JP6293073B2 - Arrival direction estimation apparatus and arrival direction estimation method - Google Patents

Description

  The present invention relates to an arrival direction estimation device and an arrival direction estimation method for accurately estimating the arrival directions of incoming waves radiated from a plurality of radiation sources.

For example, when there are multiple radiation sources that radiate radio waves, light waves, sound waves, etc., incoming signals such as radio waves radiated from multiple radiation sources are received by the array antenna, and signal processing is performed on the received signals of the array antenna. There is an arrival direction estimating apparatus that estimates the arrival directions of incoming waves radiated from a plurality of radiation sources.
As signal processing for estimating the direction of arrival of an incoming wave, ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) processing (see Non-Patent Document 1) and VESPA (Virtual ESPRIT Algorithm) are known. (Refer nonpatent literature 2).

The ESPRIT process is a method that can estimate arrival waves radiated from a plurality of radiation sources with high resolution by utilizing rotation invariance between two identical subarrays. Must be prepared, and the array arrangement is limited.
On the other hand, the VESPA process includes a fourth-order cumulant matrix of a real array that is an actual arrangement of a plurality of element antennas constituting the array antenna, and a virtual array that is a virtual arrangement in which the plurality of element antennas are moved in parallel. By utilizing the fact that rotation invariance holds between the fourth-order cumulant matrix and applying the EPSRIT process to the fourth-order cumulant matrix of the real array and the fourth-order cumulant matrix of the virtual array, The incoming wave radiated from the radiation source can be estimated with high resolution.
The VESPA process has an advantage that it is not subject to the restrictions on the array arrangement like the ESPRIT process.

  However, in the VESPA process, in order to use a fourth-order cumulant, when incoming waves radiated from a plurality of radiation sources have a high dynamic range, that is, when a signal with high power and a signal with low power are simultaneously incident on the array antenna It has been reported that the estimation accuracy of the direction of arrival of a signal with low power deteriorates even if the signal to noise ratio (SNR) of the signal with high power and low signal is high. Further, it has been reported that the estimation accuracy of the arrival direction is deteriorated even when there is a correlation between a plurality of incoming waves (see Non-Patent Document 3).

Hamid KRIM and Mats VIBERG, “Two decades of array signal processing research,” IEEE Signal Processing MAGAZINE, VOLUME 13, ISSUE 4, PP. 67-94, JULY, 1996. M.M. Dogan, J .; Mendel, “Application of cumulants to array processing-Part I: Aperture extension and array calibration,” IEEE Trans. Signal Processing, vol. 43, no. 5, pp. 1200-1216, May 1997 Gonen, E.M. & Mendel, J.M. M.M. “Subspace-Based Direction Finding Methods” in Digital Signal Processing Handbook added by Vijay K.K. Madisetti and Douglas B.M. Williams, 1999

  Since the conventional arrival direction estimation apparatus is configured as described above, when the VESPA process is performed, the arrival directions of the arrival waves radiated from a plurality of radiation sources are estimated without being restricted by the array arrangement. However, when incoming waves radiated from multiple radiation sources have a high dynamic range, or when there is a correlation between multiple incoming waves, multiple incoming waves can be separated with high accuracy. Therefore, there has been a problem that the arrival directions of a plurality of incoming waves cannot be accurately estimated.

  This invention was made in order to solve the above problems, and even when the incoming waves radiated from a plurality of radiation sources have a high dynamic range or when there is a correlation between the plurality of incoming waves, An object of the present invention is to provide an arrival direction estimation device and an arrival direction estimation method that can improve the estimation accuracy of arrival directions of a plurality of arrival waves.

  An arrival direction estimation apparatus according to the present invention performs a reception process of an incoming wave incident by an antenna and a plurality of antennas that receive incoming waves emitted from a plurality of radiation sources, and outputs an incoming wave reception signal A steering vector estimating unit for estimating a steering vector indicating directions of arrival of arriving waves radiated from a plurality of radiation sources, and a steering vector estimating unit from a reception signal output from the plurality of receiving units A projection matrix calculation unit that calculates a projection matrix for projecting into a space orthogonal to the true steering vector indicating the true arrival direction of the incoming wave using the estimated steering vector, and the arrival direction search unit, Set the steering vector determined from the antenna position and direction of arrival, and change the direction of arrival indicated by the set steering vector. Reluctant, calculates the product of the calculated projection matrix by a projection matrix calculation unit that sets the steering vector is obtained by so as to search for the direction of arrival and the product becomes zero.

  According to the present invention, a projection matrix calculation for calculating a projection matrix for projecting into a space orthogonal to a true steering vector indicating a true arrival direction of an incoming wave using the steering vector estimated by the steering vector estimation unit. Is calculated by the set steering vector and projection matrix calculation unit while changing the arrival direction indicated by the set steering vector. The product is calculated by calculating the product with the projection matrix and the arrival direction where the product is zero is searched, so that the arrival waves radiated from multiple radiation sources have a high dynamic range or multiple arrivals. Even if there is a correlation between the waves, it is possible to improve the estimation accuracy of the direction of arrival of multiple incoming waves. That.

It is a block diagram which shows the arrival direction estimation apparatus by Embodiment 1 of this invention. It is a hardware block diagram in case a part of component of an arrival direction estimation apparatus is comprised with a computer. It is a flowchart which shows the arrival direction estimation method which is the processing content of the arrival direction estimation apparatus by Embodiment 1 of this invention. It is a block diagram which shows the arrival direction estimation apparatus by Embodiment 3 of this invention.

