阅读说明：本技术 基于退化的空间arma模型的多维传感器阵列信源测向方法 (Multi-dimensional sensor array source direction finding method based on degraded space ARMA model ) 是由 姚桂锦 张海蓉 岳东旭 李玲 赵海艳 于 2021-08-23 设计创作，主要内容包括：本发明涉及一种基于退化的空间ARMA模型的多维传感器阵列信源测向方法,属于阵列信号处理中基于多维阵列的二维信源测向。包括3维体阵模型,多维阵列中任一ULA的信源相差估计,多维阵列中的ULA分类准则,多维阵列中信源相差(或角度)配对方案,多维阵列中信源仰角和方位角的计算。本发明的优点是：能够处理多维阵列中的任一ULA,二维信源测向方法能够匹配和发挥多维阵列ULA及其数据丰富的优势；给出了能够实现信源相差自动配对的ULA组合准则,所提测向方法能够处理两种方位角定义下ULA,而且对信源和传感器阵元噪声的信号性质仅要求为平稳；所提测向方法是直接处理多维阵列数据,不涉及矩阵特征值分解或奇异值分解,计算较为高效。(The invention relates to a method for measuring the direction of a source of a multi-dimensional sensor array based on a degraded space ARMA model, belonging to the field of two-dimensional source direction measurement based on a multi-dimensional array in array signal processing. The method comprises a 3-dimensional volume array model, source phase difference estimation of any ULA in a multi-dimensional array, an ULA classification criterion in the multi-dimensional array, a source phase difference (or angle) pairing scheme in the multi-dimensional array, and calculation of a source elevation angle and an azimuth angle in the multi-dimensional array. The invention has the advantages that: any ULA in the multi-dimensional array can be processed, and the advantage of the multi-dimensional array and the advantage of abundant data thereof can be matched and exerted by the two-dimensional source direction finding method; the ULA combination criterion capable of realizing automatic matching of the information source phase difference is given, the provided direction finding method can process the ULA under two azimuth angle definitions, and the signal properties of the noise of the information source and the sensor array element are only required to be stable; the direction finding method is used for directly processing the multidimensional array data, does not involve matrix eigenvalue decomposition or singular value decomposition, and is high in calculation efficiency.)

1. A multi-dimensional sensor array source direction finding method based on a degraded space ARMA model is characterized by comprising the following steps:

(I), 3-dimensional volume array model:

(1) the 3-dimensional array is composed of M multiplied by N multiplied by L isotropic sensor array elements, the number of the sensor array elements parallel to X, Y and Z-axis direction is M, N and L respectively, K far-field narrow-band stationary signal sources in space are incident to the 3-dimensional array, and the incident azimuth angle and the elevation angle are phi respectively_k，θ_kK is 1, …, K, and after setting the sensor array element at the origin of the matrix coordinate as a zero-phase array element, the kth source propagates the phase shift reaching the (m, n, l) th array element of the 3-dimensional matrixComprises the following steps:

wherein M is 1, …, M; n is 1, …, N; l is the sum of 1, …, L,andrepresenting the component phases in directions parallel to the X, Y and Z axes respectively,andis defined as the constituent phaseThe equation (1) shows that the phase of an external source incident on any sensor array element in the multidimensional array is a linear combination of 3 parameter terms;

the 3 parameter terms in the formula (1) are:

wherein the scale factorf and c represent carrier frequency and propagation velocity, Δ d_x、Δd_yAnd Δ d_zSpacing the sensor array elements in the direction parallel to X, Y and Z axis;

u in formula (2)_k、v_kAnd w_kThe method specifically comprises the following steps:

u_k＝cos(φ_k)sin(θ_k)，v_k＝sin(φ_k)sin(θ_k)，w_k＝cos(θ_k).(3)

wherein theta is_kAnd phi_kThe elevation angle and the azimuth angle of the kth information source are respectively defined as the included angle between the incident direction of the information source and the Z axis and the included angle between the projection of the incident direction on the X-Y plane array and the X axis, under the definition of the azimuth angle, except that the sensor array element data positioned on the Z axis only comprises the elevation angle theta, other sensor array element data in the multidimensional array simultaneously comprises the elevation angle theta and the azimuth angle phi, the two angles are mutually coupled, and the parameter item delta phi is_xAnd delta phi_yAlso called source elevation angle theta and azimuth angle phi, where for simplicity, the constant terms are true since they hold for all K sourcesAndθ_kand phi_kDeleting the index k;

(2) on the premise of the assumption that external incident source signals and sensor noise are stable, a signal model of the source incident on any ULA in the multi-dimensional array is a degraded space ARMA model, and the degraded space ARMA model has MYW linear equation sets and root-solving polynomials;

(II) estimating the source phase difference of any ULA in the multi-dimensional array:

(1) aiming at any ULA in the multi-dimensional array, under the precondition that an information source signal is irrelevant to sensor noise, by utilizing a correlation function of the ULA data, a linear equation set and a polynomial root are sequentially constructed and solved MYW, and the phase difference of each information source can be calculated;

(2) for any ULA in a multi-dimensional array, using its correlation function of sensor array data, a linear system of equations is constructed MYW as follows:

Hb＝r， (4)

in the formula (4), H is an I × K dimensional coefficient matrix, b and r are K × 1 and I × 1 dimensional parameters to be solved and constant term column vectors, respectively, and H, b and r have the following specific forms:

wherein (·)^TFor transpose operators, line vectors h_m＝[h_m,…,h_(m+K-1)],m＝1,…,I，h_mAnd array elements in r E {. is the mathematical expectation (.)^HIs a conjugate transpose, x_i(t) and n_i(t) is the ith sensor array element data and noise, x, of the selected ULA_n(t) referred to as reference data;

under the condition that the signal source signal and the noise are stable, a correlation function is taken for the ULA data, and R can be ensured_iAndthe same is stable; and by selecting x when the sensor noise is uncorrelated with the source signal_n(t) making MYW linear equation set in equation (4) no longer contain unknownsConvenience is brought to equation solving;

(3) to-be-solved parameterIs K incident source propagatorsThe specific functional form of the initial idempotent and symmetric function of (2) is:

solving the MYW linear equation set in the formula (4) can obtain K parameters to be solvedThis requires that the number of equations I in the MYW linear system of equations should at least satisfy I ≧ K;

(4) constructing a root-seeking polynomial according to the parameters to be sought in the formula (6)The following unary first polynomial is constructed:

f(v)＝v^K+b₁v^K-1+…+b_kv^K-k+…+b_K, (7)

easy to prove, source propagatorIs the root of a unary first polynomial f (v).

