阅读说明：本技术 一种基于恒模算法的阵元位置估计方法 (Array element position estimation method based on constant modulus algorithm ) 是由 杨益新 刘砚鸣 杨龙 汪勇 于 2019-10-16 设计创作，主要内容包括：本发明涉及一种基于恒模算法的阵元位置估计方法,根据阵元上的接收信号,以及位于坐标原点处的阵元信息,使用CMA方法估计阵列流形矩阵。求所得阵列流形矩阵的相位信息,利用第二个已知阵元信息,根据相位和角度的关系估计各个声源的入射角。将阵元真实位置表示为平面上某一位置和位置差之和,利用估计的阵列流形、估计的声源入射角及已知阵元位置信息逐个估计其余阵元位置。无需构造代价函数对每个阵元的位置进行网格搜索,计算量不依赖于原始阵元位置,与形变大小无关,简化计算复杂度,提高了运算效率,实现了对信号波达方向和阵元位置的联合估计。(The invention relates to an array element position estimation method based on a constant modulus algorithm, which is used for estimating an array manifold matrix by using a CMA method according to a received signal on an array element and array element information positioned at a coordinate origin. And obtaining the phase information of the obtained array manifold matrix, and estimating the incidence angle of each sound source according to the relation between the phase and the angle by utilizing second known array element information. And expressing the real position of the array element as the sum of a certain position and a position difference on the plane, and estimating the positions of the rest array elements one by utilizing the estimated array manifold, the estimated incident angle of the sound source and the known position information of the array element. The grid search of the position of each array element is not required to be carried out by constructing a cost function, the calculated amount does not depend on the position of the original array element and is irrelevant to the deformation size, the calculation complexity is simplified, the operation efficiency is improved, and the joint estimation of the signal arrival direction and the position of the array element is realized.)

1. An array element position estimation method based on a constant modulus algorithm is characterized by comprising the following steps:

step 1: from received signals y on array elements_i(t) and array element information at the origin of the coordinates, estimating the array manifold matrix using the CMA method

step 2: determining phase information of the resulting array manifold matrix

wherein: i | · | | represents a vector 2 norm; j is a sound source number and is the jth sound source in the N sound sources; λ is the wavelength; i | · | | represents a vector 2 norm; (.)^TRepresents a transpose of a matrix;

and step 3: estimating the position of the array element: expressing the position of the ith real array element as the sum of the position of the ith-1 array element and the position difference, and estimating the positions of the rest array elements one by using the array manifold estimated in the step 1, the sound source incidence angle estimated in the step 2 and the known array element information, wherein the method comprises the following steps:

the array manifold and the known array element positions are used for obtaining:

definition of

wherein: j is an imaginary unit, a_ijIs composed of

By p_i＝p_i-1+p_i' 3, …, M, estimating the position p of the ith array element_i(ii) a Wherein, (.)^#Representing a generalized inverse operation of the matrix.

Technical Field

The invention belongs to an array element position estimation method, relates to an array element position estimation method based on a constant modulus algorithm, realizes position estimation of other array elements of an array by utilizing incoherent narrow-band sources at two unknown positions and array elements at two known positions, and relates to the fields of signal processing, underwater acoustic measurement and the like.

Background

For the fixed sonar at the seabed, the uncontrollable factors of sonar array arrangement are many, the underwater operation precision is difficult to guarantee, and the array shape is bent and deformed. Meanwhile, the position of the sonar array element is easy to seriously deviate due to changeable underwater environmental conditions (such as tides and sea waves). Most high resolution algorithms in beamforming are premised on the fact that the array manifold is precisely known, and the deviation of the array element positions can cause the theoretical array manifold to be inconsistent with the actual manifold, so that the performance of the algorithm is reduced. Hou-xi et al (Hou, Chen vogue, Jie Qi. influence of position deviation of array elements on acoustic array performance [ J ] Acoustic and electronic engineering, 2017(01):9-12.) establish a mathematical model of the position deviation of the array elements, deduce and prove the relation between output energy, directivity index and position deviation, quantitatively analyze the influence of the position deviation of the array elements on the acoustic array performance, and give simulation results under different frequencies and different deviation amounts.

