CN109376329B - Array amplitude and phase error correction method based on quantum bird swarm evolution mechanism - Google Patents
Array amplitude and phase error correction method based on quantum bird swarm evolution mechanism Download PDFInfo
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Abstract
The invention belongs to the field of array signal processing, and particularly relates to a method for correcting array amplitude and phase errors based on a quantum bird swarm evolution mechanism. The method comprises the steps of correcting a phase error and correcting an amplitude error; the steps of each correction after establishing a received data model by using a known independent information source are as follows: initializing a quantum bird group; calculating the fitness of the quantum position of each quantum bird to obtain the local optimal quantum position of each quantum bird and the global optimal quantum position of the quantum bird group; updating the quantum position by updating the quantum rotation angle of each quantum bird; calculating the fitness of each quantum bird after the quantum position is updated, and updating the local optimal quantum position of each quantum bird and the global optimal quantum position of the quantum bird group; judging whether the maximum iteration times is reached; and outputting the global optimal quantum position and mapping the global optimal quantum position into a phase or amplitude-phase error matrix. The invention only needs a known auxiliary information source, has simple algorithm model and less operation amount, and has the advantages of high convergence speed and high convergence precision.
Description
Technical Field
The invention belongs to the field of array signal processing, and particularly relates to a method for correcting array amplitude and phase errors based on a quantum bird swarm evolution mechanism.
Background
Estimation of the direction of arrival of a signal is an important research problem in array signal processing. The MUSIC algorithm is a direction of arrival estimation algorithm based on feature decomposition, and has high estimation precision and resolution capability when an array is an ideal model, but the performance of the algorithm is obviously reduced due to errors in the array in practical application.
Most array errors are errors of amplitude and phase, wherein the amplitude error causes the height of a spectral peak to change, and the phase error causes the position of the spectral peak to change, so that the method has important significance for correcting the amplitude and phase errors of the array.
According to the existing literature, the method provided by the new array amplitude-phase error correction method based on rotation measurement, published by cheng feng et al in the journal of electronics and information (2017, Vol.39, No.8, pp.1899-1905), has the disadvantages of complex algorithm model, large calculated amount and low correction precision. The method proposed by Yangyong et al in the array model active correction method based on the simulated annealing algorithm published in the university of defense science and technology (2011, Vol.33, No.1, pp.91-94) has the disadvantages of slow convergence rate and long operation time.
Although the above-mentioned array amplitude and phase error correction method achieves better results, the algorithm model is more complex and the calculation amount is larger, so a new array amplitude and phase error correction method needs to be designed to solve the problems.
Disclosure of Invention
The invention aims to provide a method for correcting array amplitude and phase errors based on a quantum bird swarm evolution mechanism, which is high in convergence speed and convergence precision.
A method for correcting array amplitude and phase errors based on a quantum bird swarm evolution mechanism specifically comprises the following steps:
Step 3, calculating the fitness of the quantum positions of all the quantum birds, and calculating the quantum position of the ith quantum bird
Mapping to a phase error matrix
Respectively, the M-th array element phase error minimum value and the M-th array element phase error maximum value, wherein M is 1,2, … and M;
step 4, updating the quantum position of each quantum bird, wherein the quantum bird group has three behaviors, namely flight behavior, foraging behavior and warning behavior;
step 6, updating the local optimal quantum position and the global optimal quantum position of each quantum bird;
step 7, judging whether the iteration time t reaches the maximum iteration time G; if yes, judging whether the phase error is corrected, if yes, executing a step 8; if not, executing the step 10, if the maximum iteration number is not reached, making t equal to t +1, and returning to the step 4 to continue executing;
step 8, outputting the global optimal quantum position of the quantum bird group, and mapping the global optimal quantum position into a phase error
Is the optimal value of the phase error estimation of the mth array element, M is 1,2, …, M;
and step 10, outputting the global optimal quantum position of the quantum bird group, and mapping the global optimal quantum position into an amplitude-phase error matrix.
