JP5062804B2 - Arrival wave estimation method and apparatus - Google Patents
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本発明は、到来波をアレーアンテナで受信し、得られる受信信号ベクトルに基づいて、到来波の到来方向を推定する到来波推定に関する。 The present invention relates to arrival wave estimation in which an arrival wave is received by an array antenna and an arrival direction of the arrival wave is estimated based on a received signal vector obtained.
アレーアンテナを利用するレーダ装置においては、受信信号ベクトルに基づいて到来波の到来方向を推定する方法として、ＤＢＦ、Ｃａｐｏｎ、ＭＵＳＩＣ、ＥＳＰＲＩＴなどの手法が知られている。 In a radar apparatus using an array antenna, methods such as DBF, Capon, MUSIC, ESPRIT are known as methods for estimating the arrival direction of an incoming wave based on a received signal vector.
また、広がりをもつ到来波の到来方向をＣａｐｏｎ法で推定する場合に、微係数拘束条件を加えることにより受信波の到来方向を精度良く推定する技術についての提案がある（非特許文献１参照）。さらに、角度範囲の広がりをもつ到来波を考慮した積分型モードベクトルを適用したＭＵＳＩＣ法によって、到来方向と広がり角をどちらも推定できるようにした技術についての提案もある（非特許文献２）。 In addition, there is a proposal for a technique for accurately estimating the arrival direction of a received wave by adding a derivative constraint condition when estimating the arrival direction of a wide arrival wave by the Capon method (see Non-Patent Document 1). . Furthermore, there is also a proposal for a technique in which both the direction of arrival and the spread angle can be estimated by the MUSIC method using an integrated mode vector that takes into account an incoming wave having a wide angular range (Non-Patent Document 2).
上述したＤＢＦ、Ｃａｐｏｎ、ＭＵＳＩＣ、ＥＳＰＲＩＴなどの到来方向推定技術は、モードベクトルに到来波の角度広がりを考慮していない。このため、到来波の到来方向（方位）は推定できるが、広がり角を推定できない。また、角度広がりのある到来波の到来方向推定結果の精度は、角度広がりの無い到来波の到来方向を推定した場合よりも劣化する。 The arrival direction estimation techniques such as DBF, Capon, MUSIC, ESPRIT described above do not consider the angular spread of the arrival wave in the mode vector. For this reason, although the arrival direction (direction) of an incoming wave can be estimated, a spread angle cannot be estimated. In addition, the accuracy of the arrival direction estimation result of the arrival wave having the angular spread is deteriorated as compared with the case where the arrival direction of the arrival wave having no angular spread is estimated.
また、非特許文献１に記載の技術では、到来波に角度広がりがある場合でも到来方向推定精度が劣化しないように微係数拘束条件を利用している。しかし、この非特許文献１において利用されるモードベクトルも角度広がりを考慮したものではなく、従って到来方向を推定するのみで広がり角の推定はできなかった。 Further, in the technique described in Non-Patent Document 1, a derivative constraint condition is used so that the arrival direction estimation accuracy does not deteriorate even when the incoming wave has an angular spread. However, the mode vector used in Non-Patent Document 1 does not take into account the angular spread, and therefore the spread angle cannot be estimated only by estimating the direction of arrival.
一方、非特許文献２では、モードベクトルを到来波の角度広がりを考慮した積分型モードベクトルとし、これを従来のモードベクトルと置き換えたためＭＵＳＩＣ法により到来方向と広がり角を推定する。この方法は、解像度が高いＭＵＳＩＣ法を用いているため、接近した複数の到来波を分離して推定する能力が高い。しかし、その能力のために到来波を構成する素波が狭い間隔で連続して存在していない状態では複数の素波を分離して検出してしまい、到来波の広がり角を正確に推定できなくなるという問題があった。 On the other hand, in Non-Patent Document 2, since the mode vector is an integral mode vector that takes into account the angular spread of the incoming wave, and this is replaced with the conventional mode vector, the arrival direction and the spread angle are estimated by the MUSIC method. Since this method uses the MUSIC method with high resolution, it has a high ability to separate and estimate a plurality of approaching incoming waves. However, due to its ability, if the elementary waves that make up the incoming wave do not exist continuously at a narrow interval, multiple elementary waves can be detected separately, and the divergence angle of the incoming wave can be accurately estimated. There was a problem of disappearing.
また、ＭＵＳＩＣ法では到来波数をあらかじめ正確に推定する必要があり、これを正しく推定できなければ到来方向や広がり角も正しく推定できない。例えば、到来波が１波でもそれを構成する素波を２つのグループに分離した場合には、到来波を２波としなければ正確に推定できない。ここで、この到来波の推定は、一般的に自己相関行列を固有値展開して得られる固有値の大きさから推定するが、信号電力が雑音電力に比べてあまり大きくなかったり、観測時間が短いために素波間の相関が高くなってしまったりすることが多い現実の測定環境ではこの到来波数の推定が極めて難しいという問題がある。 Also, in the MUSIC method, it is necessary to accurately estimate the number of incoming waves in advance, and the arrival direction and spread angle cannot be estimated correctly unless this can be estimated correctly. For example, even if there is only one incoming wave, when the elementary waves constituting the incoming wave are separated into two groups, accurate estimation cannot be made unless the incoming wave is set to two waves. Here, this arriving wave is estimated from the size of the eigenvalue obtained by expanding the eigenvalue of the autocorrelation matrix, but the signal power is not so large compared to the noise power or the observation time is short. However, there is a problem that it is extremely difficult to estimate the number of incoming waves in an actual measurement environment where the correlation between elementary waves is often high.
さらに、到来波を構成する素波の位相が各々異なる場合には、素波の位相が全て同じと仮定しているモードベクトルとの差異により、波数推定や到来方位推定精度が劣化するという問題が生じる。特に、移動通信や移動体に搭載するレーダのように周辺環境が時々刻々と変化する状況では、素波の位相が様々に変化するため、この問題は極めて顕著に現れる。 Furthermore, when the phases of the elementary waves constituting the incoming wave are different from each other, there is a problem that the accuracy of wave number estimation and arrival direction estimation deteriorates due to the difference from the mode vector assuming that the phases of the elementary waves are all the same. Arise. In particular, in a situation where the surrounding environment changes from moment to moment, such as mobile communications and radar mounted on a moving body, this problem appears extremely remarkably because the phase of the elementary wave changes variously.
