阅读说明：本技术 基于改进music算法的近场信号源定位方法 (Near-field signal source positioning method based on improved MUSIC algorithm ) 是由 蔡晶晶 李盼盼 鲍丹 谭富伟 于 2021-08-19 设计创作，主要内容包括：本发明提出了一种基于改进MUSIC算法的近场信号源定位方法,实现步骤为：构建均匀线阵P；获得均匀线阵P的阵列输出信号矢量X(t)；获取接收数据阵列协方差矩阵的估计值获取噪声子空间矩阵U-(n)；构造代价函数V(b,c)；基于改进MUSIC算法获取代价函数解集通过绘制幅度谱图获取近场信号源的定位估计结果。本发明采用的改进MUSIC算法是通过对代价函数求导从而得到代价函数的解集,再根据代价函数的解集绘制幅度谱图获取近场信号源的定位估计结果,有效提高了近场信号源定位中波达方向和距离的估计精度。(The invention provides a near field signal source positioning method based on an improved MUSIC algorithm, which comprises the following steps: constructing a uniform linear array P; obtaining an array output signal vector X (t) of the uniform linear array P; obtaining an estimate of a received data array covariance matrix Obtaining a noise subspace matrix U n (ii) a Constructing a cost function V (b, c); obtaining cost function solution set based on improved MUSIC algorithm Obtaining near-field signal source by plotting amplitude spectrumAnd positioning the estimation result. The improved MUSIC algorithm adopted by the invention obtains a solution set of the cost function by deriving the cost function, and then draws an amplitude spectrogram according to the solution set of the cost function to obtain a positioning estimation result of the near-field signal source, thereby effectively improving the estimation precision of the direction of arrival and the distance in the positioning of the near-field signal source.)

1. A near field signal source positioning method based on an improved MUSIC algorithm is characterized by comprising the following steps:

(1) constructing a uniform linear array P:

constructing a uniform linear array P ═ P comprising M omnidirectional sensor array elements₀,...,p_m,...,p_M-1And p is₀As a reference array element, the distance between adjacent omnidirectional sensor array elements in the uniform linear array P is d, wherein M is more than or equal to 2, P_mThe (m + 1) th omnidirectional sensor array element is represented, d is less than or equal to lambda/4, and lambda is the wavelength of a narrow-band signal incident to the array;

(2) acquiring an array output signal vector X (t) of the uniform linear array P:

sampling and filtering narrow-band signals transmitted by K near-field signal sources in space by each omnidirectional sensor array element in the uniform linear array P to obtain an array output signal vector X (t):

X(t)＝[x₀(t),x₁(t),...,x_m(t),...,x_M-1(t)]^T

wherein K is more than or equal to 1 and less than or equal to M, x_m(t) denotes the m +1 th omnidirectional sensor array element p_mT represents discrete time, t is more than or equal to 1 and less than or equal to L, L represents the number of sampling points of the signal in the time domain, and the near-field signal source and the reference array element p₀In the range of[·]^TRepresenting a transpose operation;

(3) obtaining an estimate of a received data array covariance matrix

Calculating the estimated value of the covariance matrix of the received data array by using the array output signal vector X (t)

(4) Obtaining noise subspace momentsArray U_n：

Estimation of covariance matrix of received data arrayPerforming characteristic decomposition to obtain a noise subspace matrix U_n；

(5) Constructing a cost function V (b, c):

(5a) for noise subspace matrix U_nPerforming conjugate transposition and passing through U_nAnd conjugate transpose resultCalculating square matrixWherein [ ·]^HRepresenting a conjugate transpose operation;

(5b) constructing a cost function V (b, c) by a square matrix G:

V(b,c)＝a(b,c)^HGa(b,c)

wherein a (b, c) represents a steering vector,b denotes a variable containing an unknown quantity as angle θ, b ═ e^{-j2πdsinθ/λ}C represents a variable containing two unknowns, angle theta and distance r respectively,

(6) obtaining cost function solution set based on improved MUSIC algorithm

(6a) Adopting a space grid division method, and observing an airspace [0 degrees and 180 degrees ] according to the airspace sparse characteristic of a signal source]Equally spaced into Q anglesWherein, Q > K,represents the qth angular value;

(6b) through angle valueCalculating the value of variable bThen pass throughCalculating a cost function

(6c) To pairC in (3) is derived to obtain a polynomial equation

(6d) Solving polynomial equationsAnd substituting the root with the modulus value of 1 into the rootIn then letThe minimum root is used as the optimal root

(6e) Each will beAndsubstituting into V (b, c) to obtain a solution set of cost functions V (b, c) corresponding to Q angles

(7) Obtaining a positioning estimation result of the near-field signal source by drawing an amplitude spectrogram:

(7a) at an angleIs the x-axis coordinate to solve the setThe reciprocal of the first K spectral peaks is a y-axis coordinate, an amplitude spectrogram is drawn, the first K spectral peaks with larger amplitude values are searched from the amplitude spectrogram in a sequence from high to low, and the x-axis coordinate corresponding to the peak points of the spectral peaks is the estimated value of the direction of arrival of the K near-field signal sources

(7b) By passingCorresponding solution setGet the optimal rootThrough each oneAndcomputing correspondencesIs estimated from the distanceObtaining the distance estimated values of K near-field signal sources

(7c) Direction of arrival estimation in combination with near field signal sourcesAnd distance estimateAnd obtaining positioning estimation results of K near-field signal sources.

