CN109212466B - Quantum dragonfly evolution mechanism-based broadband direction finding method - Google Patents

Quantum dragonfly evolution mechanism-based broadband direction finding method Download PDF

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CN109212466B
CN109212466B CN201811017243.0A CN201811017243A CN109212466B CN 109212466 B CN109212466 B CN 109212466B CN 201811017243 A CN201811017243 A CN 201811017243A CN 109212466 B CN109212466 B CN 109212466B
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CN109212466A (en
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高洪元
臧国建
池鹏飞
刁鸣
张世铂
马雨微
苏雨萌
谢婉婷
刘子奇
孙贺麟
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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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention provides a broadband direction finding method based on a quantum dragonfly evolution mechanism, which comprises the steps of initializing quantum dragonfly evolution parameters by establishing a broadband signal sampling model, calculating the fitness of each quantum dragonfly, updating the radius of the field and the related parameters of the neighborhood quantum dragonfly for the first half of a quantum dragonfly group, updating the related parameters of each quantum dragonfly for the second half, calculating the fitness values of the positions of all the quantum dragonflies, judging whether the maximum iteration times are reached, mapping the global optimal quantum position of the quantum dragonfly group into an optimal position if the maximum iteration times are reached, and obtaining the angle to be estimated by the broadband direction of arrival estimation. The method carries out direction finding on the broadband signal, reduces the operation amount and the operation time, improves the convergence speed and the convergence precision, realizes high-precision direction finding, can simultaneously carry out direction of arrival estimation on a coherent source and an independent source, has excellent anti-noise performance and higher estimation success probability, and has direction finding performance superior to that of a broadband direction finding method based on a particle swarm algorithm.

Description

Quantum dragonfly evolution mechanism-based broadband direction finding method
Technical Field
The invention belongs to the field of array signal processing, and particularly relates to a broadband direction finding method based on a quantum dragonfly evolution mechanism.
Background
Array signal processing has wide application in the fields of communication, radar, sonar and the like, and direction-of-arrival estimation is one of important research directions in the field of array signals. The broadband signal has the advantages of large amount of carried information, easy target signal detection, parameter estimation, characteristic extraction and the like, and the application of the broadband signals such as frequency hopping signals, spread spectrum signals, linear frequency modulation signals and the like in a communication system is more and more extensive. Therefore, it is more important to study the estimation of the direction of arrival of the broadband signal.
The maximum likelihood algorithm is to calculate a covariance matrix and an orthogonal projection matrix of a signal by processing received data, and then obtain a target function of the maximum likelihood algorithm through a series of operations. However, the objective function is a multidimensional nonlinear function related to the incident angle, the solving process is complex, and the calculation amount is large.
The weighted signal subspace fitting algorithm is to solve a signal subspace and a noise subspace by performing characteristic decomposition on a covariance matrix of a received signal, and then to solve a target function by fitting between the signal subspace of the received data and a subspace formed by actual signal guide vectors. The objective function is also a multidimensional nonlinear function, the solving process is complex, and the calculation amount is large.
According to the existing literature, the method proposed by the Luojing green in the electronic information countermeasure technology (2014, Vol.29, No.1, pp.16-20 published the wideband direction finding method based on the orthogonal projection transformation) has low convergence accuracy, Rixin, Liuwenhong in the computer engineering and application (2013, Vol.49, No.20, pp.227-229) published the wideband multi-signal direction finding method research based on the frequency domain correlation and SVM has large operand, low convergence accuracy and poor performance.
Although the method obtains a good result in the broadband direction finding problem, the method has low solving precision, poor convergence performance and large calculation amount, so a new broadband direction finding method needs to be designed to solve the problems.
Disclosure of Invention
The invention aims to provide a broadband direction finding method based on a quantum dragonfly evolution mechanism, which is used for quickly and accurately finding directions of an independent information source and a coherent information source in a broadband environment.
The purpose of the invention is realized as follows:
a broadband direction finding method based on a quantum dragonfly evolution mechanism comprises the following specific implementation steps:
step 1, establishing a broadband signal sampling model;
step 2, initializing parameters of a quantum dragonfly evolution mechanism;
step 3, calculating the fitness of each quantum dragonfly to obtain a local optimal quantum position and a local worst quantum position, and a global optimal quantum position and a global worst quantum position;
step 4, updating the radius of the field and the quantum position and the quantum speed of the neighborhood quantum dragonfly in the first half of the quantum dragonfly group, updating five behavior vectors and step length vectors of each quantum dragonfly, and updating the quantum rotation angle and the quantum position of each quantum dragonfly;
step 5, updating the quantum speed and the quantum position of each quantum dragonfly for the second half of the quantum dragonfly group;
step 6, calculating the fitness values of all the quantum dragonfly positions, and updating the local optimal quantum position and the local worst quantum position, and the global optimal quantum position and the global worst quantum position;
step 7, judging whether the maximum iteration times is reached, if not, returning to the step 4 for continuing; if the quantum dragonfly group global optimal quantum position is reached, mapping the quantum dragonfly group global optimal quantum position into an optimal position to obtain an angle to be estimated by the broadband direction of arrival estimation.
The process of establishing the broadband signal sampling model in the step 1 is that under the environment of Gaussian noise, broadband signals with P far fields respectively form a directional angle theta 1 ,θ 2 ,…,θ P The signal is incident on a certain antenna array in space, the antenna array is composed of M array elements, the distance between the array elements is d, the wavelength is lambda, and the bandwidth of the incident signal is B. The first array element is taken as a reference array element, and the signal received by the mth array element is expressed as
Figure BDA0001786081700000021
Wherein s is p (t) the incident direction is θ p Of the broadband signal n p (t) represents additive noise on the mth array element,a m,p indicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
Figure BDA0001786081700000022
representing the time delay of the p source to the m array element; will observe the time T o Is divided into K subsections, and each subsection has a time T d I.e. by
Figure BDA0001786081700000023
Then the observation data are processed
Figure BDA0001786081700000024
Point discrete Fourier transform to obtain K groups of uncorrelated narrow band frequency domain components, sub-segment T d Compared with the signal and noise correlation time, the data after discrete Fourier transform is irrelevant, and the obtained broadband model is
Figure BDA0001786081700000025
Figure BDA0001786081700000026
Figure BDA0001786081700000027
Figure BDA0001786081700000028
Figure BDA0001786081700000029
Figure BDA00017860817000000210
Are each z m (t)、s p (t)、n m (t) at the kth time subsection a frequency of
Figure BDA00017860817000000211
The fourier coefficients of the time of flight,
Figure BDA00017860817000000212
is a steering matrix of size M x P, where P directions are different, the matrix is full rank,
Figure BDA00017860817000000213
steering vectors called matrices
Figure BDA0001786081700000031
Wherein P is 1,2, …, P; processing data received by the array under conditions in which the signal is uncorrelated with noise, at each frequency point
Figure BDA0001786081700000032
The covariance matrix of the frequency domain sampled data of the sensor array is obtained as
Figure BDA0001786081700000033
Using the received data to obtain an orthogonal projection matrix of
Figure BDA0001786081700000034
An angle estimation value obtained from the maximum likelihood equation is
Figure BDA0001786081700000035
Performing characteristic decomposition on the covariance matrix to obtain a signal subspace
Figure BDA0001786081700000036
And noise subspace
Figure BDA0001786081700000037
Then, according to the condition that the space formed by the signal subspace and the space formed by the array flow pattern are the same, the angle estimation value of the weighted signal subspace fitting equation is obtained as
Figure BDA0001786081700000038
Wherein tr represents the trace of the matrix, and the weight matrix satisfies
Figure BDA0001786081700000039
Figure BDA00017860817000000310
Is frequency of
Figure BDA00017860817000000311
The power of the corresponding noise is set to be,
Figure BDA00017860817000000312
is frequency of
Figure BDA00017860817000000313
And the diagonal matrix formed by large eigenvalues is decomposed by the characteristic of the corresponding signal covariance matrix. Combining a maximum likelihood equation and a weighted signal subspace fitting equation to design a novel broadband direction finding method, combining the maximum likelihood equation and the weighted signal subspace fitting equation together by different weights, and obtaining an angle estimation value of
Figure BDA00017860817000000314
Wherein w 1 +w 2 ＝1，w 1 And w 2 Is [0,1 ]]BetweenThe weighting factor of (2).
