JP2004226122A - Method and device of optimizing sensor placement and incoming direction measuring system - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a sensor placement optimizing method for placing a plurality of sensor element for suppressing minimum, the generation of false image in azimuth measurement. <P>SOLUTION: A sensor position pattern indicating the positions of a plurality of sensors constituting a sensor array and a wavelength of the maximum frequency of a desired frequency band are input, and whether the false image generates is searched for all the sensor element positions of input sensor position pattern based on the incoming azimuth of an introduced wave and the phase difference of a steering vector so that the generation degree of the false image to the maximum frequency in the specific incoming azimuth and angle of elevation of the introduced wave is calculated. By integrating the calculated generation degree for all azimuthal angles and all angle of elevation, the generation degree of false image in the sensor position pattern is calculated. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

ここで、ｒ_ｋは位置ベクトルの大きさ、θ_ｋはＸＹ平面上に投影された位置ベクトルＲ_ｋがＸ軸となす角（方位角）、φ_ｋはＸＹ平面と位置ベクトルＲ_ｋとがなす角（仰角）である。
【００１７】
今、入射波の到来方位角をα、入射波の到来仰角をεとすると、入射波の単位方位ベクトルｅ（α，ε）は、下記式（２）で表すことができる。
【００１８】
【数８】

入射波の波長がλ、到来方位がｅ（α，ε）であるとき、ｋ番目のアンテナ素子の原点との位相差Ψ_ｋは、下記式（３）で表される。
【００１９】
【数９】

同様に、ステアリングベクトルの単位方位ベクトルをｅ（α_０，ε_０）とすると、ステアリングベクトルによるｋ番目のアンテナ素子の原点との位相差Ψ_０ｋは、下記式（４）で表される。
【００２０】
【数１０】

よって、入射波の到来方位とステアリングベクトルとの位相差Φ_ｋは、下記式（５）で表すことができる。
【００２１】
【数１１】

この式（５）で表される位相差Φ_ｋが２πの整数倍になると偽像が発生する。即ち、入射波の単位方位ベクトルがｅ（α，ε）である場合、ｋ番目のアンテナ素子の原点との位相差Ψ_ｋは、上記式（３）に示した通りであり、アレイマニホールドａ_ｋ（α，ε）は、下記式（６）で表される。
【００２２】
【数１２】

同様に、ステアリングベクトルの単位方位ベクトルをｅ（α_０，ε_０）とすると、その原点との位相差Ψ_０ｋは、上記式（４）に示した通りであり、アレイマニホールドは、下記式（７）で表すことができる。
【００２３】
【数１３】

今、仮に入射波の到来方位とステアリングベクトルの位相差が２πの整数倍（２ｍπ）であるとすると、ステアリングベクトルの原点との差は、下記式（８）で表される。
【００２４】
【数１４】

この場合のアレイマニホールドは、下記式（９）で表される。
【００２５】
【数１５】

即ち、位相差が２πの整数倍になると、入射波の到来方位とステアリングベクトルの方位とが異なっていたとしてもアレイマニホールドは同じ値になるため、アンテナの出力は同じものになり、偽像が発生する。
【００２６】
ここで、Ｆ（α，α_０，ε，ε_０）を下記式（１０）のように定義する。
【００２７】
【数１６】

このＦの値が大きいほど、入射波の到来方位角α、到来仰角εのとき、方位角α_０、仰角ε_０に偽像が発生すること、つまり偽像の発生程度を示している。即ち、上記式（１０）中のΦ_ｋは、各アンテナにおける入射波の到来方位とステアリングベクトルの位相差を表しており、Φ_ｋが２πの整数倍であると「ｅｘｐ（ｊΦ_ｋ）」は「１」になる。そのため、ｎ個のアンテナの中で、入射波の到来方位とステアリングベクトルの位相差Φ_ｋが２πの整数倍であるものが多いほど、換言すれば、偽像の発生するアンテナが多いほど上記式（１０）の右辺分母の第２項は「１」に近づき、Ｆは大きい値になる。即ち、Ｆが大きい値になるほど、偽像の発生するアンテナが多くなり、偽像の発生する程度が大きくなる。
【００２８】
ここで、上記式（５）を、下記式（１１）で置き換えると、下記式（１２）が得られる。なお、Ａはアレイマニホールドを表す。
【００２９】
【数１７】

【数１８】

ここで、アンテナ素子の配置を同一の水平面上にあるとすると「φ_ｋ＝０」とおくことができ、上記式（１２）は、下記式（１３）のように簡単化することができる。
【００３０】
【数１９】