本発明は、到来波をアレーアンテナで受信し、得られる受信信号ベクトルに基づいて、到来波の到来方向を推定する到来波推定方法であって、Ｃａｐｏｎ法のモードベクトルを、到来波の角度範囲の広がりを考慮し、当該角度範囲に存在する複数の素波について加算したモードベクトルとする積分型モードベクトルとし、到来波の到来方向および広がり角を推定することを特徴とする。 The present invention relates to an arrival wave estimation method for receiving an incoming wave with an array antenna and estimating an arrival direction of the incoming wave based on an obtained received signal vector. The mode vector of the Capon method is represented by an angular range of the incoming wave. In consideration of the spread of the wave, an integrated mode vector that is a mode vector obtained by adding a plurality of elementary waves existing in the angle range is used , and the arrival direction and the spread angle of the incoming wave are estimated.
また、前記積分型モードベクトルを、到来波を構成する素波の振幅または位相変化を考慮し、当該角度範囲内に存在する素波についてそれぞれの振幅または位相を考慮して加算したモードベクトルとする積分型モードベクトルとしたことが好適である。 Further, the integral mode vector is a mode vector obtained by taking into account the amplitude or phase change of the elementary wave constituting the incoming wave and adding the elementary waves existing within the angle range in consideration of the amplitude or phase. It is preferable to use an integral mode vector.
また、前記Ｃａｐｏｎ法における推定について微係数拘束条件を加えて行うことが好適である。 In addition, it is preferable to perform estimation in the Capon method by adding a derivative constraint condition.
また、本発明は、到来波をアレーアンテナで受信し、得られる受信信号ベクトルに基づいて、到来波の到来方向を推定する到来波推定方法であって、Ｃａｐｏｎ法のモードベクトルを、到来波の角度範囲の広がりを考慮した積分型モードベクトルとし、到来波の到来方向および広がり角を推定するとともに、前記Ｃａｐｏｎ法における推定について微係数拘束条件を加えて行い、前記微係数拘束のウエイトが任意に変えられることを特徴とする。 The present invention also relates to an arrival wave estimation method for receiving an incoming wave with an array antenna and estimating an arrival direction of the incoming wave based on an obtained received signal vector. An integral mode vector that takes into account the spread of the angle range is used to estimate the arrival direction and the spread angle of the incoming wave, and to perform estimation in the Capon method with a derivative constraint condition. characterized in that it be changed.
また、前記受信信号ベクトルから自己相関行列を作成するとともに、この自己相関行列に対して、擬似雑音を加えて逆行列演算を行うことが好適である。 In addition, it is preferable that an autocorrelation matrix is created from the received signal vector and an inverse matrix operation is performed on the autocorrelation matrix by adding pseudo noise.
また、本発明は、上述のような到来波推定方法を利用して、到来波の到来方向および広がり角を推定する到来波推定装置に関する。 The present invention also relates to an arrival wave estimation device that estimates the arrival direction and the spread angle of an arrival wave using the arrival wave estimation method as described above.
なお、到来波をアレーアンテナで受信し、アレーアンテナの受信波に基づいて、到来波の到来方向を推定する到来波推定方法において、到来波を構成する素波の角度広がりおよび振幅または位相変化を考慮した積分型モードベクトルを用いて、到来波の到来方向および広がり角を推定することも好適である。 In the arrival wave estimation method for receiving an incoming wave with an array antenna and estimating the arrival direction of the incoming wave based on the received wave of the array antenna, the angular spread and amplitude or phase change of the elementary wave constituting the incoming wave is changed. It is also preferable to estimate the arrival direction and divergence angle of the incoming wave using the considered integral mode vector.
到来波推定の手段として、Ｃａｐｏｎ法を用いたことにより、到来波数の推定が不要になり、また分解能の低下により到来波を構成する素波が不必要に分離されることがない。このため、到来波数をあらかじめ正確に推定する必要がなく、到来波を構成する素波の数が減少した場合でも正確に到来方向や広がり角を推定できる。 By using the Capon method as an arrival wave estimation means, it is not necessary to estimate the number of arrival waves, and the elementary waves constituting the arrival wave are not unnecessarily separated due to a decrease in resolution. For this reason, it is not necessary to accurately estimate the number of incoming waves in advance, and the direction of arrival and the spread angle can be accurately estimated even when the number of elementary waves constituting the incoming wave is reduced.
また、積分型モードベクトルに振幅または位相項を付加して拡張し、到来波を構成する素波の振幅または位相情報を含めたモードベクトルとすることにより、到来波を構成する素波の振幅や位相が同一でなくそれぞれ異なっていても、方位または広がり角を正確に推定できる。 Also, by adding an amplitude or phase term to the integral mode vector and expanding it to make a mode vector that includes the amplitude or phase information of the elementary wave constituting the incoming wave, the amplitude of the elementary wave constituting the incoming wave or Even if the phases are not the same and are different from each other, the azimuth or the spread angle can be accurately estimated.
また、Ｃａｐｏｎ法で方位や広がり角を推定するときに微係数拘束条件を加えることにより、さらに素波が不必要に分離し難くなり、素波の数や振幅、位相などが変化しても方位や広がり角の推定に与える影響が小さくなる。従って、到来波を構成する素波の振幅や位相が様々に変化する状況でも、それらの変動の影響を受け難くなり到来波の到来方向および広がり角を正確に推定できる。 Further, by adding a derivative constraint condition when estimating the azimuth and divergence angle by the Capon method, it becomes difficult to further separate the elementary waves unnecessarily, and even if the number, amplitude, phase, etc. of the elementary waves change, the azimuth is changed. And the influence on the estimation of the spread angle is reduced. Therefore, even in a situation where the amplitude and phase of the elementary waves constituting the incoming wave are variously changed, the arrival direction and the spread angle of the incoming wave can be accurately estimated without being affected by the fluctuations.
ここで、微係数拘束付積分型Ｃａｐｏｎ法では、微係数拘束を利用しない積分型Ｃａｐｏｎ法よりも方位推定精度が劣化する場合がある。これは微係数拘束の影響が強すぎることが原因であり、微係数拘束のウエイトを任意に変えられるようにすることにより、方位推定精度が最良となるウエイトを設定することが可能となる。一方、広がり角推定では微係数拘束のウエイトを重くすると精度が良くなる傾向がある。このため、方位と広がり角の推定精度がどちらも望ましくなるようにウエイトを最適に設定することにより、方位の推定精度を向上させながら広がり角の精度劣化を抑えることが可能になる。 Here, in the integral type Capon method with a differential coefficient constraint, the direction estimation accuracy may be deteriorated as compared with the integral type Capon method that does not use the differential coefficient constraint. This is because the influence of the differential coefficient constraint is too strong, and by making the weight of the differential coefficient constraint arbitrarily changeable, it becomes possible to set the weight with the best azimuth estimation accuracy. On the other hand, in the divergence angle estimation, the accuracy tends to be improved when the weight of the derivative constraint is increased. For this reason, by setting the weight optimally so that both the estimation accuracy of the azimuth and the divergence angle is desirable, it becomes possible to suppress the deterioration of the accuracy of the divergence angle while improving the estimation accuracy of the azimuth.