The specific process for initializing the parameters of the quantum dragonfly evolution mechanism in the step 2 is that the population scale of the quantum dragonfly evolution mechanism is
Figure BDA00017860817000000315
The maximum iteration number is G, the search space dimension is P, the neighborhood radius is r, and the step vector is
Figure BDA00017860817000000316
Wherein
Figure BDA0001786081700000041
The weight factors of five behaviors of the quantum dragonfly group are respectively
Figure BDA0001786081700000042
And the weight factor of the step size vector is w 3 The quantum position of the ith quantum dragonfly is
Figure BDA0001786081700000043
The i-th quantum dragonfly has the speed of
Figure BDA0001786081700000044
Wherein
Figure BDA0001786081700000045
t is the number of iterations, and initially t is 1.
The specific process of calculating the fitness of each quantum dragonfly in the step 3 is that in the broadband direction finding, the p-th dimension of the quantum position of the ith quantum dragonfly is mapped into the broadband direction finding by a formula
Figure BDA0001786081700000046
Wherein A is max At a maximum angle of 90 DEG, A min -90 ° is the minimum angle, P ═ 1,2, …, P; calculating the fitness value of the ith quantum dragonfly position, wherein the fitness function is
Figure BDA0001786081700000047
Determining the local optimal quantum position of the ith quantum dragonfly to be
Figure BDA0001786081700000048
The ith quantum dragonfly local minimum quantum position is
Figure BDA0001786081700000049
And globally optimal qubits of
Figure BDA00017860817000000410
The global worst quantum position is
Figure BDA00017860817000000411
The global optimal quantum position is a food source quantum position, and the global optimal quantum position is a natural enemy quantum position.
The specific steps of the step 4 are as follows:
and 4.1, updating the neighborhood radius and the quantum position vector and the quantum speed vector of the neighborhood quantum dragonflies, wherein each quantum dragonflies at the center of a circle with the radius of r, and when the Euclidean distance between the two quantum dragonflies is smaller than the neighborhood radius, the two quantum dragonflies are considered to be adjacent, otherwise, the two quantum dragonflies are not adjacent. The neighborhood radius is linearly increased along with the increase of the iteration times until the whole quantum dragonfly group is all adjacent, and the update formula of the neighborhood radius is
r t ＝(A max -A min )/4+(A max -A min )×t×2/G
The quantum position of the (i) th quantum dragonfly and the q th adjacent quantum dragonfly is
Figure BDA0001786081700000051
Wherein
Figure BDA0001786081700000052
Q is the total number of adjacent quantum dragonflies of the ith quantum dragonfly, and the speed of updating the qth adjacent quantum dragonfly of the ith quantum dragonfly is
Figure BDA0001786081700000053
Step 4.2, updating five behavior vectors and step length vectors of the quantum dragonfly group, wherein the updating formula of the ith quantum dragonfly collision avoidance behavior vector is
Figure BDA0001786081700000054
Wherein
Figure BDA0001786081700000055
The update formula of the alignment behavior vector is
Figure BDA0001786081700000056
The cohesive behavior vector is updated by the formula
Figure BDA0001786081700000057
The update formula of the foraging behavior vector is
Figure BDA0001786081700000058
The vector of the behavior of avoiding the enemy is updated by the formula
Figure BDA0001786081700000059
Updating each weight factor
Figure BDA00017860817000000510
And inertial weight w 3 The formula for updating the step vector of the ith quantum dragonfly is
Figure BDA00017860817000000511
And 4.3, updating the quantum rotary gate rotation angle and the quantum position vector of each quantum dragonfly, wherein when the ith quantum dragonfly in the quantum dragonfly group has an adjacent quantum dragonfly, the p-th dimension of the quantum rotary gate rotation angle is
Figure BDA00017860817000000512
Figure BDA0001786081700000061
Wherein
Figure BDA0001786081700000062
The ith dimension of the quantum dragonfly step vector is the p dimension of the quantum position update formula of the ith vector
Figure BDA0001786081700000063
When the ith quantum dragonfly in the equivalent quantum dragonfly group does not have an adjacent quantum dragonfly, the quantum dragonfly flies around the search space in a Le' vy flight mode, and the ith quantum dragonfly quantum revolving door rotation angle is the p-dimensionIs composed of
Figure BDA0001786081700000064
Its quantum position update formula is
Figure BDA0001786081700000065
The Le' vy function is calculated as
Figure BDA0001786081700000066
Wherein r is 1 ，r 2 Is [0,1 ]]The random number in (1+ eta) is Gamma function, and the calculation formula is Γ (1+ eta) ═ eta! And η is a constant.
The specific process of the step 5 is to update the quantum velocity vector and the quantum position vector of the quantum dragonfly, and the quantum velocity p-dimension update formula of the ith quantum dragonfly is
Figure BDA0001786081700000067
Wherein
Figure BDA0001786081700000068
The ith quantum position of the quantum dragonfly and the p-dimension updating formula is
Figure BDA0001786081700000069
Wherein w 4 Is the proportion of the previous generation quantum velocity, w 5 And w 6 Weight factors, c, of the locally optimal quantum position and the globally optimal quantum position, respectively 1 And c 2 Is at [0,1 ]]Randomly generated constants in between.
The concrete process of step 6 is to calculate the fitness value of all quantum dragonflies position, if the fitness value of the ith quantum dragonflies is greater than the already-stored fitness value, replace the originally-stored fitness value with the fitness value of the ith quantum dragonflies, and replace the originally-stored local optimum quantum position with the quantum position of the ith quantum dragonflies; and (3) calculating the maximum adaptability value of the quantum dragonfly group, if the current maximum adaptability value is larger than the originally stored maximum adaptability value, replacing the originally stored maximum adaptability value with the current maximum adaptability value, and using the quantum position of the quantum dragonfly with the maximum current adaptability value as the global optimal quantum position.
The invention has the beneficial effects that: the invention designs a quantum dragonfly evolution mechanism to carry out direction finding on the broadband signal, reduces the operation amount and the operation time, improves the convergence speed and the convergence precision and realizes high-precision direction finding; the broadband direction finding method designed by the invention can simultaneously estimate the direction of arrival of a coherent source and an independent source, and has excellent anti-noise performance and higher estimation success probability; the direction finding performance of the method is superior to that of a broadband direction finding method based on a particle swarm algorithm.
Drawings
FIG. 1 is a flow chart of a broadband direction finding method based on a quantum dragonfly evolution mechanism.
FIG. 2 is a plot of RMS error as an independent source versus signal-to-noise ratio.
FIG. 3 is a plot of root mean square error of coherent source versus signal to noise ratio.
