iteration times as G, the iteration number label as G, and G belongs to [1, G ]](ii) a In the g iteration, the quantum of the l quantum spot dog in the P-dimensional search spaceIs positioned as
Figure FDA0003626294900000026
When g is 1, each dimension of the quantum position of the primary quantum dot dog is initialized to [0, 1%]A uniform random number in between;
step six: defining and calculating the distance between the quantum dot dog and the prey;
in the g iteration, each dimension of quantum positions of all the quantum spot dogs is mapped into an angle solution space range to obtain the mapping state of the quantum spot dogs
Figure FDA0003626294900000027
The projection complement operator of the search array flow pattern matrix is
Figure FDA0003626294900000028
Substituting likelihood function to obtain corresponding objective function value
Figure FDA0003626294900000029
Step seven: sequencing all the quantum dot dogs according to the distance between the quantum dot dogs and prey;
arranging all quantum spot dogs in a sequence from near to far from a prey, and setting a quantum position closest to the prey as an optimal quantum position
Figure FDA00036262949000000210
The corresponding minimum objective function value is
Figure FDA00036262949000000211
The quantum position farthest from the prey is the worst quantum position
Figure FDA00036262949000000212
The corresponding maximum objective function value is
Figure FDA00036262949000000213
Step eight: the optimization searching process of the quantum dot dog surrounding prey is realized by using the simulated quantum revolving door;
(1) defining threshold values
Figure FDA00036262949000000214
And calculating the target function value less than or equal to xi in all the quantum spot dogsgNumber of (2)
Figure FDA00036262949000000215
Each quantum dot dog considers the top Q closest to the prey in the populationgCarrying out movement by using the quantum position information of the quantum spot dog;
(2) the movement of the first quantum dot dog to the q quantum dot dog in the population corresponds to a quantum rotation angle vector of
Figure FDA00036262949000000216
Wherein the p-th dimension of the quantum rotation angle is calculated by
Figure FDA00036262949000000217
Wherein
Figure FDA00036262949000000218
Is [0,1 ]]A uniform random number therebetween; if it is calculated to obtain
Figure FDA0003626294900000031
Then order
Figure FDA0003626294900000032
ω3Sign is a symbol decision function;
(3) calculating the displacement component of the movement of the first quantum dot dog to the q quantum dot dog by using an analog quantum revolving gate as
Figure FDA0003626294900000033
Wherein the p-th dimension of the displacement component is calculated by
Figure FDA0003626294900000034
(4) The quantum spot dog determines the quantum position after movement as
Figure FDA0003626294900000035
All L quantum spot dogs in the population move in the P-dimensional search space according to the rule, so that prey enclosure is realized;
step nine: determining the quantum position of the next generation of quantum dot dog by applying a truncation selection strategy;
calculating the objective function value corresponding to the vector mapping state of the moved quantum dot dog position, and calculating the objective function value from the original quantum position
Figure FDA0003626294900000036
And post-exercise quantum position
Figure FDA0003626294900000037
In 2L quantum positions in total, selecting the L quantum positions closest to the prey as the quantum positions of the quantum spot dog of the new generation
Figure FDA0003626294900000038
Step ten: judging whether the maximum iteration number G is reached, if not, making G equal to G +1, and returning to the seventh step; if so, stopping the iterative loop, and outputting the mapping state of the optimal quantum position in the last generation as a direction finding result.
2. The quantum dot dog mechanism-based composite weighted time-frequency direction finding method according to claim 1, wherein: the first step is specifically: suppose that P far-field signals are incident on a uniform linear array consisting of M array elements, and the included angle between the incoming wave direction of the signals and the array normal is [ theta ═ theta1,θ2,…,θP]At time t, the p-th signal may be denoted as sp(t)，P is 1,2, …, P with instantaneous frequency fp(t), P ═ 1,2, …, P; under the assumption that the signal is a narrowband signal, the pth signal received by the mth array element is:
Figure FDA0003626294900000039
wherein: a ismp(θp,fp(t)) may be abbreviated as ampThe response of the mth array element to the pth signal is shown, if the array element interval is d and the first array element is used as the phase reference point, the response is shown
Figure FDA00036262949000000310
The time difference of the p-th incident signal reaching the m-th array element relative to the arrival time of the signal at the reference array element is shown, wherein c is the propagation speed of the electromagnetic wave; obtaining the array element output signal of P incident signals after the m array element is superposed
Figure FDA00036262949000000311
Wherein n ism(t) additive noise at the mth array element, considering additive noise nm(t) is the complex impulse noise subject to a symmetrical alpha stationary distribution whose characteristic function has the form ψ (t) exp (j μ t- γ | t | t |)α) Wherein alpha is a characteristic index, and alpha is more than 0 and less than or equal to 2; gamma is a dispersion coefficient, and gamma is more than 0; mu is a position parameter, - ∞ < mu < ∞.
3. The quantum dot dog mechanism-based composite weighted time-frequency direction finding method according to claim 2, wherein: the second step is specifically as follows: at the sampling time t of the k-th snapshotkThe sample value of the m-th array element signal is
Figure FDA0003626294900000041
Figure FDA0003626294900000042
Because the digital system has far sampling intervalGreater than the time that the signal sweeps across the array, so s is satisfiedp(tk-τmp)≈sp(tk) When P is 1,2, …, P, M is 1,2, …, M, K is 1,2, …, K, the array snapshot data vector is
Figure FDA0003626294900000043
Synthesizing all K snapshot sampling values into a snapshot data matrix
Figure FDA0003626294900000044
Figure FDA0003626294900000045
Can also be expressed as
Figure FDA0003626294900000046
Where A is an array flow pattern matrix of size M P, S is a signal matrix of size P K, and N is a noise matrix of size M K.
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