  Hereinafter, in order to describe the present invention in more detail, modes for carrying out the present invention will be described with reference to the accompanying drawings.

Embodiment 1 FIG.
FIG. 1 is a block diagram showing an arrival direction estimation apparatus according to Embodiment 1 of the present invention.
In the first embodiment, the radiation source 1-k (k = 1, 2,..., K) radiates radio waves, and the arrival direction estimation device uses the arrival direction of the radio waves radiated from the radiation source 1-k. The radiation source 1-k radiates light waves, sound waves, and the like, and the arrival direction estimation device estimates the arrival direction of the arrival waves such as light waves and sound waves emitted from the radiation source 1-k. You may do.
In FIG. 1, a receiving antenna 2-m (m = 1, 2,..., M) receives an incoming wave radiated from the radiation sources 1-1 to 1-K, and a radio frequency signal of the incoming wave. The receiving antennas 2-1 to 2-M constitute an M-element array antenna.

  The reception unit 3-m (m = 1, 2,..., M) performs, for example, amplification processing for amplifying the RF signal, high-frequency component of the RF signal, and the like on the RF signal output from the reception antenna 2-m. By performing reception processing such as band-pass filter processing for removing noise, frequency conversion processing for converting the frequency of the RF signal, and A / D conversion processing for converting the RF signal into a digital signal, the received signal of the incoming wave is digitally Output baseband complex signal. When the obtained digital signal is a real signal of an IF signal that is an intermediate frequency signal, a baseband complex signal may be obtained by performing, for example, Hilbert transform or digital quadrature detection.

The VESPA processing unit 4 performs VESPA processing on the baseband complex signals output from the receiving units 3-1 to 3-M, thereby allowing the incoming waves radiated from the radiation sources 1-1 to 1-K to be transmitted. incoming steering vector a (θ ₁₎ to indicate the direction theta ₁ tilde through? _K tilde estimates the tilde ~a (θ _K) tilde, by arranging the steering vector a (θ ₁₎ tilde ~a (θ _K) tilde steering A process of outputting the matrix A tilde to the projection matrix calculation unit 5 is performed.
In the text of the specification, on the relationship of electronic filing, _{"θ k",} because "a (θ _k)" Ya on top of the letter "A""~" can not be denoted by the symbol of, "θ _k It is expressed as “tilde” “a (θ _k ) tilde” “A tilde”. The VESPA processing unit 4 constitutes a steering vector estimation unit.

The projection matrix calculation unit 5 uses the steering matrix A tilde output from the VESPA processing unit 4, and the true steering vectors a (θ ₁ ) to a (θ _K indicating the true arrival directions θ _{1 to} θ _K of the incoming waves. A process of calculating a projection matrix P for projecting onto a space orthogonal to () is performed.
The arrival direction search unit 6 sets an ideal steering vector a (θ) determined from the positions of the receiving antennas 2-1 to 2-M and the arrival direction θ, and changes the arrival direction θ indicated by the steering vector a (θ). However, the product of the steering vector a (θ) and the projection matrix P calculated by the projection matrix calculation unit 5 is calculated, the arrival direction θ where the product is zero is searched, and the searched arrival direction θ is determined. A process of outputting the estimation result of the arrival direction θ _k of the incoming wave is performed.

In the example of FIG. 1, it is assumed that each of the VESPA processing unit 4, the projection matrix calculation unit 5, and the arrival direction search unit 6, which are some of the components of the arrival direction estimation device, is configured by dedicated hardware. However, the VESPA processing unit 4, the projection matrix calculation unit 5, and the arrival direction search unit 6, which are some of the components of the arrival direction estimation device, may be configured by a computer. As the dedicated hardware, for example, a semiconductor integrated circuit on which a CPU is mounted, a one-chip microcomputer, or the like can be considered.
FIG. 2 is a hardware configuration diagram in a case where some of the components of the arrival direction estimation apparatus are configured by a computer.
For example, when the VESPA processing unit 4, the projection matrix calculation unit 5, and the arrival direction search unit 6, which are some of the components of the arrival direction estimation device, are configured by a computer, the VESPA processing unit 4, the projection matrix calculation unit 5, and the arrival A program describing the processing contents of the direction search unit 6 may be stored in the memory 11 shown in FIG. 2, and the processor 12 shown in FIG. 2 may execute the program stored in the memory 11.
FIG. 3 is a flowchart showing an arrival direction estimation method which is a processing content of the arrival direction estimation apparatus according to Embodiment 1 of the present invention.

Next, the operation will be described.
Receiving antennas 2-1 to 2-M constituting an M-element array antenna receive an incoming wave of radio waves radiated from radiation sources 1-1 to 1-K and receive an RF signal of the arriving wave. Output to the units 3-1 to 3-M (step ST1 in FIG. 3).

  When the receiving unit 3-m (m = 1, 2,..., M) receives an RF signal from the receiving antenna 2-m, for example, an amplification process for amplifying the RF signal with respect to the RF signal, RF By performing reception processing such as band-pass filter processing that removes high-frequency components of the signal, frequency conversion processing that converts the frequency of the RF signal, A / D conversion processing that converts the RF signal into a digital signal, As a reception signal, a digital baseband complex signal is output to the VESPA processing unit 4 (step ST2).