例えば、この式（１３）において、周波数が１／２倍になった場合、波長λは２倍となるので、Ｒ_ｋ、Ａ、θ_ｋ及びηが一定であれば、Φ_ｋの値は１／２になる。また、式（１３）において、Ａが１／２になった場合は、Ｒ_ｋ、λ、θ_ｋ及びηが一定であれば、Φ_ｋの値は１／２になる。従って、周波数が１／２倍になることとＡが１／２倍になることとは等価である。即ち、周波数を下げることと、Ａの値を小さくすることは等価である。
【００３１】
周波数を最大としてΦ_ｋを計算すれば、Ａは０≦Ａ≦２の範囲をとるため、Φ_ｋの値は最大周波数以下を計算したことと等価の値が得られる。即ち、波長λを所望周波数帯の最大周波数の波長とすることで、Ｆは所望周波数帯の最大周波数までの偽像の発生程度を表している。
【００３２】
図２は、Ｆ（α，α_０，ε，ε_０）の変数α，α_０，ε，ε_０を、式（１１）を満足するように変数Ａ、ηで置き換え、全てのアンテナ素子が同一水平面上に存在するという条件のもとで、Ｆ（α，α_０，ε，ε_０）の値を等高線グラフで表した偽像パターンを示す。この図２において、内側の円内は最大周波数が３ＭＨｚのときの偽像パターンを表し、外側の円内が最大周波数６ＭＨｚのときの偽像パターンを表す。また、円の中心がＡ＝０、外側の円周がＡ＝２であり、角度はηを表す。
【００３３】
この偽像パターンは、円の中心以外に出現するピークが、そのアンテナ素子の配置、つまりセンサ位置パターンにおける偽像の出やすさを表しており、ピーク値が高いほど（等高線グラフが高いほど）大きい偽像が発生し、その高い値を有するピークの数が多いほど偽像が発生しやすいことを表している。
【００３４】
この図２に示した偽像パターンを利用すれば、複数のセンサ位置パターンの間で偽像の出やすさを比較することは可能である。しかしながら、上述したように、複数のセンサ位置パターンの偽像パターンを人が見比べる必要があるため、見比べる人の主観に依存してアンテナ素子の配置の良否が判断され、客観性に欠ける。また、全てのアンテナ素子が同一水平面上に存在する場合にしか適用できないため、アンテナ素子の配置の自由度が制限される。
【００３５】
そこで、本発明の第１の実施の形態に係るセンサ配置最適化方法では、アンビギュイティ指数Ｊを、Ｆ（α，α_０，ε，ε_０）を変数α，α_０，ε，ε_０の取りうる範囲で積分したものであると定義し、このアンビギュイティ指数Ｊを計算することにより、１つのセンサ配置パターンにおける全方位、全仰角における偽像の発生程度を数値で表すようにしたものである。
【００３６】
全てのα、α_０、ε、ε_０について、つまり、０≦α，α_０≦２π、０≦ε，ε_０≦π／２の範囲の全てについてＦを計算し加算したものを、アンビギュイティ指数Ｊと定義すると、このアンビギュイティ指数Ｊは下記式（１４）で表すことができる。なお、下記式（１４）における位相差Φ_ｋは、式（５）に示したものであり、式（１３）に示す位相差Φ_ｋ（φ_ｋ＝０とおいたもの）ではない。
【００３７】
【数２０】