Detailed Description
The invention is further described with reference to the accompanying drawings in which:
example 1
The invention relates to a broadband direction finding method combining a maximum likelihood equation and a weighted signal subspace fitting equation, and designing a quantum dragonfly evolution mechanism to solve a target function, wherein the broadband direction finding method based on the quantum dragonfly evolution mechanism comprises the following specific implementation steps:
step 1, establishing a broadband signal sampling model;
step 2, initializing parameters of a quantum dragonfly evolution mechanism;
step 3, calculating the fitness of each quantum dragonfly to obtain a local optimal quantum position and a local worst quantum position, and a global optimal quantum position and a global worst quantum position;
step 4, updating the radius of the field and the quantum position and the quantum speed of the neighborhood quantum dragonfly in the first half of the quantum dragonfly group, updating five behavior vectors and step length vectors of each quantum dragonfly, and updating the quantum rotation angle and the quantum position of each quantum dragonfly;
step 5, updating the quantum speed and the quantum position of each quantum dragonfly for the second half of the quantum dragonfly group;
step 6, calculating the fitness values of all the quantum dragonfly positions, and updating the local optimal quantum position and the local worst quantum position, and the global optimal quantum position and the global worst quantum position;
step 7, judging whether the maximum iteration times is reached, if not, returning to the step 4 for continuing; if the quantum dragonfly group global optimal quantum position is reached, mapping the quantum dragonfly group global optimal quantum position into an optimal position to obtain an angle to be estimated by the broadband direction of arrival estimation.
In the attached drawings, a broadband direction finding method based on a quantum dragonfly evolution mechanism is abbreviated as QDA, and a broadband direction finding method based on a particle swarm algorithm is abbreviated as PSO.
The process of establishing the broadband signal sampling model in the step 1 is that under the environment of Gaussian noise, broadband signals with P far fields respectively form a directional angle theta 1 ,θ 2 ,…,θ P The signal is incident on a certain antenna array in space, the antenna array is composed of M array elements, the distance between the array elements is d, the wavelength is lambda, and the bandwidth of the incident signal is B. With the first array element as the reference array element, the signal received by the mth array element can be expressed as
Figure BDA0001786081700000081
Wherein s is p (t) represents an incident direction of θ p Of the broadband signal n p (t) denotes additive noise on the m-th array element, a m,p Indicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
Figure BDA0001786081700000082
representing the time delay of the p source to the m array element; will observe the time T o Is divided into K subsections, and each subsection has a time T d I.e. by
Figure BDA0001786081700000083
Then the observation data are processed
Figure BDA00017860817000000817
Point discrete Fourier transform to obtain K groups of uncorrelated narrow band frequency domain components, sub-segment T d Compared with the signal and the noise which are relatively long in correlation time, the data after the discrete Fourier transform are irrelevant, and the obtained broadband model is
Figure BDA0001786081700000084
Figure BDA0001786081700000085
Figure BDA0001786081700000086
Figure BDA0001786081700000087
Figure BDA0001786081700000088
Figure BDA0001786081700000089
Are each z m (t)、s p (t)、n m (t) at the kth time subsection a frequency of
Figure BDA00017860817000000810
The fourier coefficients of the time of flight,
Figure BDA00017860817000000811
is a steering matrix of size M x P, where P directions are different, the matrix is full rank,
Figure BDA00017860817000000812
steering vectors called matrices
Figure BDA00017860817000000813
Wherein P is 1,2, …, P; processing data received by the array under conditions in which the signal is uncorrelated with noise, at each frequency point
Figure BDA00017860817000000814
The covariance matrix of the frequency domain sampled data of the sensor array is obtained as
Figure BDA00017860817000000815
Using the received data to obtain an orthogonal projection matrix of
Figure BDA00017860817000000816
An angle estimation value obtained from the maximum likelihood equation is
Figure BDA0001786081700000091
Performing characteristic decomposition on the covariance matrix to obtain a signal subspace
Figure BDA0001786081700000092
And noise subspace
Figure BDA0001786081700000093
Then, according to the condition that the space formed by the signal subspace and the space formed by the array flow pattern are the same, the angle estimation value of the weighted signal subspace fitting equation is obtained as
Figure BDA0001786081700000094
Wherein tr represents the trace of matrix, and the weight matrix satisfies
Figure BDA0001786081700000095
Figure BDA0001786081700000096
Is frequency of
Figure BDA0001786081700000097
The power of the corresponding noise is set to be,
Figure BDA0001786081700000098
is a frequency
Figure BDA0001786081700000099
And decomposing the characteristic of the corresponding signal covariance matrix, and forming a diagonal matrix by large eigenvalues. A novel broadband direction finding method is designed by combining a maximum likelihood equation and a weighted signal subspace fitting equation, the maximum likelihood equation and the weighted signal subspace fitting equation are combined together by different weights, and the obtained angle estimation value is
Figure BDA00017860817000000910
Wherein w 1 +w 2 ＝1，w 1 And w 2 Is [0,1 ]]A weighting factor in between.
The specific process for initializing the parameters of the quantum dragonfly evolution mechanism in the step 2 isThe quantum dragonfly group scale is
Figure BDA00017860817000000911
The maximum iteration number is G, the search space dimension is P, the neighborhood radius is r, and the step vector is
Figure BDA00017860817000000912
Wherein
Figure BDA00017860817000000913
The weight factors of five behaviors of the quantum dragonfly group are respectively
Figure BDA00017860817000000914
And the weight factor of the step size vector is w 3 The quantum position of the ith quantum dragonfly is
Figure BDA00017860817000000915
The i-th quantum dragonfly has the speed of
Figure BDA00017860817000000916
Wherein
Figure BDA00017860817000000917
t is the number of iterations, and initially t is 1.
The specific process of calculating the fitness of each quantum dragonfly in the step 3 is that in the broadband direction finding, the p-th dimension of the quantum position of the ith quantum dragonfly is mapped into the broadband direction finding by a formula
Figure BDA0001786081700000101
Wherein A is max At a maximum angle of 90 DEG, A min ＝-90(ii) minimum angle, P ═ 1,2, …, P; calculating the fitness value of the ith quantum dragonfly position, wherein the fitness function is
Figure BDA0001786081700000102
Determining the local optimal quantum position of the ith quantum dragonfly to be
Figure BDA0001786081700000103
The ith quantum dragonfly local minimum quantum position is
Figure BDA0001786081700000104
And globally optimal qubits of
Figure BDA0001786081700000105
The global worst quantum position is
Figure BDA0001786081700000106
The global optimal quantum position is a food source quantum position, and the global optimal quantum position is a natural enemy quantum position.
The specific steps of the step 4 are as follows:
and 4.1, updating the neighborhood radius and the quantum position vector and the quantum speed vector of the neighborhood quantum dragonflies, wherein each quantum dragonflies at the center of a circle with the radius of r, and when the Euclidean distance between the two quantum dragonflies is smaller than the neighborhood radius, the two quantum dragonflies are considered to be adjacent, otherwise, the two quantum dragonflies are not adjacent. The neighborhood radius is linearly increased along with the increase of the iteration times until the whole quantum dragonfly group is all adjacent, and the update formula of the neighborhood radius is
r t ＝(A max -A min )/4+(A max -A min )×t×2/G
The quantum position of the (i) th quantum dragonfly (q) adjacent to the quantum dragonfly is set as
Figure BDA0001786081700000107
Wherein
Figure BDA0001786081700000108
Q is the total number of adjacent quantum dragonflies of the ith quantum dragonfly, and the speed of updating the qth adjacent quantum dragonfly of the ith quantum dragonfly is
Figure BDA0001786081700000109
Step 4.2, updating five behavior vectors and step length vectors of the quantum dragonfly group, wherein the updating formula of the ith quantum dragonfly collision avoidance behavior vector is
Figure BDA0001786081700000111
Wherein
Figure BDA0001786081700000112
The updated formula of the alignment behavior vector is
Figure BDA0001786081700000113
The cohesive behavior vector is updated by the formula
Figure BDA0001786081700000114
The update formula of the foraging behavior vector is
Figure BDA0001786081700000115
The vector of the behavior of the enemy avoidance is updated into the formula
Figure BDA0001786081700000116
Updating each weight factor
Figure BDA0001786081700000117
And an inertial weight w 3 The formula for updating the step vector of the ith quantum dragonfly is
Figure BDA0001786081700000118
And 4.3, updating the quantum rotary gate rotation angle and the quantum position vector of each quantum dragonfly, wherein when the ith quantum dragonfly in the quantum dragonfly group has an adjacent quantum dragonfly, the p-th dimension of the quantum rotary gate rotation angle is
Figure BDA0001786081700000119
Figure BDA00017860817000001110
Wherein
Figure BDA00017860817000001111
The ith dimension of the quantum dragonfly step vector is the p dimension of the quantum position update formula of the ith vector
Figure BDA00017860817000001112
When the ith quantum dragonfly in the equivalent quantum dragonfly group does not have an adjacent quantum dragonfly, the quantum dragonfly flies around the search space in a Le' vy flight mode, and the p-th dimension of the rotation angle of the ith quantum dragonfly quantum rotary gate is
Figure BDA00017860817000001113
Its quantum position update formula is
Figure BDA00017860817000001114
The Le' vy function is calculated as
Figure BDA0001786081700000121
Wherein r is 1 ，r 2 Is [0,1 ]]The random number in (1+ eta) is Gamma function, and the calculation formula is Γ (1+ eta) ═ eta! And η is a constant.
