Direction of arrival estimation system, array antenna, and direction of arrival estimation device

Abstract

Estimate the angle of arrival waves using a miniaturized array antenna. 【Solution means】The array antenna 10 includes a linear array in which a plurality of antenna elements 11 are arranged in a row, and an antenna element 12 arranged on a plane perpendicular to the linear array and including any one of the plurality of antenna elements 11. The two-dimensional direction-of-arrival estimation unit 30 obtains the first angle θ of the direction of arrival from the observation signal of the linear array, and calculates a weight vector β that approximates the linear combination of the array response vector α z (θ l ) of the linear array to the antenna response α x (θ l , φ l ) of the antenna element 12 by the least squares method. Using the weight vector β, it calculates the second angle φ l that forms a pair with the first angle θ by using an evaluation function f(θ) based on the linear combination of the array response vector α z (θ) of the linear array. l to obtain, and the array response vector α z z (θ l ) of the linear array is linearly combined with the antenna response α x x (θ l , φ l ) of the antenna element 12, and the weight vector β is calculated by the least squares method. Based on the linear combination of the array response vector α z z (θ) of the linear array using the weight vector β, the evaluation function f(θ) is used to calculate the second angle φ l l that forms a pair with the first angle θ l .

Description

[Technical Field]

[0001] This disclosure relates to a direction of arrival estimation system, an array antenna, and a direction of arrival estimation device. [Background technology]

[0002] Two-dimensional direction of arrival estimation is used in many fields, including radar, sonar, and wireless communication. When performing two-dimensional direction of arrival estimation, it is necessary to determine the arrangement of elements in an array antenna and resolve the paired angles. Non-patent document 1 proposes a two-dimensional direction of arrival estimation method based on the propagator method using a double-parallel array consisting of two linear arrays. However, the method in non-patent document 1 requires additional calculations for pair matching.

[0003] Non-Patent Document 2 describes an improvement that automatically performs pair matching. Furthermore, Non-Patent Document 3 proposes a two-dimensional direction of arrival estimation method based on the propagator method, using an L-shaped array formed by orthogonally connecting two linear arrays. The method in Non-Patent Document 3 can automatically perform pair matching. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Y. Wu, G. Liao and HC So, “A Fast Algorithm for Direction of Arrival Estimation”, Signal Processing, vol. 83, no. 8, pp. 1827-1831, 2003. [Non-Patent Document 2] J. Li, X. Zhang and H. Chen, “Improved two-dimensional DOA estimation algorithm for two-parallel uniform linear arrays using propagator method”, Signal Processing, vol. 92, pp. 3032-3038, Dec. 2012. [Non-Patent Document 3] N. Tayem and HM Kwon, “L-Shape 2-Dimensional Arrival Angle Estimation With Propagator Method”, IEEE Transactions on Antennas and Propagation, vol. 53, pp. 1622-1630, May. 2005. [Non-Patent Document 4] W.-K. Ma, T.-H. Hsieh and C.-Y. Chi, “DOA Estimation of Quasi-Stationary Signals With Less Sensors Than Sources and Unknown Spatial Noise Covariance: A Khatri-Rao Subspace Approach”, IEEE Transactions on Signal Processing, vol. 58, No. 4, pp. 2168-2180, 2010 [Overview of the project] [Problems that the invention aims to solve]

[0005] The methods described in Non-Patent Documents 1-3 estimate angles by utilizing rotational invariance between linear subarrays that overlap under translation. Therefore, since eigenvalue decomposition is required to estimate rotational invariance, there was a problem in that the computational load was large.

[0006] Furthermore, the propagator method, a subspace method, differs from other subspace methods (e.g., the MUSIC method and the ESPRIT method) in that it does not require eigenvalue decomposition of the autocorrelation matrix generated from the observed signals of the array. However, both methods require prior information on the number of signals (arrival wavenumber) in order to divide the autocorrelation matrix into a signal subspace and a noise subspace.

[0007] This disclosure is made in view of the above and aims to estimate the angle of an incoming wave using a miniaturized array antenna. [Means for solving the problem]

[0008] An approach direction estimation system according to one aspect of the present disclosure is an approach direction estimation system comprising an array antenna and an approach direction estimation device, wherein the array antenna comprises a linear array in which a plurality of first antenna elements are arranged in a row, and a second antenna element disposed on a plane perpendicular to the linear array and including any of the plurality of first antenna elements, and the approach direction estimation device determines a first angle of the direction of arrival of a signal from the observed signal of the linear array, calculates a weight vector that brings the linear combination of the array response vectors of the linear array closer to the antenna response of the second antenna element, and calculates a second angle paired with the first angle using an evaluation function based on the linear combination of the array response vectors of the linear array using the weight vector.

[0009] An array antenna according to one aspect of the present disclosure comprises a linear array in which a plurality of first antenna elements are arranged in a row, and a second antenna element disposed on a plane perpendicular to the linear array and including any of the plurality of first antenna elements.

[0010] An arrival direction estimation device according to one aspect of the present disclosure receives an observation signal from an array antenna comprising a linear array in which a plurality of first antenna elements are arranged in a row, and a second antenna element arranged on a plane perpendicular to the linear array and including any of the plurality of first antenna elements. The device obtains a first angle of the arrival direction of the signal from the observation signal of the linear array, calculates a weight vector that brings the linear combination of the array response vectors of the linear array closer to the antenna response of the second antenna element, and calculates a second angle that pairs with the first angle using an evaluation function based on the linear combination of the array response vectors of the linear array using the weight vector. [Effects of the Invention]

[0011] According to this disclosure, the angle of the incoming wave can be estimated using a miniaturized array antenna. [Brief explanation of the drawing]