Root-finding f (v) to obtainThen the kth source differs by phaseThe following equation is used to solve:

(III) ULA classification criterion in the multi-dimensional array:

(1) determining an ULA classification criterion in a multi-dimensional array according to an information source phase difference function form, and providing a plurality of information source phase difference estimation modes according to the ULA classification criterion, so as to find a solution for the problem of angle automatic pairing in two-dimensional information source direction finding, wherein in the multi-dimensional array, starting array elements, the located space positions and the possessed information source phase function forms of various ULAs may be different, but according to the information source phase difference function form, the various ULAs can be effectively classified, and all the ULAs with the same information source phase difference function form belong to one class; correspondingly, the ULA data belonging to the same class are processed, and the information source phase difference in the same function form can be estimated;

(2) in the multidimensional array, the source phase difference can be expressed as a linear combination of a plurality of component phase differences in a functional form, wherein each component phase difference can be directly estimated by finding corresponding ULA data, so that the source phase difference has the following two estimation modes based on an explicit functional form of the phase difference and a linear combination form thereof: directly estimating by searching and utilizing corresponding ULA data based on an explicit function form of the phase difference per se; firstly, estimating component phase difference, and calculating the estimated component phase difference by using a linear combination formula;

(IV) source phase difference or angle pairing scheme in the multidimensional array:

(1) the automatic pairing of the source phase differences or angles is converted into a constraint parameter, the constraint parameter is embodied into a linear combination of two phase differences to be paired, and the automatic pairing is realized by comparing the results of the source phase differences obtained by two estimation modes one by one, so that the automatic pairing of the source phase differences or angles is realized by at least searching and using 3 phase differences, wherein two are the phase differences to be paired, and the other is used for pairing;

(2) aiming at the scheme for automatically pairing the information source phase difference or angle, an ULA (ultra-low amplitude amplifier) selection principle for realizing automatic pairing of the information source phase difference or angle is provided, namely: at least 3 specific ULAs are selected in the multi-dimensional array, the 3 ULAs should have source phase differences in different function forms, and for convenience of calculation and comparison, the 3 source phase differences preferably satisfy a linear combination relation;

and (V) calculating the elevation angle and the azimuth angle of the source in the multi-dimensional array:

in the multidimensional array, the phase difference of each specific information source is an explicit function of the elevation angle and/or azimuth angle of the specific information source, and the form of the function of the phase difference of the information source only changes along with the type of the ULA, so that the two-dimensional information source direction finding is actually converted into the problem that the elevation angle and the azimuth angle are calculated by the phase difference of two matched pairs after the automatic matching of the phase difference or the angle of the information source is completed;

after the automatic matching of the source phase difference or angle is realized, two ULAs are selected from any of the 3 selected ULAs, and the source elevation angle and the azimuth angle are directly calculated by utilizing the source propagation sub and phase difference formulas corresponding to the two selected ULAs and the estimated values of the source propagation sub and phase difference formulas.

Technical Field

The invention belongs to two-dimensional information source direction finding based on a multi-dimensional array in array signal processing, and can be widely applied to the research related to target parameter estimation, positioning, identification and tracking in the fields of radar, sonar, communication, seismic exploration, automatic driving and the like.

Background

Array signal processing based on various sensor arrays is a modern signal processing technology which is rapidly developed in recent three or forty years, and is widely applied to many actual engineering fields such as radar, sonar, mobile communication, geological exploration, biomedicine, automatic driving and the like. The source Direction of arrival (Estimation of Direction of arrival) is a basic content in array signal processing, and has important military, civil and civil values.

The multi-dimensional array can provide an elevation angle and an azimuth angle, and can carry out more detailed description on an external incident information source, so that the direction finding of the two-dimensional information source (also called information source elevation angle and azimuth angle joint estimation, two-dimensional direction of arrival estimation and two-dimensional DoA estimation) is closer to the practical engineering application, and has more theoretical significance and practical value.

A multi-dimensional array including a two-dimensional area array and a three-dimensional volume array includes a large number of Uniform Linear Arrays (ULA), which is an advantage of the multi-dimensional array; in addition, the array design and optimization can be realized only by orderly selecting and setting the sensor array elements on a multi-dimensional scale. Therefore, proposing and developing a two-dimensional source direction finding method capable of fully playing and matching the advantages of the multi-dimensional array is a problem to be solved urgently in both theory and practical application.

At present, the conventional idea is to decompose the complicated two-dimensional source direction finding problem into two simpler and easily-processed single-angle estimation problems. In order to realize two-dimensional information source direction finding decomposition operation, comprehensive consideration and solution need to be carried out from two angles of a single-angle estimation method and a matched array geometric structure, most of the existing single-angle estimation methods are proposed and developed based on an Azimuth-only ULA model, the existing single-angle estimation methods are generally considered to be mature at present, two-dimensional information source direction finding is preferably and directly used, but the Azimuth-only ULA model is simple, the information source phase shift is a single-term function only containing an Azimuth angle, and the phase shift is directly proportional to the phase difference; while the source phase shift of various ULA in a multi-dimensional array tends to be linear with respect to their phase shift, the phase shift and phase difference are a function of the source azimuth and elevation, and the azimuth and elevation are coupled to each other (except for the ULA located on the Z-axis). Therefore, the single angle estimation method based on the Azimuth-only ULA model is difficult to be applied directly to any ULA in a multi-dimensional array.

For this reason, a generally accepted compromise is to find ULA that contain only a single angle within the multi-dimensional array. It can be seen that the ULA on the Z axis in the multidimensional array only contains the elevation angle, and the elevation angle of the information source can be estimated by directly using a single-angle estimation method; if the azimuth angle is defined by the angle between the incident direction of the source and the X-axis, the ULA on the X-axis only contains the azimuth angle of the source. Therefore, two orthogonal ULA on the X and Z axes form a simple ULA combination, which is called an L-shaped array, and the L-shaped array is an array capable of matching with a single angle estimation method, which can directly process the array data, and a large part of two-dimensional source direction finding methods are proposed and researched based on the L-shaped array.

Conventional single angle estimation methods such as Subspace-based methods (including MUSIC methods, ESPRIT and its modifications or variations) can be directly applied to two-dimensional direction of arrival estimation, and other methods include mpm (matrix pencil method), pm (promoter method), and mwe (Subspace-based method with estimated contribution) methods and CODE (Cross-correlation based 2D DOA estimation) methods, which are more or less borrowing the rotation invariant technique of ESPRIT.

The non-L-shaped array is also concerned in two-dimensional information source direction finding, the representative array is a double parallel line shape, the principle is that a diagonal unitary matrix containing information source phase difference is separated out by utilizing two parallel ULAs, and the double parallel line shape is different from the L-shaped array in that the two ULAs are not required to be positioned on coordinate axes.

The greatest advantage of multi-dimensional arrays is that a large number of alternative ULA, various ULA arrays and combinations can be provided for two-dimensional source direction finding, but only a small number of arrays including L-shaped arrays and double parallel lines are currently used, which means that the existing two-dimensional source direction finding method does not currently have the capability of processing any ULA and data thereof in the multi-dimensional array, and cannot match and exert the advantages of the multi-dimensional array, which is a waste of resources and efficiency of the multi-dimensional array.

Source elevation to azimuth pairing is another key issue in two-dimensional source direction finding research. The array (for example, an L-shaped array) commonly used in the current two-dimensional source direction finding method generally consists of two ULA. Processing one ULA data can obtain a disordered source single-angle estimation value set, and processing two ULAs separately can obtain two decoupled angle estimation value sets. Thus, angular pairing is the picking and pairing of elevation and azimuth from the same source in two decoupled and unordered sets of estimates. Currently, angle pairing is mainly realized by setting a cost function and using a complex two-dimensional search or nonlinear optimization algorithm.