When receiving the baseband complex signal from the receiving units 3-1 to 3 -M, the VESPA processing unit 4 performs VESPA processing on the baseband complex signal, thereby causing the radiation sources 1-1 to 1 -K. The steering vector a (θ ₁ ) tilde to a (θ _K ) tilde indicating the arrival directions θ ₁ tilde to θ _K tilde of the incoming wave radiated from is estimated, and the steering vector a (θ ₁ ) tilde to a (θ _K ) The steering matrix A tilde in which tildes are arranged is output to the projection matrix calculation unit 5 (step ST3).
Hereinafter, a process for estimating the steering vector a (θ ₁ ) tilde to a (θ _K ) tilde by the VESPA processing unit 4 will be specifically described.

式（１）において、Ａは放射源１−１〜１−Ｋから放射された到来波の真の到来方向を示す真のステアリングベクトルａ（θ_ｋ）が波数分並べられているＭ×Ｋのステアリング行列である。ｓ（ｔ）は到来波の信号、ｎ（ｔ）はノイズ信号である。 First, assuming that M baseband complex signals output from the reception units 3-1 to 3-M are reception data x (t), the reception data x (t) is expressed as the following equation (1). Is done. t is a time sample.

In Expression (1), A is an M × K in which true steering vectors a (θ _k ) indicating the true arrival directions of the incoming waves radiated from the radiation sources 1-1 to 1-K are arranged for the wave number. Steering matrix. s (t) is an incoming wave signal and n (t) is a noise signal.

Here, the cumulant matrix C is defined as the following formula (2).

In Expressions (3) to (5), C ₁ is a component of a cumulant for an actual array that is an actual arrangement of the receiving antennas 2-1 to ₂ -M, and C ₂ is a receiving antenna 2-1 to ₂ -M. Is a cumulant component for a virtual array that is a virtual arrangement that has been translated.
u and v are guiding sensor numbers indicating two sensors whose reception characteristics are known, cum is a symbol indicating cumulant, and E is an expected value.
Assuming that a plurality of incoming waves are uncorrelated with each other, Γ is a diagonal matrix in which fourth-order cumulants γ _k are arranged in diagonal terms, and is expressed as the following equation (6).
Φ is a diagonal matrix in which phase differences φ _k depending on the arrival direction of the guiding sensor and each incoming wave are arranged in a diagonal term, and is expressed as the following Expression (7).

Δはガイディングセンサ間隔、λは到来波の波長、θ_ｋは＃ｋ波目の到来方向である。

Δ is the guiding sensor interval, λ is the wavelength of the incoming wave, and θ _k is the arrival direction of the #k wave.

式（９）のＵは２Ｍ×２Ｍ行の列、式（１１）のＶはＭ×Ｍの行列である。式（１０）のｄｉａｇは対角行列の対角項を表している。 When the singular value decomposition is performed on the cumulant matrix C, the following expression (8) is obtained.

U in Equation (9) is a 2M × 2M row column, and V in Equation (11) is an M × M matrix. “Diag” in Expression (10) represents a diagonal term of the diagonal matrix.

式（２）を式（１２）に代入すると、式（１２）は下記の式（１３）のように変形することができる。

Here, if different singular vectors are orthogonal, the following formula (12) is established.

By substituting equation (2) into equation (12), equation (12) can be transformed into equation (13) below.

さらに、行列ＵのＵ_１とＵ_２が直交することを考慮すると、式（１４）より、行列Ｂの列ベクトルで張られる空間と、Ｕ_１の列ベクトルで張られる空間は、同一になることが分かる。
したがって、下記の式（１５）を満足するＫ×Ｋ次元の正則行列Ｔが存在する。

Using the fact that AΓ in Expression (13) is full rank, Expression (12) means the following Expression (14).

Further, considering that U ₁ and U ₂ of the matrix U are orthogonal, the space spanned by the column vector of the matrix B and the space spanned by the column vector of U ₁ are the same from the equation (14). I understand.
Therefore, there exists a K × K-dimensional regular matrix T that satisfies the following equation (15).

And the upper half of U _1, is regarded as the eigenvector corresponding to the sub-arrays of the lower half of U _1, equation (15) is found to be identical to the property satisfied by the signal subspace ESPRIT process.
Therefore, Φ can be estimated by using LS (Least Square) -ESPRIT or TLS (Total Last Square) -ESPRIT in ESPRIT processing.

Here, the estimation of Φ using TLS-ESPRIT will be briefly described. Details of this estimation are disclosed in Non-Patent Document 4 below.
[Non-Patent Document 4]
M.M. Dogan, J, Mendel, “Application of cumulants to array processing—Part III: Blind Beamforming for Coherent Signals,” IEEE Trans. Signal Processing, vol. 45, no. 9, pp. 2252-2264, May 1997

式（１７）のＥ_Ｈの固有値展開を行って、ゼロに等しいＫ個の固有値に属する固有ベクトルから行列Ｖ_ＸＹを構成する。

そして、行列Ｖ_ＸＹの上半分をＧ_Ｘ、行列Ｖ_ＸＹの下半分をＧ_Ｙとおくと、ＴＬＳ解Ψは、下記の式（１９）のように求まる。

Performing eigenvalue decomposition of E _H of formula (17), constituting the matrix V _XY eigenvectors belonging to K eigenvalues equal to zero.

Then, half _{G X} on the matrix _{V XY,} when put the _{G Y} the lower half of the matrix _{V XY,} the TLS solution [psi, calculated as the following equation (19).