2. The improved MUSIC algorithm-based near field signal source localization method of claim 1, wherein the step (3) of calculating the estimated value of the covariance matrix of the received data array is performed

3. The improved MUSIC algorithm-based near field signal source localization method of claim 1, wherein the estimated value of the covariance matrix of the received data array in step (4)Performing characteristic decomposition, wherein the decomposition formula is as follows:

wherein, Λ_sAnd Λ_nEigenvalue diagonal matrices, U, of the signal subspace and the noise subspace, respectively_sAnd U_nRespectively a signal subspace matrix and a noise subspace matrix.

Technical Field

The invention belongs to the technical field of signal processing, relates to a near-field signal source positioning method, and particularly relates to a near-field signal source positioning method based on an improved MUSIC algorithm, which can be used for acquiring signal orientation parameters.

Background

Array signal processing is an important branch of modern signal processing, research contents of the array signal processing comprise signal detection, parameter estimation, spatial filtering, target imaging and the like, and the array signal processing is widely applied to numerous military and civil fields such as radars, sonars, communication, navigation, seismic exploration, radio astronomy, electronic medical treatment and the like. The method can be divided into a far-field signal source and a near-field signal source according to the distance between a signal source and a receiving array, compared with the far-field signal source, the processing of signals emitted by the near-field signal source is more complex, the near-field signal source is located in a Fresnel region, the emitted signals need to be accurately described by spherical waves relative to the aperture of the array, the wavefront shape has a nonlinear change characteristic along with the position of the array, the position of the signal source needs to be determined by the distance and the direction of arrival, and therefore the positioning of the near-field signal source can be attributed to the problem of joint estimation of the distance of the signal source and the direction of arrival. Near-field signal source positioning is widely applied in the fields of electronic monitoring, seismic detection, sound source positioning and the like. The near-field signal source positioning algorithm mainly comprises a maximum likelihood estimation method, a weighted linear prediction method, a multiple signal classification (MUSIC) algorithm, an algorithm for Estimating Signal Parameters (ESPRIT) by a rotation invariant technology and the like. The MUSIC algorithm belongs to a high-resolution subspace estimation method, and the basic idea is to perform characteristic decomposition on a covariance matrix of any array received data so as to obtain a signal subspace corresponding to a signal component and a noise subspace orthogonal to the signal component, then construct a spatial spectrum function by utilizing a guide vector of the signal subspace and the orthogonality of the noise subspace, and detect a signal through spectrum peak search.

The MUSIC algorithm has high resolution, estimation accuracy and stability, so the MUSIC algorithm is widely used, for example, a patent application with the application publication number of CN107255796A and the name of 'a narrow-band near-field signal source positioning method under non-uniform noise' discloses a narrow-band near-field signal source positioning method under non-uniform noise, the method utilizes a received data array covariance matrix to construct a Toeplitz matrix, combines the MUSIC algorithm which directly utilizes a guide vector and a noise subspace matrix to construct a spatial spectrum function to estimate a direction estimation value of a near-field narrow-band signal source, and then constructs the Toeplitz matrix again and combines the MUSIC algorithm to obtain a distance estimation value of the near-field narrow-band signal source. The method effectively solves the problem of noise non-uniformity during positioning of the near-field signal source, but has the defects that no constraint is carried out on the guide vector, the guide vector and the noise subspace matrix are directly utilized to construct a spatial spectrum function, so that the accuracy of the direction of arrival estimation and the distance estimation of the near-field signal source is low, the construction process of the Topritz matrix is complex, and the calculation complexity is high.

Disclosure of Invention

The invention aims to overcome the defects in the prior art, provides a near-field signal source positioning method based on an improved MUSIC algorithm, and aims to improve the positioning precision and reduce the calculation complexity.