In practice, the pairing of source elevation and azimuth can be seen as a constraint. For multidimensional array data, the constraint can translate a linear combination parameter newly set as two parameters to be paired, and to estimate the new parameter, the corresponding ULA and its data need to be additionally selected and provided. Thus, to implement source elevation and azimuth pairing, theoretically at least 3 ULA's need to be chosen, where two ULA's are used to estimate the parameters to be paired (e.g., azimuth and elevation) and the other is used for pairing. In contrast, in the conventional two-dimensional source direction finding method, the angle estimation and pairing both use the original two ULA, and the ULA data that has been used for estimating the elevation angle and the azimuth angle of the source is reused for determining the pairing of the elevation angle and the azimuth angle of the source, which is questionable in principle.

It can be seen that the propagation physical characteristics of the external incident source, including the complex composition of the source phase and the coupling manner of its internal elevation and azimuth, determine the estimation method and its matching formation, and in addition, the two definitions of the source azimuth also cause the phase and the coupling manner of its internal elevation and azimuth to change. In summary, the two-dimensional source direction finding is far more complex in theory and method than the single-angle DoA estimation based on the Azimuth-only ULA model.

The sensor array signal processing comprises two-dimensional signal source direction finding, which is a physical problem and a signal processing problem and is a cross disciplinary problem, the physical basis of the sensor array is that sensor array elements are orderly arranged in space, the phase of an external incident signal source is induced to regularly change along with the orderly arrangement of the sensor array elements in space, specifically, for a multi-dimensional array, the phase of the incident signal source and the phase difference of the incident signal source are in a linear relation, and a linear coefficient is a sensor array element space position angle mark.

Disclosure of Invention

The invention provides a multi-dimensional sensor array source direction finding method based on a degraded space ARMA model, which can match and give full play to the two-dimensional source direction finding of the advantages of a multi-dimensional array.

The technical scheme adopted by the invention is as follows: comprises the following steps:

(I), 3-dimensional volume array model:

(1) directly considering a 3-dimensional array without loss of generality, the array is composed of M multiplied by N multiplied by L isotropic sensor array elements, the number of the sensor array elements parallel to X, Y and Z-axis direction is M, N and L respectively, K far-field narrow-band stationary information sources in space are incident to the 3-dimensional array, and the incident azimuth angle and the incident elevation angle are (phi) respectively_k，θ_k) K is 1, …, K, and after setting the sensor array element at the origin of the matrix coordinate as a zero-phase array element, the kth source propagates the phase shift reaching the (m, n, l) th array element of the 3-dimensional matrixComprises the following steps:

wherein M is 1, …, M; n is 1, …, N; l is 1, …, L.Andrepresenting the component phases in directions parallel to the X, Y and Z axes respectively,andis defined as the constituent phaseThe parameter item of (2). Equation (1) shows that the phase of an external source incident on any sensor array element in the multidimensional array is a linear combination of 3 parameter terms;

the 3 parameter terms in the formula (1) are:

wherein the scale factorf and c represent carrier frequency and propagation velocity, Δ d_x、Δd_yAnd Δ d_zSpacing the sensor array elements in the direction parallel to X, Y and Z axis;

u in formula (2)_k、v_kAnd w_kThe method specifically comprises the following steps:

u_k＝cos(φ_k)sin(θ_k)，v_k＝sin(φ_k)sin(θ_k)，w_k＝cos(θ_k). (3)

wherein theta is_kAnd phi_kThe elevation angle and the azimuth angle of the kth information source are respectively defined as an included angle between an incident direction of the information source and a Z axis and an included angle between a projection of the incident direction on the X-Y plane array and an X axis, under the definition of the azimuth angle, except that sensor array element data positioned on the Z axis only comprises the elevation angle theta, other sensor array element data in the multidimensional array simultaneously comprises the elevation angle theta and the azimuth angle phi, the two angles are mutually coupled, and for the convenience of the following discussion, a parameter item delta phi is defined_xAnd delta phi_yAlso called source elevation angle theta and azimuth angle phi, where for simplicity, the constant terms are true since they hold for all K sourcesAndθ_kand phi_kThe index k is deleted.

(2) On the premise of the assumption that external incident source signals and sensor noise are stable, theories show that a signal model of the source incident on any ULA in the multidimensional array is a degraded space ARMA (automatic moving-average) model, and the degraded space ARMA model has MYW (Modified Yule-Walker) linear equation set and a root-seeking polynomial;

(II) estimating the source phase difference of any ULA in the multi-dimensional array:

(1) the invention can process any ULA in the multidimensional array and data thereof, and estimate the phase difference of external incident information sources, which is the basis and premise for solving the problem of two-dimensional information source direction finding, and is also a distinct characteristic different from the existing two-dimensional information source direction finding method, and the characteristic can fully utilize and play the advantage of abundant data of the multidimensional array;

aiming at any ULA in the multi-dimensional array, under the precondition that an information source signal is irrelevant to sensor noise, by utilizing a correlation function of the ULA data, a linear equation set and a polynomial root are sequentially constructed and solved MYW, and the phase difference of each information source can be calculated;

(2) for any ULA in a multi-dimensional array, using its correlation function of sensor array data, a linear system of equations is constructed MYW as follows:

hb ═ r, (4) in formula (4), H is an I × K dimensional coefficient matrix, and b and r are K × 1 and I × 1 dimensional parameters to be solved and constant term column vectors, respectively. H. The specific forms of b and r are as follows:

wherein (·)^TFor transpose operators, line vectors h_m＝[h_m,…,h_(m+K―1)],m＝1,…,I，h_mAnd array elements in r E {. is the mathematical expectation (.)^HIs a conjugate transpose, x_i(t) and n_i(t) is the ith sensor array element data and noise, x, of the selected ULA_n(t) referred to as reference data;

under the condition that the signal source signal and the noise are stable, a correlation function is taken for the ULA data, and R can be ensured_iAndthe same is stable; and when the sensor noise is not related to the information source signal, x can be reasonably selected_n(t) making MYW linear equation set in equation (4) no longer contain unknownsConvenience is brought to equation solving;

(3) to-be-solved parameterIs K incident source propagatorsThe specific functional form of the initial idempotent and symmetric function of (2) is:

solving the MYW linear equation set in the formula (4) can obtain K parameters to be solvedThis requires that the number of equations I in the MYW linear system of equations should at least satisfy I ≧ K;

(4) constructing a root-seeking polynomial according to the parameters to be sought in the formula (6)The following unary first polynomial is constructed:

f(v)＝v^K+b₁v^K―1+…+b_kv^K―k+…+b_K, (7)

easy to prove, source propagatorIs the root of a unary first polynomial f (v);

root-finding f (v) to obtainThen the kth source differs by phaseThe following equation is used to solve:

(III) ULA classification criterion in the multi-dimensional array:

(1) the invention can process any ULA data of the multidimensional array, firstly determine the ULA classification criterion in the multidimensional array according to the function form of the source phase difference, and provide a plurality of source phase difference estimation modes according to the ULA classification criterion, thereby finding a solution for the problem of automatic angle pairing in the direction finding of two-dimensional source; accordingly, the source phase difference in the same functional form can be estimated by processing the ULA data belonging to the same class.