The method for correcting the array amplitude-phase error based on the quantum bird swarm evolution mechanism specifically comprises the following steps of 1, establishing a spatial uniform linear array, wherein the number of array elements is M, the spacing between the array elements is d, the wavelength is lambda, a narrow-band far-field signal is incident at a direction angle theta, the noise is Gaussian noise, and the receiving k-th snapshot data by the array can be expressed as follows: y (k) ═ as (k) + n (k), where y (k) ═ y 1 (k),y 2 (k),…,y M (k)] T ，y m (k) Is the receiving signal of the m-th array element, s (k) is the narrow-band far-field input signal, n (k) ═ n 1 (k),n 2 (k),…,n M (k)] T Is a Gaussian white noise vector, n m (k) The M is white Gaussian noise, M is 1,2, … and M, and is independent of the signal source, when the array elements have no amplitude phase error, the array steering vector is
When the array elements have amplitude phase errors, the array steering vector is a (theta) to gamma a 0 (theta) in the formula
As a diagonal matrix, p m 、
Is the amplitude error of the m-th array element,Phase error, M-1, 2, …, M; using the first array element as the reference array element, the rho can be known 1 ＝1，
And carrying out phase error correction.
In the method for correcting the array amplitude-phase error based on the quantum bird swarm evolution mechanism, the fitness function in the step 3 is as follows:
covariance matrix of received data
Estimate, where L is the fast beat number and R is U for R feature decomposition S ∑ S U S +U N ∑ N U N ,U S Being a signal subspace, U N In order to make the noise subspace, the local optimal quantum position of the ith quantum bird is set as
At the beginning of the process, t is 0,
i＝1,2,…,N b global initial optimal qubits of a quantum bird population
The method for correcting the array amplitude-phase error based on the quantum bird swarm evolution mechanism specifically comprises the following steps of: setting the flying distance as F, F belongs to [0,2 ]]Quantum bird groups every F q The second iteration flies to another place when the iteration number t is F q When the number is integral multiple, the quantum bird group selects flight behavior; when the quantum bird group flies to a new place to search for food, one part of the quantum birds become producers to search for food, and the other part of the quantum birds become discussers to follow the producers to search for food. The quantum bird population fitness is arranged from high to low, the first 20% of the quantum birds become producers, and the rest become discussionThe first step is to obtain a first product; for the producer, the m-dimension updating formula of the quantum rotation angle of the ith quantum bird is
c 1 Is a constant of a positive number,
is [0,1 ]]Random number of (i) 2,3, …, N b M is 1,2, …, M; for the entrepreneur, the mth dimension updating formula of the quantum rotation angle of the ith quantum bird is
Wherein
Represents the m-dimension quantum position of the q-th quantum bird in the producer in the t iteration,
is [0,1 ]]M is 1,2, …, M.
The method for correcting the array amplitude-phase error based on the quantum bird swarm evolution mechanism specifically comprises the following steps of in step 4: when the number of iterations t is not F q When is integral multiple of
Is [0,1 ]]Constant of [ 1 ], randomly generated [0,1 ]]Random number in between
When in use
When the ith quantum bird selects foraging behavior, the mth dimension updating formula of the quantum rotation angle of the ith quantum bird is
c 2 、c 3 Is a constant of a positive number of bits,
is [0,1 ]]M is 1,2, …, M.
The method for correcting the array amplitude and phase errors based on the quantum bird swarm evolution mechanism specifically comprises the following steps of: when the number of iterations t is not F q Is an integer multiple of
Then, the i-th quantum bird selects the alert behavior, and the m-dimension updating formula of the quantum rotation angle of the i-th quantum bird is as follows
Wherein
Is [0,2 ]]A constant value of (a) to (b),
is uniformly distributed in [0,1 ]]The number of the cells between (c) and (d),
is uniformly distributed in [ -1,1 [)]The number of the intermediate positions is equal to or greater than,
is the average of the local optimal quantum positions of all the quantum birds in the t-th iteration,
for the sum of the fitness of the local optimal quantum positions of all the quantum birds in the t iteration,
is the t th iteration
Only the locally optimal quantum position of the quantum bird,
is as follows
The fitness of the locally optimal quantum position of the quantum-only bird,
the fitness of the local optimal quantum position of the ith quantum bird is shown, and epsilon is the minimum normal number generated by a computer.