In order to achieve the purpose, the technical scheme adopted by the invention comprises the following steps:

(1) constructing a uniform linear array P:

constructing a uniform linear array P ═ P comprising M omnidirectional sensor array elements₀,...,p_m,...,p_M-1And p is₀As a reference array element, the distance between adjacent omnidirectional sensor array elements in the uniform linear array P is d, wherein M is more than or equal to 2, P_mThe (m + 1) th omnidirectional sensor array element is represented, d is less than or equal to lambda/4, and lambda is the wavelength of a narrow-band signal incident to the array;

(2) acquiring an array output signal vector X (t) of the uniform linear array P:

sampling and filtering narrow-band signals transmitted by K near-field signal sources in space by each omnidirectional sensor array element in the uniform linear array P to obtain an array output signal vector X (t):

X(t)＝[x₀(t),x₁(t),...,x_m(t),...,x_M-1(t)]^T

wherein K is more than or equal to 1 and less than or equal to M, x_m(t) denotes the m +1 th omnidirectional sensor array element p_mT represents discrete time, t is more than or equal to 1 and less than or equal to L, L represents the number of sampling points of the signal in the time domain, and the near-field signal source and the reference array element p₀In the range of[·]^TRepresenting a transpose operation;

(3) obtaining an estimate of a received data array covariance matrix

Calculating the estimated value of the covariance matrix of the received data array by using the array output signal vector X (t)

(4) Obtaining a noise subspace matrix U_n：

Estimation of covariance matrix of received data arrayPerforming characteristic decomposition to obtain a noise subspace matrix U_n；

(5) Constructing a cost function V (b, c):

(5a) for noise subspace matrix U_nPerforming conjugate transposition and passing through U_nAnd conjugate transpose resultCalculating square matrixWherein [ ·]^HRepresenting a conjugate transpose operation;

(5b) constructing a cost function V (b, c) by a square matrix G:

V(b,c)＝a(b,c)^HGa(b,c)

wherein a (b, c) represents a steering vector,b denotes a variable containing an unknown quantity as angle θ, b ═ e^{-j2πdsinθ/λ}C represents a variable containing two unknowns, angle theta and distance r respectively,

(6) obtaining cost function solution set based on improved MUSIC algorithm

(6a) Adopting a space grid division method, and observing an airspace [0 degrees and 180 degrees ] according to the airspace sparse characteristic of a signal source]Equally spaced into Q anglesWherein, Q > K,represents the qth angular value;

(6b) through angle valueCalculating the value of variable bThen pass throughCalculating a cost function

(6c) To pairC in (3) is derived to obtain a polynomial equation

(6d) Solving polynomial equationsAnd substituting the root with the modulus value of 1 into the rootIn then letThe minimum root is used as the optimal root

(6e) Each will beAndsubstituting into V (b, c) to obtain a solution set of cost functions V (b, c) corresponding to Q angles

(7) Obtaining a positioning estimation result of the near-field signal source by drawing an amplitude spectrogram:

(7a) at an angleIs the x-axis coordinate to solve the setThe reciprocal of the first K spectral peaks is a y-axis coordinate, an amplitude spectrogram is drawn, the first K spectral peaks with larger amplitude values are searched from the amplitude spectrogram in a sequence from high to low, and the x-axis coordinate corresponding to the peak points of the spectral peaks is the estimated value of the direction of arrival of the K near-field signal sources

(7b) By passingCorresponding solution setGet the optimal rootThrough each oneAndcomputing correspondencesIs estimated from the distanceObtaining the distance estimated values of K near-field signal sources

(7c) Direction of arrival estimation in combination with near field signal sourcesAnd distance estimateAnd obtaining positioning estimation results of K near-field signal sources.

Compared with the prior art, the invention has the following advantages:

(1) the positioning result of the near-field signal source acquired by the method is realized based on the improved MUSIC algorithm, the method utilizes the cost function constructed by the noise subspace matrix to carry out derivation to obtain a group of cost function solution sets, the derivation of the cost function in the improved MUSIC algorithm is equivalent to the restriction of each value in the guide vector, the problem that the precision is low due to the fact that the guide vector is not restricted in the prior art and the space spectrum function is constructed by directly utilizing the guide vector and the noise subspace matrix is solved, and the arrival direction estimation and distance estimation precision in the positioning of the near-field signal source is improved.

(2) The noise subspace matrix obtained by the method is realized by performing characteristic decomposition on the estimated value of the received data array covariance matrix, so that the defect that the calculation process for obtaining the noise subspace matrix is too complicated by performing characteristic decomposition on the Topritz matrix constructed by the received data array covariance matrix in the prior art is overcome, and the positioning efficiency is ensured.

Drawings

FIG. 1 is a flow chart of an implementation of the present invention;

fig. 2 is a schematic structural diagram of a uniform linear array received signal model adopted in the embodiment of the present invention.

Detailed Description

The invention is described in further detail below with reference to the figures and the specific embodiments.