また、到来波を構成する素波の相関が非常に高かったり、観測時間や回数が少なかったりすると自己相関行列が正則にならない。しかし、この自己相関行列の対角成分に擬似雑音を加えることにより、自己相関行列を正則にでき、そのような状況でも、自己相関行列に擬似雑音を加えることにより逆行列演算を行うことが可能になる。 Also, the autocorrelation matrix does not become regular if the correlation of the elementary waves constituting the incoming wave is very high, or if the observation time and number of times are short. However, by adding pseudo-noise to the diagonal component of this auto-correlation matrix, the auto-correlation matrix can be made regular, and even in such situations, inverse matrix operations can be performed by adding pseudo-noise to the auto-correlation matrix. become.
以下、本発明の実施形態について、図面に基づいて説明する。 Hereinafter, embodiments of the present invention will be described with reference to the drawings.
図１は、実施形態に係る到来波推定を行う受信装置の構成を示すブロック図である。Ｋ本の受信アンテナ素子１０−１〜１０−Ｋには、受信部１２−１〜１２−Ｋがそれぞれ接続されている。従って、到来波はＫ本の受信アンテナ素子１０−１〜１０−Ｋによってそれぞれ受信され、受信部１２−１〜１２−Ｋから受信信号がそれぞれ出力される。受信部１２−１〜１２−Ｋには、Ａ／Ｄ変換器１４−１〜１４−Ｋがそれぞれ接続されており、受信部１２−１〜１２−Ｋからのアナログの受信信号はＡ／Ｄ変換器１４−１〜１４−Ｋによってデジタル受信信号ｘ1〜ｘKに変換される。Ａ／Ｄ変換器１４−１〜１４−Ｋからのデジタル受信信号ｘ1〜ｘKからなる受信信号ベクトル（ｘ1，ｘ2，ｘ3、・・・，ｘK）は、信号処理装置１６に入力される。信号処理装置１６は、入力される受信信号ベクトル（ｘ1，ｘ2，ｘ3、・・・，ｘK）について、演算処理を行い、到来波の到来方向および広がり角を算出する。 FIG. 1 is a block diagram illustrating a configuration of a receiving apparatus that performs arrival wave estimation according to the embodiment. Receiving units 12-1 to 12-K are connected to the K receiving antenna elements 10-1 to 10-K, respectively. Accordingly, the incoming waves are received by the K receiving antenna elements 10-1 to 10-K, respectively, and the reception signals are output from the receiving units 12-1 to 12-K, respectively. A / D converters 14-1 to 14-K are connected to the receiving units 12-1 to 12-K, respectively, and analog received signals from the receiving units 12-1 to 12-K are A / D signals. The signals are converted into digital received signals x 1 to x K by the converters 14-1 to 14 -K. Comprises a digital reception signal x 1 ~x K from the A / D converters 14-1 to 14-K received signal vector (x 1, x 2, x 3, ···, x K) , the signal processing device 16 Is input. The signal processing device 16 performs arithmetic processing on the input received signal vectors (x 1 , x 2 , x 3 ,..., X K ), and calculates the arrival direction and spread angle of the incoming wave.
「到来波の到来方向と広がり角の推定」
ここで、信号処理装置１６における到来波の到来方向と広がり角の推定について、以下に説明する。
"Estimation of arrival direction and divergence angle"
Here, estimation of the arrival direction and the spread angle of the incoming wave in the signal processing device 16 will be described below.
本実施形態においては、素波の振幅と位相の角度分布を考慮した積分型モードベクトルを適用したＣａｐｏｎ法により、到来波の到来方向と広がり角の推定を行う。 In this embodiment, the arrival direction and the spread angle of an incoming wave are estimated by the Capon method to which an integral mode vector that takes into account the angular distribution of the amplitude and phase of the elementary wave is applied.
まず、図２に示すように、受信アンテナが配置された環境に角度広がりのある到来波が到来したと仮定する。 First, as shown in FIG. 2, it is assumed that an incoming wave having an angular spread has arrived in the environment where the receiving antenna is arranged.
ここで、到来波の中心方位はθ、広がり角はΔθとする。また、到来波はＭ個の素波からなり、各素波の振幅はＡｍ、位相はφｍとする。また、素波の到来波の中心方位θを基準とした角度をθｍとする。また、図２においては、受信アンテナ素子１０−１が受信している状態を示している。受信アンテナ素子１０間の間隔はｄであり、各受信アンテナ素子１０によって受信される到来波はこの間隔ｄおよび到来波方位に応じて位相が変化する。 Here, the center direction of the incoming wave is θ, and the spread angle is Δθ. The incoming wave is composed of M elementary waves, and the amplitude of each elementary wave is Am and the phase is φm. In addition, an angle based on the center direction θ of the incoming wave of the elementary wave is defined as θm. FIG. 2 shows a state in which the receiving antenna element 10-1 is receiving. The interval between the receiving antenna elements 10 is d, and the phase of the incoming wave received by each receiving antenna element 10 changes according to the interval d and the incoming wave direction.
「到来波が１波しかないとした場合の受信信号」
図２のような到来波を図１に示したような受信装置によって受信した場合の、各受信アンテナ素子１０から得られるチャネルごとの受信信号ｘ1〜ｘKは次式（数１）のように表される。なお、下式においては、ベクトルを太字で表す（以下同じ）が、文字コードで表す明細書中の文章には太字が使用できないため、通常フォントを使用する。また、ｎはノイズベクトルである。
"Received signal when there is only one incoming wave"
When the incoming wave as shown in FIG. 2 is received by the receiving apparatus as shown in FIG. 1, the received signals x 1 to x K for each channel obtained from each receiving antenna element 10 are expressed by the following equation (Equation 1). It is expressed in In the following expression, the vector is represented in bold (the same applies hereinafter), but since the bold text cannot be used in the text in the specification represented by the character code, a normal font is used. N is a noise vector.
「波源の広がりを考慮しない従来のモードベクトル」
また、到来波の広がりを考慮していない場合、モードベクトルａは到来方位θのみを用いて受信アンテナ素子１０−１を位相基準として次式（数２）のように表される。
"Conventional mode vector without considering the spread of wave source"
When the spread of the incoming wave is not taken into consideration, the mode vector a is expressed by the following equation (Equation 2) using only the incoming direction θ and the receiving antenna element 10-1 as a phase reference.
