CN104616059B - A kind of Wave arrival direction estimating method based on quantum particle swarm - Google Patents

Abstract

The invention discloses a kind of Wave arrival direction estimating method based on quantum particle swarm, step includes：Set up array signal model, array relevant parameter is set, maximal possibility estimation is set up then according to array signal data, then initialize, the fitness function of each particle is calculated, quantum particle swarm speed and position is updated, then judges whether to reach maximum iteration, then information source incident angle vector estimate is exported, and then calculates the mean square deviation at incident direction angle.The present invention make use of the quantum behavior of particle in searching process, overcome standard particle group's algorithm and be easily trapped into local minimum shortcoming, estimated accuracy is high, for solving the problems, such as that Mutual coupling achieves preferable effect, new resolving ideas are provided to obtain high-resolution Mutual coupling.

Description

Direction-of-arrival estimation method based on quantum particle swarm

Technical Field

The invention relates to the technical field of array signal processing and intelligence, in particular to a direction of arrival estimation technology based on quantum particle swarm.

Background

At present, the estimation of the direction of arrival based on an array mainly comprises a traditional method, a subspace method, a maximum likelihood method and a MUSIC algorithm. The traditional method needs more array elements to ensure high resolution, thereby limiting the application of the method; the subspace method fully utilizes the spatial structure of the received data, decomposes the data into a signal subspace and a noise subspace, and has the performance superior to that of the traditional method; the maximum likelihood method has better robustness, and can obtain better performance even when the signal-to-noise ratio is lower, but the maximum likelihood method needs huge calculation amount, so that the application of the maximum likelihood method is limited in engineering; the MUSIC algorithm presents difficulties with multi-dimensional spectral peak searching.

The Quantum Particle Swarm Optimization (QPSO) is a new emerging group intelligent computing method in recent years, combines the basic theory of quantum physics, applies the quantum theory to the standard particle swarm optimization algorithm, and provides a new particle swarm optimization algorithm model from the perspective of quantum mechanical wave function, which is a new improvement on the standard PSO algorithm, has the particle search performance far superior to that of the basic PSO algorithm, and has been applied in the fields of function optimization, neural network training and the like.

In view of the above-mentioned shortcomings or shortcomings of the conventional array-based direction of arrival estimation techniques, the applicant of the present invention has been engaged in the technical accumulation of the present industry for many years, and actively studies how to apply the quantum-behaved particle swarm algorithm to the estimation of the direction of arrival, so as to improve the shortcomings of the prior art, and finally develops the present invention under careful consideration of various conditions.

Disclosure of Invention

The invention aims to solve the problem of nonlinear complex optimization in the existing direction-of-arrival estimation algorithm, and provides a direction-of-arrival estimation method based on quantum particle swarm.

In order to achieve the purposes and effects, the invention adopts the following technical contents:

a method for estimating the direction of arrival based on quantum particle swarm comprises the following steps:

(1) determining array element numberNumber of plane wave signals P, central wavelength of signal lambda, number of snapshotsSpacing d between adjacent array elements, combining pairs of received signalsPerforming feature decomposition on the maximum likelihood estimation of the data covariance matrix to obtain a signal subspace S and a noise subspace G;

(2) initializing; determining the population size M of the particle swarm, wherein the initial position vector of the particle is z_iThe velocity vector corresponding to the particle is v_iI 1,2, …, M, maximum speed V_maxThe number of iterations K is 1, and the maximum number of iterations K_maxLocal optimum position of each particleAnd global optimal position of the whole population

(3) Calculating a fitness function of each particle; positioning M particles at z_iM is substituted as the estimated value of the direction of arrival angle θ, i is 1,2, …, and the spectrum estimation fitness function of the MUSIC algorithm is substituted

Obtaining an individual fitness function value of each particle;

wherein, I is an identity matrix,

(4) updating the group velocity and position of the quantum particles; on the (k + 1) th iteration, the particle updates the velocity and position according to the following formula:

wherein i is 1,2, …, M, α is contraction and expansion coefficient, r is₁,r₂,r₃,r₄Take [0,1]Are uniformly distributed with the random numbers in between,for the best position the ith particle experiences, the best position to experience for all particle populations;

(5) if the maximum iteration number K is equal to K_maxIf the information source is the optimal arrival direction angle estimation value, the optimization is finished, the obtained first P global optimal position vectors are the optimal arrival direction angle estimation value, namely the information source incidence angle vector estimation value is output, and then the mean square error of the incidence direction angle is calculated; otherwise, k ═ k +1, go to step 3.