このアンビギュイティ指数Ｊは、１つのセンサ配置パターンを有するセンサアレイの偽像の発生程度を表わし、このアンビギュイティ指数Ｊの値が大きいほどそのセンサアレイの偽像の発生程度は大きくなる。
【００３８】
次に、偽像の発生程度を最も少なくすることができる最適なセンサ配置パターンを求める手順を、図３に示すフローチャートを参照しながら説明する。この手順は、図４に示すコンピュータを用いて実行される。このコンピュータ１は、入力部２、計算部３、メモリ４、センサ配置決定部５を有しており、本発明のセンサ配置最適化装置に対応する。
【００３９】
まず、アレイアンテナで取り扱う周波数帯の最大周波数の波長λ_ｍが入力部２から入力される（ステップＳ１０）。次に、センサ配置パターンが入力部２から入力される（ステップＳ１１）。センサ配置パターンとしては、具体的には、センサ配置パターンを構成するアンテナ素子のアンテナ位置Ｒ_ｋ（１，２，…，ｎ）が入力される。
【００４０】
次に、アンビギュイティ指数Ｊが計算部３により算出される（ステップＳ１２）。このアンビギュイティ指数Ｊの算出は、ステップＳ１０及びＳ１１でそれぞれ入力された波長λ_ｍ及びアンテナ位置Ｒ_ｋ（１，２，…，ｎ）をパラメータとし、上記式（１４）に従った計算を実行することにより行われる。ここで算出されたアンビギュイティ指数Ｊは、メモリ４に格納される。
【００４１】
次に、予め用意された全てのセンサ位置パターンのアンビギュイティ指数Ｊの算出が完了したかどうか図示しない判定部により判定される（ステップＳ１３）。そして、完了していないことが判断されると、ステップＳ１１に戻り、以下同様の処理が繰り返される。ステップＳ１１〜Ｓ１３の繰り返し実行により、メモリ４に複数のセンサ位置パターンにそれぞれ対応する複数のアンビギュイティ指数Ｊが格納される。
【００４２】
ステップＳ１３で全てのセンサ位置パターンのアンビギュイティ指数Ｊの算出が完了したことが判断されると、次に、メモリ４に格納された複数のアンビギュイティ指数Ｊの中から最小値を有するものがセンサ配置決定部５により検索される（ステップＳ１４）。そして、検索されたアンビギュイティ指数Ｊに対応するセンサ位置パターンが最適なセンサ位置パターン、即ち、偽像の発生程度が最も少ないアンテナ素子の配置パターンとしてセンサ配置決定部５により決定される（ステップＳ１５）。決定されたアンテナ素子の配置パターンを有するアレイアンテナが実際の到来方向測定装置に適用される。
【００４３】
以上説明したように、本発明の第１の実施の形態に係るセンサ配置最適化方法及びその装置によれば、アンビギュイティ指数Ｊを表す式（１４）にセンサアレイのアンテナ位置Ｒ_ｋ（１，２，…，ｎ）、所望周波数帯の最大周波数の波長λ_ｍを代入することで、所望周波数帯の全方位、全仰角の偽像の発生度合いを一度に定量的に判断することが可能になる。
【００４４】
従って、図２に示す偽像パターンを利用する場合のような、複数のセンサ位置パターンの偽像パターンを人が見比べることに起因する客観性の欠如を排除できる。また、全てのアンテナ素子が同一水平面上に存在する場合に限らず適用できるので、アンテナ素子の配置の自由度が増加する。
【００４５】
（第２の実施の形態）
本発明の第２の実施の形態に係る到来方位測定装置では、上述した第１の実施の形態に係るセンサ配置最適化装置であるコンピュータ１を備え、第１の実施の形態に係るセンサ配置最適化装置により決定されたアンテナ配置を有するアレイアンテナが使用される。
【００４６】
なお、以下では、説明を簡単にするために、アンテナ素子の数を「４」とし、入射信号の数ｎを「４」として説明するが、アンテナ素子の数及び入射信号の数はこれらに限定されず任意である。
【００４７】
図４は、本発明の第２の実施の形態に係る到来方位測定装置の構成を示すブロック図である。この到来方位測定装置は、コンピュータ１、第１〜第４アンテナ１１〜１４、第１〜第４帯域制限ろ波器２１〜２４、ベクトル生成部２７、相関量算出部２８、サンプリング部３０及び到来方位演算部４７から構成されている。コンピュータ１は、センサ配置最適化装置であり、偽像の発生程度の最小のものを最適なセンサ配置パターンとする。即ち、センサ配置最適化装置により決定されたアンテナ配置を有するアレイアンテナが使用される。
【００４８】
第１〜第４アンテナ１１〜１４としては、バーチカルアンテナ、ダイポールアンテナといった無指向性のアンテナ、及び任意の指向性を持ったアンテナ等が用いられ、種々の方位からの電波を受信する。これら第１〜第４アンテナ１１〜１４を設置する間隔や高さは、上述した第１の実施の形態に係るセンサ配置最適化方法により決定される。第１〜第４アンテナ１１〜１４は、空中からの複数の入射信号（電波）Ｓ１〜Ｓ４を受信し、これらが混合された混合信号を第１〜第４帯域制限ろ波器２１〜２４に送る。
【００４９】
第１〜第４帯域制限ろ波器２１〜２４は、第１〜第４アンテナ１１〜１４からの混合信号に含まれる所定帯域の周波数成分のみを通過させてサンプリング部３０に送る。なお、各第１〜第４帯域制限ろ波器２１〜２４が通過させる周波数帯域は同じである。
【００５０】
帯域制限制御器２５は、通過させる周波数帯域、つまり通過させる周波数成分の範囲を指定するための制御信号を生成する。この帯域制限制御器２５で生成された制御信号は、第１〜第４帯域制限ろ波器２１〜２４に送られる。第１〜第４帯域制限ろ波器２１〜２４は、帯域制限制御器２５からの制御信号に従って、入力された混合信号に含まれる所定帯域の周波数成分のみを通過させる。
【００５１】
この帯域制限制御器２５は、任意の帯域の周波数成分を通過させるような制御信号を生成できるように構成されている。従って、帯域制限制御器２５からの制御信号を適宜変更することにより、第１〜第４帯域制限ろ波器２１〜２４を通過する周波数帯域を任意に変化させることができる。
【００５２】
サンプリング部３０は、第１〜第４中間周波数変換器３１〜３４、局部発振器３５、第１〜第４Ａ／Ｄ変換器４１〜４４及び発振器４５から構成されている。
【００５３】
局部発振器３５は、受信電波を中間周波数に変換するために必要とする発信周波数を有する信号を生成する。この局部発振器３５で生成された信号は、第１〜第４中間周波数変換器３１〜３４に送られる。
【００５４】
第１〜第４中間周波数変換器３１〜３４の各々は、何れも図示を省略するが、高周波増幅器、周波数混合器及び中間周波数増幅器から構成されている。
【００５５】
高周波増幅器は、受信周波数帯の高周波を、次段の周波数混合器の入力電圧として適当な大きさになるように増幅する。周波数混合器は、高周波増幅器で増幅された信号と局部発振器３５の出力信号とを混合し、それらの和又は差の周波数を作ることにより中間周波数の信号に変換する。中間周波数増幅器は、受信電波の周波数を、より低い中間周波数に変換して増幅する。これにより、安定で高利得の増幅を行うことができ、感度を向上させることができる。
【００５６】
上記のように構成される第１〜第４中間周波数変換器３１〜３４から出力される信号は、第１〜第４Ａ／Ｄ変換器４１〜４４にそれぞれ送られる。
【００５７】
発振器４５は、第１〜第４中間周波数変換器３１〜３４からの信号をサンプリングするためのサンプリングクロックを生成する。この発振器４５で生成されたサンプリングクロックは第１〜第４Ａ／Ｄ変換器４１〜４４に送られる。
【００５８】
第１〜第４Ａ／Ｄ変換器４１〜４４は、発振器４５からの信号をサンプリングクロックとして、第１〜第４中間周波数変換器３１〜３４からのアナログ信号をサンプリングすることにより、デジタル信号にそれぞれ変換する。第１〜第４Ａ／Ｄ変換器４１〜４４の各々から出力されるデジタル信号は、到来方位演算部４７に供給される。
【００５９】
ベクトル生成部２７は、第１〜第４帯域制限ろ波器２１〜２４からの信号に基づいて、各アンテナ１１〜１４における複数の入射信号の位相応答を行列で表したステアリングベクトルを生成する。
【００６０】
相関量算出部２８は、ベクトル生成部２７で生成されたステアリングベクトルに基づいてステアリングベクトルの複素共役転置行列を求め、複素共役転置行列とステアリングベクトルとを演算することによりステアリングベクトルの自己内相関量を求める。以下、この相関量算出部２８の動作を説明する。
【００６１】
今、ｎ個（ｎは２以上の整数）のアンテナ素子のアレイに同時にｍ個（ｍは２以上の整数）の信号が入射する場合を仮定する。この状態は、下記式（１５）で表すことができる。
【００６２】
【数２１】

ここで、Ｘ１〜ｎは各アンテナで観測される時系列データ、Ａ＝［ａ（θ１），…ａ（θｍ）］はアンテナの配置と特性とで決まるｎ行×ｍ列の信号混合の行列、Ｓ１〜ｍ（ｔ）はｍ個の入射信号、Ｎ１〜ｎ（ｔ）は各アンテナにおける雑音である。
【００６３】
一般に、スーパーレゾリューションによる方位測定やヌルステアリングにおいては、上記式（１５）における「Ａ」に相当する情報が直接的又は間接的に推定される。
【００６４】
ここで、［Ａ］をステアリングベクトルａとする。このステアリングベクトルａは、ステアリングベクトル生成部２７で生成される。このステアリングベクトルａは、各アンテナ１１〜１４における複数の入射信号の位相応答を行列で表したものであり、［４×３６０］の行列、即ち、下記式（１６）で表される。
【００６５】
【数２２】