ここで、ｋは受信アンテナ素子１０の番号であり、各受信アンテナ素子１０における受信波の位相は、１番目の受信アンテナ素子１０−１に対し、（２π／λ）ｄ（ｋ−１）ｓｉｎθだけずれる。また、Ｔは転置、ｄは受信アンテナ素子間隔、λは到来波の波長を示す。 Here, k is the number of the receiving antenna element 10, and the phase of the received wave at each receiving antenna element 10 is (2π / λ) d (k-1) sinθ with respect to the first receiving antenna element 10-1. Just shift. T represents transposition, d represents the distance between the receiving antenna elements, and λ represents the wavelength of the incoming wave.
「角度広がりと素波の振幅変化を考慮した積分型モードベクトル」
上述した非特許文献２における到来波を構成する素波の振幅を与えた積分型モードベクトルは次式（数３）のように表される。なお、波源は、波源分布内で連続的に無数に存在すると仮定している。
"Integral mode vector taking into account angular spread and changes in the amplitude of elementary waves"
The integral mode vector giving the amplitude of the elementary wave constituting the incoming wave in Non-Patent Document 2 described above is expressed by the following equation (Equation 3). It is assumed that the wave source exists innumerably continuously in the wave source distribution.
上記式において、１段目は支配的な素波がＭ個に限られている場合であり、２，３段目は素波が連続的に存在する場合を仮定している。 In the above equation, the first stage is a case where the number of dominant waves is limited to M, and the second and third stages are assumed to have a continuous existence of elementary waves.
「角度広がりと素波の振幅と位相変化を考慮した積分型モードベクトル」
振幅や位相の与え方の一例として、広がりのある到来波の発生状況から推測して与えることが考えられる。そこで、下式で示される新たなモードベクトルを考える。
"Integral mode vector taking into account angular spread and amplitude and phase change of the wave"
As an example of how to give amplitude and phase, it is conceivable to give it by guessing from the state of occurrence of a wide arrival wave. Therefore, a new mode vector represented by the following equation is considered.
なお、数４において、上記数３と同様に１段目は支配的な素波がＭ個に限られている場合であり、２、３段目は素波が連続的に存在する場合を仮定している。 In Equation 4, as in Equation 3 above, the first stage assumes that the number of dominant waves is limited to M, and the second and third stages assume that there are continuous waves. is doing.
「Ｃａｐｏｎ法の角度スペクトラム」
そして、本実施形態では、上述の角度とその位相変化考慮した積分型モードベクトルを従来から存在するＣａｐｏｎ法に適用する。この場合、本モードベクトルは、従来の到来波の広がりを考慮していないモードベクトルや広がりと素波の振幅を考慮した積分型モードベクトルに単純に置き換えて利用できる。
"Angle spectrum of Capon method"
In the present embodiment, the integral mode vector considering the angle and the phase change is applied to the existing Capon method. In this case, this mode vector can be used simply by replacing it with a conventional mode vector that does not take into account the spread of the incoming wave, or an integrated mode vector that takes into account the spread and the amplitude of the elementary wave.
このようにして、上述した角度とその位相変化考慮した積分型モードベクトルをＣａｐｏｎ法に適用した場合における、受信信号から到来方位と広がり角を推定する角度スペクトラムの導出式を次式（数５）に示す。 In this way, when the integral mode vector in consideration of the angle and its phase change is applied to the Capon method, the derivation formula of the angle spectrum for estimating the arrival direction and the spread angle from the received signal is expressed by the following equation (Equation 5). Shown in
この式に示すように、自己相関行列Ｒxxとモードベクトルａ（θ）から、角度スペクトラムを計算することができる。そして、θ，Δθを変化させたときのピークの位置から到来方位θおよび広がり角Δθを推定することができる。なお、ピーク高さが電力推定値となる。この計算は上述の通り、従来のＣａｐｏｎ法と同じに到来方向および広がり角について感度が一定という条件の下にそれ以外の信号の干渉を最小化する拘束付き最小化法になっている。 As shown in this equation, the angle spectrum can be calculated from the autocorrelation matrix Rxx and the mode vector a (θ). The arrival direction θ and the spread angle Δθ can be estimated from the peak positions when θ and Δθ are changed. Note that the peak height is the estimated power value. As described above, this calculation is a constrained minimization method that minimizes interference of other signals under the condition that the sensitivity is constant with respect to the direction of arrival and the spread angle as in the conventional Capon method.
「擬似雑音を加えた相関行列」
観測時間が短くて受信信号ベクトルが１つしかないなどの理由で自己相関行列が正則でない場合がある。この場合に、次式（数６）に示すように自己相関行列に擬似雑音を加えることにより逆行列演算ができるようになる。
"Correlation matrix with pseudo-noise"
The autocorrelation matrix may not be regular because the observation time is short and there is only one received signal vector. In this case, the inverse matrix operation can be performed by adding pseudo noise to the autocorrelation matrix as shown in the following equation (Equation 6).
「推定結果の例」
上述のようにして得られた、位相を考慮した積分型モードベクトルを適用したＣａｐｏｎ法による、広がりのある到来波の到来方向および広がり角推定結果の一例について説明する。
"Example of estimation results"
An example of the arrival direction and spread angle estimation result of the spread arrival wave by the Capon method using the integral mode vector in consideration of the phase obtained as described above will be described.
すなわち、到来波を構成する素波の位相変化を到来波の広がりの範囲において−４５°〜４５°で変化させた場合の推定結果を示す。 That is, an estimation result in the case where the phase change of the elementary wave constituting the incoming wave is changed from −45 ° to 45 ° in the range of the arrival wave spread is shown.
まず、設定値として、次のようなものを採用した。 First, the following values were adopted as set values.
到来波数：１、到来波の到来方向θ：０°、到来波の広がり角Δθ：３．６°、素波数Ｍ：３〜１５、到来波の広がり角に対する振幅変化：ガウス分布、到来波の広がり角に対する位相変化：−４５°〜４５°、受信アンテナ素子配置：直線状アレーアンテナ、受信アンテナ素子数Ｋ：９、受信アンテナ素子間隔：１波長である。 Number of incoming waves: 1, arrival direction of incoming wave: 0 °, spread angle of incoming wave Δθ: 3.6 °, number of elementary waves M: 3-15, amplitude change with respect to spread angle of incoming wave: Gaussian distribution, arrival wave Phase change with respect to divergence angle: −45 ° to 45 °, receiving antenna element arrangement: linear array antenna, number of receiving antenna elements K: 9, receiving antenna element interval: 1 wavelength.