(2) In the multidimensional array, the source phase difference can be expressed as a linear combination of a plurality of component phase differences in a functional form, wherein each component phase difference can be directly estimated by finding corresponding ULA data, so that the source phase difference has the following two estimation modes based on an explicit functional form of the phase difference and a linear combination form thereof: directly estimating by searching and utilizing corresponding ULA data based on an explicit function form of the phase difference per se; firstly, estimating component phase difference, and calculating the estimated component phase difference by using a linear combination formula;

(IV) source phase difference or angle pairing scheme in the multidimensional array:

(1) the invention converts the automatic pairing of the information source phase difference or the angle into a constraint parameter, embodies the constraint parameter into the linear combination of two phase differences to be paired, and realizes the automatic pairing by comparing the information source phase difference results obtained by two estimation modes one by one, therefore, the invention provides the following steps: the method comprises the steps of realizing automatic matching of information source phase differences or angles, searching and using at least 3 phase differences, wherein two phase differences are phase differences to be matched, and the other phase difference is used for matching;

(2) aiming at the scheme for automatically pairing the information source phase difference or angle, the invention provides an ULA (ultra low amplitude analysis) selection principle for realizing automatic pairing of the information source phase difference or angle, namely: at least 3 specific ULAs are selected in the multi-dimensional array, the 3 ULAs should have source phase differences in different function forms, and for convenience of calculation and comparison, the 3 source phase differences preferably satisfy a linear combination relation;

and (V) calculating the elevation angle and the azimuth angle of the source in the multi-dimensional array: in the multidimensional array, the phase difference of each specific information source is an explicit function of the elevation angle and/or azimuth angle of the specific information source, and the form of the function of the phase difference of the information source only changes along with the type of the ULA, so that the two-dimensional information source direction finding is actually converted into the problem that the elevation angle and the azimuth angle are calculated by the phase difference of two matched pairs after the automatic matching of the phase difference or the angle of the information source is completed;

after the automatic matching of the source phase difference or angle is realized, two ULAs are selected from any of the 3 selected ULAs, and the source elevation angle and the azimuth angle are directly calculated by utilizing the source propagation sub and phase difference formulas corresponding to the two selected ULAs and the estimated values of the source propagation sub and phase difference formulas.

The information source phase difference estimation method and the two-dimensional information source direction finding method provided by the invention are also suitable for various two-dimensional sensor area arrays.

According to the method, by utilizing the characteristic that the linear change of the information source phase is induced by the ordered spatial arrangement of the sensor array elements, under the condition that the information source signal and the sensor noise are stable, a method capable of processing any ULA data in a multi-dimensional array and estimating the information source phase difference is provided firstly through implementing spatial difference on the information source phase; for all the ULAs in the multi-dimensional array, firstly determining a classification criterion according to the source phase difference function form: the ULAs with the same source phase difference function form belong to the same class, and the ULAs of the same class have the same root-seeking polynomial and source phase difference estimation performance; the invention provides a two-dimensional information source direction-finding information source phase difference or angle automatic pairing general scheme and an ULA combination principle thereof; and provides a two-dimensional source direction finding method which can match and give full play to the advantages of the multi-dimensional array.

The invention has the advantages that: the proposed information source phase difference estimation method can process any ULA in the multi-dimensional array, and the two-dimensional information source direction finding method can match and play the advantages of the multi-dimensional array ULA and rich data thereof; and the ULA combination criterion capable of realizing automatic source phase difference or angle pairing is given, and the method has guiding significance for practical direction finding application.

In terms of algorithm, the direction-finding method only requires the signal properties of the noise of the information source and the sensor array element to be stable; and simultaneously, independent, correlated and coherent information sources and independent and coherent mixed information sources can be processed.

In addition, the provided direction finding method is used for directly processing the multidimensional array data, matrix eigenvalue decomposition or singular value decomposition is not involved, and the calculation is more efficient.

Drawings

FIG. 1 is a diagram of the ULA used on three area arrays X-Y, X-Z and Y-Z in a 3-dimensional volume array in an example;

FIG. 2 is a plot of source phase difference search for non-axial ULAs parallel to coordinate axes within X-Y, X-Z and Y-Z3 planar arrays;

FIG. 3 is a graph of source-disparity search results for the ULA on the anti-diagonals in 3 area arrays, X-Y, X-Z and Y-Z;

fig. 4 is a source phase difference estimation performance graph for a multi-dimensional array selected ULA.

Detailed Description

Comprises the following steps:

(I), 3-dimensional volume array model:

for the sake of no loss of generality, a 3-dimensional array is directly considered, the array is composed of M multiplied by N multiplied by L isotropic sensor array elements, the number of the sensor array elements parallel to X, Y and Z-axis direction is M, N and L respectively, K far-field narrow-band stationary sources in space are incident to the 3-dimensional array, and the incident azimuth angle and elevation angle are (phi) respectively_k，θ_k) K is 1, …, K, and after setting the sensor array element at the origin of the matrix coordinate as a zero-phase array element, the kth source propagates the phase shift reaching the (m, n, l) th array element of the 3-dimensional matrixComprises the following steps:

wherein M is 1, …, M; n is 1, …, N; l is 1, …, L.Andrepresenting the phase of the component parallel to the X, Y and Z axes, respectively, without reference to the ULA, we will refer toAndis defined as the constituent phaseThe parameter item of (2). Equation (1) shows that the external source phase incident on any sensor array element in the multidimensional array is a linear combination of 3 parameter terms.

The 3 parameter terms in the formula (1) are:

wherein the scale factorf and c represent carrier frequency and propagation velocity, Δ d_x、Δd_yAnd Δ d_zAre spaced apart in the sensor array elements parallel to the X, Y and Z-axis directions.

U in formula (2)_k、v_kAnd w_kThe method specifically comprises the following steps:

u_k＝cos(φ_k)sin(θ_k)，v_k＝sin(φ_k)sin(θ_k)，w_k＝cos(θ_k). (3)

wherein theta is_kAnd phi_kThe elevation angle and the azimuth angle of the kth information source are respectively defined as an included angle between the incident direction of the information source and the Z axis and an included angle between the projection of the incident direction on the X-Y plane array and the X axis. Under the above definition of azimuth, in addition to the sensor array element data located on the Z-axis only including the elevation angle θ, other sensor array element data in the multidimensional array includes both the elevation angle θ and the azimuth angle φ, and the two angles are coupled to each other (for convenience of the following discussion, the parameter term Δ φ_xAnd delta phi_yAlso known as the coupling terms of source elevation theta and azimuth phi. Since this holds for all K sources, the constant term is simpleAndθ_kand phi_kThe index k is deleted);

there are two common definitions of source azimuth in practice, besides the definition of φ, there is another definition φ', namely: the angle between the incident direction of the source and the X-axis, defined by the azimuth angle phi', u in formula (3)_kAnd v_kThe specific function form of the azimuth angle needs to be correspondingly changed, and the transformation relation between two definitions of the azimuth angle phi and phi' meets the following conditions:

cos(φ′_k)＝cos(φ_k)sin(θ_k), (4)

any ULA in a multi-dimensional array is one-dimensional, which means that only one sensor array element spatial position angle scale in the source phase formula incident on any ULA changes orderly. Thus, the source phase can be uniformly expressed as:

in the formula (5)Andfor corresponding source phase difference and constant phase, due to phaseFor k sources, only the index m is reserved in the invention to emphasize phaseDependence on the subscript m;

according to the formulas (1) and (5), any ULA in the multidimensional array is mainly divided into the following two types according to the variation of the sensor array element spatial position angle mark:

type 1: only 1 ordered change exists in the 3 sensor array element spatial position angle labels, and the type 1 mainly refers to the ULA (ultra Wide array) which is positioned and parallel to 3 coordinate axes such as X, Y and Z in the multi-dimensional array;

for example, let a ULA with its array element spatial position angle l parallel to the Z axis be from l₀Increment to L, L₀Is a constant integer satisfying l₀<L, constant integer m for angle marking parallel to the X and Y axes₀And n₀Indicates the source phase incident on the ULA(for the sake of simplicity, the symbols are omittedThe superscript k, and the corner mark k will also be recovered if the following is required, which is not described herein again) can be expressed as:

whereinFor the source phase difference to be,defined as source phaseA constant phase of (d);

more specifically, let m₀＝1,n₀1 and l₀Constant phase 1Then the source phase The ULA corresponding to the source phase is Elevation-only ULA which is positioned on the Z axis of the multi-dimensional array and starts from the coordinate origin, the Elevation-only ULA data only contains the Elevation angle theta, and analysis shows that any ULA positioned on or parallel to the Z axis has the formula (6)Of a phase difference ofConstant phaseMiddle corner mark m₀And n₀Actually describing the spatial position of the ULA in the multi-dimensional array, its starting array element is marked by the corner mark l₀Description is given;

similarly, the phase of any ULA lying on or parallel to the X axisCan be expressed as:

m in the formula (7) is a change angle mark,is a source phase difference, constant phase Corner mark n₀And l₀The spatial position, m, of the corresponding ULA is depicted₀The ULA start array element is indicated;

when m is₀＝1,、n₀1 and l₀Constant phase when 1Source phase change toThe corresponding ULA is located on the X-axis and starts at the origin of the multidimensional array coordinate, and likewise, any ULA located on or parallel to the X-axis has the phase in equation (7)Of a phase difference of

Similarly, for any ULA located at or parallel to the Y axis, there are:

in the formula (8), n is a change angle mark,is a source phase difference, constant phase

When m is₀＝1,、n₀1 and l₀When the number is equal to 1, the alloy is put into a container,source phaseThe corresponding ULA is located on the Y-axis and starts at the origin of the multidimensional array coordinate. Similarly, any ULA in the multi-dimensional array that is at or parallel to the Y axis has the phase in equation (8)Of a functional form of phase difference of

As can be seen from equations (6), (7) and (8), the ULA starting from the multidimensional array origin of coordinates and located on the coordinate axis differs mainly from the ULA starting from the non-origin of coordinates and located on the coordinate axis or parallel to the coordinate axis by zero and non-zero constant phases, the source phase of the ULA starting from the multidimensional array origin of coordinates is relatively simple in functional form and easy to handle, especially the Elevation-only ULA located on the Z-axis because the constant phase is zero;

type 2: in the information source phase formula (1), two or three sensor array element space position angle markers change synchronously;

type 2 refers primarily to ULA located on and parallel to various diagonal lines on an area or volume array;

multi-dimensional arrays can provide a large number of ULA's on and parallel to various diagonals, and the present invention is primarily described in terms of ULA's on the X-Y, Y-Z and X-Z area array anti-diagonals and starting at the area array origin of coordinates.

Setting the angular marks m and n of the sensor array element space position of the ULA from the X-Y plane array coordinate origin m₀＝n₀When the synchronous increase is started as 1, the phaseCan be expressed as:

phase difference between neutral sources in formula (9)Since the ULA is in the X-Y plane array, the corner mark l₀1, again starting at the origin of the area array coordinates, so the ULA phaseConstant phase ofEqual to zero, phase of the source in equation (9)Analysis of the ULA on the anti-diagonal of the X-Y array and starting from the origin of coordinates shows that the sources in the multidimensional array that are parallel to the ULA on the anti-diagonal of the X-Y array all differ by a factor ofSimilarly, the ULAs parallel to the diagonal of the X-Y array are all phase-shifted byPhase differenceAndis thatAndtwo linear combinations of (1);

ULA located on the reverse diagonal of the Y-Z plane array and starting at the origin of coordinates, its source phaseComprises the following steps:

wherein the source phase difference isSimilarly, the source-to-source phase difference of the ULA parallel to the Y-Z plane array anti-diagonals in the multidimensional array is all asSimilarly, the ULAs parallel to the diagonal of the Y-Z array are all phase-shifted by

ULA located on the opposite diagonal of the X-Z array and starting at the origin of coordinates, its source phaseComprises the following steps:

wherein the source phase difference isSimilarly, sources within the multidimensional array that are parallel to the ULA on the anti-diagonals of the Y-Z plane array all differ by as much asSimilarly, the ULAs parallel to the diagonal of the X-Z array are all phase-shifted by

For 3D body array, also having various ULAs on or parallel to body diagonal, the corresponding source phase difference function form has 3 sensor array elements space position angle scale synchronous change, therefore, the source phase difference isAnda combination coefficient of +1 or-1, for example:

etc., not listed one by one here.

The invention can process any ULA and data thereof in the multidimensional array and estimate the phase difference of external incident information sources, which is the basis and premise for solving the problem of two-dimensional information source direction finding.

On the premise of the assumption that external incident source signals and sensor noise are stable, a signal model of a source incident on any ULA in the multidimensional array is a degraded space ARMA (autoregisterive moving-average) model, and the degraded space ARMA model has MYW (Modified Yule-Walker) linear equation set and a root-seeking polynomial;

(II) estimating the source phase difference of any ULA in the multi-dimensional array: aiming at any ULA in the multi-dimensional array, under the precondition that an information source signal is not related to sensor noise, by utilizing a correlation function of the ULA data and sequentially constructing and solving MYW a linear equation set and a polynomial root solving, the phase difference of each information source can be calculated, and the following is a specific implementation scheme provided by the invention for processing any ULA data in the multi-dimensional array:

for any ULA in a multi-dimensional array, using its correlation function of the sensor array data, a linear system of equations is constructed MYW as follows:

hb ═ r, (13) in formula (13), H is an I × K dimensional coefficient matrix, and b and r are K × 1 and I × 1 dimensional parameters to be solved and constant term column vectors, respectively. H. The specific forms of b and r are as follows:

wherein (·)^TFor transpose operators, line vectors h_m＝[h_m,…,h_(m+K―1)],m＝1,…,N。h_mAnd array elements in r E {. is the mathematical expectation (.)^HIs a conjugate transpose, x_i(t) and n_i(t) is the ith sensor array element data and noise, x, of the selected ULA_n(t) referred to as reference data;

at the source signalUnder the condition that sum noise is stable, a correlation function is taken for the ULA data, and R can be ensured_iAndthe same is stable; and when the sensor noise is not related to the information source signal, x can be reasonably selected_n(t) making MYW linear equation set in equation (13) no longer contain unknownsConvenience is brought to equation solving;

to-be-solved parameterIs K incident source propagatorsThe specific functional form of the initial idempotent and symmetric function of (2) is:

solving the MYW linear equation set in the formula (14) can obtain K parameters to be solvedThis requires that the number of equations I in the MYW linear system of equations should at least satisfy I ≧ K;

constructing a root-seeking polynomial according to the parameters to be sought in the formula (15)The following unary first polynomial is constructed:

f(v)＝v^K+b₁v^K―1+…+b_kv^K―k+…+b_K, (16)

easy to prove, source propagatorIs the root of a unary first polynomial f (v);

root-finding f (v) to obtainThen the kth source differs by phaseThe following equation is used to solve:

thus, with any ULA data in the multi-dimensional array, the equation unknown parameters are first estimated MYW by constructing and solving a linear system of equationsSecond using the estimatedConstructing and rooting a unary first polynomial f (v) to obtain an information source propagatorFinally known byCalculating all signal source phase differences, which are the steps of any ULA signal source phase difference estimation method provided by the invention;