The specific process of the step 5 is to update the quantum velocity vector and the quantum position vector of the quantum dragonfly, and the updating formula of the p-th dimension of the quantum velocity of the ith quantum dragonfly is
Figure BDA0001786081700000122
Wherein
Figure BDA0001786081700000123
The ith quantum position of the quantum dragonfly and the p-dimension updating formula is
Figure BDA0001786081700000124
Wherein w 4 Is the proportion of the previous generation quantum velocity, w 5 And w 6 Weight factors, c, of the locally optimal quantum position and the globally optimal quantum position, respectively 1 And c 2 Is at [0,1 ]]With randomly generated constants.
The concrete process of step 6 is to calculate the fitness value of all quantum dragonflies position, if the fitness value of the ith quantum dragonflies is greater than the already-stored fitness value, replace the originally-stored fitness value with the fitness value of the ith quantum dragonflies, and replace the originally-stored local optimum quantum position with the quantum position of the ith quantum dragonflies; and (3) calculating the maximum adaptability value of the quantum dragonfly group, if the current maximum adaptability value is larger than the originally stored maximum adaptability value, replacing the originally stored maximum adaptability value with the current maximum adaptability value, and using the quantum position of the quantum dragonfly with the maximum current adaptability value as the global optimal quantum position.
The simulation calculation is carried out on the invention, and the specific parameters of the model are set as follows:
the broadband far-field signal has the lowest frequency of 80Hz, the highest frequency of 180Hz, the antenna arrays are uniform linear arrays, the array element spacing is half wavelength, the number of the antennas is 8, the signal propagation speed is 1500m/s, the fast beat number is 1024, the number of the information sources is 2, the signal incidence angles are 20 degrees and 10 degrees respectively, the incidence signal is a linear frequency modulation signal, and the noise is Gaussian noise.
The parameters of the broadband direction finding method based on the quantum dragonfly algorithm are set as follows: quantum dragonfly population scale
Figure BDA0001786081700000125
The iteration number G is 60, the initial step vector xi is 0, the initial neighborhood radius r is 1.5, the collision avoidance behavior weight s is 0.2, the alignment behavior weight a is 0.2, the cohesion behavior weight c is 0.3, the food source weight f is 1, the natural enemy weight z is 1, and the step vector weight w is 3 0.8, 1.5 in Le' vy function.
Parameter setting of a broadband direction finding method based on a particle swarm algorithm: weight factor w 4 ＝1，w 5 ＝2，w 6 ＝2。
Fig. 2 and 3 are root mean square error and signal to noise ratio plots for an independent source and a coherent source, respectively. As can be seen from the simulation diagram, the root mean square error of the broadband direction finding based on the quantum dragonfly algorithm is smaller than that of the particle swarm algorithm no matter the source is an independent source or a coherent source.
Example 2
The invention relates to a broadband direction finding method based on a quantum dragonfly evolution mechanism, and belongs to the field of array signal processing.
Array signal processing has wide application in the fields of communication, radar, sonar and the like, and direction-of-arrival estimation is one of important research directions in the field of array signals. The broadband signal has the advantages of large amount of carried information, easy target signal detection, parameter estimation, characteristic extraction and the like, and the application of the broadband signals such as frequency hopping signals, spread spectrum signals, linear frequency modulation signals and the like in a communication system is more and more extensive. Therefore, it is more important to study the estimation of the direction of arrival of the broadband signal.
The maximum likelihood algorithm is to calculate a covariance matrix and an orthogonal projection matrix of a signal by processing received data, and then obtain a target function of the maximum likelihood algorithm through a series of operations. However, the objective function is a multidimensional nonlinear function related to the incident angle, the solving process is complex, and the calculation amount is large.
The weighted signal subspace fitting algorithm is to solve a signal subspace and a noise subspace by performing characteristic decomposition on a covariance matrix of a received signal, and then to solve a target function by fitting between the signal subspace of the received data and a subspace formed by actual signal guide vectors. The objective function is also a multidimensional nonlinear function, the solving process is complex, and the calculation amount is large.
According to the existing literature, the method proposed by the Luojing green in the electronic information countermeasure technology (2014, Vol.29, No.1, pp.16-20 published the wideband direction finding method based on the orthogonal projection transformation) has low convergence accuracy, Rixin, Liuwenhong in the computer engineering and application (2013, Vol.49, No.20, pp.227-229) published the wideband multi-signal direction finding method research based on the frequency domain correlation and SVM has large operand, low convergence accuracy and poor performance.
Although the method obtains a good result in the broadband direction finding problem, the method has low solving precision, poor convergence performance and large calculation amount, so a new broadband direction finding method needs to be designed to solve the problems.
The invention provides a broadband direction finding method combining a weighted signal subspace fitting equation and a maximum likelihood equation, and then a quantum dragonfly evolution mechanism is designed to solve a target function of the method. According to simulation results, the method realizes rapid high-precision direction finding of the independent information source and the coherent information source in a broadband environment.
The invention is realized by the following technical scheme, which mainly comprises the following steps:
the method comprises the following steps: under the environment of Gaussian noise, broadband signals with P far fields respectively have a directional angle theta 1 ,θ 2 ,…,θ P The signal is incident on a certain antenna array in space, the antenna array is composed of M array elements, the distance between the array elements is d, the wavelength is lambda, and the bandwidth of the incident signal is B. With the first array element as the reference array element, the signal received by the mth array element can be expressed as
Figure BDA0001786081700000141
Wherein s is p (t) the incident direction is θ p Of the broadband signal n p (t) denotes additive noise on the m-th array element, a m,p Indicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
Figure BDA0001786081700000142
representing the time delay for the p-th source to reach the m-th array element.
Will observe the time T o Is divided into K subsections, and each subsection has a time T d I.e. by
Figure BDA0001786081700000143
Then the observation data are processed
Figure BDA0001786081700000144
Point discrete Fourier transform to obtain K groups of uncorrelated narrow band frequency domain components, sub-segment T d Compared with the signal and noise correlation time, the data after the discrete Fourier transform is irrelevant, and the broadband model can be obtained as
Figure BDA0001786081700000145
In the formula
Figure BDA0001786081700000147
Figure BDA0001786081700000148
Are each z m (t)、s p (t)、n m (t) at the kth time subsection a frequency of
Figure BDA0001786081700000149
Fourier coefficients of time.