従って、図３に示すように、到来波の広がり角に対する位相変化は、図２に示すθｍ＝１．８°では素波の位相ｐ（θ）は４５°、θｍ＝−１．８°では素波の位相ｐ（θ）は−４５°であり、その間について直線的関係となっている。 Therefore, as shown in FIG. 3, the phase change with respect to the divergence angle of the incoming wave is as follows. When θm = 1.8 ° shown in FIG. 2, the phase p (θ) of the elementary wave is 45 °, and when θm = −1.8 °. The phase p (θ) of the elementary wave is −45 °, and there is a linear relationship therebetween.
そして、モードベクトルについて、次のように位相変化を与えた場合における、到来方向推定結果および広がり角推定結果（素子数別）を図４，５に示す。ここで、＃１：位相変化なし（従来の積分型モードベクトル）、＃２：−１８°（＠−Δθ／２）〜１８°（＠Δθ／２）、＃３：−４５°（＠−Δθ／２）〜４５°（＠Δθ／２）、＃４：−９０°（＠−Δθ／２）〜９０°（＠Δθ／２）、＃５：−１８０°（＠−Δθ／２）〜１８０°（＠Δθ／２）である。 4 and 5 show arrival direction estimation results and divergence angle estimation results (by the number of elements) when the phase change is applied to the mode vector as follows. Here, # 1: no phase change (conventional integral mode vector), # 2: −18 ° (@ −Δθ / 2) to 18 ° (@ Δθ / 2), # 3: −45 ° (@ − Δθ / 2) to 45 ° (@ Δθ / 2), # 4: −90 ° (@ −Δθ / 2) to 90 ° (@ Δθ / 2), # 5: −180 ° (@ −Δθ / 2) ~ 180 ° (@ Δθ / 2).
このように、到来波数を推定する必要がないため、素波数にかかわらず到来方向、広がり角のどちらも安定して推定できることがわかる。また、位相を考慮した積分型モードベクトルに与えた位相が到来波の位相変化と同じである場合の推定結果が最も精度良く推定できていることが分かる。それに対して位相を考慮しない従来の積分型モードベクトルを用いた場合は特に広がり角の推定で誤差が大きいことが分かる。さらに、本実施例では、到来波が１波の場合を仮定したが、従来の到来方向推定と同様に、到来波が複数となった場合でも、分離して推定することが可能である。 Thus, since it is not necessary to estimate the number of incoming waves, it can be seen that both the direction of arrival and the spread angle can be stably estimated regardless of the number of elementary waves. It can also be seen that the estimation result when the phase given to the integral mode vector considering the phase is the same as the phase change of the incoming wave can be estimated with the highest accuracy. On the other hand, when a conventional integral mode vector that does not consider the phase is used, it can be seen that the error is particularly large in the estimation of the spread angle. Furthermore, in the present embodiment, it is assumed that the number of incoming waves is one. However, similarly to the conventional arrival direction estimation, even when there are a plurality of incoming waves, it is possible to estimate separately.
なお上記の結果において「位相変化なしの場合」は、位相を考慮しない場合における積分型モードベクトルを適用したＣａｐｏｎ法と同じである。 In the above result, “the case where there is no phase change” is the same as the Capon method to which the integral mode vector is applied when the phase is not considered.
なお、上述した位相を考慮したモードベクトルは、Ｃａｐｏｎ法だけでなくＤＢＦ法、ＬＰ法、ＭＵＳＩＣ法やＥＳＰＲＩＴ法などの良く知られる各種の到来方向推定手段にも同様に適用して、到来波の到来方向または広がり角を推定することが可能である。 Note that the above-described mode vector considering the phase is similarly applied to various well-known arrival direction estimation means such as the DBF method, the LP method, the MUSIC method, and the ESPRIT method as well as the Capon method. It is possible to estimate the direction of arrival or the spread angle.
さらに、上記自己相関行列に擬似雑音を加える手法は、ＭＵＳＩＣ法やＥＳＰＲＩＴ法のように自己相関行列の固有値・固有ベクトル展開が必要となる場合にも同様に適用できる。 Further, the method of adding pseudo noise to the autocorrelation matrix can be similarly applied to the case where eigenvalue / eigenvector expansion of the autocorrelation matrix is required as in the MUSIC method or ESPRIT method.
「積分型モードベクトルを適用した微係数拘束条件を加えたＣａｐｏｎ法（微係数拘束付積分型Ｃａｐｏｎ法）による到来波の到来方向と広がり角の推定」
この例では、微係数拘束条件を加えて、素波同士の位相変化の影響などを抑制する。上述の場合と同様に、到来波の広がりを考慮し、到来波を構成する素波の振幅を与えた積分型モードベクトルは上述した数３のように表される。１段目は支配的な素波がＭ個に限られている場合であり、２、３段目は素波が連続的に存在する場合を仮定している。
“Estimation of arrival direction and divergence angle of incoming wave by Capon method with integral coefficient vector applied with integral mode vector (integral Capon method with differential coefficient constraint)”
In this example, a derivative constraint condition is added to suppress the influence of the phase change between the elementary waves. Similarly to the above-described case, the integral mode vector in which the amplitude of the elementary wave constituting the incoming wave is given in consideration of the spread of the incoming wave is expressed as the above-described Expression 3. The first stage is a case where the number of dominant elementary waves is limited to M, and the second and third stages assume a case where there are continuous elementary waves.
そして、微係数拘束条件を加えて積分型モードベクトルをＣａｐｏｎ法に適用した場合における、受信信号から到来方向と広がり角を推定する角度スペクトラムの導出式を次式（数７）に示す。 Then, an equation for deriving an angle spectrum for estimating the arrival direction and the spread angle from the received signal in the case where the integral mode vector is applied to the Capon method by adding the derivative constraint condition is shown in the following equation (Expression 7).
このような微係数拘束条件を加えた角度スペクトラムの導出式を利用して、上述と同様の演算によって、到来波の到来方向および広がり角を推定することができる。 Using the angle spectrum derivation formula to which such a derivative constraint condition is added, the arrival direction and the spread angle of the incoming wave can be estimated by the same calculation as described above.
また、上述の場合と同様に、観測時間が短くて受信信号ベクトルが１つしかない場合には、自己相関行列に擬似雑音を加えることで、演算対象となる行列を正則にできる。 Similarly to the above case, when the observation time is short and there is only one received signal vector, the matrix to be calculated can be made regular by adding pseudo noise to the autocorrelation matrix.