(III) ULA classification criterion in the multi-dimensional array: the invention can process any ULA data of the multidimensional array, determines the ULA classification criterion in the multidimensional array according to the information source phase difference function form, provides various information source phase difference estimation modes according to the ULA classification criterion, and finds a solution for finally solving the problem of angle automatic pairing in the direction finding of the two-dimensional information source;

in the multidimensional array, the starting array elements, the spatial positions and the source phase function forms of various ULAs may be different, but the various ULAs can be effectively classified according to the function forms of source phase differences, and all the ULAs with the same function forms of the source phase differences belong to one class; correspondingly, the ULA data belonging to one type are processed, and the information source phase difference in the same function form can be estimated;

for example, in a multi-dimensional array, all ULA's parallel to the X-axis belong to a class that can be used to estimate phase differencesAlso, all ULA parallel to the Y axis can be estimatedAll the ULAs parallel to the Z axis can be estimated

(IV) source phase difference or angle pairing scheme in the multidimensional array: in a multidimensional array, the source phase difference can be expressed in a functional form as a linear combination of a plurality of component phase differences, each of which can be directly estimated by finding the corresponding ULA data. Therefore, based on the explicit function form of the phase difference itself and the linear combination form thereof, the source phase difference has the following two estimation modes:

directly estimating by searching and utilizing corresponding ULA data based on an explicit function form of the phase difference per se; firstly, estimating component phase difference, and calculating the estimated component phase difference in an indirect mode by using a linear combination formula;

for example, source phase differenceOne way is direct estimation, which is directly estimated from the ULA on or parallel to the anti-diagonals within the X-Y plane array; indirect estimation isSeen as a component phase differenceAndlinear combination of components, phase differenceAndsource phase difference can be estimated from the ULA at or parallel to the X and Y axes, respectivelyCan be estimatedAndusing linear combination formulasCalculating to obtain;

it is worth noting that various source phase differences estimated by using the ULA data are all decoupled and unordered, which shows that in an indirect estimation mode, only under the premise that component phase differences are matched, the source phase differences can be calculated and given in a linear combination mode. On the contrary, the same information source phase difference results obtained by the two estimation modes are equal to each other, and the results obtained by the two estimation modes are compared one by one, so that automatic pairing of the information source phase difference (or angle) can be realized. Therefore, the invention provides a phase difference (or angle) automatic pairing scheme based on multi-dimensional array multi-ULA data;

the invention converts the automatic pairing of the source phase difference or the angle into a constraint parameter, embodies the constraint parameter into the linear combination of two phase differences to be paired, and realizes the automatic pairing by comparing the source phase difference results obtained by two estimation modes one by one. Therefore, the present invention proposes: the method comprises the steps of realizing automatic matching of information source phase differences or angles, searching and using at least 3 phase differences, wherein two phase differences are phase differences to be matched, and the other phase difference is used for matching;

aiming at the scheme for automatically pairing the source phase difference (or angle), the invention provides an ULA (ultra low amplitude analysis) selection principle for realizing automatic pairing of the source phase difference or angle, namely: at least 3 specific ULAs are selected in the multi-dimensional array, the 3 ULAs should have source phase differences in different function forms, and for convenience of calculation and comparison, the 3 source phase differences preferably satisfy a linear combination relation;

and (V) calculating the elevation angle and the azimuth angle of the source in the multi-dimensional array: in a multi-dimensional array, each particular source disparity is an explicit function of its elevation and/or azimuth, and the source disparity function form varies only with the ULA class. Therefore, after the automatic matching of the phase difference (or angle) of the information sources is completed, the two-dimensional information source direction finding actually becomes a problem that the elevation angle and the azimuth angle of the information source are calculated by the phase difference of two matched pairs;

after the automatic matching of the phase difference or angle of the information sources is realized, two ULAs are selected from the 3 selected ULAs, and the elevation angle and the azimuth angle of the information sources are directly calculated by corresponding information source propagation sub and phase difference estimated values;

for example: in the X-Y area array, the ULA parallel to the X and Y axes is selected, and the corresponding ULA data is used for estimating to obtain an estimated value of the kth source propagation sub-pairCorresponding to an estimated value of phase difference pair Using propagatorsAndrespectively differ from each otherAndexplicit relational expression ofAnd the following formula can be obtained:

the calculation formula of the k-th source azimuth estimate is:

the k azimuth angle is calculated by equation (19)After calculation, willSubstitution into (17) or (18) can result in:

or

For another example: in an X-Z array, by parallel to the X and Z axesThe estimation value of k information source propagation sub-pair obtained by estimating the data of the ULA isCorresponding to an estimated value of phase difference pairUsing propagatorsAndrespectively differ from each otherAndexplicit relational expression ofAndthen:

the calculation formula of the k source elevation angle estimated value is as follows:

elevation angle of k-th by equation (24)After calculation, willSubstituting (22) can obtain:

similarly, the k-th source azimuth estimate can be calculated from equation (25)

The source phase difference estimation method provided by the invention can also process the ULA data under another coordinate definition phi 'of the azimuth angle, and the definition of the azimuth angle phi' is as follows: and the included angle between the incident direction of the information source and the X axis of the multidimensional array. The principles and steps of the source phase difference estimation method and the two-dimensional source direction finding method are completely the same as those mentioned above.

The source phase difference estimation method and the two-dimensional source direction finding method provided by the invention are also suitable for various two-dimensional sensor area arrays, and the array direction finding method based on the target source propagation phase shift difference technology needs the given number of target sources in advance.

The effectiveness of the method provided by the invention is verified by the following two-dimensional information source direction-finding example.

Two-dimensional information source direction-finding calculation example based on 3-dimensional array adopts the three-dimensional square array of equal sensor array element interval here, for simplifying the calculation, supposing that the sensor array element number along 3 directions such as X, Y and Z axle is 8, has 3 far-field narrow-band information sources to incide to this square array, and equal sensor array element interval adopts two kinds: λ is signal wavelength, SNR is 5dB, signal source signal and sensor noise are both simulated by zero-mean complex Gaussian white noise, each sensor array element noise has the same variance, and azimuth angle phi of 3 signal sources_kAnd elevation angle theta_k(k is 1,2,3) is (phi)₁,θ₁)＝(95°,45°)，(φ₂,θ₂) Equal to (63 °,12 °) and (Φ)₃,θ₃)＝(150°,71°)。

Here, theUsing the first sensor data of each ULA as reference data, a sequence of correlation functions { h } of sensor array data is selected since the signal is uncorrelated with noise₂,h₃,┄,h_MThe system does not contain unknown noise variance and can be used for constructing MYW linear equations, so that the noise variance is not required to be considered when solving the equations.