なお、このステアリングベクトルａは、例えばシュミレーションにより測定しても良い。このステアリングベクトルａは、アンテナのメインローブの方向を決めるものである。
【００６６】
相関量算出部２８は、ベクトル生成部２７で生成されたステアリングベクトルに基づいてステアリングベクトルの複素共役転置行列を求め、複素共役転置行列とステアリングベクトルとを演算することによりステアリングベクトルの自己内相関量Ｐを求める。
【００６７】
この自己内相関量Ｐは、下記式（１７）で表される。
【００６８】
【数２３】

ここで、上添字Ｈは複素共役転置を表す。そして、自己内相関量Ｐは、下記式（１８）に示すように［３６０×３６０］の行列となる。
【００６９】
【数２４】

この行列の対角成分が自己相関部分であり、その他の成分が相互相関部分となる。そして、自己内相関量から相互相関量が抽出される。この相互相関量からステアリングベクトルａの相関関係が求まる。例えば、相互相関量ｐ４０・２は、ステアリングベクトルａの４０ｄｅｇと２ｄｅｇとの成分の相関値を表す。相関関係が強い場合には、相互相関量ｐ４０・２の値は大きくなり、相関関係が弱い場合には、相互相関量ｐ４０・２の値は小さくなる。
【００７０】
相互相関量ｐ４０・２が大きい値を示した場合には、到来波が４０ｄｅｇから到来した場合、４０ｄｅｇ以外の２ｄｅｇからも到来したという、本来の到来方位以外にも偽像として方位を示すアンビギュティ（曖昧性）が発生する。
【００７１】
到来方位演算部４７は、第１〜第４Ａ／Ｄ変換器４１〜４４からの信号と相関量算出部２８で算出された自己内相関量とに基づいて、ＭＵＳＩＣ等のアルゴリズムを用いて入射信号の到来方位を測定する。この到来方位演算部４７の処理を図６を参照して詳細に説明する。
【００７２】
ＭＵＳＩＣ法は相関行列の固有値と固有ベクトルとを用いた推定法である。図６に示すようにアンテナ間隔ｄのＭ素子等間隔リニアアレーに平面波がＫ波到来していて、各到来波の信号波形と到来角がＦｋ（ｔ），θｋ（ｋ＝１，２…，Ｋ）と表されるとき、各アンテナにおける各到来波の位相応答を表す方向ベクトルａ（θｋ）は、下記式（１９）で与えられる。
【００７３】
【数２５】

ここで、上添字Ｔは転置を表す。よって、入力ベクトルは下記式（２０）〜式（２４）で表される。
【００７４】
【数２６】

上式においてＮ（ｔ）は熱雑音ベクトルであり、その成分は平均が０で分散（電力）がσ^２の独立な複素ガウス過程である。このとき、アンテナ間の相関特性を表す相関行列は下記式（２５）及び式（２６）で与えられる。
【００７５】
【数２７】

ここで、上添字Ｈは複素共役転置を表す。到来波が互いに無関係であれば信号相関行列ＳのランクはＫとなる。また、方向行列ＡもランクはＫである。従って、この場合の相関行列ＲｘｘはランクＫの非負定値エルミート行列となる。この行列の固有値λｉ（ｉ＝１，２…，Ｍ）は実数となり、下記式（２７）の関係を有する。
【００７６】
【数２８】

従って、相関行列の固有値を求め、熱雑音電力σ^２より大きい固有値の数から到来波数Ｋを推定することができる。また、固有値λｉ（ｉ＝１，２…，Ｍ）に対応する固有ベクトルをｅｉ（ｉ＝１，２…，Ｍ）とすると、Ｍ次元のエルミート空間の正規直交基底ベクトルとして扱われる。この空間は信号空間ｓｐａｎ｛ｅ１，…ｅＫ｝と雑音空間ｓｐａｎ｛ｅＫ＋１，…ｅＭ｝との二つの部分空間にわけることができ、信号空間と雑音空間とは互いに直交補空間の関係にある。
【００７７】
ｓｐａｎ｛ｅ１，…ｅＫ｝はベクトルｅｉ（ｉ＝１，２…，Ｍ）で張られる空間とする。また、信号空間は方向ベクトルを用いて、ｓｐａｎ｛ａ（θ１），…，ａ（θｋ）｝と表すことができる。従って、熱雑音電力に等しい固有値に対応する固有ベクトルは全て到来波の方向ベクトルと直交することになる。そこで、下記式（２８）のような評価関数を定義する。
【００７８】
【数２９】