ここで、積分型モードベクトルを適用した微係数拘束条件を加えたＣａｐｏｎ法による、広がりのある到来波の到来方向および広がり角推定結果の一例について、位相を考慮しない積分型モードベクトルを適用したＣａｐｏｎ法の結果と比較して図６，７に示す。 Here, Capon to which an integral mode vector that does not consider the phase is applied to an example of the arrival direction and spread angle estimation result of a wide arrival wave by the Capon method to which a derivative constraint condition to which the integral mode vector is applied is added. Compared with the results of the method, it is shown in FIGS.
ここで、設定値は、次の通りである。到来波数：１、到来波の到来方向θ：０°、到来波の広がり角Δθ：３．６°、素波数Ｍ：３〜１５、到来波の広がり角に対する振幅変化：ガウス分布、到来波の広がり角に対する位相変化：−４５°〜４５°、受信アンテナ配置：直線状アレーアンテナ、受信アンテナ素子数Ｋ：９、受信アンテナ素子間隔：１波長。 Here, the set values are as follows. Number of incoming waves: 1, arrival direction of incoming wave: 0 °, spread angle of incoming wave Δθ: 3.6 °, number of elementary waves M: 3-15, amplitude change with respect to spread angle of incoming wave: Gaussian distribution, arrival wave Phase change with respect to spread angle: −45 ° to 45 °, receiving antenna arrangement: linear array antenna, number of receiving antenna elements K: 9, receiving antenna element spacing: 1 wavelength.
このように微係数拘束条件を加えたＣａｐｏｎ法を用いた結果は単にＣａｐｏｎ法を用いた結果よりも到来方向推定精度が若干劣化したが、推定誤差０．５°以下を維持しており、広がり角推定精度は向上している。なお、どちらの推定法も位相を考慮しない積分型モードベクトルを用いている。 As described above, although the result of using the Capon method with a derivative constraint condition is slightly deteriorated in the direction of arrival estimation accuracy than the result of using the Capon method, the estimation error is maintained at 0.5 ° or less. The angle estimation accuracy is improved. Both estimation methods use an integral mode vector that does not consider the phase.
これより、微係数という拘束条件を設けたことにより、到来波を構成する素波の位相変化とモードベクトルの位相変化の違いによる推定結果への悪影響を吸収できていることがわかる。この例では、位相を考慮しない数３をモードベクトルに用いたが、当然数４でも同様の効果が得られる。 From this, it can be seen that by providing the constraint condition of the derivative, the adverse effect on the estimation result due to the difference between the phase change of the elementary wave constituting the incoming wave and the phase change of the mode vector can be absorbed. In this example, Equation 3 that does not consider the phase is used for the mode vector, but naturally the same effect can be obtained with Equation 4 as well.
「微係数拘束のウェイトの変更」
上述のように、微係数拘束条件を加えることで、図６、７に示されるように、推定の精度を向上することができる。ここで、別の評価結果を図８（ａ）、（ｂ）に示す。図８（ａ）が広がり角推定結果、図８（ｂ）が到来方向推定結果である。
"Changing weights for derivative constraints"
As described above, by adding the derivative constraint condition, the accuracy of estimation can be improved as shown in FIGS. Here, another evaluation result is shown in FIGS. FIG. 8A shows the spread angle estimation result, and FIG. 8B shows the arrival direction estimation result.
このグラフの縦軸は、図４〜図７とは違い到来波の広がり角に対する位相変化を乱数で１００回試行による２乗平均平方根誤差（ＲＭＳＥ）で表している。この評価は、到来波の広がり角に比例して−４５°〜４５°で線形に変化させて与えていた素波の位相を、任意の乱数でランダムに与えたものである。これらの結果から「微係数拘束付積分型Ｃａｐｏｎ法」の推定精度を「積分型Ｃａｐｏｎ法」と比較すると、微係数拘束付積分型Ｃａｐｏｎ法では、到来波を構成する素波数によらず、広がり角推定では推定精度は良くなり、到来方向推定ではほぼ同等の精度が得られていることが分かる。 Unlike FIG. 4 to FIG. 7, the vertical axis of this graph represents the phase change with respect to the divergence angle of the incoming wave as a random mean square root error (RMSE) by 100 trials. In this evaluation, the phase of the element wave that is linearly changed from −45 ° to 45 ° in proportion to the spread angle of the incoming wave is randomly given by an arbitrary random number. From these results, comparing the estimation accuracy of the “integral Capon method with a differential coefficient constraint” with the “integral Capon method”, the integral Capon method with a differential coefficient constraint spreads regardless of the number of elementary waves constituting the incoming wave. It can be seen that the estimation accuracy is improved in the angle estimation, and almost the same accuracy is obtained in the direction of arrival estimation.
なお、この評価の際の設定値は、次の通りである。到来波数：１、到来波の方位θ：０°、到来波の広がり角Δθ：３．６°、素波数Ｍ：３〜１５、到来波の広がり角に対する素波の振幅変化：ガウス分布、到来波の広がり角に対する素波の位相変化：任意（乱数）、受信アンテナ配置：直線状アレーアンテナ、受信アンテナ素子数Ｋ：９、受信アンテナ素子間隔：１波長、試行回数：１００回。 The set values for this evaluation are as follows. Number of incoming waves: 1, direction of incoming wave θ: 0 °, divergence angle of incoming wave Δθ: 3.6 °, number of elementary waves M: 3-15, amplitude change of elementary wave with respect to divergence angle of incoming wave: Gaussian distribution, arrival Phase change of elementary wave with respect to wave spread angle: Arbitrary (random number), receiving antenna arrangement: linear array antenna, number of receiving antenna elements K: 9, receiving antenna element interval: 1 wavelength, number of trials: 100 times.
図８のような結果となる理由について検討した結果ところ、次のことが分かった。上記の２種類の推定法は、どちらも到来方向推定に用いる角度スペクトラムの走査において凸型のカーブを描き、そのピークから推定方位を得ている。しかし、図９に示すように、微係数拘束付積分型Ｃａｐｏｎ法では微係数が０となる極値を拘束条件として利用しているために、到来波の振幅や位相等の状況によっては、ピーク付近において凹型のカーブを描いてしまい、極値周辺のピークから推定方位を得るために推定誤差が大きくなる場合がある。そのため、微係数拘束付積分型Ｃａｐｏｎ法の到来方向推定精度が積分型Ｃａｐｏｎ法よりも劣化する場合があり、ＲＭＳＥは良くならなかった。 As a result of examining the reason for the result as shown in FIG. 8, the following was found. In both of the above-described two estimation methods, a convex curve is drawn in scanning of an angle spectrum used for arrival direction estimation, and an estimated direction is obtained from the peak. However, as shown in FIG. 9, in the integral type Capon method with a differential coefficient constraint, an extreme value with a differential coefficient of 0 is used as a constraint condition. Therefore, depending on the situation such as the amplitude and phase of the incoming wave, the peak In some cases, a concave curve is drawn in the vicinity, and the estimation error becomes large in order to obtain the estimated direction from the peak around the extreme value. For this reason, the arrival direction estimation accuracy of the integral type Capon method with a differential coefficient constraint may be deteriorated compared to the integral type Capon method, and the RMSE is not improved.