1. Source phase difference estimation

The multidimensional array can provide abundant and various ULAs for two-dimensional source direction finding, and the method can process any ULA data, which is a distinct feature and advantage of the invention. In the calculation example, 3 representative groups of ULAs are specifically selected, wherein the 3 groups of ULAs are respectively taken from 3 area arrays of X-Y, X-Z and Y-Z in FIG. 1, wherein 3 ULAs are selected in each area array, namely two non-axial ULAs parallel to the coordinate axes of the area array and an ULA located on the anti-diagonal line of the area array.

Because more ULA are selected in the calculation example, in order to avoid confusion and facilitate the following explanation and analysis, each selected ULA is named, and the ULA naming rule is explained by specifically combining 3 selected ULA on an X-Y plane array, as shown in fig. 1, non-axis ULA parallel to X and Y axes are selected in the X-Y plane array and respectively used as X and Y axes^n＝2And Y^m＝2Name, X^n＝2The superscript n-2 indicates the Y-axis coordinate of the ULA on the X-Y array; also, as shown in fig. 1, m ═ 2 indicates a ula y^m＝2X-axis coordinates on the X-Y plane, ULA on the anti-diagonals of the X-Y plane, where D is used_XYNaming; by similar nomenclature, 3 ULAs selected on an X-Z array, each designated by X^l＝2、Z^m＝2And D_XZDenotes, wherein the non-axis ULA parallel to the Z-axis is Z^m＝2With X-axis coordinate m 2, non-axis ULAX parallel to the X-axis^l＝2The Z-axis coordinate is l-2, and the ULA on the inverse diagonal line of the X-Z planar array is D_XZ(ii) a The 3 ULAs selected on the Y-Z array are respectively Y^l＝2、Z^n＝2And D_YZThe naming rules and the ULA location are not described in detail here.

In comparison with the conventional elevation-only ULA on the Z axis, Z was selected in the calculation^m＝2And Z^n＝2Is a non-axial ULA parallel to the Z-axis, with source phase difference equal to eleIdentical for the motion-only ULA, but with a non-zero constant phase, Z, due to the non-axis^m＝2And Z^n＝2The source phase shift of (a) is more complex in functional form than the elevation-only ULA.

In order to visually display and analyze the calculation example results, after a linear equation set of MYW is constructed and solved for the selected ULA, a root-finding curve is drawn for the root-finding polynomial by adopting a point-by-point numerical root-finding method. As shown in fig. 2, the ordinate is normalized amplitude, which is the reciprocal of the absolute value of the root-finding polynomial, the amplitude has a sharp peak to represent that the root of the polynomial is found, and the abscissa of the peak is the estimated value of the phase difference of a certain signal source, and of course, for the root-finding polynomial of which the first term is less than 5, the phase difference of the signal source can be directly calculated by using the root-finding formula. In the example, since the array element spacing of the cubic array along the X, Y and Z-axis 3 directions is set to be equal, the source phase difference of the ULA parallel to X, Y and Z-axis can be simplified to u respectively_x＝cosφsinθ，v_ySin phi sin theta and w_zCos θ, considering the azimuth angle φ ∈ [0, π ∈ [ ]]Elevation angle theta is equal to 0, pi/2]Then u is_x∈[―1,1]，v_y∈[0,1]And w_z∈[0,1]；

As shown in fig. 2(a), (b) and (c), when the spacing between the sensor array elements is larger than 0.45 λ, the amplitude peak and the position are clearer and are easy to distinguish and judge. For example, the peak position of the amplitude of the thick line in fig. 2(a) is (-0.82, -0.06,0.10), which is the non-axial ULAX in the X-Y array^n＝2The peak position of the amplitude of the thin line is (0.19,0.47,0.71), and is non-axial ULAY in the X-Y plane array^m＝23 source phase difference estimates.

When the sensor array element spacing becomes smaller than 0.30 λ, the resolution of the amplitude peak and its position is reduced, which is not easy to be determined, for example, when the sensor array element spacing is 0.30 λ in fig. 2(a), X^n＝2And Y^m＝2The corresponding o line can not even correctly judge the number of the information sources according to the peak value of the curve; however, for other ULA, even if the sensor array element interval is 0.30 λ, the number of sources, the peak value and the position thereof can be clearly determined, so as to obtain more accurate source phase difference estimation values, such as the thick o line in fig. 2(b) and the thin o line in fig. 2 (c).

As indicated above, for a multi-dimensional array, since a large amount of ULA data is available, even when the sensor array element spacing setting is small or the signal SNR is low, it is still possible to perform source direction finding using the multi-ULA data, but if a two-dimensional source direction finding method can only be based on a specific ULA or array shape, when the sensor array element spacing is small or the SNR is low, the source direction finding is likely to not be performed or to obtain an erroneous result. Therefore, for multi-dimensional arrays, especially for MIMO large-scale antenna arrays, one of the most basic requirements for the direction-finding method is that the method should have the capability of processing any ULA and its data, and the source phase difference estimation method proposed by the present invention can fully meet the above requirements.

As can be seen from fig. 2(a), (b) and (c), ULA having the same source phase difference function form belong to a class, and although these ULA may be in different area arrays or distributed at different positions on the same area array, they can all be used to estimate the same phase difference. E.g. ULAX parallel to the X-axis^n＝2Distributed in an X-Y array, X^l＝2Within the X-Z array (bold lines in FIGS. 2(a) and (b)), both can be used to estimate the source phase difference u_xIt can be seen that the 3 peak positions of the two sets of curves are nearly identical when the sensor array element spacing is 0.45 λ. ULAY parallel to the Y axis^m＝2Distributed in an X-Y planar array, Y^l＝2Within the Y-Z area array (thin lines in FIG. 2(a) and thick lines in (c)), for estimating v_yAgain, the 3 peak positions of the two sets of curves are nearly identical when the pitch is 0.45 λ. ULAZ parallel to the Z axis^m＝2Distributed in an X-Z planar array, Z^n＝2Within the Y-Z area array (thin lines in FIGS. 2(b) and (c)), for estimating w_zCos θ. The method has the advantages that the ULAs in the multidimensional array are various and large in quantity, but have regularity in source multi-parameter estimation including direction finding, and research and finding of the regularity are of great significance for the source multi-parameter estimation.

Source phase differences of ULA on the 3 planar array anti-diagonals were estimated separately (fig. 3(a), and (b)). For ULAD on the anti-diagonals of the X-Y, X-Z and Y-Z planar arrays_XY、D_XZAnd D_YZThe source phase difference is u_x+y＝cosφsinθ+sinφsinθ，u_x+zCos phi sin theta + cos theta and u_y+zSin phi sin theta + cos theta. It follows that ULA's source phase differences, which lie on or parallel to the diagonal, have a linear combination.