したがって、式（１５）より、放射源１−１〜１−Ｋから放射された到来波の到来方向θ_１チルダ〜θ_Ｋチルダを示すステアリングベクトルａ（θ_１）チルダ〜ａ（θ_Ｋ）チルダを推定することができる。
下記の式（２１）は、実アレーについてのステアリングベクトルａ（θ_１）チルダ〜ａ（θ_Ｋ）チルダが並べられたステアリング行列Ａ_１チルダであり、式（２２）は、仮想アレーについてのステアリングベクトルａ（θ_１）チルダ〜ａ（θ_Ｋ）チルダが並べられたステアリング行列Ａ_２チルダである。
式（２３）は、実アレーに係るステアリングベクトルと仮想アレーに係るステアリングベクトルとの平均のステアリングベクトルが並べられたステアリング行列Ａチルダである。 From the eigenvalue obtained by eigenvalue expansion of the TLS solution Ψ, Φ can be estimated as in the following equation (20).

Therefore, from equation (15), steering vectors a (θ ₁ ) tilde to a (θ _K ) tilde indicating arrival directions θ ₁ tilde to θ _K tilde of the incoming waves radiated from the radiation sources 1-1 to 1-K. Can be estimated.
Equation (21) below is a steering matrix A ₁ tilde in which steering vectors a (θ ₁ ) tilde to a (θ _K ) tilde for the real array are arranged, and Equation (22) is the steering for the virtual array. This is a steering matrix A ₂ tilde in which vectors a (θ ₁ ) tilde to a (θ _K ) tilde are arranged.
Expression (23) is a steering matrix A tilde in which average steering vectors of the steering vector related to the real array and the steering vector related to the virtual array are arranged.

ステアリング行列Ａチルダの各列ベクトルである推定のステアリングベクトルａ（θ_ｋ）チルダは、複数の到来波の間で相関が無く、ダイナミックレンジが小さい場合には、真の到来方向θ_ｋに対応するステアリングベクトルａ（θ_ｋ）と一致する。
ここでは、ＶＥＳＰＡ処理部４が、ＴＬＳ−ＥＳＰＲＩＴに基づいてステアリングベクトルａ（θ_ｋ）チルダを推定するものを示したが、ＬＳ−ＥＳＰＲＩＴに基づいても、ステアリングベクトルａ（θ_ｋ）チルダを推定することができる。
なお、ＶＥＳＰＡ処理部４により推定されたステアリングベクトルａ（θ_ｋ）チルダは、放射源１−１〜１−Ｋから放射された到来波が高いダイナミックレンジを有する場合や、到来波１−１〜１−Ｋの間に相関がある場合には、複数の到来波を高精度に分離することができないため、この実施の形態１では、以下の処理を実施する。

The estimated steering vector a (θ _k ) tilde, which is each column vector of the steering matrix A tilde, corresponds to the true arrival direction θ _k when there is no correlation among the plurality of incoming waves and the dynamic range is small. It coincides with the steering vector a (θ _k ).
Here, VESPA processing unit 4, showed that estimates a steering vector a (θ _k) tilde based on TLS-ESPRIT, be based on the LS-ESPRIT, steering vector a (θ _k) estimated tilde can do.
Note that the steering vector a (θ _k ) tilde estimated by the VESPA processing unit 4 is used when the incoming waves radiated from the radiation sources 1-1 to 1-K have a high dynamic range, or the incoming waves 1-1 to 1-1. When there is a correlation between 1-K, a plurality of incoming waves cannot be separated with high accuracy. Therefore, in the first embodiment, the following processing is performed.

When the VESPA processing unit 4 estimates the steering vector a (θ _k ) tilde, the projection matrix calculation unit 5 uses the steering matrix A tilde in which the steering vector a (θ _k ) tilde is arranged, calculating the arrival direction theta ₁ through? true steering vector a (theta ₁₎ showing a _K ~a (θ _K) projection matrix P for projecting into the space orthogonal to (step ST4).
That is, the projection matrix calculation unit 5 calculates a projection matrix P as shown in the following equation (25) using the steering matrix A tilde.

When there is a correlation between a plurality of incoming waves or when the dynamic range is large, the estimated steering vector a (θ _k ) tilde, which is each column vector of the steering matrix A tilde, is the true steering vector a (θ _k ) does not match.
At this time, the steering matrix A in which the true steering vectors a (θ ₁ ) to a (θ _k ) are arranged, and the steering vector a (θ ₁ ) tilde to a (θ _K estimated by the projection matrix calculation unit 5. The steering matrix A tilde in which tildes are arranged has the relationship of the following formula (24).

式（２５）において、Ｉは単位行列である。 Z in Expression (24) is a K × K matrix, and Expression (24) means that a true steering vector a (θ _k ) exists in a space spanned by the column vector of the steering matrix A.
Here, if the projection matrix P is defined as the following equation (25), when the matrix Z is a regular matrix, the projection matrix P of the equation (25) is expressed as a true steering vector a (θ _k ). It can be seen that the matrix is projected onto an orthogonal space, that is, a noise subspace.

In Expression (25), I is a unit matrix.

ここで、Ｘ^Ｔは、行列あるいはベクトルＸの転置を表し、Ｐ_ｍはｍ素子番目の受信アンテナ２−ｍの位置座標を示している２次元ベクトルである。 When the projection matrix calculation unit 5 calculates the projection matrix P, the arrival direction search unit 6 is ideally determined from the positions of the reception antennas 2-1 to 2-M and the arrival direction θ as shown in the following equation (26). A correct steering vector a (θ) is set (step ST5). That is, a steering vector a (θ) close to the true steering vector a (θ _k ) indicating the true arrival direction θ _k of the incoming wave is set.

Here, X ^T represents a transpose of a matrix or vector X, P _m is the two-dimensional vector represents the m elements th position coordinates of the receiver antenna 2-m.