Referring to fig. 1, the present invention includes the steps of:

step 1) constructing a uniform linear array P:

constructing a uniform linear array P ═ P comprising M omnidirectional sensor array elements₀,...,p_m,...,p_M-1And p is₀As a reference array element, the distance between adjacent omnidirectional sensor array elements in the uniform linear array P is d, wherein M is more than or equal to 2, P_mThe (m + 1) th omnidirectional sensor array element is represented, d is less than or equal to lambda/4, and lambda is the wavelength of a narrow-band signal incident to the array;

the structure of the uniform line array receiving signal model in this embodiment is shown in fig. 2, and a uniform line array P ═ P including M ═ 7 omnidirectional sensor array elements is { P ═₀,p₁,...,p₆And (6) positioning the uniform linear array P on a one-dimensional coordinate axis, and referring to an array element P₀Placed at one-dimensional origin of coordinates, except for p₀The other array elements are sequentially arranged on a one-dimensional coordinate axis in sequence, and if the uniform linear array P receives a signal transmitted by the near-field signal source X, the near-field signal source X is far away from the reference array element P₀Is a distance r_XReference array element p₀The included angle between the signal transmitted by the near field signal source X and the one-dimensional coordinate axis is the direction of arrival angle theta_X。

Step 2), obtaining an array output signal vector X (t) of the uniform linear array P:

sampling and filtering narrow-band signals transmitted by K near-field signal sources in space by each omnidirectional sensor array element in the uniform linear array P to obtain an array output signal vector X (t):

X(t)＝[x₀(t),x₁(t),...,x_m(t),...,x_M-1(t)]^T

wherein K is more than or equal to 1 and less than or equal to M, x_m(t) denotes the m +1 th omnidirectional sensor array element p_mT represents discrete time, t is more than or equal to 1 and less than or equal to L, L represents the number of sampling points of the signal in the time domain, and the near-field signal source and the reference array element p₀In the range of[·]^TRepresenting a transpose operation;

step 3) obtaining the estimated value of the covariance matrix of the received data array

Calculating the estimated value of the covariance matrix of the received data array by using the array output signal vector X (t)

Step 4) obtaining a noise subspace matrix U_n：

Estimation of covariance matrix of received data arrayPerforming characteristic decomposition to obtain a noise subspace matrix U_n：

Wherein, Λ_sAnd Λ_nEigenvalue diagonal matrices, U, of the signal subspace and the noise subspace, respectively_sAnd U_nRespectively a signal subspace matrix and a noise subspace matrix.

Step 5) constructing a cost function V (b, c):

(5a) for noise subspace matrix U_nPerforming conjugate transposition and passing through U_nAnd conjugate transpose resultCalculating square matrixWherein [ ·]^HRepresenting a conjugate transpose operation;

(5b) constructing a cost function V (b, c) by a square matrix G:

V(b,c)＝a(b,c)^HGa(b,c)

wherein a (b, c) represents a steering vector,b denotes a variable containing an unknown quantity as angle θ, b ═ e^{-j2πdsinθ/λ}C represents a variable containing two unknowns, angle theta and distance r respectively,

step 6) obtaining cost function solution set based on improved MUSIC algorithm

(6a) Adopting a space grid division method, and observing an airspace [0 degrees and 180 degrees ] according to the airspace sparse characteristic of a signal source]Equally spaced into Q anglesWherein, Q > K,represents the qth angular value;

(6b) through angle valueCalculating the value of variable bThen pass throughCalculating a cost function

(6c) To pairC in (3) is derived to obtain a polynomial equation

(6d) Solving polynomial equationsAnd substituting the root with the modulus value of 1 into the rootIn then letThe minimum root is used as the optimal root

Polynomial equationThe root of (a) is a complex number, comprising an imaginary part and a real part, and modulo the root is the absolute value of the complex number, which is equal to the square root of the sum of the squares of the real and imaginary parts.

(6e) Each will beAndsubstituting into V (b, c) to obtain a solution set of cost functions V (b, c) corresponding to Q angles

Step 7) obtaining a positioning estimation result of the near field signal source by drawing an amplitude spectrogram:

(7a) at an angleIs the x-axis coordinate to solve the setThe reciprocal of the first K spectral peaks is a y-axis coordinate, an amplitude spectrogram is drawn, the first K spectral peaks with larger amplitude values are searched from the amplitude spectrogram in a sequence from high to low, and the x-axis coordinate corresponding to the peak points of the spectral peaks is the estimated value of the direction of arrival of the K near-field signal sources

(7b) By passingCorresponding solution setGet the optimal rootThrough each oneAndcomputing correspondencesIs estimated from the distanceObtaining the distance estimated values of K near-field signal sources

(7c) Direction of arrival estimation in combination with near field signal sourcesAnd distance estimateAnd obtaining positioning estimation results of K near-field signal sources.