[0012] [Figure 1] Figure 1 shows an example of an array antenna configuration. [Figure 2] Figure 2 shows numerical examples of the absolute value of the evaluation function f(θ). [Figure 3] Figure 3 shows a numerical example of the evaluation function f(θ). [Figure 4] Figure 4 shows numerical examples of the absolute value of the evaluation function g(θ). [Figure 5] Figure 5 shows a numerical example of the evaluation function g(θ). [Figure 6] Figure 6 shows an example of the configuration of the two-dimensional direction of arrival estimation system of Example 1. [Figure 7] Figure 7 shows an example of the configuration of the two-dimensional direction of arrival estimation system of Example 2. [Figure 8] Figure 8 shows an example of the configuration of the two-dimensional direction of arrival estimation system of Example 3. [Figure 9] Figure 9 shows an example of the configuration of the two-dimensional direction of arrival estimation system of Example 4. [Figure 10]Figure 10 shows an example of an array antenna configuration. [Figure 11] Figure 11 shows an example of an array antenna configuration. [Figure 12] Figure 12 shows an example of an array antenna configuration. [Figure 13] Figure 13 shows numerical examples of the absolute value of the evaluation function f(θ). [Figure 14] Figure 14 shows a numerical example of the evaluation function f(θ). [Figure 15] Figure 15 shows an example of the configuration of the two-dimensional direction of arrival estimation system of Example 5. [Modes for carrying out the invention]

[0013] [Array Antenna] Referring to Figure 1, an example of the array antenna configuration of this embodiment will be described.

[0014] The array antenna 10 in Figure 1 consists of K antenna elements 111, 112, ..., 11 arranged in a row. K The system comprises a linear array (hereinafter referred to as a linear array) and an antenna element 12 positioned on a plane perpendicular to the direction in which the antenna elements 11 are arranged, and which includes one of the antenna elements 11. In Figure 1, the antenna element 111 is positioned at the origin, the antenna elements 11 are arranged at equal intervals in the z-axis direction from the origin, and the antenna element 12 is positioned at a location away from the origin on the x-axis. The antenna element 111 positioned at the origin is used as the phase reference. Note that the antenna elements 111,···,11 K Any of these can be used as the phase reference. That is, antenna elements 111,...,11 K Either of these may be placed as the origin. The spacing between the antenna elements 11 and the spacing between the phase-referenced antenna element 111 and antenna element 12 may be set to half the wavelength of the incoming wave to be detected.

[0015] The array antenna 10 of this embodiment can reduce the number of antenna elements to the same extent as that of a linear array with respect to an existing array shape (for example, a parallel array, an L-shaped array). As a result, the size of the array antenna 10 can be reduced.

[0016] Hereinafter, a method for estimating the arrival direction of an incoming wave based on the observation signal of the array antenna 10 will be described. The arrival direction (arrow 100 in FIG. 1) is represented by a pair of a first angle (elevation angle θ in FIG. 1) and a second angle (azimuth angle φ in FIG. 1). The mathematical formulas shown in each method may be approximated by any means.

[0017] [Automatic pairing matching method] The observation signal of the array antenna 10 at time t is expressed by the following equations (1) and (2). x in equation (1) z (t) is the observation signal of the linear array, and x in equation (2) x (t) is the observation signal of the antenna element 12.

[0018] [Number]

[0019] Here, s(t) ∈ C L (C refers to C with a double line and represents the set of all complex numbers. The same applies hereinafter.) is the signal component vector, and n z (t) ∈ C K is the noise component vector corresponding to the linear array, and n x (t) ∈ C is the noise component corresponding to the antenna element 12, and each is additive white noise with an average of 0 and a variance of σ 2 . A z ∈ C K×L is the array response matrix of the linear array, and A x ∈ C L is the antenna response vector of the antenna element 12 and is expressed by the following equations (3) and (4).

[0020] [Number]

[0021] Here, L is the incoming wavenumber, and θ is the angle of arrival. l (l=1,2,...,L) and azimuth angle φ l Let's represent it as (l=1,2,...,L).

[0022] α z (θ l ) is the array response vector of a linear array, and is expressed by the following equations (5) and (6). [·] T This represents transposition.

[0023]

number

[0024] α x (θ l ,φ l ) is the antenna response of antenna element 12, and is expressed by the following equation (7).

[0025]

number

[0026] Here, ν l and μ l The following equations (8) and (9) are given, where Δz is the distance between adjacent antenna elements 11 in the z-axis direction, and Δx is the distance between antenna element 111 and antenna element 12 with respect to the phase.

[0027]

number

[0028] Linear array response vector α z (θ l ) and the antenna response α of antenna element 12 x (θ l ,φ l The linear dependency relationship expressed by equation (10) holds for ).

[0029]

number

[0030] Here, β=(β1,β2,...,β K ) T ∈C K This is the least squares solution that minimizes the objective function of equation (11), and is expressed by equation (12).

[0031]

number

[0032] [·] H is the complex conjugate transpose, [·] † ||·||² represents the generalized inverse matrix, and ||·||² represents the Euclidean norm. rank(A z )=L <Kより、A z Since the inverse matrix does not exist, we use the generalized inverse matrix A instead. z † It is represented by [this].

[0033] Using equation (12), equation (10) becomes α x (θ l ,φ l )=A x A z † α z (θ l ) can be expressed as A z † α z (θ l ) is a vector where the l-th element is 1 and all other elements are 0. Therefore, A x From the alpha of the first wave component x (θ l ,φ l Each of these is extracted independently.

[0034] Next, we will explain how to estimate the least squares solution. The observed signal x of the linear array... z From (t), the autocorrelation matrix R is expressed by the following equation (13) zz ∈C K×K We seek.

[0035]

number

[0036] Here, R ss =E[s(t)s(t)] H ]=diag(p1,p2,...,p L ), R sn =E[s(t)n z (t) H ]=0, R nn =E[n z (t)n z (t) H ]=σ 2 I is p l (l=1,2,...,L) are signal powers, and I∈R K×K (R refers to the double-lined R, representing the set of all real numbers. The same applies hereafter.) is the identity matrix. E[·] represents the expectation value, and diag(·) represents the diagonal matrix.