When the arrival direction search unit 6 sets the steering vector a (θ), the steering vector a (θ) and the projection matrix calculation unit 5 calculate the arrival direction θ indicated by the set steering vector a (θ). The product of the calculated projection matrix P is calculated, the arrival direction θ in which the product is zero is searched, and the searched arrival direction θ is output as the estimation result of the arrival direction θ _k of the incoming wave (step ST6). .
Hereinafter, the process of estimating the arrival direction θ _k by the arrival direction searching unit 6 will be specifically described.

Since the projection matrix P calculated by the projection matrix calculation unit 5 is a matrix for projecting onto a space orthogonal to the true steering vector a (θ _k ), the arrival direction indicated by the set steering vector a (θ) If θ matches the true arrival direction θ _k of the incoming wave, the product of the set steering vector a (θ) and the projection matrix P becomes a zero vector, and the inner product of the zero vectors becomes zero.
Therefore, when the azimuth spectrum S (θ) as shown in the following equation (29) is calculated using the same concept as the MUSIC algorithm which is a known multiple signal classification process, the arrival indicated by the steering vector a (θ) If the direction θ coincides with the true arrival direction θ _k of the incoming wave and the product of the steering vector a (θ) and the projection matrix P becomes a zero vector, the denominator of the equation (29) becomes 0, and the direction The spectrum S (θ) has a peak.

Therefore, the arrival direction searching unit 6 searches for the arrival direction θ in which the azimuth spectrum S (θ) has a maximum value, and outputs the searched arrival direction θ as an estimation result of the true arrival direction θ _k of the arrival wave.
In this way, by searching for the arrival direction θ where the azimuth spectrum S (θ) has a maximum value, the true arrival directions θ _{1 to} θ _K of a plurality of arrival waves can be separated and estimated.
Note that a ^H (θ) a (θ) in the numerator of the formula (29) is a coefficient for normalization similar to the MUSIC spectrum, and the antenna pattern by the receiving antennas 2-1 to 2-M is omnidirectional. In the case of the characteristic, it is equal to the number of elements of the receiving antenna 2-m.

As apparent from the above, according to the first embodiment, the true steering vector indicating the true arrival directions θ _{1 to} θ _K of the incoming wave using the steering matrix A tilde output from the VESPA processing unit 4. A projection matrix calculation unit 5 that calculates a projection matrix P for projecting into a space orthogonal to a (θ ₁ ) to a (θ _K ) is provided, and the arrival direction search unit 6 includes reception antennas 2-1 to 2-M. An ideal steering vector a (θ) determined from the position and the arrival direction θ is set, and while changing the arrival direction θ indicated by the steering vector a (θ), the steering vector a (θ) and the projection matrix calculation unit 5 Since the product with the projection matrix P calculated by the above is calculated and the arrival direction θ in which the product becomes zero is searched, the arrival waves radiated from the radiation sources 1-1 to 1-K are high. Dynamic range If you have, the radiation source even if there is a correlation between the incoming waves radiated from 1-1 to 1-K, and separating a plurality of incoming waves with high accuracy, the arrival direction of a plurality of incoming waves theta ₁ ~ There is an effect that θ _K can be accurately estimated.

In this first embodiment, the arrival direction searching unit 6 changes the steering vector a (θ) and the projection matrix P calculated by the projection matrix calculation unit 5 while changing the arrival direction θ indicated by the steering vector a (θ). The one-dimensional arrival direction θ _k is estimated by searching for the arrival direction θ where the product is zero, and the azimuth angle θ _k and the elevation angle φ of the arrival wave are shown. You may make it estimate _k .
In this case, the arrival direction searching unit 6 sets the steering vector a (θ, φ) instead of the equation (26).
At this time, P _m in Expression (27) is a three-dimensional vector indicating the three-dimensional position coordinates of the m-th element receiving antenna 2-m.
Further, L (θ, φ) as shown in the following equation (30) is used instead of L (θ) in equation (27).

Then, the arrival direction search unit 6 changes the azimuth angle θ and the elevation angle φ indicated by the set steering vector a (θ, φ), while changing the azimuth spectrum S (θ, φ, The azimuth angle θ and the elevation angle φ at which φ) is the maximum are searched, and the searched azimuth angle θ and elevation angle φ are output as estimation results of the azimuth angle θ _k and the elevation angle φ _k of the incoming wave. .

式（３２）において、“〇”の記号はベクトルの要素毎の積を表している。 In the first embodiment, the arrival direction search unit 6 sets an ideal steering vector a (θ) determined from the positions of the reception antennas 2-1 to 2-M and the arrival direction θ. When the antenna pattern b (θ) by the receiving antennas 2-1 to 2-M can be measured in advance, as shown in the following equation (32), the receiving antennas 2-1 to 2-M An ideal steering vector a (θ) tilde that is determined from the position, the arrival direction θ, and the antenna pattern b (θ) may be set.

In equation (32), the symbol “◯” represents the product of each vector element.

受信アンテナ２−１〜２−Ｍによるアンテナパターンｂ（θ）を用いて、ステアリングベクトルａ（θ）を設定することで、ステアリングベクトルａ（θ）の設定精度が向上するため、積が零になる到来方向θを短時間で探索することができる。 In this case, the arrival direction searching unit 6 searches for the arrival direction θ in which the azimuth spectrum S (θ) as shown in the following equation (33) becomes a maximum value.