Step 6 specifically includes calculating an updated fitness value of the quantum position of each quantum bird, if the fitness value is larger than the fitness value of the local optimal quantum position of each quantum bird, updating the local optimal quantum position by using the updated quantum position, and otherwise, keeping the local optimal quantum position of the previous generation to the next generation; and calculating the maximum value of the fitness after the quantum positions of the quantum bird group are updated, if the maximum value of the fitness is greater than the fitness of the globally optimal quantum position, updating the globally optimal quantum position by using the corresponding quantum position, otherwise, keeping the globally optimal quantum position of the previous generation to the next generation.
In the method for correcting the array amplitude-phase error based on the quantum bird swarm evolution mechanism, step 9 specifically comprises the initialization of the quantum bird swarm evolution mechanism parameters for solving the amplitude error, and the quantum position of the ith quantum bird is
Randomly generating the quantum positions of all the quantum birds
Wherein the order
The amplitude error of the first array element of the mapping is 1, i is 1,2, …, N b . Will be provided with
Mapping to amplitude-phase error matrix
Respectively, the minimum value and the maximum value of the amplitude error of the mth array element, wherein M is 1,2, … and M; using fitness function
Calculating the fitness, and setting the local optimal quantum position of the ith quantum bird to be
The overall initial optimal quantum position of the quantum bird group is
And step four is executed.
The invention has the beneficial effects that:
the invention solves the problem of array amplitude-phase error correction, designs the quantum bird swarm machine as an evolution strategy, has the advantages of high convergence speed and high convergence precision, and can be popularized and applied to other continuous problems. Meanwhile, the invention only needs a known auxiliary information source, and has simple algorithm model and less computation. Simulation results also show that compared with the array amplitude-phase error correction method based on the particle swarm optimization, the method can obtain a more accurate amplitude-phase error matrix, and can effectively correct the steering vector or the steering matrix during direction finding.
Drawings
FIG. 1 is a flow chart of an array amplitude and phase error correction method based on a quantum bird swarm evolution mechanism;
FIG. 2 is a plot of phase RMS error versus signal-to-noise ratio;
FIG. 3 is a plot of RMS error amplitude versus signal-to-noise ratio;
FIG. 4 shows the measured azimuth angle changes of the two signal sources before and after correction by using the amplitude-phase error correction method based on the quantum-bird swarm evolution mechanism under the conditions that the azimuth angles of the two signal sources are respectively 10 degrees, 20 degrees and the signal-to-noise ratio is 5 dB;
FIG. 5 shows the measured azimuth angle changes of the signal sources before and after correction by using the amplitude-phase error correction method based on the quantum-bird swarm evolution mechanism under the conditions that the azimuth angles of the three signal sources are respectively 10 degrees, 20 degrees and 30 degrees, and the signal-to-noise ratio is 5 dB.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
For convenience of description, the array amplitude and phase error correction method based on the quantum bird swarm evolution mechanism is abbreviated as QBSA, and the array amplitude and phase error correction method based on the particle swarm optimization is abbreviated as PSO.