[0037] Also, the observed signal x of the linear array z (t) and the observed signal x of antenna element 12 x From (t), the cross-correlation matrix R is expressed by the following equation (14) zx ∈C K We seek.

[0038]

number

[0039] Here, A z E[s(t)n x (t) H ],E[n z (t)s(t) H ]A x H ,E[n z (t)n x (t) H From the cross-correlation matrix, all of the values ​​are zero. Therefore, the estimated least squares solution β (with a ^ above it) can be obtained from equation (15). [·] -1 This represents the inverse matrix.

[0040] [Number]

[0041] Noise variance σ 2 When it is small enough to be ignored, the following equation (16) holds, so equation (15) holds.

[0042] [Number]

[0043] The estimated value β (with a hat on top) of the least-squares solution has been obtained, but the array response vector α of the linear array z (θ l ) and the antenna response α of antenna element 12 x (θ l , φ l ) are unknown. Therefore, assuming an arbitrary elevation angle as θ, the evaluation function f(θ) of the following equation (17) is evaluated.

[0044] [Number]

[0045] The evaluation function f(θ) becomes the following equation (18) when θ = θ l .

[0046] <​​​​​​​​​​​​​​​​​​​​​

[0049] That is, in the automatic pairing method of the present embodiment, the array response vector α z (θ l ) of the linear array is linearly combined with the antenna response α x (θ l , φ l ) of the antenna element 12, and the weight vector β that approximates the antenna response α z (θ) of the linear array using the weight vector β is calculated by the least squares method, and the evaluation function f(θ) based on the linear combination of the array response vector α l (θ) of the linear array using the weight vector β is used to calculate the second angle φ l that forms a pair with the first angle θ z (t), x x (t) to calculate the autocorrelation matrix R zz and the cross-correlation matrix R zx , calculate the least squares solution β (with a hat on top) that minimizes the objective function from the autocorrelation matrix R zz and the cross-correlation matrix R zx , obtain the evaluation function f(θ) with the array response vector A z of the linear array with the least squares solution β (with a hat on top) and an arbitrary angle as arguments, use the evaluation function f(θ) to estimate the first angle θ l , and calculate the second angle φ l that forms a pair with the first angle θ l . Note that the first angle θ l can be obtained by the conventional method, and the second angle φ l that forms a pair with the first angle θ obtained by the conventional method l can also be calculated.

[0050] [Method for improving estimation accuracy] When the number of samples of the observation signal x z (t) is not infinite, the autocorrelation matrix of Equation (13) can be expressed by the following Equation (20).

[0051] [Equation]

[0052] Here, R ss =E[s(t)s(t)] H ](a dot above R, a dot above E), R sn =E[s(t)n z (t) H ](a dot above R, a dot above E), R nn =E[n z (t)n z (t) H ] (with a dot above R and a dot above E). E[·] (with a dot above E) represents a finite expected value. A contains angular information. z R sn (R sn Above (·) is noise dispersion σ 2 When the angle is large, or when the angles of the incoming waves are close, it can be a factor that degrades the estimation accuracy.

[0053] R zz The signal component is R S =A z R ss A z H (R ss Place a '·' above it, and group everything else together as R N =A z R sn +(A z R sn ) H +R nn (R sn and R nn If we place a hyphen (·) above the given value, the estimated least squares solution of equation (15) can be transformed into equation (21).

[0054]

number

[0055] Here, ε is the error contained in β (above ^). Also, X = R S † R N This is the coefficient matrix, where X and (I+X) -1 The two functions are commutative. β = R S † R zx(A checkmark above β) represents the minimum norm solution. rank(R S )=L <Kより、R S Since the inverse matrix does not exist, we use the generalized inverse matrix R instead. S † It is represented by [this].

[0056] Let's consider obtaining the estimated least squares solution of equation (15) by correcting it as shown in equation (23).

[0057]

number

[0058] Here, F∈C K×K This is the minimum solution to the Frobenius norm. Equation (23) can be transformed from equation (21) to equation (24).

[0059]

number

[0060] Here, Y=R zz -1 F is the coefficient matrix. To cancel out the error ε with its estimate ε (^ above), by comparing equations (22) and (25), we can minimize the following objective function: ||·|| F This represents the Frobenius norm.

[0061]

number

[0062] The case where the objective function is minimized, i.e., X = (IY) -1 If Y holds, the minimum solution to the Frobenius norm can be found by equation (27).

[0063]

number

[0064] In this case, the estimated least squares solution is β(with two ^s above) = β(with a · above), and the error ε is canceled out by this estimated value ε(with ^s above).

[0065] Next, we will explain the method for estimating the minimum solution to the Frobenius norm. (Known elevation angle θ) l A is used as the estimate of the array response matrix by (l=1,2,...,L). z (Above ^) is constructed, and the estimated value of the autocorrelation matrix of the signal components is obtained by the following equation (28).

[0066]

number

[0067] Here, σ 2 The (^) above is an estimate of the noise dispersion and must be obtained by any method. The estimate of the signal component term is R S =A z R ss A z H (R S , A z , R ss If we represent it as ^) above, the estimated values ​​of the interference and noise component terms are R N =R zz -R S (R N and R S Since it can be obtained as ^) above, the estimated value of the coefficient matrix is ​​X=R S † R N (X, R S , R N This can be expressed as ^) above. Thus, the estimated value of the minimum solution to the Frobenius norm can be obtained by the following equation (29).

[0068]

number

[0069] Using the estimated F(^) of the least squares solution of the Frobenius norm, the estimated corrected least squares solution can be obtained by the following equation (30).

[0070]

number

[0071] We evaluate the following evaluation function g(θ) using the corrected least squares solution estimate β (with two ^s above it).

[0072]

number

[0073] The evaluation function g(θ) is defined by the known elevation angle θ. l Substituting (l=1,2,...,L) into the equation gives the following:

[0074]

number

[0075] Furthermore, using the evaluation function g(θ), the elevation angle θ is given by the following equation (33): l The estimated azimuth angle φ that pairs with it l This is required.