これはＭＵＳＩＣスペクトラムと呼ばれ、到来角θに対するスペクトラムのＫ個のピークが到来方位θｋ（ｋ＝１，２…Ｋ）となる。なお、上記式（２７）からもわかるように、熱雑音電力に等しい最小固有値が少なくとも一つ必要なので、アレーのセンサ数はＭ≧Ｋ＋１が必要条件となる。
【００７９】
ここで、式（２８）の分子の部分が、上記式（１７）の自己内相関量Ｐとなる。このため、到来方位演算部４７は、相関量算出部２８で算出された自己内相関量Ｐを用いて上記式（２８）に示すＭＵＳＩＣスペクトラムを求め、該ＭＵＳＩＣスペクトラムに基づいて複数の入射信号の到来方位を求める。
【００８０】
即ち、偽像の発生程度が最も小さくなるように最適配置された第１〜第４アンテナ１１〜１４を用いることにより、自己内相関量Ｐの内の相互相関量は所定値以下に設定されるので、図７に示すように、ＭＵＳＩＣスペクトラム上における偽像は最小限に押えらて、該スペクトラム上には所望信号（複数の入射信号）のみのピークＰ１のみが現れる。このため、ピークＰ１における方位が複数の入射信号の到来方位となり、複数の入射信号の到来方位を正確に推定できる。
【００８１】
【発明の効果】
以上詳細したように、本発明に係るセンサ配置最適化方法及びその装置によれば、センサ位置パターン及び所望周波数帯の最大周波数の波長を入力するだけで、そのセンサ位置パターンの全方位角及び全仰角について、最大周波数帯以下の周波数による偽像の発生程度が自動的に求められるので、センサ配置の良否が判断者の主観に依存することはなく、偽像の発生程度を客観的に判断できる。また、センサ位置パターンの全方位角及び全仰角について偽像の発生程度が求められるのでセンサが同一水平面上に存在する必要はなく、センサ配置の自由度が増加する。
【００８２】
また、本発明に係る到来方位測定装置によれば、偽像の発生程度が最も小さくなるように配置されたセンサ素子を用いて入射信号の到来方位が測定されるので、偽像が発生することに起因して入射信号の到来方位を誤ることがなくなり、確実に入力信号の到来方位を測定できる。
【図面の簡単な説明】
【図１】本発明の第１の実施の形態に係るセンサ配置最適化方法において、アンテナ素子の位置ベクトルを説明するための図である。
【図２】本発明の第１の実施の形態に係るセンサ配置最適化方法において得られる偽像パターンの一例を示す図である。
【図３】本発明の第１の実施の形態に係るセンサ配置最適化方法において、センサ位置パターンを求める手順を示すフローチャートである。
【図４】本発明の第１の実施の形態に係るセンサ配置最適化方法を実現するセンサ配置最適化装置の構成を示すブロック図である。
【図５】本発明の第２の実施の形態に係る到来方位測定装置の構成を示すブロック図である。
【図６】本発明の第２の実施の形態に係る到来方位測定装置における、ＭＵＳＩＣによる到来方位推定を説明するための図である。
【図７】本発明の第２の実施の形態に係る到来方位測定装置における、到来角に対するＭＵＳＩＣスペクトラムを示す図である。
【符号の説明】
１ コンピュータ
２ 入力部
３ 計算部
４ メモリ
５ センサ配置決定部
１１〜１４ 第１〜第４アンテナ
２１〜２４ 第１〜第４帯域制限ろ波器
２５ 帯域制限制御器
２７ ベクトル生成部
２８ 相関量算出部
３１〜３４ 第１〜第４中間周波数変換器
３５ 局部発振器
４１〜４４ 第１〜第４Ａ／Ｄ変換器
４５ 発振器
４７ 到来方位演算部
６０ 出力処理部
６１〜６４ 第１〜第４Ｄ／Ａ変換器[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a sensor arrangement optimizing method and apparatus for optimizing the arrangement of sensors used in a sensor array system, and an arrival direction measuring apparatus for measuring an arrival direction of an incident signal using an optimally arranged sensor element.
[0002]
[Prior art]
2. Description of the Related Art Conventionally, there has been known a receiving device that measures an arrival direction of an incident wave using a sensor array having an antenna as a sensor. In this receiver, when a set of sensor array systems in which a plurality of sensors are arranged at a predetermined interval attempts to receive an incident signal in a wide frequency range, the sensor interval is arranged within a half wavelength interval of the received signal, and a low frequency It becomes impossible to secure the opening length even with a band. In this case, when azimuth estimation is performed using an algorithm for estimating the direction of arrival, for example, the MUSIC method, a true image is generated in the original azimuth and a false image is generated in addition to the original azimuth. As a result, the azimuth where the incident signal has not arrived may be erroneously estimated as the arrival azimuth of the incident signal.
[0003]
Therefore, in order to determine the optimal arrangement of the sensor array, a false image pattern representing a false image occurrence state is drawn according to an algorithm for calculating the arrival direction of the incident signal, and the position of the sensor is determined with reference to the false image pattern. In some cases, the optimal arrangement of the sensor array is determined by trial and error (for example, see Non-Patent Document 1).
[0004]
[Non-patent document 1]
D. H. BRANDWOOD "AMBIGITY PATTERNS OF PLANAR ANTENNA ARRAYS OFPARALLEL ELEMENTS", Antennas and Propagation, 4-7 April 1995. Conference Publication No. 407, Page (s): 432-436, IEEE 1995.
[0005]
[Problems to be solved by the invention]
However, according to the method disclosed in Non-Patent Document 1 described above, when the frequency range of a desired incident signal extends over a wide range, in order to know the degree of occurrence of a false image, it is necessary to determine the incidence direction of each frequency in the desired frequency band for each arrival direction. The calculation must be performed in accordance with the algorithm for calculating the arrival direction of the incident signal to draw the false image pattern, which requires a huge amount of calculation. In addition, since a person judges the quality of the sensor arrangement by looking at the drawn false image pattern, there is a problem that the quality of the sensor arrangement depends on the subjectivity of the judge and lacks objectivity. Further, the method disclosed in Non-Patent Document 1 has a limitation that the sensors must be present on the same horizontal plane, and thus has a problem that the degree of freedom of sensor arrangement is reduced.
[0006]
SUMMARY OF THE INVENTION The present invention has been made to solve the above-described problem, and an object of the present invention is to provide a sensor arrangement optimizing method and an apparatus therefor capable of arranging a plurality of sensor elements so as to minimize occurrence of false images in azimuth measurement. Another object of the present invention is to provide a direction-of-arrival measuring device that measures the direction of arrival of an incident signal using a sensor element optimally arranged.
[0007]
[Means for Solving the Problems]
A sensor arrangement optimizing method according to a first aspect of the present invention includes an inputting step of inputting a sensor position pattern representing a position of a plurality of sensor elements constituting a sensor array and a wavelength of a maximum frequency in a desired frequency band; By determining whether a false image is generated based on the phase difference between the arrival direction of the incident wave and the steering vector with respect to the positions of all the sensor elements of the sensor position pattern input in the input step, the predetermined arrival direction of the incident wave is obtained. A first calculation step of calculating the degree of occurrence of the false image up to the maximum frequency at the elevation angle, and integrating the calculated degree of occurrence of the false image for all azimuths and all elevation angles, thereby forming the false image of the sensor position pattern. And a second calculation step of calculating the degree of occurrence.
[0008]
According to the sensor arrangement optimizing method according to the first aspect, only by inputting the sensor position pattern and the wavelength of the maximum frequency in the desired frequency band, the azimuth and the elevation angle of the sensor position pattern are equal to or less than the maximum frequency. Since the degree of occurrence of a false image due to the frequency is automatically obtained, the quality of the sensor arrangement does not depend on the subjectivity of the judge, and the degree of occurrence of the false image can be objectively determined. In addition, since the degree of occurrence of a false image is obtained for all azimuth angles and all elevation angles of the sensor position pattern, the sensors do not need to be on the same horizontal plane, and the degree of freedom of sensor arrangement increases.
[0009]
Further, the sensor arrangement optimizing device according to the second aspect of the present invention is an input unit for inputting a sensor position pattern representing a position of a plurality of sensor elements constituting a sensor array and a wavelength of a maximum frequency of a desired frequency band, By determining whether or not a false image is generated based on the phase difference between the arrival direction of the incident wave and the steering vector with respect to the positions of all the sensor elements of the sensor position pattern input by the input unit, a predetermined value of the incident wave is determined. A first calculation unit for calculating the degree of occurrence of a false image up to the maximum frequency in the arrival direction and the elevation angle, and integrating the calculated degree of the false image with respect to all azimuths and elevation angles to obtain a false value in the sensor position pattern. A second calculation unit that calculates a degree of occurrence of an image.
[0010]
According to the sensor arrangement optimizing device according to the second aspect, the same operation and effect as those of the sensor arrangement optimizing method according to the first aspect are exhibited.
[0011]
In addition, the arrival direction measuring device according to the third aspect of the present invention comprises: an input unit for inputting a sensor position pattern indicating a position of a plurality of sensor elements constituting a sensor array and a wavelength of a maximum frequency in a desired frequency band; By determining whether or not a false image is generated based on the phase difference between the wave arrival direction and the steering vector with respect to the positions of all the sensor elements of the sensor position pattern input by the input unit, the predetermined arrival of the incident wave A first calculator for calculating the degree of occurrence of a false image up to the maximum frequency in azimuth and elevation, and a false image in the sensor position pattern by integrating the calculated degree of occurrence of the false image for all azimuth and elevation angles A second calculating unit for calculating the degree of occurrence of the image, and calculating by the second calculating unit based on a plurality of sensor position patterns input by the input unit. And a determining unit that determines the smallest one of the plurality of obtained false images as the final sensor position pattern, and the plurality of sensor elements arranged in the sensor position pattern determined by the determining unit. A vector generation unit that generates a steering vector based on a signal from the vector generation unit; a correlation amount calculation unit that calculates an autocorrelation amount based on a steering vector from the vector generation unit; and a signal from the plurality of sensor elements and the correlation. An arrival direction calculation unit for obtaining the arrival direction of the incident signal based on the self-internal correlation amount from the amount calculation unit.
[0012]
According to the direction-of-arrival measuring device according to the third aspect, the direction of arrival of the incident signal is measured using the sensor element arranged so that the degree of occurrence of the false image is minimized. As a result, the arrival direction of the incident signal is not erroneously determined, and the arrival direction of the input signal can be reliably measured.
[0013]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In the embodiment described below, an antenna element is used as a sensor element. Note that the sensor element is not limited to the antenna element, and a microphone or other sensor can be used.
[0014]
(First Embodiment)
A part of the algorithm for obtaining a false image disclosed in Non-Patent Document 1 described above is also used in the sensor arrangement optimizing method and apparatus according to the embodiment of the present invention. Therefore, first, the contents disclosed in Non-Patent Document 1 will be described.
[0015]
First, in the three-dimensional space shown in FIG. 1, the position vector R of the k-th antenna element forming the sensor array _k (K = 1, 2,..., N) is defined as in the following equation (1).
[0016]
(Equation 7)