Figure BDA00017860817000001410
Is a steering matrix of size M × P, which is full rank when P directions are different;
Figure BDA00017860817000001411
Figure BDA00017860817000001424
referred to as the steering vector of the matrix.
Processing data received by the array under conditions in which the signal is uncorrelated with noise, at each frequency point
Figure BDA00017860817000001412
The covariance matrix of the frequency domain sampled data of the sensor array is obtained as
Figure BDA00017860817000001413
Using the received data to obtain an orthogonal projection matrix of
Figure BDA00017860817000001414
An angle estimation value obtained from the maximum likelihood equation is
Figure BDA00017860817000001415
Performing characteristic decomposition on the covariance matrix to obtain a signal subspace
Figure BDA00017860817000001416
Sum noise elementSpace(s)
Figure BDA00017860817000001417
Then according to the condition that the space formed by the signal subspace is the same as the space formed by the array flow pattern, obtaining an angle estimation value of a weighted signal subspace fitting equation as
Figure BDA00017860817000001418
Wherein tr represents the trace of the matrix, and the weight matrix satisfies
Figure BDA00017860817000001419
Figure BDA00017860817000001420
Is frequency of
Figure BDA00017860817000001421
The power of the corresponding noise is set to be,
Figure BDA00017860817000001422
is frequency of
Figure BDA00017860817000001423
And the diagonal matrix formed by large eigenvalues is decomposed by the characteristic of the corresponding signal covariance matrix. A novel broadband direction finding method is designed by combining a maximum likelihood equation and a weighted signal subspace fitting equation, the maximum likelihood equation and the weighted signal subspace fitting equation are combined together by different weights, and the obtained angle estimation value is
Figure BDA0001786081700000151
w 1 And w 2 Is [0,1 ]]A weighting factor in between.
Step two: initializing parameters of a quantum dragonfly evolution mechanism: the quantum dragonfly population scale is
Figure BDA0001786081700000152
The maximum iteration number is G, the search space dimension is P, the neighborhood radius is r, and the step vector is
Figure BDA0001786081700000153
The weight factors of five behaviors of the quantum dragonfly group are respectively
Figure BDA0001786081700000154
And the weight factor of the step size vector is w 3 The quantum position of the ith quantum dragonfly is
Figure BDA0001786081700000155
The i-th quantum dragonfly has the speed of
Figure BDA0001786081700000156
Wherein
Figure BDA0001786081700000157
t is the number of iterations, and initially t is 1.
Step three: and calculating the fitness of all the quantum dragonfly positions. In the broadband direction finding, the p-th dimension of the quantum position of the ith quantum dragonfly is mapped into the broadband direction finding formula
Figure BDA0001786081700000158
Wherein A is max At a maximum angle of 90 DEG, A min -90 ° is the minimum angle, P-1, 2, …, P. Calculating the fitness value of the ith quantum dragonfly position, wherein the fitness function is
Figure BDA0001786081700000159
Determining the local optimal quantum position of the ith quantum dragonfly to be
Figure BDA00017860817000001510
And the ith quantum dragonfly local minimum quantum position is
Figure BDA00017860817000001511
And globally optimal qubits of
Figure BDA00017860817000001512
And a global minimum quantum position of
Figure BDA00017860817000001513
The global optimal quantum position is a food source quantum position, and the global optimal quantum position is a natural enemy quantum position.
Step four: the first half of the quantum dragonfly group performs the following operations:
1) and updating the quantum position vector and the quantum velocity vector of the neighborhood radius and the neighborhood quantum dragonfly. Each quantum dragonfly is positioned at the center of a circle with the radius r, and when the Euclidean distance between the two quantum dragonflies is smaller than the radius of the neighborhood, the two quantum dragonflies are considered to be adjacent, otherwise, the two quantum dragonflies are not adjacent. The neighborhood radius is linearly increased along with the increase of the iteration times until the whole quantum dragonfly group is all adjacent, and the update formula of the neighborhood radius is r t ＝(A max -A min )/4+(A max -A min ) X t × 2/G; the quantum position of the (i) th quantum dragonfly and the q th adjacent quantum dragonfly is
Figure BDA00017860817000001514
Q is the total number of adjacent quantum dragonflies of the ith quantum dragonfly, and the speed of updating the qth adjacent quantum dragonfly of the ith quantum dragonfly is
Figure BDA00017860817000001515
2) And updating five behavior vectors and step vectors of the quantum dragonfly group. The updating formula of the ith quantum dragonfly collision avoidance behavior vector is
Figure BDA0001786081700000161
The updated formula of the alignment behavior vector is
Figure BDA0001786081700000162
The cohesive behavior vector is updated by the formula
Figure BDA0001786081700000163
The update formula of the foraging behavior vector is
Figure BDA0001786081700000164
The vector of the behavior of the enemy avoidance is updated into the formula
Figure BDA0001786081700000165
Updating each weight factor
Figure BDA0001786081700000166
And inertial weight w 3 . The step vector updating formula of the ith quantum dragonfly is
Figure BDA0001786081700000167
3) And updating the rotation angle and the quantum position vector of the quantum rotary gate of each quantum dragonfly. When the ith quantum dragonfly in the quantum dragonfly group has the adjacent quantum dragonfly, the p-th dimension of the rotation angle of the quantum rotary gate is
Figure BDA0001786081700000168
Figure BDA00017860817000001617
Wherein
Figure BDA0001786081700000169
The ith dimension of the quantum dragonfly step vector is the p dimension of the quantum position update formula of the ith vector
Figure BDA00017860817000001610
When the ith quantum dragonfly in the equivalent quantum dragonfly group does not have an adjacent quantum dragonfly, the quantum dragonfly flies around the search space in a Le' vy flight mode, and the p-th dimension of the rotation angle of the ith quantum dragonfly quantum rotary gate is
Figure BDA00017860817000001611
Its quantum position update formula is
Figure BDA00017860817000001612
The Le' vy function is calculated as
Figure BDA00017860817000001613
Figure BDA00017860817000001614
Wherein r is 1 ，r 2 Is [0,1 ]]The random number in Gamma function is Γ (1+ η), and its calculation formula is Γ (1+ η) ═ η! And η is a constant.
Step five: the second half of the quantum dragonfly population is operated as follows:
and updating the quantum velocity vector and the quantum position vector of the quantum dragonfly. The quantum speed dimension p of the ith quantum dragonfly is updated by the formula
Figure BDA00017860817000001615
The p-dimension updating formula of the quantum position of the ith quantum dragonfly is
Figure BDA00017860817000001616
Wherein w 4 Is the proportion of the previous generation quantum velocity, w 5 And w 6 Weight factors, c, of the locally optimal quantum position and the globally optimal quantum position, respectively 1 And c 2 Is at [0,1 ]]With randomly generated constants.
Step six: calculating the fitness value of all the quantum dragonflies, if the fitness value of the ith quantum dragonfly is larger than the stored fitness value, replacing the originally stored fitness value with the fitness value of the ith quantum dragonfly, and replacing the originally stored local optimal quantum position with the quantum position of the ith quantum dragonfly; and (3) calculating the maximum adaptability value of the quantum dragonfly group, if the current maximum adaptability value is larger than the originally stored maximum adaptability value, replacing the originally stored maximum adaptability value with the current maximum adaptability value, and using the quantum position of the quantum dragonfly with the maximum current adaptability value as the global optimal quantum position.
Step seven: judging whether the maximum iteration times is reached, if not, returning to the fourth step to continue the operation; if the estimated angle of the broadband direction of arrival is reached, mapping the global optimal quantum position of the quantum dragonfly group into the optimal position to obtain the estimated angle of the broadband direction of arrival.