[0076]

number

[0077] In other words, in the estimation accuracy improvement method of this embodiment, the estimated value β (with two ^s above) of the least squares solution is corrected by the Frobenius norm minimum solution F, and the first angle θ is obtained using the evaluation function g(θ) which uses the estimated value β (with two ^s above) of the least squares solution. l The second angle φ that pairs with it l This calculates the observed signal x received by the array antenna 10. More specifically, in the estimation accuracy improvement method of this embodiment, z (t),x x (t) Autocorrelation matrix R zz and the cross-correlation matrix R zx Calculate the known first angle θ lUsing this, we calculate the Frobenius norm minimum solution F that minimizes the objective function, and then calculate the autocorrelation matrix R zz and the cross-correlation matrix R zx Then, we calculate the least squares solution β (with two ^s above) that minimizes the objective function from the Frobenius norm minimum solution F, and the least squares solution β (with two ^s above) and the first angle θ l Array response vector α of a linear array with argument z From (θ), we obtain an evaluation function g(θ) with the first angle θ as an argument, and use the evaluation function g(θ) to determine the first angle θ l The second angle φ that pairs with it l Calculate the first angle θ. l This can be obtained using evaluation functions f(θ) and g(θ), or by conventional methods.

[0078] [Numerical examples of the evaluation function f(θ)] The properties of the evaluation function f(θ) will be explained using numerical examples.

[0079] For the array antenna 10, the number of antenna elements 11 in the linear array is K=14, and the total number of antenna elements 11 and 12 in the array antenna 10 is K+1=15. The number of incoming waves is L=2, the signal power of the first wave is p1=1, the direction of arrival (pair of elevation angle θ and azimuth angle φ) is (θ1,φ1)=(90°,70°), the signal power of the second wave is p2=1, the direction of arrival is (θ2,φ2)=(100°,80°), and the noise dispersion is σ 2 I set it to =0.1.

[0080] Figure 2 shows a numerical example of |f(θ)|. The horizontal axis represents the first angle (elevation angle), and the vertical axis represents the absolute value of the evaluation function f(θ). The peaks of |f(θ)| appear at the elevation angles θ1=90° of the first wave and θ2=100° of the second wave. Therefore, from |f(θ)|, θ l It is possible to estimate this.

[0081] Figure 3 shows a numerical example of f(θ). The real part is plotted on the horizontal axis and the imaginary part on the vertical axis. The point that f(θ) takes is the α that lies on the unit circle when its argument is close to the elevation angle θ1 = 90° of the first wave and the elevation angle θ2 = 100° of the second wave. x (θ1, φ1) and αx It is close to the point (θ2, φ2). Therefore, from f(θ), α x (θ l ,φ l ) can be estimated.

[0082] [Numerical examples of the evaluation function g(θ)] Next, we will explain the properties of the evaluation function g(θ) using numerical examples.

[0083] For the array antenna 10, the number of antenna elements 11 in the linear array is K=14, and the total number of antenna elements 11 and 12 in the array antenna 10 is K+1=15. The number of incoming waves is L=2, the signal power of the first wave is p1=1, the direction of arrival is (θ1,φ1)=(95°,70°), the signal power of the second wave is p2=1, the direction of arrival is (θ2,φ2)=(100°,80°), and the noise dispersion is σ 2 I set it to =10.

[0084] Figure 4 shows a numerical example of |g(θ)|. The horizontal axis represents the first angle (elevation angle), and the vertical axis represents the absolute value of the evaluation function g(θ). As a comparison, Figure 4 also shows a numerical example of |f(θ)| under the same conditions. Compared with |f(θ)|, it can be seen that |g(θ)| can separate peaks even when the arrival directions of the two incoming waves are close and the noise dispersion is large.

[0085] Figure 5 shows a numerical example of g(θ). The real part is plotted on the horizontal axis and the imaginary part on the vertical axis. As a comparative example, Figure 5 also shows a numerical example of f(θ) under the same conditions. Compared to f(θ), g(θ) has α that lies on the unit circle even when the arrival directions of the two incoming waves are close and the noise dispersion is large. x (θ1, φ1) and α x It can be seen that it is close to the point (θ2, φ2).

[0086] In this way, the estimation accuracy can be improved by using the evaluation function g(θ).

[0087] [Example 1] Referring to Figure 6, an example of the configuration of the two-dimensional direction of arrival estimation device of Example 1 will be described. In Example 1, the first angle and the second angle are estimated using the automatic pair matching method described above. The two-dimensional direction of arrival estimation device shown in the figure comprises an array antenna 10, a receiving unit 20, and a two-dimensional direction of arrival estimation unit 30.

[0088] The array antenna 10 consists of K antenna elements 111,...,11 arranged in a row, similar to the one shown in Figure 1. K The system comprises a linear array and antenna elements 12 arranged on a plane orthogonal to the linear array. Each antenna element 11, 12 receives the incoming wave.

[0089] The incoming wave signal received by the array antenna 10 is sent to the receiving unit 20.

[0090] The receiving unit 20 includes a receiver 21 and an observation signal generation unit 22.

[0091] The receiver 21 performs low-noise amplification on the incoming wave signal, mixes it with a local oscillator signal of a predetermined frequency to convert it into a baseband signal, and further samples the baseband signal at a predetermined sampling period to convert it into a digital signal.

[0092] The observation signal generation unit 22 generates the observation signal x of a linear array corresponding to equation (1) from the digital signal. z (t) and the observed signal x of antenna element 12 corresponding to equation (2) x Generate (t).

[0093] Observation signal x generated by the receiving unit 20 z (t),x x (t) is sent to the 2D direction of arrival estimation unit 30.

[0094] The two-dimensional direction of arrival estimation unit 30 includes an autocorrelation matrix calculation unit 31, a cross-correlation matrix calculation unit 32, a least-squares solution calculation unit 33, an evaluation function calculation unit 34, a spectral analysis unit 35, and a second angle estimation unit 36.