There are two main types of current array calibration methods, one is an active calibration method, and the other is a self-calibration method. The active calibration method utilizes a sound source with an accurately known spatial position to carry out calibration, the calculation amount is small, but the method needs to place an auxiliary sound source, the requirement on equipment is higher, and errors possibly occurring in sound source information can influence the estimation result of the array element position. In the self-calibration method, position information of an auxiliary sound source is not needed, but the estimation precision is poor and the calculation amount is large because the position information is the joint estimation of the direction of arrival and the position of an array element. In addition, it often has some limitations on the array structure (canadian. the direction of arrival estimation algorithm in the presence of array errors research [ D ]. wo scientific and technical university of china, doctrine 2014.).

An active correction method [ J ] of an underwater multi-element linear array error based on a simulated annealing method, a ship scientific technology, 2018,40(17): 107-.

Weiss (A.J. Weiss and B.Friedlander, Array shape calibration using sources in unknown locations-a maximum likelihood alignment, IEEE Transactionson Acoustics, Speech, and Signal Processing, 1989; 37(12):1958 and 1966.) proposes an Array element position self-calibration method, and a cost function is defined based on a maximum likelihood criterion for iterative solution. The method belongs to the field of constructing a cost function between a signal arrival direction and an array element position, and uses the most value point of the cost function as an estimation limiting condition.

The invention limits the array element spacing, estimates the array manifold based on a Constant Modulus Algorithm (CMA), provides an array element self-calibration method without searching the array element position, and effectively reduces the operation complexity.

Disclosure of Invention

Technical problem to be solved

In order to avoid the defects of the prior art, the invention provides an array element position estimation method based on a constant modulus algorithm, which is an array self-calibration method. In order to reduce the calculation complexity of the algorithm, aiming at a sonar array with array element spacing smaller than half wavelength, incoherent narrow-band sources at two unknown positions and array elements at two known positions are utilized, the directions of the two sound sources are estimated firstly, then the positions of the rest array elements are estimated in an iterative manner, and the problem of phase ambiguity is avoided due to the limitation of the array element spacing.

Technical scheme

An array element position estimation method based on a constant modulus algorithm is characterized by comprising the following steps:

step 1: from received signals y on array elements_i(t) and array element information at the origin of the coordinates, estimating the array manifold matrix using the CMA method

Wherein i is array element number, and t is time;

step 2: determining phase information of the resulting array manifold matrixUsing position information p of a second known array element₂＝[||p₂||,0]^TAnd obtaining the incident angle of each sound source as follows:

wherein: i | · | | represents a vector 2 norm; j is a sound source number and is the jth sound source in the N sound sources; λ is the wavelength; i | · | | represents a vector 2 norm; (.)^TRepresents a transpose of a matrix;

and step 3: estimating the position of the array element: expressing the position of the ith real array element as the sum of the position of the ith-1 array element and the position difference, and estimating the positions of the rest array elements one by using the array manifold estimated in the step 1, the sound source incidence angle estimated in the step 2 and the known array element information, wherein the method comprises the following steps:

the array manifold and the known array element positions are used for obtaining:

definition of

Φ'_i＝[φ'_i1… φ'_iN]^TThen, the position difference of the array elements is:

wherein: j is an imaginary unit, a_ijIs composed of

Is an element of

n_j＝[cos(θ_j),sin(θ_j)]^TJ is 1,2, … N is the direction of each sound source; theta_jIs an azimuth angle, and satisfies-pi/2 < theta_j＜π/2；

By p_i＝p_i-1+p_i' M, estimating the position p of the ith array element_i(ii) a Wherein, (.)^#Representing a generalized inverse operation of the matrix.

Advantageous effects

The array element position estimation method based on the constant modulus algorithm provided by the invention estimates the array manifold matrix by using a CMA method according to the received signals on the array elements and the array element information at the coordinate origin. And obtaining the phase information of the obtained array manifold matrix, and estimating the incidence angle of each sound source according to the relation between the phase and the angle by utilizing second known array element information. And (3) expressing the real position of the array element as the sum of a certain position and a position difference on the plane, and estimating the positions of the rest array elements one by using the array manifold estimated in the step 1, the sound source incidence angle estimated in the step 2 and the known position information of the array element.