The invention has at least the following beneficial effects:

compared with the standard particle swarm algorithm, the particle swarm optimization method has more states, the particles do not have a certain motion track and can appear at any position in a search space with a certain determined probability, and the position can be far away from a local attraction point and even better than the global optimal position in the current population, so that the diversity of the particles is greatly increased, the premature convergence of the algorithm is avoided, the optimization search efficiency and performance are greatly improved, and the global search capability of the algorithm is enhanced. Therefore, the invention can better realize the estimation of the direction of arrival.

Other objects and advantages of the present invention will be further understood from the technical disclosure of the present invention. In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.

Drawings

FIG. 1 is a flow chart of a direction of arrival estimation method of the present invention.

FIG. 2 is a diagram of the mean square error of the estimation of the direction of arrival angle versus the signal-to-noise ratio in an embodiment of the present invention.

Detailed Description

The following description will be provided to enable one of ordinary skill in the art to make and use the present invention as provided in the following detailed description. It should be noted that modifications and variations can be made by those skilled in the art without departing from the spirit of the present invention without departing from the scope of the present invention.

Consider oneThe linear uniform array of array elements has P narrow-band plane wave signals in space, and the baseband envelope of the received signal of the ith array element can be expressed as

Wherein,λ is the central wavelength of the signal, d is the distance between adjacent array elements, and θ_kIs the angle between the kth signal source direction and the array normal (i.e. the direction of arrival angle), s_kIs the baseband envelope of the kth signal source, w_i(t) is the additive received noise on the ith array element.

Expression (1) is expressed as a vector as follows:

X(t)＝A(θ)s(t)+w(t) (2)

wherein,s(t)＝[s₁(t),…,s_P(t)]^T，t denotes transposition. A (theta) isA matrix of order with column vectors of

Wherein,

the maximum likelihood estimation from the covariance matrix is:

wherein,is the snapshot number, and H is the complex conjugate transpose. The characteristic decomposition of R is as follows:

R＝UΣU^H＝SΣ_SS^H+GΣ_NG^H(5)

wherein U ═ S | G]S is a subspace spanned by the feature vectors corresponding to the large feature values, namely a signal subspace; g is a subspace spanned by the feature vectors corresponding to the small feature values, i.e. the noise subspace. Due to the presence of noise, the steering vectors of the signal subspace and the noise subspace are not completely orthogonal. Thus, the direction of arrival is achieved with a minimum optimization search:according to the nature SS^H+GG^HIn the actual optimization algorithm, the spectral estimation fitness function of the MUSIC algorithm is calculated as I

Wherein I is an identity matrix. The angle theta corresponding to the minimum value of f (theta) is the estimated direction of arrival angle.

In one embodiment, consider oneLinear uniform array of array elements, where the distance d between adjacent array elements is 1, there are 1 narrow-band plane wave signals in space, the central wavelength of the signal is 2, and its amplitude is 1The angular frequency of the signal is 1.0 and the initial phase of the signal is pi/3, the actual direction of arrival angles of the signal with respect to the array are pi/4, respectively. And performing characteristic decomposition on the data covariance matrix by using the baseband envelope of the received signal to obtain a signal subspace S and a noise subspace G.

The working flow of the method of the invention is shown in fig. 1, and the specific implementation can be divided into the following steps:

step 1: setting a fast tempoAccording to given array element numberThe number P of plane wave signals, the central wavelength lambda of the signals, the distance d between adjacent array elements and the maximum likelihood estimation of the data covariance matrix are combined with the received signals to carry out feature decomposition to obtain a signal subspace S and a noise subspace G.