Compared with the prior art, the invention has the following advantages:
(1) the invention designs a quantum dragonfly evolution mechanism to carry out direction finding on the broadband signal, reduces the operation amount and improves the convergence speed and the convergence precision.
(2) The broadband direction finding method designed by the invention can simultaneously estimate the direction of arrival of a coherent source and an independent source, and has excellent anti-noise performance and higher estimation success probability.
(3) Simulation results show that the direction finding performance of the broadband direction finding method is superior to that of the broadband direction finding method based on the particle swarm optimization.
FIG. 1 is a flow chart of a broadband direction finding method based on a quantum dragonfly evolution mechanism. The invention relates to a broadband direction finding method combining a maximum likelihood equation and a weighted signal subspace fitting equation, and a quantum dragonfly evolution mechanism is designed to solve a target function. The scheme adopted by the invention for solving the problems comprises the following steps:
the method comprises the following steps: under the environment of Gaussian noise, broadband signals with P far fields respectively have a directional angle theta 1 ,θ 2 ,…,θ P The signal is incident on a certain antenna array in space, the antenna array is composed of M array elements, the distance between the array elements is d, the wavelength is lambda, and the bandwidth of the incident signal is B. With the first array element as the reference array element, the signal received by the mth array element can be expressed as
Figure BDA0001786081700000171
Wherein s is p (t) the incident direction is θ p Of the broadband signal n p (t) denotes additive noise on the m-th array element, a m,p Indicating the signal strength at the m-th element as a function of the spatial loss from the p-th source to the various sensors,
Figure BDA0001786081700000172
representing the time delay for the p-th source to reach the m-th array element.
Will observe the time T o Divided into K subsections, each time being T d I.e. by
Figure BDA0001786081700000173
Then the observation data are processed
Figure BDA0001786081700000174
Point discrete Fourier transform to obtain K groups of uncorrelated narrow band frequency domain components, sub-segment T d Compared with the signal and noise correlation time, the data after the discrete Fourier transform is irrelevant, and the broadband model can be obtained as
Figure BDA0001786081700000175
In the formula
Figure BDA0001786081700000181
Figure BDA0001786081700000182
Are each z m (t)、s p (t)、n m (t) at the kth time subsection a frequency of
Figure BDA0001786081700000183
Fourier coefficients of time.
Figure BDA0001786081700000184
Is a steering matrix of size M × P, which is full rank when P directions are different;
Figure BDA0001786081700000185
Figure BDA00017860817000001825
referred to as the steering vector of the matrix.
Processing data received by the array under conditions where the signal is uncorrelated with noise, at each frequency point
Figure BDA0001786081700000186
The covariance matrix of the frequency domain sampled data of the sensor array is obtained as
Figure BDA0001786081700000187
Using the received data to obtain an orthogonal projection matrix of
Figure BDA0001786081700000188
An angle estimation value obtained from the maximum likelihood equation is
Figure BDA0001786081700000189
Performing characteristic decomposition on the covariance matrix to obtain a signal subspace
Figure BDA00017860817000001810
And noise subspace
Figure BDA00017860817000001811
Then, according to the condition that the space formed by the signal subspace and the space formed by the array flow pattern are the same, the angle estimation value of the weighted signal subspace fitting equation is obtained as
Figure BDA00017860817000001812
Wherein tr represents the trace of matrix, and the weight matrix satisfies
Figure BDA00017860817000001813
Figure BDA00017860817000001814
Is frequency of
Figure BDA00017860817000001815
The power of the corresponding noise is set to be,
Figure BDA00017860817000001816
is frequency of
Figure BDA00017860817000001817
And the diagonal matrix formed by large eigenvalues is decomposed by the characteristic of the corresponding signal covariance matrix. Designing a new broadband direction finding method by combining a maximum likelihood equation and a weighted signal subspace fitting equation, wherein the maximum likelihood equation and the weighted signal subspace fitting equation are differentAre combined together to obtain an angle estimate of
Figure BDA00017860817000001818
w 1 And w 2 Is [0,1 ]]A weighting factor in between.
Step two: initializing parameters of a quantum dragonfly evolution mechanism: the quantum dragonfly population scale is
Figure BDA00017860817000001819
The maximum iteration number is G, the search space dimension is P, the neighborhood radius is r, and the step vector is
Figure BDA00017860817000001820
The weight factors of five behaviors of the quantum dragonfly group are respectively
Figure BDA00017860817000001821
And the weight factor of the step size vector is w 3 The quantum position of the ith quantum dragonfly is
Figure BDA00017860817000001822
The i-th quantum dragonfly has the speed of
Figure BDA00017860817000001823
Wherein
Figure BDA00017860817000001824
t is the number of iterations, and initially t is 1.
Step three: and calculating the fitness of all the quantum dragonfly positions. In the broadband direction finding, the p-th dimension of the quantum position of the ith quantum dragonfly is mapped into the broadband direction finding formula
Figure BDA0001786081700000191
Wherein A is max At a maximum angle of 90 DEG, A min -90 ° is the minimum angle, P-1, 2, …, P. Calculating the fitness value of the ith quantum dragonfly position, wherein the fitness function is
Figure BDA0001786081700000192
Determining the local optimal quantum position of the ith quantum dragonfly to be
Figure BDA0001786081700000193
And the ith quantum dragonfly local minimum quantum position is
Figure BDA0001786081700000194
And globally optimal qubits of
Figure BDA0001786081700000195
And a global minimum quantum position of
Figure BDA0001786081700000196
The global optimal quantum position is a food source quantum position, and the global optimal quantum position is a natural enemy quantum position.
Step four: the first half of the quantum dragonfly group performs the following operations:
1) and updating the quantum position vector and the quantum velocity vector of the neighborhood radius and the neighborhood quantum dragonfly. Each quantum dragonfly is positioned at the center of a circle with the radius r, and when the Euclidean distance between the two quantum dragonflies is smaller than the radius of the neighborhood, the two quantum dragonflies are considered to be adjacent, otherwise, the two quantum dragonflies are not adjacent. The neighborhood radius is linearly increased along with the increase of the iteration times until the whole quantum dragonfly group is all adjacent, and the update formula of the neighborhood radius is r t ＝(A max -A min )/4+(A max -A min ) X t x 2/G; the quantum position of the (i) th quantum dragonfly and the q th adjacent quantum dragonfly is
Figure BDA0001786081700000197
Q is the total number of adjacent quantum dragonflies of the ith quantum dragonfly, and the speed of updating the qth adjacent quantum dragonfly of the ith quantum dragonfly is
Figure BDA0001786081700000198
2) And updating five behavior vectors and step vectors of the quantum dragonfly group. Ith quantum dragonfly collision avoidance behavior directionThe updated formula of the quantity is
Figure BDA0001786081700000199
The update formula of the alignment behavior vector is
Figure BDA00017860817000001910
The cohesive behavior vector is updated by the formula
Figure BDA00017860817000001911
The update formula of the foraging behavior vector is
Figure BDA00017860817000001912
The vector of the behavior of avoiding the enemy is updated by the formula
Figure BDA00017860817000001913
Updating each weight factor
Figure BDA00017860817000001914
And inertial weight w 3 . The ith quantum dragonfly step vector updating formula is
Figure BDA00017860817000001915
3) And updating the rotation angle and the quantum position vector of the quantum rotary gate of each quantum dragonfly. When the ith quantum dragonfly in the quantum dragonfly group has the adjacent quantum dragonfly, the p-th dimension of the rotation angle of the quantum rotary gate is
Figure BDA0001786081700000201
Figure BDA00017860817000002010
Wherein
Figure BDA0001786081700000202
The ith dimension of the quantum dragonfly step vector is the p dimension of the quantum position update formula of the ith vector
Figure BDA0001786081700000203
Equivalent weightWhen the ith quantum dragonfly in the sub dragonfly group does not have an adjacent quantum dragonfly, the quantum dragonfly flies around the search space in a Le' vy flight mode, and the p-th dimension of the rotation angle of the ith quantum dragonfly quantum revolving door is
Figure BDA0001786081700000204
Its quantum position update formula is
Figure BDA0001786081700000205
The Le' vy function is calculated as
Figure BDA0001786081700000206
Figure BDA0001786081700000207
Wherein r is 1 ，r 2 Is [0,1 ]]The random number in Gamma function is Γ (1+ η), and its calculation formula is Γ (1+ η) ═ η! And η is a constant.