As shown in fig. 1, which is a flow chart of an array amplitude and phase error correction method based on a quantum bird swarm evolution mechanism, the invention adopts the quantum bird swarm evolution mechanism to correct the array amplitude and phase error, and the technical scheme comprises the following steps:
And 2, initializing parameters of a quantum bird group evolution mechanism for solving the phase error. The quantum bird group size is N b The maximum iteration number is G, and the quantum position of the ith quantum bird is
Wherein t is the number of iterations, the quantum positions of all the quantum birds are randomly generated to satisfy
Wherein the order
The phase error of the first mapped array element is 0rad, i is 1,2, …, N b 。
And 3, calculating the fitness of the quantum positions of all the quantum birds. Quantum position of ith quantum bird
Mapping to a phase error matrix
The minimum value and the maximum value of the M-th array element phase error are respectively, and M is 1,2, … and M. The fitness function is:
covariance matrix of received data
Estimate, where L is the fast beat number and R is U for R feature decomposition S ∑ S U S +U N ∑ N U N ,U S Is a signal subspace, U N Is the noise subspace. Let the i-th quantum bird have the local optimal quantum position as
Initially, t is equal to 0 and,
the global initial optimal quantum position of the quantum bird group is
And 4, updating the quantum position of each quantum bird. The quantum bird group has three behaviors, namely a flying behavior, a foraging behavior and a warning behavior.
Flight behavior: let the flying distance be F, F ∈ [0,2 ]]Quantum bird groups every F q The number of iterations is F q And when the number is integral multiple of the number, the quantum bird group selects flight behavior. When the quantum bird group flies to a new place to search food, one part of the quantum birds becomes producers to search food, and the other part of the quantum birds becomes entrepreneurs to follow the producers to search food. Quantum bird population fitness is arranged from high to low, the first 20% of quantum birds become producers, and the rest become discussers. For the producer, the m-dimension updating formula of the quantum rotation angle of the ith quantum bird is
c 1 Is a constant of a positive number of bits,
is [0,1 ]]I is 2,3, …, N b M is 1,2, …, M; for the entrepreneur, the mth dimension updating formula of the quantum rotation angle of the ith quantum bird is
Wherein
Represents the m-dimension quantum position of the q-th quantum bird in the producer in the t iteration,
is [0,1 ]]M is 1,2, …, M.
Foraging behavior: when the number of iterations t is not F q When the integer multiple of
Is [0,1 ]]Constant between, randomly generated [0,1 ]]Random number in between
When in use
When the foraging behavior is selected by the ith quantum bird. The mth dimension updating formula of the quantum rotation angle of the ith quantum bird is
c 2 、c 3 Is a constant of a positive number of bits,
is [0,1 ]]M is 1,2, …, M.
Alert behavior: when the number of iterations t is not F q Is an integer multiple of
And in time, the i-th quantum bird selects the alert behavior. The mth dimension updating formula of the quantum rotation angle of the ith quantum bird is
Wherein
Is [0,2 ]]A constant value of (a) to (b),
to be uniformly divided intoIs distributed on [0,1 ]]The number of the intermediate positions is equal to or greater than,
is uniformly distributed in [ -1,1 [)]The number of the intermediate positions is equal to or greater than,
is the average of the local optimal quantum positions of all the quantum birds in the t-th iteration,
the sum of the fitness of the local optimal quantum positions of all the quantum birds in the t-th iteration,
is the t th iteration
Only the locally optimal quantum position of the quantum bird,
is as follows
The fitness of the locally optimal quantum position of the quantum-only bird,
the fitness of the local optimal quantum position of the ith quantum bird is shown, and epsilon is the minimum normal number generated by a computer.
The m-dimension updating formula of the quantum position of the ith quantum bird is
m＝1，2，…，M。
And 5, calculating the fitness of the new quantum position of each quantum bird. Quantum position of ith quantum bird
Mapping to a phase or amplitude-phase error matrix
Using fitness function
Calculating a fitness measure, the value of which is also representative of
The fitness of (2).
And 6, updating the local optimal quantum position and the global optimal quantum position of each quantum bird. And calculating the updated fitness value of the quantum position of each quantum bird, if the updated fitness value is larger than the fitness value of the local optimal quantum position, updating the local optimal quantum position by using the updated quantum position, and otherwise, keeping the local optimal quantum position of the previous generation to the next generation. And calculating the maximum fitness value after the quantum position of the quantum bird group is updated, if the fitness value is larger than the fitness value of the global optimal quantum position, updating the global optimal quantum position by using the corresponding quantum position, and otherwise, keeping the global optimal quantum position of the previous generation to the next generation.