Comparing fig. 3(a) and (b), the amplitude peaks and their positions are generally more easily resolved and determined when the sensor array element spacing is 0.45 λ, but noting at the same time that the urad on the X-Y array anti-diagonals in fig. 3(b)_XYThe source phase difference (o line) of the method has 4 amplitude peak values, and actually only 3 source values, which indicates that a 'false' peak is additionally generated, which is a new phenomenon when the proposed method processes ULAs on various diagonals, and is called as a source phase difference multivalued phenomenon, and the multivalued property of the source phase difference is a main reason for angle estimation error or angle multivalued property.

In array signal processing, in order to avoid source phase difference (and angle) multivalue, it is generally required to set the sensor array element spacing not greater than 0.50 λ, λ is the signal wavelength, but in multidimensional arrays, although the sensor array element spacing is set according to the above requirements, when processing some ULA, especially ULA on various diagonals of an area array or a body array, source phase difference multivalue may still occur, which is a very notable problem in two-dimensional source direction finding theory and application research.

By adopting larger sensor array element spacing, on one hand, the information source phase difference can possibly generate a multi-valued phenomenon, and on the other hand, the resolution and the accuracy of the information source phase difference estimation can be effectively improved. Therefore, how to eliminate the multivalue of the source phase difference (angle) and improve the estimation resolution and accuracy is an important link of the two-dimensional source direction finding. The inventor proposes that: comparing and analyzing multiple ULA data is one possible solution to eliminate phase difference ambiguity. The invention can process any ULA data, so that the solution for eliminating source difference multivalue has more practical operability.

Since source phase difference multivalue appears in ULA located on or parallel to various diagonal lines, and source phase differences corresponding to the ULA often have a linear combination form, the proposed specific solution is: firstly, estimating to obtain component phase difference, calculating the upper limit and the lower limit of a multivalued information source phase difference range according to a satisfied linear combination form and the component phase difference estimated value, narrowing the range and eliminating 'pseudo' phase difference.

For example, ULAD on the anti-diagonals of an X-Y planar array_XYThe source phase difference of the sensor array element has a multi-valued phenomenon (figure 3(b) o line) when the distance between the sensor array elements is 0.45 lambda. To eliminate the multivalue phenomenon, the inventors utilized ULAD_XYSource phase difference u_x+yThe range is narrowed to eliminate the ambiguity, which is a linear combination of cos phi sin theta + sin phi sin theta. The method comprises the following specific steps: for ULAX^n＝2Source phase difference u_xCos phi sin theta, its estimated value (-0.82, -0.06, 0.10); for ULAY^m＝2Source phase difference v_ySin phi sin theta, the estimates are (0.19,0.47,0.71), and the inverse diagonal ULAD on the X-Y plane array_XYHas a source phase difference of u_x+yCos phi sin theta + sin phi sin theta with the lower limit of the range u_xAnd u_yThe sum of the lower limits of (a), calculated as (-0.82+0.19) ═ 0.63; in a similar manner, ULAD_XYThe upper limit of the source phase difference range of (0.10+0.71) is 0.81, so the ULAD_XYCan be narrowed to [ -0.63,0.81 ]]Accordingly, it is determined that a 'false' value appears at position 1.88 on the o-line in fig. 3 (b).

2. Source phase difference pairing and angle estimation in multi-dimensional array

Because the source phase differences estimated from the ULA data are decoupled and out of order, the phase difference estimated values from the same source need to be picked out for the subsequent calculation of the azimuth angle and elevation angle of the source, and the picking process is called source phase difference (or angle) pairing. Source phase difference (or angle) pairing is a key link for two-dimensional source direction finding.

The method provided by the invention can process any ULA data in a multidimensional array, and accordingly, the inventor provides an automatic source phase difference (or angle) pairing method, namely: at least 3 ULA are selected in the multi-dimensional array, the 3 ULA should belong to different categories. For simplicity and convenience of pairing calculation, the source phase difference of one ULA is preferably set as a linear combination of the other two phase differences. Therefore, two estimation modes exist in the combined information source phase difference, and the results obtained by the two estimation modes are compared one by one, so that automatic phase difference pairing can be realized.

For example, we can select 3 ULAXs in the X-Y area array parallel to the X and Y axes and the anti-diagonals, respectively^n＝2、Y^m＝2And D_XYAs a combination for automatic pairing of source phase differences, the selected 3 ULAs belong to different classes with respective phase differences u_x、u_yAnd u_x+y。

Phase difference u_x、v_yAnd u_x+yCan be directly estimated from X^n＝2、Y^m＝2And D_XYIt is estimated that the values are noted in FIG. 2(a) and FIG. 3(b), and are (-0.82, -0.06,0.10), (0.19,0.47,0.71), and (-0.34, 0.28, 0.64), respectively. Phase difference u_x、v_yAnd u_x+yAt the same time satisfy u_x+y＝u_x+u_yHandle u_xAnd u_yIs combined and added, and the result of the addition is obtained by the direct estimation method_x+yAnd comparing the estimated values one by one to realize automatic pairing. Through calculation, the matching result (u) of the phase difference of 3 information sources_x1,v_y1)＝(-0.82,0.47)，(u_x2,v_y2)＝(-0.06,0.71)，(u_x3,v_y3)＝(0.10,0.19)。

After completing source phase difference pairing, the azimuth angle and elevation angle estimated values of 3 sources are calculated by using the formulas (19) and (20) or (21)(k ═ 1,2, and 3) are (150.18 °,70.93 °), (94.83 °,45.44 °), and (62.24 °,12.40 °), respectively.

If the 3 signal source phase differences do not satisfy the linear combination relationship, automatic pairing of the signal source phase differences (or angles) can be realized as long as the selected 3 ULA belong to different categories, and compared with the case that the 3 signal source phase differences directly satisfy the linear combination relationship, the automatic pairing under the nonlinear combination relationship needs to involve angle sine (cosine) conversion, and the calculation is complicated.

3. Source phase difference estimation performance in multi-dimensional array

The method takes the selected ULA as an object, numerically inspects the information source phase difference estimation performance and the characteristics of the method, adopts Root-mean-square error (RMSE) to reflect the information source phase difference estimation performance, and the curve listed in the graph is the statistical average result of 200 Monte Carlo tests.

ULAX is given in FIG. 4(a)^n＝2And X^l＝2、Y^m＝2And Y^l＝2、Z^m＝2And Z^n＝2The source of (a) differs by the RMSE curve. As shown in the figure, the source phase difference estimation performance of the ULAs belonging to the same class is completely consistent. Fig. 4(b) shows the source phase difference RMSE curve for ULA on the 3 anti-diagonals of the planar array, and fig. 4(a) and (b) illustrate that the phase difference estimation performance is quite different for different types of ULA. Therefore, the ULA is reasonably selected, designed and combined, and the two-dimensional information source direction-finding estimation performance can be effectively improved.

The above calculation shows that the method can process any ULA data in the multi-dimensional array, and the provided two-dimensional source direction finding can fully utilize and exert the rich advantages of the multi-dimensional array ULA. Therefore, for two-dimensional source direction finding theory and application research based on multi-dimensional arrays, research should be carried out from the aspects of selecting and designing ULA combinations and improving method estimation performance, and not only based on specific ULA or ULA array forms.