Step 2: and (5) initializing. Setting the population size M of the particle swarm to be 20, the dimension size D to be 1, and the initial position vector of the particle to be z_i∈[0,π/2]The velocity vector corresponding to the particle is v_i∈ (0,0.01), i ═ 1,2, …, M, maximum speed V_max0.01, 1, and K, the maximum number of iterations_maxDetermining the local optimum position of each particle 80And global optimal position of the whole population

And step 3: a fitness function for each particle is calculated. Positioning M particles at z_i(i ═ 1,2, …, M) is substituted into (6) as the estimated value of the direction of arrival angle θ, to obtain a value of fitness function for each particle;

wherein, I is an identity matrix,

and 4, step 4: the quantum particle group velocity and position are updated. On the (k + 1) th iteration, the particle updates the velocity and position according to the following formula:

wherein i is 1,2, …, M is the population scale, generally 20-40, α is the contraction and expansion coefficient，r₁,r₂,r₃,r₄Take [0,1]Are uniformly distributed with the random numbers in between,for the best position (individual extremum) experienced by the ith particle, the best position (global extremum) experienced by all particle populations.

And 5: if the maximum number of iterations is reached (K ═ K)_max) If so, the optimization is finished, and the obtained first P global optimal position vectors are the optimal arrival direction angle estimation values, namely, the information source incident angle vector estimation values are output, and then the mean square error of the incident direction angles is calculated; otherwise, k: ═ k +1, go to step 3.

Fig. 2 shows a diagram of the mean square error of the estimation of the direction of arrival angle and the signal-to-noise ratio in the embodiment of the present invention. Therefore, the accuracy of the estimation of the direction of arrival by using the scheme of the invention is high.

In conclusion, the quantum behavior of the particles is utilized in the optimization process, the defect that the standard particle swarm algorithm is easy to fall into the local minimum value is overcome, the estimation precision is high, and a good effect is achieved for solving the estimation problem of the direction of arrival. The high-resolution direction-of-arrival estimation is always a bottleneck for improving the performance of the communication system, and the invention provides a new solution for obtaining the high-resolution direction-of-arrival estimation.

What has been described above is only a preferred embodiment of the present invention, and the present invention is not limited to the above examples. It is to be understood that other modifications and variations directly derivable or suggested by those skilled in the art without departing from the spirit and concept of the present invention are to be considered as included within the scope of the present invention.

Claims (1)

1. A method for estimating a direction of arrival based on a quantum particle swarm is characterized by comprising the following steps:

(1) determining array element numberNumber of plane wave signals P, central wavelength of signal lambda, number of snapshotsSpacing d between adjacent array elements, combining the received signalsPerforming feature decomposition on the maximum likelihood estimation of the data covariance matrix to obtain a signal subspace S and a noise subspace G, wherein the signal subspace S is a subspace spanned by feature vectors corresponding to large eigenvalues, and the noise subspace G is a subspace spanned by feature vectors corresponding to small eigenvalues;

(2) initializing; determining the population size M of the particle swarm, wherein the initial position vector of the particle is z_iThe velocity vector corresponding to the particle is v_iI 1,2, …, M, maximum speed V_maxThe number of iterations K is 1, and the maximum number of iterations K_maxLocal optimum position of each particleAnd global optimal position of the whole population

(3) Calculating a fitness function of each particle; positioning M particles at z_iM is substituted as the estimated value of the direction of arrival angle θ, i is 1,2, …, and the spectrum estimation fitness function of the MUSIC algorithm is substituted

$f\left(\mathrm{\θ}\right)=\frac{a^H\left(\mathrm{\θ}\right)a\left(\mathrm{\θ}\right)}{a^H\left(\mathrm{\θ}\right)(I-{\mathrm{SS}}^H)a\left(\mathrm{\θ}\right)}$

Obtaining an individual fitness function value of each particle;

wherein, I is an identity matrix,

(4) updating the group velocity and position of the quantum particles; on the (k + 1) th iteration, the particle updates the velocity and position according to the following formula:

$v_i^{k+1}=\frac{2r_1{p}_i^k+2.1r_2{p}_g^k}{2r_1+2.1r_2};$

wherein i is 1,2, …, M, α is contraction and expansion coefficient, r is₁,r₂,r₃,r₄Take [0,1]Are uniformly distributed with the random numbers in between,for the best position the ith particle experiences, the best position to experience for all particle populations;

(5) if the maximum iteration number K is equal to K_maxIf the information source is the optimal arrival direction angle estimation value, the optimization is finished, the obtained first P global optimal position vectors are the optimal arrival direction angle estimation value, namely the information source incidence angle vector estimation value is output, and then the mean square error of the incidence direction angle is calculated; otherwise, k ═ k +1, go to step 3.