そこで、本実施形態においては、広がり角推定で積分型Ｃａｐｏｎ法よりも良い精度が得られるという特徴を維持しながら、この極端に精度が劣化した到来方向推定を行わないことを目指している。 Therefore, in the present embodiment, it is aimed to avoid the arrival direction estimation with extremely deteriorated accuracy while maintaining the feature that the divergence angle estimation can obtain better accuracy than the integral Capon method.
ここで、積分型モードベクトルを利用するとともに角度スペクトラムの走査に微係数拘束を加えてＣａｐｏｎ法に適用した微係数拘束付積分型Ｃａｐｏｎ法における、受信信号から到来方向と広がり角を推定する角度スペクトラムの導出式は、上述した数７のように表される。 Here, in the integral type Capon method with a differential coefficient constraint applied to the Capon method by using an integral mode vector and adding a differential coefficient constraint to the scanning of the angle spectrum, the angle spectrum for estimating the arrival direction and the spread angle from the received signal The derivation formula is expressed as shown in Equation 7 above.
一方、微係数拘束のウエイトを変えられることを特徴とした微係数軟拘束付積分型Ｃａｐｏｎ法における、受信信号から到来方向と広がり角を推定する角度スペクトラムの導出式を次式（数８）に示す。 On the other hand, in the integral-type Capon method with a differential coefficient soft constraint characterized in that the weight of the differential coefficient constraint can be changed, an equation for deriving an angle spectrum for estimating the direction of arrival and the spread angle from the received signal is given by Show.
ここで、αは微係数拘束のウェイトである。そこで、この数８の式（１）におけるウェイトαの値を変化することにより、微係数拘束のウエイトを変化することができる。なお、微係数拘束付積分型Ｃａｐｏｎ法では、Ｄ（θ，Δθ）＝０となる極値を、θやΔθを推定する拘束条件としており、上述の数７における行列Ｃの中のＤ（θ，Δθ）にウェイトをかけても、結果としてαが推定において考慮されないことになる。 Here, α is the weight of the derivative constraint. Therefore, the weight of the derivative constraint can be changed by changing the value of the weight α in Expression (1) of Equation 8. In the integral Capon method with a differential coefficient constraint, an extreme value at which D (θ, Δθ) = 0 is used as a constraint condition for estimating θ and Δθ, and D (θ in the matrix C in Equation 7 above is used. , Δθ) is weighted, as a result, α is not considered in the estimation.
また、数８において、逆行列の部分を展開することにより式（２）を得ることができる。 Further, in Expression 8, Expression (2) can be obtained by expanding the inverse matrix portion.
式（１）では逆行列演算内にθとΔθの成分が存在するため、角度スペクトラムを求める場合にθおよびΔθを変化させる度に逆行列演算を行う必要があり、従来の方法と比較して非常に計算コストが高くなる。 In Equation (1), θ and Δθ components exist in the inverse matrix calculation. Therefore, when obtaining the angle spectrum, it is necessary to perform the inverse matrix calculation every time θ and Δθ are changed. Compared with the conventional method, The calculation cost is very high.
一方、式（２）では自己相関行列の逆行列のみを求めれば良く、逆行列演算内にθとΔθを含まないため、計算コストは従来の微係数拘束付積分型Ｃａｐｏｎ法と変わらず、現実的な計算コストで、演算が可能になる。 On the other hand, in Equation (2), only the inverse matrix of the autocorrelation matrix needs to be obtained, and θ and Δθ are not included in the inverse matrix calculation. Therefore, the calculation cost is the same as that of the conventional integral-capon method with a differential coefficient constraint. Calculation is possible at a reasonable calculation cost.
なお、観測時間が短くて受信信号ベクトルが１つしかないなどの理由により、自己相関行列が正則でなく逆行列が計算できない場合もあるが、上述の数６に示すように、自己相関行列に擬似雑音を加えることにより逆行列演算ができるようになる。 Note that the autocorrelation matrix may not be regular because the observation time is short and there is only one received signal vector, and the inverse matrix cannot be calculated. Inverse matrix operation can be performed by adding pseudo noise.
「推定結果」
本実施形態による、微係数軟拘束付（ウェイト変更可能）積分型Ｃａｐｏｎ法による、角度広がりを有する到来波の到来方向および広がり角推定を計算機シミュレーションで実施した。その一例の条件と結果を、積分型Ｃａｐｏｎ法および微係数拘束付積分型Ｃａｐｏｎ法と比較して図１０（ａ）、（ｂ）に示す。なお、図９（ａ）、（ｂ）において、微係数軟拘束付Ｃａｐｏｎ法の結果は、信号内のノイズレベルや擬似雑音のレベルによって異なり、およそ、それらのレベルに対して１／１００〜１／１０００程度とすることが望ましい。ここでは一例としてα＝５×１０-6，α＝９×１０-6とした結果を示す。
"Estimation results"
The arrival direction and divergence angle estimation of an incoming wave having an angular spread by the integral Capon method with derivative soft constraint (weight changeable) according to the present embodiment was performed by computer simulation. The conditions and results of the example are shown in FIGS. 10A and 10B in comparison with the integral Capon method and the integral Capon method with a differential coefficient constraint. 9 (a) and 9 (b), the result of the Capon method with the derivative soft constraint varies depending on the noise level in the signal and the level of the pseudo noise, and is approximately 1/100 to 1 with respect to those levels. / 1000 or so is desirable. Here, as an example, the results of α = 5 × 10 −6 and α = 9 × 10 −6 are shown.
これらの結果から、本実施形態に係る微係数軟拘束付積分型Ｃａｐｏｎ法は、到来波を構成する素波数によらず、広がり角の推定精度の劣化をある程度抑えて積分型Ｃａｐｏｎ法よりも良いという特徴を維持しながら、到来方向推定精度は積分型Ｃａｐｏｎ法や微係数拘束付積分型Ｃａｐｏｎ法よりも向上できていることが分かる。また数８のウエイトαを変化することにより、到来方向と広がり角の推定精度が変化していることも分かる。 From these results, the integral-type Capon method with a derivative soft constraint according to the present embodiment is better than the integral-type Capon method by suppressing degradation of the spread angle estimation accuracy to some extent, regardless of the number of rays constituting the incoming wave. It can be seen that the direction-of-arrival estimation accuracy can be improved as compared with the integral type Capon method and the integral type Capon method with a differential coefficient constraint while maintaining the above feature. It can also be seen that the estimation accuracy of the arrival direction and the spread angle is changed by changing the weight α in Equation (8).