Setting the steering vector a (θ) using the antenna pattern b (θ) by the receiving antennas 2-1 to 2-M improves the setting accuracy of the steering vector a (θ), so the product becomes zero. Can be searched in a short time.

Embodiment 2. FIG.
In the first embodiment, the VESPA processing unit 4 outputs the average steering vector a (θ _k ) tilde of the steering vector related to the real array and the steering vector related to the virtual array, and the projection matrix calculation unit 5 Using the average steering vector a (θ _k ) tilde output from the processing unit 4, true steering vectors a (θ ₁ ) to a (θ _K ) indicating the true arrival directions θ _{1 to} θ _K of the incoming wave. Although a projection matrix P for calculating a projection matrix P for projecting to a space orthogonal to the above is shown, the projection matrix calculation unit 5 performs an actual operation from the steering vector a (θ _k ) tilde related to the actual array calculated by the VESPA processing unit 4. calculates the projection matrix P ₁ of the array steering vector a according to a virtual array calculated by VESPA processor 4 (θ _k) Ji It may be calculated projection matrix P ₂ according to a virtual array from da.
Specifically, it is as follows.

When the projection matrix calculation unit 5 receives the steering matrix A ₁ tilde in which the steering vector a (θ _k ) tilde related to the real array is arranged from the VESPA processing unit 4, as shown in the following equation (34), A projection matrix P for projecting onto a space orthogonal to the true steering vectors a (θ ₁ ) to a (θ _K ) indicating the true arrival directions θ _{1 to} θ _K of the incoming wave using the steering matrix A ₁ tilde. ₁ is calculated.

When the projection matrix calculation unit 5 receives the steering matrix A ₂ tilde in which the steering vector a (θ _k ) tilde related to the virtual array is arranged from the VESPA processing unit 4, as shown in the following equation (35): Then, using the steering matrix A ₂ tilde, a projection for projecting onto a space orthogonal to the true steering vectors a (θ ₁ ) to a (θ _K ) indicating the true arrival directions θ _{1 to} θ _K of the incoming wave to calculate the matrix _{P 2.}

The arrival direction search unit 6 sets the steering vector a (θ) of Expression (26), as in the first embodiment.
Here, the steering vector a (θ) in Expression (26) is set, but the steering vector a (θ) tilde in Expression (32) may be set.
When the arrival direction search unit 6 sets the steering vector a (θ), the steering vector a (θ) and the projection matrix calculation unit 5 calculate the arrival direction θ indicated by the set steering vector a (θ). A product with the projected matrix P ₁ is calculated, and an arrival direction θ in which the product becomes zero is searched. In practice, to calculate the inner product of vectors obtained by multiplying the projection matrix P ₁ and the steering vector.
That is, the arrival direction searching unit 6 searches for the arrival direction θ where the azimuth spectrum S ₁ (θ) as shown in the following formula (36) becomes a maximum value.

Further, the arrival direction searching unit 6 changes the arrival direction θ indicated by the set steering vector a (θ), and changes the steering vector a (θ) and the projection matrix P ₂ calculated by the projection matrix calculation unit 5. The product is calculated, and the arrival direction θ where the product becomes zero is searched.
That is, the arrival direction search unit 6 searches for an arrival direction θ in which the azimuth spectrum S ₂ (θ) as shown in the following formula (37) becomes a maximum value.

When the arrival direction search unit 6 searches for the arrival direction θ where the azimuth spectrum S ₁ (θ) has a maximum value and the arrival direction θ where the azimuth spectrum S ₂ (θ) has a maximum value, The average value is output as the estimation result of the arrival direction θ _k of the incoming wave.
According to the second embodiment, similarly to the first embodiment, the arrival waves radiated from the radiation sources 1-1 to 1-K have a high dynamic range, or the radiation sources 1-1 to 1- Even when there is a correlation between incoming waves radiated from K, it is possible to separate a plurality of incoming waves with high accuracy and accurately estimate the arrival directions θ _{1 to} θ _K of the plurality of incoming waves. Play.

Here, the arrival direction search unit 6 searches for the arrival direction θ where the azimuth spectrum S ₁ (θ) has a maximum value, and searches for the arrival direction θ where the azimuth spectrum S ₂ (θ) has a maximum value. Although the output of the average value of the two arrival directions θ is shown, the arrival direction θ in which the azimuth spectrum S (θ) as shown in the following equation (38) becomes a maximum value may be searched.

In the first embodiment, the direction-of-arrival search unit 6 uses the projection matrix P. However, as the projection matrix used by the direction-of-arrival search unit 6, the projection matrix calculated using the steering vector related to the real array is used. and P _1, may be used mean a is averaged projection matrix and a projection matrix P ₂ calculated using the steering vector of the virtual array.
That is, an azimuth spectrum obtained by replacing the projection matrix P in Equation (33) with 1/2 * (P ₁ + P ₂ ) can also be used.

Embodiment 3 FIG.
In the first and second embodiments, the VESPA processing unit 4 performs the VESPA processing on the baseband complex signals output from the reception units 3-1 to 3-M, thereby causing the radiation sources 1-1 to 1-1. Although the estimation of the steering vector a (θ ₁ ) tilde to a (θ _K ) tilde indicating the arrival directions θ ₁ tilde to θ _K tilde of the incoming wave radiated from 1-K is shown, the receiving unit 3-1 By performing ESPRI processing on the baseband complex signal output from ˜3-M, arrival directions θ ₁ tilde to θ _K tilde of incoming waves radiated from radiation sources 1-1 to _{1- K} are obtained. Steering vectors a (θ ₁ ) tilde to a (θ _K ) tilde may be estimated.