Where r _k Is the magnitude of the position vector, θ _k Is the position vector R projected on the XY plane _k Is the angle (azimuth) that the X axis makes, φ _k Is the XY plane and the position vector R _k The angle (elevation angle) between them.
[0017]
Assuming that the incoming azimuth angle of the incident wave is α and the incoming elevation angle of the incident wave is ε, the unit azimuth vector e (α, ε) of the incident wave can be expressed by the following equation (2).
[0018]
(Equation 8)

When the wavelength of the incident wave is λ and the arrival direction is e (α, ε), the phase difference from the origin of the k-th antenna element Ψ _k Is represented by the following equation (3).
[0019]
(Equation 9)

Similarly, the unit azimuth vector of the steering vector is e (α ₀ , Ε ₀ ), The phase difference from the origin of the k-th antenna element due to the steering vector Ψ _0k Is represented by the following equation (4).
[0020]
(Equation 10)

Therefore, the phase difference Φ between the direction of arrival of the incident wave and the steering vector _k Can be represented by the following equation (5).
[0021]
[Equation 11]

The phase difference Φ represented by the equation (5) _k Is an integral multiple of 2π, a false image occurs. That is, when the unit azimuth vector of the incident wave is e (α, ε), the phase difference と from the origin of the k-th antenna element is obtained. _k Is as shown in the above equation (3), and the array manifold a _k (Α, ε) is represented by the following equation (6).
[0022]
(Equation 12)

Similarly, the unit azimuth vector of the steering vector is e (α ₀ , Ε ₀ ), The phase difference from the origin Ψ _0k Is as shown in the above equation (4), and the array manifold can be represented by the following equation (7).
[0023]
(Equation 13)

Now, assuming that the phase difference between the arrival direction of the incident wave and the steering vector is an integral multiple of 2π (2mπ), the difference between the steering vector and the origin is expressed by the following equation (8).
[0024]
[Equation 14]

The array manifold in this case is represented by the following equation (9).
[0025]
(Equation 15)

That is, when the phase difference becomes an integral multiple of 2π, the array manifold has the same value even if the direction of arrival of the incident wave and the direction of the steering vector are different, so that the output of the antenna becomes the same and a false image is generated. appear.
[0026]
Here, F (α, α ₀ , Ε, ε ₀ ) Is defined as in the following equation (10).
[0027]
(Equation 16)