And 7, judging whether the iteration time t reaches the maximum iteration time G. If yes, judging whether the phase error is corrected, if yes, executing step eight; if not, execute step ten. And if the maximum iteration number is not reached, making t equal to t +1, and returning to the step four to continue execution.
Step 8, outputting the global optimal quantum position of the quantum bird group, and mapping the global optimal quantum position into a phase error
Is the optimal value of the phase error estimate for the mth array element, M being 1,2, …, M.
And 9, correcting the amplitude error. And initializing the parameter of the quantum bird group evolution mechanism for solving the amplitude error. The quantum position of the ith quantum bird is
Randomly generating the quantum positions of all the quantum birds
Wherein order
The amplitude error of the first array element of the mapping is 1, i is 1,2, …, N b . Will be provided with
Mapping to amplitude-phase error matrix
The minimum value and the maximum value of the amplitude error of the mth array element are respectively, and M is 1,2, … and M. Using fitness function
Calculating the fitness, and setting the local optimal quantum position of the ith quantum bird to be
The overall initial optimal quantum position of the quantum bird group is
And step four is executed.
And step 10, outputting the global optimal quantum position of the quantum bird group, and mapping the global optimal quantum position into an amplitude-phase error matrix.
The specific parameters of the model are set as follows: the antenna array is a uniform linear array, the number of array elements is 8, the spacing between the array elements is half wavelength, the incident azimuth angle of a far-field independent information source is 10 degrees, and the number of snapshots is 100.
The quantum bird swarm algorithm parameters are set as follows: population size N b 100, 1000 maximum iterations G, flight distance F e 0.5,0.15]，
F q ＝5，c 1 ＝0.05，c 2 ＝0.03,c 3 ＝0.12，
m＝1，2，…，M。
Fig. 2 and 3 are graphs of the rms error in phase and amplitude versus the signal-to-noise ratio, respectively, of the array. As can be seen from the figure, the root mean square error based on the quantum bird swarm evolution mechanism is smaller than that based on the particle swarm optimization regardless of the amplitude and the phase, and the correction of the phase error is easily influenced by the signal-to-noise ratio, so the correction is carried out in the environment with larger signal-to-noise ratio. Fig. 4 and 5 respectively show that the variation of the azimuth angle of the measured information source before and after correction is performed by using the array amplitude-phase error correction method based on the quantum birdgroup evolution mechanism under the conditions that two information sources with azimuth angles of 10 degrees and 20 degrees and three information sources with azimuth angles of 10 degrees, 20 degrees and 30 degrees are used and the signal-to-noise ratio is 5dB, it can be known from the figure that the more the number of the information sources is, the greater the influence of the array amplitude-phase error on the measurement of the azimuth angle of the information source is, the amplitude-phase error can be effectively corrected by the method, and the azimuth angle of the information source can be measured more accurately.
The method solves the defects of complex algorithm model, large calculated amount and the like in the conventional method in the array amplitude and phase error correction problem, and corrects the amplitude and phase error by using a quantum birdgroup evolution mechanism. The method firstly corrects phase errors and then corrects amplitude errors, and the steps of correcting each time after establishing a received data model by utilizing a known independent information source are as follows: initializing a quantum bird group; calculating the fitness of the quantum position of each quantum bird to obtain the local optimal quantum position of each quantum bird and the global optimal quantum position of the quantum bird group; updating the quantum position by updating the quantum rotation angle of each quantum bird; calculating the updated fitness of the quantum position of each quantum bird, and updating the local optimal quantum position of each quantum bird and the global optimal quantum position of the quantum bird group; judging whether the maximum iteration times is reached; and outputting the global optimal quantum position and mapping the global optimal quantum position into a phase or amplitude-phase error matrix. The algorithm model is simple, the calculated amount is small, and the amplitude and phase errors of the array are corrected by using less calculation time.