4 is a block diagram showing a direction-of-arrival estimation apparatus according to Embodiment 3 of the present invention. In FIG. 4, the same reference numerals as those in FIG.
The ESPRI processing unit 7 performs ESPRI processing on the baseband complex signals output from the receiving units 3-1 to 3 -M, so that the incoming waves radiated from the radiation sources 1-1 to 1 -K are transmitted. incoming steering vector a (θ ₁₎ to indicate the direction theta ₁ tilde through? _K tilde estimates the tilde ~a (θ _K) tilde, by arranging the steering vector a (θ ₁₎ tilde ~a (θ _K) tilde steering A process of outputting the matrix A tilde to the projection matrix calculation unit 5 is performed. The ESPRI processing unit 7 constitutes a steering vector estimation unit.

In the example of FIG. 4, it is assumed that each of the ESPRI processing unit 7, the projection matrix calculation unit 5, and the arrival direction search unit 6, which are some of the components of the arrival direction estimation device, is configured by dedicated hardware. However, the ESPRI processing unit 7, the projection matrix calculation unit 5, and the arrival direction search unit 6, which are some of the components of the arrival direction estimation apparatus, may be configured by a computer. As the dedicated hardware, for example, a semiconductor integrated circuit on which a CPU is mounted, a one-chip microcomputer, or the like can be considered.
For example, when the ESPRI processing unit 7, the projection matrix calculation unit 5, and the arrival direction search unit 6 that are part of the components of the arrival direction estimation device are configured by a computer, the ESPRI processing unit 7, the projection matrix calculation unit 5, and the arrival A program describing the processing contents of the direction search unit 6 may be stored in the memory 11 shown in FIG. 2, and the processor 12 shown in FIG. 2 may execute the program stored in the memory 11.

Next, the operation will be described.
Since the configuration other than the ESPRI processing unit 7 is the same as in the first and second embodiments, only the processing contents of the ESPRI processing unit 7 will be described here.
Since the ESPRI processing unit 7 performs ESPRI processing on the baseband complex signals output from the receiving units 3-1 to 3-M, the M element including the receiving antennas 2-1 to 2-M This is applicable only when the array antenna can be divided into two subarrays # 1 and # 2 of the same type.

When the ESPRI processing unit 7 receives the reception data x (t) represented by the equation (1) from the reception units 3-1 to 3-M, as shown in the following equation (39), the reception data x ( The correlation matrix Rxx of t) is calculated.

式（４０）において、Ａ_１はサブアレー＃１に対応するステアリングベクトルであり、Φは到来波の到来方向とサブアレー間隔に対応する位相差が対角項に並んでいる対角行列である。また、Ｔは正則な行列である。
式（４０）は式（１５）と同様であるため、以下、上記実施の形態１と同様に、式（１６）〜式（２３）の処理を実施することで、ステアリングベクトルａ（θ_１）チルダ〜ａ（θ_Ｋ）チルダを推定することができる。 ESPRI processing unit 7, when calculating the correlation matrix Rxx received data x (t), the correlation matrix Rxx seek signal eigenvectors _{E s} by eigenvalue decomposition, the two of the same type from the signal eigenvectors _{E s} subarrays # 1, eigenvector _E X corresponding to # 2, extracts the _{E Y,} as shown in the following equation (40), the eigenvector _E X, calculating the matrix D from _{E Y.}

In the formula (40), A ₁ is a steering vector corresponding to the sub-array # 1, [Phi is the phase difference corresponding to the direction of arrival and subarray interval of the incoming wave is a diagonal matrix are arranged in diagonal. T is a regular matrix.
Since the expression (40) is the same as the expression (15), the steering vector a (θ ₁ ) is executed by performing the processes of the expressions (16) to (23) as in the first embodiment. A tilde to a (θ _K ) tilde can be estimated.

  In the present invention, within the scope of the invention, any combination of the embodiments, or any modification of any component in each embodiment, or omission of any component in each embodiment is possible. .

  1-k radiation source, 2-m reception antenna (antenna), 3-m reception unit, 4 VESPA processing unit (steering vector estimation unit), 5 projection matrix calculation unit, 6 arrival direction search unit, 7 ESPRI processing unit (steering) Vector estimation unit), 11 memories, 12 processors.

Claims (9)