As the value of F becomes larger, the azimuth α ₀ , Elevation angle ε ₀ Indicates the occurrence of a false image, that is, the degree of occurrence of the false image. That is, Φ in the above equation (10) _k Represents the arrival direction of the incident wave at each antenna and the phase difference between the steering vector and Φ _k Is an integer multiple of 2π, “exp (jΦ _k ) "Becomes" 1 ". Therefore, of the n antennas, the phase difference Φ between the arrival direction of the incident wave and the steering vector _k Is more than an integer multiple of 2π, in other words, the more the number of antennas where false images occur, the closer the second term of the denominator on the right side of the above equation (10) becomes to “1”, and F becomes a large value. . That is, the larger the value of F, the greater the number of antennas where false images occur, and the greater the degree of occurrence of false images.
[0028]
Here, when the above equation (5) is replaced with the following equation (11), the following equation (12) is obtained. A represents an array manifold.
[0029]
[Equation 17]

(Equation 18)

Here, assuming that the antenna elements are arranged on the same horizontal plane, "φ _k = 0 ”, and the above equation (12) can be simplified as the following equation (13).
[0030]
[Equation 19]

For example, in the equation (13), when the frequency is halved, the wavelength λ is doubled. _k , A, θ _k And η are constant, then Φ _k Becomes １ ／. In addition, in the equation (13), when A becomes １ ／, R _k , Λ, θ _k And η are constant, then Φ _k Becomes １ ／. Therefore, increasing the frequency by と is equivalent to increasing A by ２. That is, lowering the frequency and reducing the value of A are equivalent.
[0031]
Φ at maximum frequency _k Is calculated, A takes a range of 0 ≦ A ≦ 2. _k Is equivalent to a value calculated below the maximum frequency. That is, by setting the wavelength λ to the wavelength of the maximum frequency in the desired frequency band, F represents the degree of occurrence of a false image up to the maximum frequency in the desired frequency band.
[0032]
FIG. 2 shows that F (α, α ₀ , Ε, ε ₀ ) Variables α, α ₀ , Ε, ε ₀ Is replaced by variables A and η so as to satisfy Expression (11), and under the condition that all antenna elements exist on the same horizontal plane, F (α, α ₀ , Ε, ε ₀ 3) shows a false image pattern in which the value of ()) is represented by a contour graph. In FIG. 2, the inner circle represents a false image pattern when the maximum frequency is 3 MHz, and the outer circle represents a false image pattern when the maximum frequency is 6 MHz. The center of the circle is A = 0, the outer circumference is A = 2, and the angle represents η.
[0033]
In this false image pattern, a peak appearing at a position other than the center of the circle indicates the arrangement of the antenna elements, that is, the easiness of appearance of a false image in the sensor position pattern. The higher the peak value (the higher the contour graph, the higher the contour line graph). A large false image is generated, and the greater the number of peaks having the higher value, the easier the false image is generated.
[0034]
If the false image pattern shown in FIG. 2 is used, it is possible to compare the likelihood of false image appearance among a plurality of sensor position patterns. However, as described above, since it is necessary for a person to compare the false image patterns of the plurality of sensor position patterns, the quality of the arrangement of the antenna elements is determined depending on the subjectivity of the person to be compared, which lacks objectivity. In addition, since it is applicable only when all the antenna elements are present on the same horizontal plane, the degree of freedom of the arrangement of the antenna elements is limited.
[0035]
Therefore, in the sensor arrangement optimizing method according to the first embodiment of the present invention, the ambiguity index J is set to F (α, α ₀ , Ε, ε ₀ ) To the variables α, α ₀ , Ε, ε ₀ The ambiguity index J is calculated by calculating the ambiguity index J so that the degree of occurrence of a false image in all directions and all elevation angles in one sensor arrangement pattern is represented by a numerical value. Things.
[0036]
All α, α ₀ , Ε, ε ₀ , That is, 0 ≦ α, α ₀ ≦ 2π, 0 ≦ ε, ε ₀ If the result of calculating and adding F for the entire range of ≦ π / 2 is defined as an ambiguity index J, the ambiguity index J can be expressed by the following equation (14). The phase difference Φ in the following equation (14) _k Is shown in equation (5), and the phase difference Φ shown in equation (13) _k (Φ _k = 0).
[0037]
(Equation 20)