Step five: the second half of the quantum dragonfly population performs the following operations:
and updating the quantum velocity vector and the quantum position vector of the quantum dragonfly. The p-th dimension updating formula of the quantum speed of the ith quantum dragonfly is
Figure BDA0001786081700000208
The p-dimension updating formula of the quantum position of the ith quantum dragonfly is
Figure BDA0001786081700000209
Wherein w 4 Is the proportion of the previous generation quantum velocity, w 5 And w 6 Weight factors, c, of the locally optimal quantum position and the globally optimal quantum position, respectively 1 And c 2 Is at [0,1 ]]With randomly generated constants.
Step six: calculating the fitness value of all the quantum dragonflies, if the fitness value of the ith quantum dragonfly is larger than the stored fitness value, replacing the originally stored fitness value with the fitness value of the ith quantum dragonfly, and replacing the originally stored local optimal quantum position with the quantum position of the ith quantum dragonfly; and (3) calculating the maximum adaptability value of the quantum dragonfly group, if the current maximum adaptability value is larger than the originally stored maximum adaptability value, replacing the originally stored maximum adaptability value with the current maximum adaptability value, and using the quantum position of the quantum dragonfly with the maximum current adaptability value as the global optimal quantum position.
Step seven: judging whether the maximum iteration times is reached, if not, returning to the step four to continue the operation; if the estimated angle of the broadband direction of arrival is reached, mapping the global optimal quantum position of the quantum dragonfly group into the optimal position to obtain the estimated angle of the broadband direction of arrival.
The specific parameters of the model are set as follows:
the broadband far-field signal has the lowest frequency of 80Hz, the highest frequency of 180Hz, the antenna array is a uniform linear array, the array element spacing is half wavelength, the number of the antennas is 8, the signal propagation speed is 1500m/s, the fast beat number is 1024, the number of the information sources is 2, the signal incidence angles are 20 degrees and 10 degrees respectively, the incidence signal is a linear frequency modulation signal, and the noise is Gaussian noise.
The parameters of the broadband direction finding method based on the quantum dragonfly algorithm are set as follows: quantum dragonfly population scale
Figure BDA0001786081700000211
The iteration number G is 60, the initial step vector xi is 0, the initial neighborhood radius r is 1.5, the collision avoidance behavior weight s is 0.2, the alignment behavior weight a is 0.2, the cohesion behavior weight c is 0.3, the food source weight f is 1, the natural enemy weight z is 1, and the step vector weight w is 3 0.8, 1.5 in Le' vy function.
Parameter setting of a broadband direction finding method based on a particle swarm algorithm: weight factor w 4 ＝1，w 5 ＝2，w 6 ＝2。
Fig. 2 and 3 are root mean square error and signal to noise ratio plots for an independent source and a coherent source, respectively. As can be seen from the simulation diagram, the root mean square error of the broadband direction finding based on the quantum dragonfly algorithm is smaller than that of the particle swarm algorithm no matter the source is an independent source or a coherent source.
The invention utilizes a quantum dragonfly evolution mechanism to estimate the direction of arrival of the broadband signal, and solves the defects of complex solving process, large calculation amount, low convergence precision and the like of the traditional method. The method comprises the steps of establishing a mathematical sampling model of the broadband signal; initializing a quantum dragonfly population; calculating the fitness of each quantum dragonfly to obtain a local optimal quantum position, a local worst quantum position, a global optimal quantum position and a global worst quantum position; updating the neighborhood radius, the quantum position and the quantum speed of the neighborhood quantum dragonfly, the behavior vector and the step vector of each quantum dragonfly, and the rotation angle and the quantum position of the quantum rotary gate of each quantum dragonfly; updating the quantum rotation angle and the quantum position of each quantum dragonfly; calculating the fitness of each quantum dragonfly, and updating the local optimal quantum position, the local worst quantum position, the global optimal quantum position and the global worst quantum position; judging whether the maximum iteration times is reached; and outputting the global optimal quantum position and mapping the global optimal quantum position to the broadband direction finding. The invention carries out direction finding on the broadband signal by using a quantum dragonfly evolution mechanism, reduces the operation amount and the operation time, obtains higher convergence precision and higher convergence speed, effectively solves some problems in the traditional direction finding method, and realizes high-precision direction finding.

Claims (1)

1. A broadband direction finding method based on a quantum dragonfly evolution mechanism is characterized by comprising the following specific implementation steps:
step 1, establishing a broadband signal sampling model;
step 2, initializing parameters of a quantum dragonfly evolution mechanism;
step 3, calculating the fitness of each quantum dragonfly to obtain a local optimal quantum position and a local worst quantum position, and a global optimal quantum position and a global worst quantum position;
step 4, updating the radius of the field and the quantum position and the quantum speed of the neighborhood quantum dragonfly in the first half of the quantum dragonfly group, updating five behavior vectors and step length vectors of each quantum dragonfly, and updating the quantum rotation angle and the quantum position of each quantum dragonfly;
step 5, updating the quantum speed and the quantum position of each quantum dragonfly for the second half of the quantum dragonfly group;
step 6, calculating the fitness values of all the quantum dragonfly positions, and updating the local optimal quantum position and the local worst quantum position, and the global optimal quantum position and the global worst quantum position;
step 7, judging whether the maximum iteration times is reached, if not, returning to the step 4 for continuing; if the global optimal quantum position of the quantum dragonfly group is reached, mapping the global optimal quantum position of the quantum dragonfly group into an optimal position to obtain an angle to be estimated by the broadband direction of arrival estimation;
the process of establishing the broadband signal sampling model in the step 1 is that under the environment of Gaussian noise, broadband signals with P far fields respectively form a directional angle theta 1 ,θ 2 ,…,θ P The signal is incident to a certain antenna array in space, the antenna array consists of M array elements, the spacing between the array elements is d, the wavelength is lambda, and the bandwidth of an incident signal is B; the first array element is taken as a reference array element, and the signal received by the mth array element is expressed as
Figure FDA0003626282530000011
Wherein s is p (t) the incident direction is θ p Of the broadband signal n p (t) denotes additive noise on the m-th array element, a m,p Indicating the signal strength present at the mth array element with different spatial losses from the pth source to the various sensors,
Figure FDA0003626282530000012
representing the time delay of the p source to the m array element; will observe the time T o Is divided into K subsections, and each subsection has a time T d I.e. by
Figure FDA0003626282530000013
Then the observation data are processed
Figure FDA0003626282530000014
Point discrete Fourier transform to obtain K groups of uncorrelated narrow band frequency domain components, sub-segment T d Compared with the signal and the noise which are relatively long in correlation time, the data after the discrete Fourier transform are irrelevant, and the obtained broadband model is
Figure FDA0003626282530000015
Figure FDA0003626282530000016
Figure FDA0003626282530000017
Figure FDA0003626282530000021
Figure FDA0003626282530000022
Figure FDA0003626282530000023