The invention has the beneficial effects that: on the basis of the CMA method, the array structure is limited under the existing condition, the distance between the array elements is required to be smaller than half wavelength, the position of the next array element is iteratively estimated by utilizing the position of the previous array element, therefore, the grid search of the position of each array element is not required to be carried out by constructing a cost function, the calculated amount does not depend on the position of the original array element and is not related to the size of deformation, the calculation complexity is simplified, the operation efficiency is improved, and the joint estimation of the signal wave arrival direction and the position of the array element is realized.

Drawings

FIG. 1 is a schematic diagram of array element calibration;

FIG. 2 is a general flow chart of an array element position calibration method;

FIG. 3 shows the estimation result of the position of an array element under the condition of a specific implementation example;

figure 4 is the MUSIC azimuth spectrum before and after array element calibration.

Detailed Description

The invention will now be further described with reference to the following examples and drawings:

1. the signal model applicable to the invention is as follows:

n far-field incoherent narrow-band sources are arranged in the same plane, the array is provided with M array elements, the spacing between the array elements is less than half wavelength, and the positions of the first two array elements are accurately known, so that the positions of the array elements can be expressed as

p_i(t)＝[x_i(t),z_i(t)]^T,i＝1,2,…,M

Wherein, (.)^TThe transposition of the matrix is represented, t is time, i is the array element number, and x and z are respectively the horizontal and vertical coordinates of the array element under the rectangular coordinate system.

The direction of each sound source is denoted n_j＝[cos(θ_j),sin(θ_j)]^TJ is 1,2, … N, azimuth angle θ_jSatisfy-pi/2 < theta_jAnd < pi/2, j is the sound source number.

A in the guide vector_ij(t) can be represented as

Where j is an imaginary unit and λ is the wavelength. The position of the first array element is taken as the origin of the whole coordinate system, which has

Defining narrow-band incoherent signal s (t) s emitted by sound source₁(t),…,s_N(t)]^TThen, the received signals y (t) on M array elements are equal to [ y ═ y₁(t),…,y_M(t)]^TIs y (t) ═ A (t) s (t) + η (t)

Wherein the array manifold matrix

η (t) is the noise received by the array, and it is assumed that the noise received by each array element is a ergodic, smooth and zero-mean random process, and the signal and the noise are not the sameAnd (4) correlating.

2. The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

1) estimating array manifold matrix according to the received signals y (t) on the array elements and the information of the array elements at the original points of the coordinates

① obtaining sampling covariance matrix from received signals on array elements

Performing characteristic decomposition and solving a signal subspace U_NIn which N is_sFor the number of sample points, E (-) represents the expectation.

② Structure

Will K_iStraightened out and transposed as the ith row of the matrix K, havingZero space of K is found

Wherein u is_iIs the ith row of the signal subspace, w_jIs the jth column of the object matrix W, (. DEG)^HRepresents the conjugate transpose of the matrix, () represents the conjugate of the matrix,

represents the kronecker product, 0_M-1Is an M-1 row-column vector with elements of 0.

③ A plurality of handlesAs a set of radicals, define

R_kIs b is_kThe inverse of the straightening is performed,

two sets of parameters a are selected as required_jTo obtain R₁And R₂Such that ∑₁Is reversible and

having different diagonal elements, to obtain

Where Σ (·) represents the sum (·)^-1Representing the inversion of a matrix, vec^-1(-) denotes the inverse of the matrix straightening,

④ pairs

Characteristic decomposition to obtain

Where Σ' is the eigenvalue, V is the eigenvector, W and V^-TCorrespondingly, the difference between the two is the ordering difference and the coefficient difference. According to a_1j1 standardized U_NV^-TObtaining an estimated array manifoldThe method is U_NV^-TDivided by the elements of the respective first row.

2) And estimating the incidence angle of each sound source according to the relation between the phase and the angle.

⑤ determining the phase of the array manifoldUsing the position p of the second known array element₂＝[||p₂||,0]^TThe incident angle of each sound source can be obtained as

Where | · | | represents a vector 2 norm.

3) Estimating array element position

⑥ are obtained from the array manifold and the known positions of the two array elements

Definition of

Φ'_i＝[φ'_i1… φ'_iN]^TThen the position difference of the array elements is generally expressed as

By p_i＝p_i-1+p_iA, M may estimate the position p of the ith array element_i. Wherein, (.)^#Representing a generalized inverse operation of the matrix.