[0095] The autocorrelation matrix calculation unit 31 calculates the observed signal x of the linear array. z (t) corresponds to the autocorrelation matrix R in equation (13) zz Calculate.

[0096] The cross-correlation matrix calculation unit 32 calculates the observed signal x of the linear array. z (t) and the observed signal x of antenna element 12 x (t) to the cross-correlation matrix R corresponding to equation (14) zx Calculate.

[0097] The least squares solution calculation unit 33 calculates the autocorrelation matrix R zz and the cross-correlation matrix R zx From this, we calculate the least squares solution β(^ above) (corresponding to equation (15)) that minimizes the objective function of equation (11).

[0098] The evaluation function calculation unit 34 calculates the array response vector α of a linear array with the least squares solution β (with a ^ sign above) and an arbitrary angle θ as arguments. z From (θ), we calculate the evaluation function f(θ) of equation (17), which takes an arbitrary angle θ as an argument. One or more arbitrary numbers can be specified as the number of arbitrary angles.

[0099] The spectral analysis unit 35 generates a spectrum using the evaluation function f(θ) and searches for peaks to determine the first angle θ l The spectral analysis unit 35 may also be called the first angle estimation unit.

[0100] The second angle estimation unit 36 ​​uses the first angle θ l The evaluation function f(θ) of equation (18) with argument l Using the calculation result of ), from equation (19), the second angle φ l Calculate.

[0101] Through the above process, the two-dimensional direction of arrival estimation unit 30 automatically determines the first pair-matched angle θ l and the second angle φ l Outputs.

[0102] [Example 2] Referring to Figure 7, an example of the configuration of the two-dimensional direction of arrival estimation device of Example 2 will be described. In Example 2, the first angle is estimated using a conventional method, and the automatic pair matching method described above is used to estimate the second angle. The two-dimensional direction of arrival estimation device shown in the figure comprises an array antenna 10, a receiving unit 20, and a two-dimensional direction of arrival estimation unit 30. The array antenna 10 and the receiving unit 20 are the same as in Example 1, so redundant explanations will be omitted.

[0103] The two-dimensional direction of arrival estimation unit 30 of Example 2 includes an autocorrelation matrix calculation unit 31, a cross-correlation matrix calculation unit 32, a least-squares solution calculation unit 33, an evaluation function calculation unit 34, a second angle estimation unit 36, and a one-dimensional direction of arrival estimation unit 37. It differs from Example 1 in that the first angle estimation unit includes a one-dimensional direction of arrival estimation unit 37 instead of a spectral analysis unit 35.

[0104] The autocorrelation matrix calculation unit 31, the cross-correlation matrix calculation unit 32, and the least-squares solution calculation unit 33, similar to Example 1, take the observed signal x z (t),x x From (t), the autocorrelation matrix R zz and the cross-correlation matrix R zx Calculate the autocorrelation matrix R zz and the cross-correlation matrix R zx From this, we calculate the least squares solution β(above ^) that minimizes the objective function of equation (11).

[0105] The one-dimensional direction of arrival estimation unit 37 uses the autocorrelation matrix R zz From this, the first angle is estimated using any direction of arrival estimation method. Well-known direction of arrival estimation methods such as the beamformer method, Capon method, linear prediction method, MUSIC method, ESPRIT method, and propagator method can be used. Other methods may also be used. By choosing a direction of arrival estimation method that boasts high angular resolution, the estimation accuracy of the first angle can be improved. From the relationship in equation (10), improving the estimation accuracy of the first angle contributes to improving the calculation accuracy of the second angle.

[0106] The evaluation function calculation unit 34 calculates the least squares solution β (with a ^ above) and the array response vector α of the linear array. z (θl ) From the first angle θ l The evaluation function f(θ) of equation (18) with argument l ) calculate.

[0107] The second angle estimation unit 36 ​​evaluates the function f(θ) l Using the calculation result of ), from equation (19), the second angle φ l Calculate.

[0108] Through the above process, the two-dimensional direction of arrival estimation unit 30 determines the first angle θ estimated by the arbitrary direction of arrival estimation method. l And the second angle φ estimated by the automatic pair matching method of this embodiment l Outputs.

[0109] [Example 3] Referring to Figure 8, an example of the configuration of the two-dimensional direction of arrival estimation device of Example 3 will be described. Example 3 differs from Example 1 in that it improves the estimation accuracy by using the evaluation function g(θ) of equation (31). The two-dimensional direction of arrival estimation device shown in the figure comprises an array antenna 10, a receiving unit 20, and a two-dimensional direction of arrival estimation unit 30. The array antenna 10 and the receiving unit 20 are the same as in Example 1, so redundant explanations will be omitted.

[0110] The two-dimensional direction of arrival estimation unit 30 of Example 3 includes an autocorrelation matrix calculation unit 31, a cross-correlation matrix calculation unit 32, a least-squares solution calculation unit 33, an evaluation function calculation unit 34, a spectral analysis unit 35, a second angle estimation unit 36, a Frobenius norm minimum solution calculation unit 41, a least-squares solution calculation unit 42, and an evaluation function calculation unit 43. It differs from Example 1 in that it includes a Frobenius norm minimum solution calculation unit 41, a least-squares solution calculation unit 42, and an evaluation function calculation unit 43 after the spectral analysis unit 35.

[0111] The autocorrelation matrix calculation unit 31, the cross-correlation matrix calculation unit 32, the least-squares solution calculation unit 33, the evaluation function calculation unit 34, and the spectral analysis unit 35, similar to Example 1, take the observed signal x z (t),x x From (t), the autocorrelation matrix R zz and the cross-correlation matrix Rzx Calculate the autocorrelation matrix R zz and the cross-correlation matrix R zx From this, we calculate the least squares solution β(above) that minimizes the objective function of equation (11), and the array response vector α of the linear array with the least squares solution β(above) and an arbitrary angle θ as arguments. z From (θ), an evaluation function f(θ) is calculated with an arbitrary angle θ as an argument, and a spectrum is generated using the evaluation function f(θ), and the peak is searched for to determine the first angle θ l We estimate this.