入力信号に含まれる雑音や擬似雑音のレベルよりもα｜Ｄ｜の大きさが小さいと推定にほとんど影響を与えないため、積分型Ｃａｐｏｎ法と同様の結果となるウエイトαは、雑音レベル、スナップショット数、擬似雑音レベル等に基づいて最適に設定されることが望ましい。なお、｜Ｄ｜は、Ｄのノルムを示す。 If the magnitude of α | D | is smaller than the level of noise or pseudo noise included in the input signal, the estimation α is hardly affected. Therefore, the weight α, which is the same result as that of the integrated Capon method, is the noise level, snap. It is desirable to set optimally based on the number of shots, pseudo noise level, and the like. | D | represents the norm of D.
ここで、微係数軟拘束付積分型Ｃａｐｏｎ法において計算された、到来方向推定の角度スペクトラムの例を図１１に示す。このときの設定値は、次の通りである。到来波数：１、到来波の方位θ：０°、到来波の広がり角Δθ：３．６°、素波数Ｍ：９、到来波の広がり角に対する素波の振幅変化：ガウス分布、到来波の広がり角に対する素波の位相変化：任意（乱数）、受信アンテナ配置：直線状アレーアンテナ、受信アンテナ素子数Ｋ：９、受信アンテナ素子間隔：１波長。 Here, FIG. 11 shows an example of the angle spectrum for estimating the direction of arrival, calculated by the integral Capon method with a derivative soft constraint. The set values at this time are as follows. Number of incoming waves: 1, azimuth of incoming wave: 0 °, divergence angle of incoming wave Δθ: 3.6 °, elementary wave number M: 9, amplitude change of elementary wave with respect to divergence angle of incoming wave: Gaussian distribution, incoming wave Phase change of elementary wave with respect to divergence angle: Arbitrary (random number), receiving antenna arrangement: linear array antenna, number of receiving antenna elements K: 9, receiving antenna element interval: 1 wavelength.
微係数拘束付積分型Ｃａｐｏｎ法では微係数拘束が強いため、すでに図９に示したように方位推定で用いる角度スペクトラムがピークを描かず凹型の極値を示してしまう場合がある。この場合到来方向は、極値の周辺のピークから導いてしまうため、凹型となると推定精度が劣化する。 Since the integral type Capon method with a derivative coefficient is strong, the coefficient coefficient constraint is strong, and as shown in FIG. 9, the angle spectrum used in the azimuth estimation may not show a peak but may indicate a concave extreme value. In this case, since the arrival direction is derived from the peak around the extreme value, the estimation accuracy deteriorates if the arrival direction is concave.
一方、本実施形態に係る微係数軟拘束付積分型Ｃａｐｏｎ法では、微係数のウエイトを調整する。これによって、図１１に示したように最適な角度スペクトラムのピークが得られており、より到来方向の推定精度を向上させることが可能になっていることが分かる。 On the other hand, in the integral type Capon method with a derivative soft constraint according to the present embodiment, the weight of the derivative is adjusted. As a result, the optimum peak of the angular spectrum is obtained as shown in FIG. 11, and it can be seen that the estimation accuracy of the arrival direction can be further improved.
１０ 受信アンテナ素子、１２ 受信部、１４ Ａ／Ｄ変換器、１６ 信号処理装置。 10 receiving antenna elements, 12 receiving units, 14 A / D converters, 16 signal processing devices.
Claims (6)
Ｃａｐｏｎ法のモードベクトルを、到来波の角度範囲の広がりを考慮し、当該角度範囲に存在する複数の素波について加算したモードベクトルとする積分型モードベクトルとし、到来波の到来方向および広がり角を推定することを特徴とする到来波推定方法。 An incoming wave estimation method for receiving an incoming wave with an array antenna and estimating an arrival direction of the incoming wave based on an obtained received signal vector,
The mode vector of the Capon method is an integral mode vector that takes into account the spread of the angle range of the incoming wave and is added to a plurality of elementary waves existing in the angle range, and the arrival direction and the spread angle of the incoming wave are An arrival wave estimation method characterized by estimating.
前記積分型モードベクトルを、到来波を構成する素波の振幅または位相変化を考慮し、当該角度範囲内に存在する素波についてそれぞれの振幅または位相を考慮して加算したモードベクトルとする積分型モードベクトルとしたことを特徴とする到来波推定方法。 The arrival wave estimation method according to claim 1,
Integral type, wherein the integral mode vector is a mode vector obtained by taking into account the amplitude or phase change of the elementary wave constituting the incoming wave, and adding each of the elementary waves existing within the angle range in consideration of the amplitude or phase. An arrival wave estimation method characterized by being a mode vector.
前記Ｃａｐｏｎ法における推定について微係数拘束条件を加えて行うことを特徴とする到来波推定方法。 In the arrival wave estimation method according to claim 1 or 2,
An arrival wave estimation method characterized in that estimation in the Capon method is performed by adding a derivative constraint condition.
Ｃａｐｏｎ法のモードベクトルを、到来波の角度範囲の広がりを考慮した積分型モードベクトルとし、到来波の到来方向および広がり角を推定するとともに、
前記Ｃａｐｏｎ法における推定について微係数拘束条件を加えて行い、
前記微係数拘束のウエイトが任意に変えられることを特徴とする到来波推定方法。 An incoming wave estimation method for receiving an incoming wave with an array antenna and estimating an arrival direction of the incoming wave based on an obtained received signal vector,
The mode vector of the Capon method is an integrated mode vector that takes into account the spread of the angle range of the incoming wave, and the arrival direction and the spread angle of the incoming wave are estimated,
The estimation in the Capon method is performed by adding a derivative constraint condition,
An arrival wave estimation method characterized in that the derivative-constraint weight is arbitrarily changed.
前記受信信号ベクトルから自己相関行列を作成するとともに、この自己相関行列に対して、擬似雑音を加えて逆行列演算を行うことを特徴とする到来波推定方法。 In the arrival wave estimation method according to any one of claims 1 to 4,
An incoming wave estimation method, wherein an autocorrelation matrix is created from the received signal vector, and an inverse matrix operation is performed on the autocorrelation matrix by adding pseudo noise.
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