A plurality of antennas that receive incoming waves radiated from a plurality of radiation sources; and
A plurality of receiving units that perform reception processing of an incoming wave incident by the antenna and output a reception signal of the incoming wave;
A steering vector estimation unit that estimates a steering vector indicating an arrival direction of incoming waves radiated from the plurality of radiation sources from reception signals output from the plurality of reception units;
Using a steering vector estimated by the steering vector estimation unit, a projection matrix calculation unit for calculating a projection matrix for projecting to a space orthogonal to a true steering vector indicating a true arrival direction of the incoming wave;
A steering vector determined from the antenna position and the arrival direction is set, and the product of the set steering vector and the projection matrix calculated by the projection matrix calculation unit is calculated while changing the arrival direction indicated by the set steering vector. An arrival direction estimation apparatus comprising: an arrival direction search unit that searches for an arrival direction in which the product is zero.   The arrival direction estimation apparatus according to claim 1, wherein the arrival direction search unit sets a steering vector determined from a position, an arrival direction, and an antenna pattern of the antenna.   The steering vector estimation unit performs a VESPA (Virtual ESPRIT Algorithm) process on the reception signals output from the plurality of reception units, thereby determining the arrival directions of the arrival waves radiated from the plurality of radiation sources. The direction-of-arrival estimation apparatus according to claim 1 or 2, wherein a steering vector is estimated.   The steering vector estimator performs ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) processing on the received signals output from the plurality of receivers, thereby arriving from the plurality of radiation sources. The arrival direction estimation apparatus according to claim 1 or 2, wherein a steering vector indicating the arrival direction of the wave is estimated. The steering vector estimation unit estimates a steering vector indicating an arrival direction of an incoming wave radiated from the plurality of radiation sources for an actual array that is an actual arrangement of the plurality of antennas, and the plurality of antennas are parallel to each other. For a virtual array that is a moved virtual arrangement, a steering vector indicating an arrival direction of an incoming wave radiated from the plurality of radiation sources is estimated, and a steering vector related to the real array and a steering vector related to the virtual array are estimated And output the average steering vector with
The projection matrix calculation unit uses the average steering vector output from the steering vector estimation unit to generate a projection matrix for projecting into a space orthogonal to a true steering vector indicating a true arrival direction of the incoming wave. The arrival direction estimation apparatus according to any one of claims 1 to 4, wherein the arrival direction estimation apparatus calculates the arrival direction. The steering vector estimation unit estimates a steering vector indicating an arrival direction of an incoming wave radiated from the plurality of radiation sources for an actual array that is an actual arrangement of the plurality of antennas, and the plurality of antennas are parallel to each other. For a virtual array that is a moved virtual arrangement, a steering vector indicating an arrival direction of incoming waves emitted from the plurality of radiation sources is estimated,
The projection matrix calculation unit uses the steering vector related to the real array estimated by the steering vector estimation unit to project to a space orthogonal to the true steering vector indicating the true arrival direction of the incoming wave A projection matrix for calculating a matrix and projecting into a space orthogonal to a true steering vector indicating a true arrival direction of the incoming wave using a steering vector related to the virtual array estimated by the steering vector estimation unit To calculate
The arrival direction search unit changes an arrival direction indicated by the set steering vector, and calculates a reciprocal of a product of the set steering vector and the projection matrix related to the real array and the virtual array calculated by the projection matrix calculation unit. The calculation method calculates an evaluation value obtained by averaging the reciprocal of the product of the real array and the projection matrix related to the virtual array, and searches for an arrival direction in which the evaluation value becomes a maximum. The arrival direction estimation apparatus according to any one of items 4 to 5. The steering vector estimation unit estimates a steering vector indicating an arrival direction of an incoming wave radiated from the plurality of radiation sources for an actual array that is an actual arrangement of the plurality of antennas, and the plurality of antennas are parallel to each other. For a virtual array that is a moved virtual arrangement, a steering vector indicating an arrival direction of incoming waves emitted from the plurality of radiation sources is estimated,
The projection matrix calculation unit uses the steering vector related to the real array estimated by the steering vector estimation unit to project to a space orthogonal to the true steering vector indicating the true arrival direction of the incoming wave A projection matrix for calculating a matrix and projecting into a space orthogonal to a true steering vector indicating a true arrival direction of the incoming wave using a steering vector related to the virtual array estimated by the steering vector estimation unit To calculate
The arrival direction search unit calculates a product of the set steering vector and a projection matrix related to the real array calculated by the projection matrix calculation unit while changing the arrival direction indicated by the set steering vector, and The direction of arrival where the product becomes zero is searched, and the product of the set steering vector and the projection matrix related to the virtual array calculated by the projection matrix calculation unit is calculated, and the direction of arrival where the product becomes zero is calculated. 5. The average direction of arrival of the direction of arrival related to the searched real array and the direction of arrival related to the searched virtual array is calculated. The direction of arrival estimation apparatus described. The steering vector estimation unit estimates a steering vector indicating an arrival direction of an incoming wave radiated from the plurality of radiation sources for an actual array that is an actual arrangement of the plurality of antennas, and the plurality of antennas are parallel to each other. For a virtual array that is a moved virtual arrangement, a steering vector indicating an arrival direction of incoming waves emitted from the plurality of radiation sources is estimated,
The projection matrix calculation unit uses a steering vector related to the real array and the virtual array estimated by the steering vector estimation unit, respectively, in a space orthogonal to a true steering vector indicating a true arrival direction of the incoming wave. Calculating a projection matrix for projecting, calculating an averaged projection matrix by averaging the projection matrices calculated using the steering vectors related to the real array and the virtual array,
The arrival direction search unit calculates a product of the set steering vector and the averaged projection matrix calculated by the projection matrix calculation unit while changing the arrival direction indicated by the set steering vector, and the product is The arrival direction estimation apparatus according to any one of claims 1 to 4, wherein an arrival direction that becomes zero is searched. When incoming waves radiated from a plurality of radiation sources are incident on a plurality of antennas, a plurality of receivers perform reception processing of the incoming waves incident by the antennas and output the received signals of the incoming waves And
A steering vector estimation unit estimates a steering vector indicating an arrival direction of incoming waves radiated from the plurality of radiation sources, from reception signals output from the plurality of reception units,
A projection matrix calculation unit uses the steering vector estimated by the steering vector estimation unit to calculate a projection matrix for projecting onto a space orthogonal to the true steering vector indicating the true arrival direction of the incoming wave,
An arrival direction search unit sets a steering vector determined from the position and direction of the antenna, and changes the arrival direction indicated by the set steering vector, and the projection calculated by the set steering vector and the projection matrix calculation unit An arrival direction estimation method that calculates a product with a matrix and searches for an arrival direction in which the product becomes zero.

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