[0112] The Frobenius norm minimum solution calculation unit 41 calculates the Frobenius norm minimum solution F (corresponding to equation (29)) that minimizes the objective function of equation (26).

[0113] The least squares solution calculation unit 42 calculates the autocorrelation matrix R zz and the cross-correlation matrix R zx From the minimum Frobenius norm solution F, we calculate the least squares solution β (with two ^s above) (corresponding to equation (30)) that minimizes the objective function in equation (11).

[0114] The evaluation function calculation unit 43 calculates the array response vector α of a linear array with the least-squares solution β (with two ^s above it) and the first angle θ as arguments. z From (θ), the first angle θ l The evaluation function g(θ) of equation (32) with argument l ) calculate.

[0115] The second angle estimation unit 36 ​​evaluates the function g(θ) l Using the calculation result of ), from equation (33), the second angle φ l Calculate.

[0116] Through the above process, the two-dimensional direction of arrival estimation unit 30 automatically determines the first pair-matched angle θ l and the second angle φ l Outputs.

[0117] The two-dimensional direction of arrival estimation device of Example 3 can improve the accuracy of direction of arrival estimation by using the evaluation function g(θ) of equation (31).

[0118] [Example 4] Referring to Figure 9, an example of the configuration of the two-dimensional direction of arrival estimation device of Example 4 will be described. Example 4 differs from Example 2 in that it improves the estimation accuracy by using the evaluation function g(θ) of equation (31). The two-dimensional direction of arrival estimation device shown in the figure comprises an array antenna 10, a receiving unit 20, and a two-dimensional direction of arrival estimation unit 30. The array antenna 10 and the receiving unit 20 are the same as in Example 1, so redundant explanations will be omitted.

[0119] The two-dimensional arrival direction estimation unit 30 of Example 4 includes an autocorrelation matrix calculation unit 31, a cross-correlation matrix calculation unit 32, a second angle estimation unit 36, a one-dimensional arrival direction estimation unit 37, a Frobenius norm minimum solution calculation unit 41, a least squares solution calculation unit 42, and an evaluation function calculation unit 43. It differs from Example 3 in that it includes a one-dimensional arrival direction estimation unit 37 instead of a least squares solution calculation unit 33, an evaluation function calculation unit 34, and a spectral analysis unit 35.

[0120] The autocorrelation matrix calculation unit 31 and the cross-correlation matrix calculation unit 32, similar to Example 1, use the observed signal x z (t),x x From (t), the autocorrelation matrix R zz and the cross-correlation matrix R zx Calculate.

[0121] The one-dimensional direction of arrival estimation unit 37 uses the same autocorrelation matrix R as in Example 2. zz From this, the first angle is estimated using an arbitrary direction of arrival estimation method.

[0122] The Frobenius norm minimum solution calculation unit 41, the least squares solution calculation unit 42, and the evaluation function calculation unit 43, similar to Example 3, calculate the Frobenius norm minimum solution F (corresponding to equation (29)) that minimizes the objective function of equation (26), calculate the least squares solution β (with two ^s above) (corresponding to equation (30)) that minimizes the objective function of equation (11), and the first angle θ lThe evaluation function g(θ) of equation (32) with argument l ) calculate.

[0123] The second angle estimation unit 36 ​​evaluates the function g(θ) l Using the calculation result of ), from equation (33), the second angle φ l Calculate.

[0124] Through the above process, the two-dimensional direction of arrival estimation unit 30 determines the first angle θ estimated by the arbitrary direction of arrival estimation method. l And the second angle φ estimated by the automatic pair matching method of this embodiment l Outputs.

[0125] The two-dimensional direction of arrival estimation device of Example 4 can improve the accuracy of direction of arrival estimation by using the evaluation function g(θ) of equation (31).

[0126] Furthermore, each processing block of the two-dimensional direction of arrival estimation unit 30 in Examples 1-4 may be configured as hardware, or it may be configured as at least one computer equipped with an arithmetic processing unit, a storage device, etc., and the processing of each part may be executed by a program. This program is stored in the storage device of the two-dimensional direction of arrival estimation unit 30, and can be recorded on a computer-readable non-temporary recording medium such as a magnetic disk, optical disk, or semiconductor memory, or it can be provided via a network.

[0127] In addition, in all of the examples 1-4, the array antenna 10 may be a double parallel array formed by arranging two conventional linear arrays side by side, or an L-shaped array formed by connecting two linear arrays orthogonally. In this case, one of the two linear arrays is used as the linear array of this embodiment, and one of the antenna elements of the other linear array is used as the K+1th antenna element 12. In other words, the array antenna 10 may be an array antenna comprising a linear array and at least one antenna element 12 separate from the linear array.

[0128] As described above, the two-dimensional direction of arrival estimation device of this embodiment comprises an array antenna 10, a receiving unit 20, and a two-dimensional direction of arrival estimation unit 30. The array antenna 10 comprises a linear array in which a plurality of antenna elements 11 are arranged in a line, and an antenna element 12 arranged on a plane perpendicular to the linear array and containing any of the plurality of antenna elements 11. The two-dimensional direction of arrival estimation unit 30 calculates the first angle θ of the direction of arrival from the observation signal of the linear array. l We find the array response vector α of the linear array. z (θ l The linear combination of ) is the antenna response α of antenna element 12 x (θ l ,φ l The weight vector β that approaches ) is calculated using the least squares method, and the array response vector α of the linear array using the weight vector β is calculated. z The first angle θ is obtained using an evaluation function f(θ) based on a linear combination of (θ). l The second angle φ that pairs with it l This calculates the following. As a result, compared to existing two-dimensional direction of arrival estimation methods (e.g., methods based on subspace methods), it does not require calculation of rotation invariance, eigenvalue decomposition, or prior information on the arriving wavenumber, thus reducing the computational load and enabling the automatic estimation of pair-matched angles.