Are each z m (t)、s p (t)、n m (t) at the kth time sub-segment, at a frequency of
Figure FDA0003626282530000024
The fourier coefficients of the time of flight,
Figure FDA0003626282530000025
is a steering matrix of size M x P, where P directions are different, the matrix is full rank,
Figure FDA0003626282530000026
steering vectors called matrices
Figure FDA0003626282530000027
Wherein P is 1,2, …, P; processing data received by the array under conditions where the signal is uncorrelated with noise, at each frequency point
Figure FDA0003626282530000028
The covariance matrix of the frequency domain sampled data of the sensor array is obtained as
Figure FDA0003626282530000029
Using the received data to obtain an orthogonal projection matrix of
Figure FDA00036262825300000210
An angle estimation value obtained from the maximum likelihood equation is
Figure FDA00036262825300000211
Performing characteristic decomposition on the covariance matrix to obtain a signal subspace
Figure FDA00036262825300000212
And noise subspace
Figure FDA00036262825300000213
Then, according to the condition that the space formed by the signal subspace and the space formed by the array flow pattern are the same, the angle estimation value of the weighted signal subspace fitting equation is obtained as
Figure FDA00036262825300000214
Wherein tr represents the trace of the matrix, and the weight matrix satisfies
Figure FDA00036262825300000215
Figure FDA00036262825300000216
Is frequency of
Figure FDA00036262825300000217
The power of the corresponding noise is set to be,
Figure FDA00036262825300000218
is frequency of
Figure FDA00036262825300000219
The diagonal matrix formed by large eigenvalues is decomposed by the characteristic of the corresponding signal covariance matrix; a novel broadband direction finding method is designed by combining a maximum likelihood equation and a weighted signal subspace fitting equation, the maximum likelihood equation and the weighted signal subspace fitting equation are combined together by different weights, and the obtained angle estimation value is
Figure FDA00036262825300000220
Wherein w 1 +w 2 ＝1，w 1 And w 2 Is [0,1 ]]A weighting factor in between;
the specific process for initializing the parameters of the quantum dragonfly evolution mechanism in the step 2 is that the population scale of the quantum dragonfly evolution mechanism is
Figure FDA0003626282530000031
The maximum iteration number is G, the search space dimension is P, the neighborhood radius is r, and the step vector is
Figure FDA0003626282530000032
Wherein
Figure FDA0003626282530000033
The weight factors of five behaviors of the quantum dragonfly group are respectively
Figure FDA0003626282530000034
And the weight factor of the step size vector is w 3 The quantum position of the ith quantum dragonfly is
Figure FDA0003626282530000035
The i-th quantum dragonfly has the speed of
Figure FDA0003626282530000036
Wherein
Figure FDA0003626282530000037
t is iteration times, and the initial time t is 1;
the specific process of calculating the fitness of each quantum dragonfly in the step 3 is that in the broadband direction finding, the p-th dimension of the quantum position of the ith quantum dragonfly is mapped into the broadband direction finding by a formula
Figure FDA0003626282530000038
Wherein A is max At a maximum angle of 90 DEG, A min -90 ° is the minimum angle, P ═ 1,2, …, P; computing the ith quantum dragonflyA fitness value of the dragonfly position as a function of
Figure FDA0003626282530000039
Determining the local optimal quantum position of the ith quantum dragonfly to be
Figure FDA00036262825300000310
The ith quantum dragonfly local minimum quantum position is
Figure FDA00036262825300000311
And globally optimal qubits of
Figure FDA00036262825300000312
The global worst quantum position is
Figure FDA00036262825300000313
The global optimal quantum position is a food source quantum position, and the global optimal quantum position is a natural enemy quantum position;
the specific steps of the step 4 are as follows:
step 4.1, updating a neighborhood radius and a quantum position vector and a quantum velocity vector of a neighborhood quantum dragonfly, wherein each quantum dragonfly is positioned at the center of a circle with the radius r, and when the Euclidean distance between the two quantum dragonflies is smaller than the neighborhood radius, the two quantum dragonflies are considered to be adjacent, otherwise, the two quantum dragonflies are not adjacent; the neighborhood radius is linearly increased along with the increase of the iteration times until the whole quantum dragonfly group is all adjacent, and the update formula of the neighborhood radius is
r t ＝(A max -A min )/4+(A max -A min )×t×2/G
The quantum position of the (i) th quantum dragonfly and the q th adjacent quantum dragonfly is
Figure FDA0003626282530000041
Wherein
Figure FDA0003626282530000042
Q is the total number of adjacent quantum dragonflies of the ith quantum dragonfly, and the speed of updating the qth adjacent quantum dragonfly of the ith quantum dragonfly is
Figure FDA0003626282530000043
Step 4.2, updating five behavior vectors and step length vectors of the quantum dragonfly group, wherein the updating formula of the ith quantum dragonfly collision avoidance behavior vector is
Figure FDA0003626282530000044
Wherein
Figure FDA0003626282530000045
The update formula of the alignment behavior vector is
Figure FDA0003626282530000046
The cohesive behavior vector is updated by the formula
Figure FDA0003626282530000047
The update formula of the foraging behavior vector is
Figure FDA0003626282530000048
The vector of the behavior of avoiding the enemy is updated by the formula
Figure FDA0003626282530000049
Updating each weight factor
Figure FDA0003626282530000051
And inertial weight w 3 The step vector updating formula of the ith quantum dragonfly is
Figure FDA0003626282530000052
And 4.3, updating the quantum rotation angle and the quantum position vector of each quantum dragonfly, wherein when the ith quantum dragonfly in the quantum dragonfly group has an adjacent quantum dragonfly, the p-dimension of the quantum rotation angle is
Figure FDA0003626282530000053
P is 1,2, …, P, wherein
Figure FDA0003626282530000054
The ith dimension of the quantum dragonfly step vector is the p dimension of the quantum position update formula of the ith vector
Figure FDA0003626282530000055
When the ith quantum dragonfly in the equivalent quantum dragonfly group does not have an adjacent quantum dragonfly, the quantum dragonfly flies around the search space in a Le' vy flight mode, and the pth dimension of the quantum rotation angle of the ith quantum dragonfly is
Figure FDA0003626282530000056
Its quantum position update formula is
Figure FDA0003626282530000057
The Le' vy function is calculated according to the formula
Figure FDA0003626282530000058
Wherein r is 1 ，r 2 Is [0,1 ]]The random number in (1+ eta) is Gamma function, and the calculation formula is Γ (1+ eta) ═ eta! η is a constant;
the specific process of the step 5 is to update the quantum velocity vector and the quantum position vector of the quantum dragonfly, and the quantum velocity p-dimension update formula of the ith quantum dragonfly is
Figure FDA0003626282530000059
Wherein
Figure FDA00036262825300000510
The ith quantum position of the quantum dragonfly and the p-dimension updating formula is
Figure FDA00036262825300000511
Wherein w 4 Is the proportion of the previous generation quantum velocity, w 5 And w 6 Weight factors, c, of the locally optimal quantum position and the globally optimal quantum position, respectively 1 And c 2 Is at [0,1 ]]A randomly generated constant therebetween;
the concrete process of step 6 is to calculate the fitness value of all quantum dragonflies position, if the fitness value of the ith quantum dragonflies is greater than the already-stored fitness value, replace the originally-stored fitness value with the fitness value of the ith quantum dragonflies, and replace the originally-stored local optimum quantum position with the quantum position of the ith quantum dragonflies; and (3) calculating the maximum adaptability value of the quantum dragonfly group, if the current maximum adaptability value is larger than the originally stored maximum adaptability value, replacing the originally stored maximum adaptability value with the current maximum adaptability value, and using the quantum position of the quantum dragonfly with the maximum current adaptability value as the global optimal quantum position.
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