Claims (8)
1. A method for correcting array amplitude and phase errors based on a quantum bird swarm evolution mechanism is characterized by comprising the following steps: the method specifically comprises the following steps:
step 1, establishing a data receiving model according to a known information source;
step 2, initializing the quantum bird swarm evolution mechanism parameters for solving the phase error; the quantum bird group size is N b The maximum iteration number is G, and the quantum position of the ith quantum bird is
Wherein t is iteration times, and the quantum positions of all quantum birds are randomly generated to satisfy
M is 1,2, …, M, wherein
The first mapped array element has a phase error of 0rad, i ═ 1,2, …, N b ；
Step 3, carrying out fitness calculation on the quantum positions of all the quantum birds, and carrying out fitness calculation on the quantum position of the ith quantum bird
Mapping to a phase error matrix
Respectively the m-th array element phase error minimum sumMaximum, M ═ 1,2, …, M;
step 4, updating the quantum position of each quantum bird, wherein the quantum bird group has three behaviors, namely flight behavior, foraging behavior and warning behavior;
step 5, calculating the fitness of the new quantum position of each quantum bird, and calculating the quantum position of the ith quantum bird
Mapped as a phase or amplitude-phase error matrix
Using fitness function
Calculating a fitness measure whose value is also representative of
The fitness of (2);
step 6, updating the local optimal quantum position and the global optimal quantum position of each quantum bird;
step 7, judging whether the iteration time t reaches the maximum iteration time G; if yes, judging whether the phase error is corrected, if yes, executing a step 8; if not, executing the step 10, if the maximum iteration number is not reached, making t equal to t +1, and returning to the step 4 to continue executing;
step 8, outputting the global optimal quantum position of the quantum bird group, and mapping the global optimal quantum position into a phase error
Is the phase error estimation optimum value of the mth array element, M is 1,2, …, M;
step 9, correcting the amplitude error;
and step 10, outputting the global optimal quantum position of the quantum bird group, and mapping the global optimal quantum position into an amplitude-phase error matrix.
2. The method for correcting the array amplitude and phase errors based on the quantum birdgroup evolutionary mechanism as claimed in claim 1, wherein: the step 1 specifically includes establishing a spatial uniform linear array, where the number of array elements is M, the array element spacing is d, the wavelength is λ, a narrow-band far-field signal is incident at a direction angle θ, the noise is gaussian noise, and the receiving of the kth snapshot data by the array can be represented as: y (as) (k) + n (k), wherein y (k) ═ y 1 (k),y 2 (k),…,y M (k)] T ，y m (k) Is the receiving signal of the m-th array element, s (k) is the narrow-band far-field input signal, n (k) ═ n 1 (k),n 2 (k),…,n M (k)] T Is a Gaussian white noise vector, n m (k) The M is 1,2, …, M, and is independent of signal source, when array element has no amplitude phase error, array guide vector is
When the array elements have amplitude phase errors, the array steering vector is a (theta) to gamma a 0 (theta) in the formula
As a diagonal matrix, p m 、
The amplitude error and the phase error of the mth array element are shown, and M is 1,2, … and M; the first array element is taken as a reference array element, and rho can be known 1 ＝1，
And carrying out phase error correction.
3. The method for correcting the array amplitude-phase error based on the quantum birdgroup evolutionary mechanism as claimed in claim 1, wherein the fitness function in step 3 is:
covariance matrix of received data
Estimate, where L is the fast beat number, with R ═ U for R feature decomposition S ∑ S U S +U N ∑ N U N ,U S Is a signal subspace, U N In order to make the noise subspace, the local optimal quantum position of the ith quantum bird is set as
At the beginning of the process, t is 0,
i＝1,2,…,N b the global initial optimal quantum position of the quantum bird group is
4. The method for correcting array amplitude and phase errors based on the quantum bird swarm evolution mechanism according to claim 1, wherein the flight behavior in step 4 is specifically: setting the flying distance as F, F belongs to [0,2 ]]Quantum bird groups every F q The number of iterations is F q When the number is integral multiple, the quantum bird group selects flight behavior; when the quantum bird group flies to a new place to search food, one part of the quantum birds become producers to search food, and the other part of the quantum birds become entrepreneurs to follow the producers to search food; the quantum bird population fitness is arranged from high to low, the first 20 percent of the quantum birds become producers, and the rest of the quantum birds become discussers; for the producer, the m-dimension updating formula of the quantum rotation angle of the ith quantum bird is
c 1 Is a constant of a positive number,
is [0,1 ]]I is 2,3, …, N b M is 1,2, …, M; for the entrepreneur, the mth dimension updating formula of the quantum rotation angle of the ith quantum bird is
Wherein
Represents the m-dimension quantum position of the q-th quantum bird in the producer in the t iteration,
is [0,1 ]]M is 1,2, …, M.