[0129] The array antenna 10 of this embodiment can reduce the number of antenna elements to the same extent as a linear array, and can also reduce the array size, compared to existing array shapes (for example, parallel arrays or L-shaped arrays).

[0130] The two-dimensional direction of arrival estimation unit 30 of this embodiment obtains the second angle φ by correcting the least-squares solution with the Frobenius norm minimum solution. l This can improve the estimation accuracy.

[0131] [Virtual Array] As a method for virtually expanding the aperture length or compensating for missing elements under a limited number of elements, Khatri-Rao product (hereinafter referred to as KR product) extended array processing is known (Non-Patent Literature 4). In KR product extended array processing, the autocorrelation matrix is ​​obtained by taking a snapshot of the observed signal of the array, and the autocorrelation matrix is ​​vectorized to generate a new observed signal (hereinafter referred to as the virtual array signal) as a snapshot. Compared to the original observed signal, the virtual array signal has an increased number of different phase terms and its dimensions are expanded, so the aperture length appears to be expanded or the missing elements are compensated for.

[0132] The following describes how to apply KR product extended array processing to the two-dimensional arrival direction estimation device of this embodiment.

[0133] Figure 10 shows an example of an array antenna 10 in which some antenna elements 11 of a linear array are missing. In the array antenna 10 of Figure 10, antenna element 110 is placed at the origin (phase reference), antenna elements 111, 114, and 116 are arranged in the z-axis direction from the origin, and antenna element 12 is placed at a position away from the origin on the x-axis. Three antenna elements 112, 113, and 115 are missing and are treated as virtual antenna elements 11. For simplicity, the arriving wave is assumed to be one wave from the elevation angle θ and azimuth angle φ, and noise components are not considered.

[0134] The observed signals of the linear array at time t can be expressed by the following equations (34) and (35).

[0135]

number

[0136] Here, s(t) is the signal component, λ is the wavelength of the incoming wave, and Δz is the distance between adjacent antenna elements 11 (including virtual antenna elements 11) in the z-axis direction. The exponent values ​​are 0, 1, 4, and 6, which correspond to the positions of antenna elements 110, 111, 114, and 116 in Figure 10.

[0137] x z(t) and its complex conjugate transpose x z (t) H The outer product with it can be expressed by the following equation (36).

[0138]

Number

[0139] The weight w(t) using the observation signal x0 of the antenna element 110 at the origin is obtained by the following equation (37).

[0140]

Number

[0141] When multiplying the non - overlapping elements of equation (36) by the weight w(t), the following equation (38) expressed as s(t) is obtained as the virtual array signal.

[0142]

Number

[0143] By leaving the elements in the positive direction of the z - axis from equation (38), the following equation (39) is obtained.

[0144]

Number

[0145] The values of the exponents of each element are consecutive numbers from 0 to 6, which correspond to the antenna elements 11 in Fig. 10 (including the virtual antenna element 11).

[0146] On the other hand, the observation signals of the antenna element 12 in the x - axis direction can be expressed by the following equations (40) and (41).

[0147]

Number

[0148] Here, Δx is the distance between antenna element 110 and antenna element 12 at the origin.

[0149] virtual array signal y z (t) and observed signal x x (t) has a common coefficient s(t), so the virtual array signal y obtained using the above procedure z (t) can be used in the two-dimensional direction of arrival estimation device of this embodiment.

[0150] [Evaluation of virtual array signals] The effect of the virtual array signal is evaluated for each of the array antennas 10A in Figure 11 and 10B in Figure 12 using the evaluation function f(θ) of equation (17). Array antenna 10A in Figure 11 has no missing elements in the linear array antenna elements 11, while array antenna 10B in Figure 12 has missing elements in the linear array antenna elements 11. The number of linear array antenna elements 11 in both Figure 11 and Figure 12 is 7. Therefore, the aperture length of array antenna 10B is larger than the aperture length of array antenna 10A.

[0151] Let the number of incoming waves be L=2, the signal power of the first wave be p1=1, the direction of arrival (the pair of elevation angle θ and azimuth angle φ) be (θ1,φ1)=(95°,70°), the signal power of the second wave be p2=1, the direction of arrival be (θ2,φ2)=(100°,80°), and the noise dispersion be σ 2 The value was set to =0.1. In Figure 11, the array antenna 10A has no missing antenna elements 11, so the observed signal was used as is. In Figure 12, the array antenna 10B has missing antenna elements 11, so a virtual array signal was generated and used as the observed signal.

[0152] Figure 13 shows numerical examples of |f(θ)|. The horizontal axis represents the first angle (elevation angle), and the vertical axis represents the absolute value of the evaluation function f(θ). Figure 13 illustrates numerical examples of |f(θ)| for array antenna 10A (element arrangement example A) and array antenna 10B (element arrangement example B). Comparing array antenna 10A and array antenna 10B, it can be seen that array antenna 10A, with its smaller aperture length, cannot separate the peaks, but array antenna 10B, with its virtually enlarged aperture length, can separate the peaks even when the arrival directions of the two incoming waves are close by using a virtual array signal.

[0153] Figure 14 shows numerical examples of f(θ). The real part is plotted on the horizontal axis and the imaginary part on the vertical axis. Figure 14 illustrates numerical examples of f(θ) for array antenna 10A (element arrangement example A) and array antenna 10B (element arrangement example B). When comparing array antenna 10A and array antenna 10B, array antenna 10B uses a virtual array signal, so that even when the arrival directions of the two arriving waves are close, α exists on the unit circle. x (θ1, φ1) and α x It can be seen that it is close to the point (θ2, φ2).

[0154] [Example 5] Referring to Figure 15, an example of the configuration of the two-dimensional direction of arrival estimation device of Example 5 will be described. Example 5 differs from Examples 1 to 4 in that it is equipped with a virtual array signal calculation unit 50. The two-dimensional direction of arrival estimation device shown in the figure comprises an array antenna 10, a receiving unit 20, a virtual array signal calculation unit 50, and a two-dimensional direction of arrival estimation unit 30. The array antenna 10 may be one in which the aperture length is virtually enlarged or one in which antenna elements 11 are missing. The two-dimensional direction of arrival estimation unit 30 may be one of those from Examples 1 to 4. The array antenna 10, the receiving unit 20, and the two-dimensional direction of arrival estimation unit 30 are the same as in Examples 1 to 4, so redundant explanations will be omitted.

[0155] The virtual array signal calculation unit 50 calculates the observed signal x of the linear array. z (t) and its complex conjugate transpose x z (t) HVectorize the non-duplicate elements of the cross product with [vector], and multiply by the weight w(t) obtained from the observed signal x0 of the antenna element 110 at the origin of the linear array to calculate the virtual array signal y z (t).

[0156] The two-dimensional direction-of-arrival estimation unit 30 inputs the virtual array signal y z (t) of the linear array and the observed signal x x (t) of the antenna element 12, and automatically calculates and outputs the first angle θ l and the second angle φ l .

[0157] As described above, by multiplying the virtual array signal generated by subjecting the observed signal x z (t) of the linear array to the KR product extended array processing by the weight w(t) obtained from the observed signal x0 of the antenna element 110 at the origin of the linear array, the KR product extended array processing can be applied to the two-dimensional direction-of-arrival estimation method of the present embodiment. As a result, the aperture length of the array antenna 10 can be virtually enlarged, or the missing of the antenna element 11 can be complemented. z (t), the virtual array signal y

Explanation of Signs

[0158] 10 Array antenna 11, 12 Antenna elements 20 Receiver 21 Receiver 22 Observed signal generation unit 30 Two-dimensional direction-of-arrival estimation unit 31 Autocorrelation matrix calculation unit 32 Cross-correlation matrix calculation unit 33 Least squares solution calculation unit 34 Evaluation function calculation unit 35 Spectrum analysis unit 36 Second angle estimation unit 37 One-dimensional direction-of-arrival estimation unit<F 41 Frobenius norm minimum solution calculation unit 42 Least squares solution calculation unit 43 Evaluation Function Calculation Unit 50 Virtual Array Signal Calculation Unit

Claims

1. An arrival direction estimation system comprising an array antenna and an arrival direction estimation device, The aforementioned array antenna is A linear array in which multiple first antenna elements are arranged in a line, A second antenna element is provided, which is a plane perpendicular to the linear array and is arranged on a plane that includes any of the plurality of first antenna elements. The aforementioned direction of arrival estimation device is, From the observed signals of the linear array, determine the first angle of the direction of arrival of the signal. A weight vector is calculated to bring the linear combination of the array response vectors of the linear array closer to the antenna response of the second antenna element. The second angle paired with the first angle is calculated using an evaluation function based on a linear combination of the array response vectors of the linear array using the weight vectors. Direction of arrival estimation system.

2. The direction of arrival estimation system according to claim 1, The direction of arrival estimation device calculates the first angle based on the absolute value of the evaluation function. Direction of arrival estimation system.

3. The direction of arrival estimation system according to claim 1, The aforementioned direction of arrival estimation device is obtained by correcting the weight vector with the minimum solution of the Frobenius norm. Direction of arrival estimation system.

4. The direction of arrival estimation system according to claim 2, The aforementioned direction of arrival estimation device is obtained by correcting the weight vector with the minimum solution of the Frobenius norm. Direction of arrival estimation system.

5. An arrival direction estimation system according to any one of claims 1 to 4, The direction of arrival estimation device generates a virtual array signal by multiplying the non-overlapping elements of the cross product of the observed signal of the linear array and its complex conjugate transpose by a weight obtained from the observed signal of the first antenna element, which is phase-referenced to the linear array, and using the virtual array signal, calculates the first angle and the second angle. Direction of arrival estimation system.

6. A linear array in which multiple first antenna elements are arranged in a line, A second antenna element is provided, which is located on a plane perpendicular to the linear array and includes one of the plurality of first antenna elements. Array antenna.

7. The array antenna according to claim 6, From the observed signals of the linear array, determine the first angle of the direction of arrival of the signal. A weight vector is calculated to bring the linear combination of the array response vectors of the linear array closer to the antenna response of the second antenna element. The second angle paired with the first angle is calculated using an evaluation function based on a linear combination of the array response vectors of the linear array using the weight vectors. Array antenna.

8. An array antenna is provided which includes a linear array in which a plurality of first antenna elements are arranged in a line, and a second antenna element arranged on a plane perpendicular to the linear array and containing any of the plurality of first antenna elements, and which receives the observed signal of the array antenna. From the observed signals of the linear array, determine the first angle of the direction of arrival of the signal. A weight vector is calculated to bring the linear combination of the array response vectors of the linear array closer to the antenna response of the second antenna element. The second angle paired with the first angle is calculated using an evaluation function based on a linear combination of the array response vectors of the linear array using the weight vectors. Direction of arrival estimation device.

9. The direction of arrival estimation device according to claim 8, The first angle is calculated based on the absolute value of the evaluation function. Direction of arrival estimation device.

10. The direction of arrival estimation device according to claim 8, The aforementioned direction of arrival estimation device is obtained by correcting the weight vector with the minimum solution of the Frobenius norm. Direction of arrival estimation device.

11. The direction of arrival estimation device according to claim 9, The aforementioned direction of arrival estimation device is obtained by correcting the weight vector with the minimum solution of the Frobenius norm. Direction of arrival estimation device.

12. An arrival direction estimation device according to any one of claims 8 to 11, A virtual array signal is generated by multiplying the non-overlapping elements of the cross product of the observed signal of the linear array and its complex conjugate transpose by a weight obtained from the observed signal of the first antenna element, which is phase-referenced to the linear array, and the first angle and the second angle are calculated using this virtual array signal. Direction of arrival estimation device.

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