5. The method for correcting array amplitude-phase errors based on the quantum bird swarm evolution mechanism according to claim 1, wherein the foraging behavior in step 4 is specifically as follows: when the number of iterations t is not F q When the integer multiple of
Is [0,1 ]]Constant of [ 1 ], randomly generated [0,1 ]]Random number in between
When in use
When the ith quantum bird selects foraging behavior, the mth dimension updating formula of the quantum rotation angle of the ith quantum bird is
c 2 、c 3 Is a constant of a positive number of bits,
is [0,1 ]]M is 1,2, …, M.
6. The method for correcting the array amplitude-phase error based on the quantum birdgroup evolutionary mechanism according to claim 1, wherein the alert behavior in step 4 specifically comprises: when the number of iterations t is not F q Is an integer multiple of
Then, the i-th quantum bird selects the alert behavior, and the m-dimension updating formula of the quantum rotation angle of the i-th quantum bird is as follows
Wherein
Is [0,2 ]]A constant of the number of the first and second electrodes,
is uniformly distributed in [0,1 ]]The number of the intermediate positions is equal to or greater than,
is uniformly distributed in [ -1,1 [)]The number of the cells between (c) and (d),
is the average of the local optimal quantum positions of all the quantum birds in the t-th iteration,
the sum of the fitness of the local optimal quantum positions of all the quantum birds in the t-th iteration,
is the t th iteration
Only the locally optimal quantum position of the quantum bird,
is as follows
The fitness of the locally optimal quantum position of the quantum-only bird,
and e is the fitness of the local optimal quantum position of the ith quantum bird, and the minimum normal number generated by the computer.
7. The method for correcting the array amplitude and phase errors based on the quantum birdgroup evolutionary mechanism as claimed in claim 1, wherein: the step 6 specifically comprises the steps of calculating the updated fitness value of the quantum position of each quantum bird, if the updated fitness value is larger than the fitness value of the local optimal quantum position, updating the local optimal quantum position by using the updated quantum position, and otherwise, keeping the local optimal quantum position of the previous generation to the next generation; and calculating the maximum value of the fitness after the quantum positions of the quantum bird group are updated, if the maximum value of the fitness is greater than the fitness of the globally optimal quantum position, updating the globally optimal quantum position by using the corresponding quantum position, otherwise, keeping the globally optimal quantum position of the previous generation to the next generation.
8. The method for correcting the array amplitude and phase errors based on the quantum birdgroup evolutionary mechanism as claimed in claim 1, wherein: the step 9 specifically includes the initialization of the parameters of the quantum bird group evolution mechanism for solving the amplitude error, the first stepThe quantum positions of the i-quantum birds are
Randomly generating the quantum positions of all the quantum birds
M is 1,2, …, M, wherein
The amplitude error of the first array element of the mapping is 1, i is 1,2, …, N b (ii) a Will be provided with
Mapping to amplitude-phase error matrix
Respectively, the minimum value and the maximum value of the amplitude error of the mth array element, wherein M is 1,2, … and M; using fitness function
Calculating the fitness, and setting the local optimal quantum position of the ith quantum bird to be
i＝1,2,…,N b The global initial optimal quantum position of the quantum bird group is
Step 4 is performed.
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