The ambiguity index J indicates the degree of occurrence of a false image in a sensor array having one sensor arrangement pattern. The greater the value of the ambiguity index J, the greater the degree of occurrence of a false image in the sensor array.
[0038]
Next, a procedure for obtaining an optimum sensor arrangement pattern that can minimize the degree of occurrence of a false image will be described with reference to the flowchart shown in FIG. This procedure is executed using the computer shown in FIG. The computer 1 has an input unit 2, a calculation unit 3, a memory 4, and a sensor arrangement determination unit 5, and corresponds to the sensor arrangement optimization device of the present invention.
[0039]
First, the wavelength λ of the maximum frequency of the frequency band handled by the array antenna _m Is input from the input unit 2 (step S10). Next, a sensor arrangement pattern is input from the input unit 2 (step S11). As the sensor arrangement pattern, specifically, the antenna position R of the antenna element forming the sensor arrangement pattern _k (1, 2,..., N) are input.
[0040]
Next, the ambiguity index J is calculated by the calculation unit 3 (step S12). The calculation of the ambiguity index J is based on the wavelength λ input in steps S10 and S11, respectively. _m And antenna position R _k The calculation is performed by using (1, 2,..., N) as parameters and executing the calculation according to the above equation (14). The ambiguity index J calculated here is stored in the memory 4.
[0041]
Next, it is determined by a determination unit (not shown) whether the calculation of the ambiguity indices J for all the sensor position patterns prepared in advance has been completed (step S13). If it is determined that the processing is not completed, the process returns to step S11, and the same processing is repeated. By repeatedly executing steps S11 to S13, a plurality of ambiguity indices J respectively corresponding to the plurality of sensor position patterns are stored in the memory 4.
[0042]
If it is determined in step S13 that the calculation of the ambiguity indices J for all the sensor position patterns has been completed, then the one having the smallest value among the plurality of ambiguity indices J stored in the memory 4 is determined. Is retrieved by the sensor arrangement determining unit 5 (step S14). Then, the sensor arrangement pattern corresponding to the retrieved ambiguity index J is determined by the sensor arrangement determination unit 5 as the optimal sensor position pattern, that is, the arrangement pattern of the antenna elements with the least occurrence of false images (step S15). An array antenna having the determined antenna element arrangement pattern is applied to an actual direction of arrival measuring device.
[0043]
As described above, according to the sensor arrangement optimizing method and the apparatus thereof according to the first embodiment of the present invention, the antenna position R of the sensor array is expressed by the equation (14) representing the ambiguity index J. _k (1, 2,..., N), the wavelength λ of the maximum frequency in the desired frequency band _m , It is possible to quantitatively determine the degree of occurrence of false images in all directions and all elevation angles in the desired frequency band at once.
[0044]
Therefore, it is possible to eliminate the lack of objectivity caused by a person comparing the false image patterns of the plurality of sensor position patterns, as in the case of using the false image pattern shown in FIG. Further, the present invention is applicable not only to the case where all the antenna elements are present on the same horizontal plane, so that the degree of freedom of arrangement of the antenna elements is increased.
[0045]
(Second embodiment)
The direction-of-arrival measuring apparatus according to the second embodiment of the present invention includes the computer 1 which is the sensor arrangement optimizing apparatus according to the above-described first embodiment, and the sensor arrangement optimizing apparatus according to the first embodiment. An array antenna having an antenna arrangement determined by the optimization device is used.
[0046]
In the following, for the sake of simplicity, the number of antenna elements is assumed to be “4” and the number n of incident signals is assumed to be “4”, but the number of antenna elements and the number of incident signals are limited to these. Not optional.
[0047]
FIG. 4 is a block diagram showing a configuration of an arrival direction measuring device according to the second embodiment of the present invention. This direction-of-arrival measuring device includes a computer 1, first to fourth antennas 11 to 14, first to fourth band-limited filters 21 to 24, a vector generator 27, a correlation amount calculator 28, a sampling unit 30, and an incoming device. The azimuth calculation unit 47 is configured. The computer 1 is a sensor arrangement optimizing device, and sets a computer having a minimum degree of occurrence of a false image as an optimal sensor arrangement pattern. That is, an array antenna having the antenna arrangement determined by the sensor arrangement optimizing device is used.
[0048]
As the first to fourth antennas 11 to 14, non-directional antennas such as vertical antennas and dipole antennas, and antennas having arbitrary directivity are used, and receive radio waves from various directions. The intervals and heights at which the first to fourth antennas 11 to 14 are installed are determined by the above-described sensor arrangement optimizing method according to the first embodiment. The first to fourth antennas 11 to 14 receive a plurality of incident signals (radio waves) S1 to S4 from the air, and transmit mixed signals obtained by mixing the signals to the first to fourth band-limited filters 21 to 24. send.
[0049]
The first to fourth band-limited filters 21 to 24 pass only frequency components of a predetermined band included in the mixed signals from the first to fourth antennas 11 to 14 and send the signals to the sampling unit 30. The frequency bands passed by the first to fourth band limiting filters 21 to 24 are the same.
[0050]
The band limitation controller 25 generates a control signal for designating a frequency band to be passed, that is, a range of frequency components to be passed. The control signal generated by the band limit controller 25 is sent to first to fourth band limit filters 21 to 24. The first to fourth band-limited filters 21 to 24 pass only frequency components of a predetermined band included in the input mixed signal according to a control signal from the band-limit controller 25.
[0051]
The band limitation controller 25 is configured to generate a control signal that allows a frequency component in an arbitrary band to pass. Therefore, by appropriately changing the control signal from the band limit controller 25, the frequency band passing through the first to fourth band limit filters 21 to 24 can be arbitrarily changed.
[0052]
The sampling unit 30 includes first to fourth intermediate frequency converters 31 to 34, a local oscillator 35, first to fourth A / D converters 41 to 44, and an oscillator 45.
[0053]
Local oscillator 35 generates a signal having a transmission frequency required to convert a received radio wave to an intermediate frequency. The signal generated by the local oscillator 35 is sent to first to fourth intermediate frequency converters 31 to 34.
[0054]
Although not shown, each of the first to fourth intermediate frequency converters 31 to 34 includes a high frequency amplifier, a frequency mixer, and an intermediate frequency amplifier.
[0055]
The high-frequency amplifier amplifies a high frequency in a reception frequency band so as to have an appropriate magnitude as an input voltage of the next-stage frequency mixer. The frequency mixer mixes the signal amplified by the high-frequency amplifier and the output signal of the local oscillator 35, and converts the signal into an intermediate frequency signal by creating a sum or difference frequency. The intermediate frequency amplifier converts the frequency of the received radio wave to a lower intermediate frequency and amplifies it. Thereby, stable and high-gain amplification can be performed, and sensitivity can be improved.
[0056]
The signals output from the first to fourth intermediate frequency converters 31 to 34 configured as described above are sent to the first to fourth A / D converters 41 to 44, respectively.
[0057]
The oscillator 45 generates a sampling clock for sampling signals from the first to fourth intermediate frequency converters 31 to 34. The sampling clock generated by the oscillator 45 is sent to first to fourth A / D converters 41 to 44.
[0058]
The first to fourth A / D converters 41 to 44 respectively convert the analog signals from the first to fourth intermediate frequency converters 31 to 34 into digital signals by using the signal from the oscillator 45 as a sampling clock. Convert. The digital signals output from each of the first to fourth A / D converters 41 to 44 are supplied to the arrival direction calculation unit 47.
[0059]
The vector generation unit 27 generates a steering vector that expresses a phase response of a plurality of incident signals at each of the antennas 11 to 14 in a matrix based on signals from the first to fourth band-limited filters 21 to 24.
[0060]
The correlation amount calculation unit 28 calculates a complex conjugate transpose matrix of the steering vector based on the steering vector generated by the vector generation unit 27, and calculates the self-internal correlation amount of the steering vector by calculating the complex conjugate transpose matrix and the steering vector. Ask for. Hereinafter, the operation of the correlation amount calculator 28 will be described.
[0061]
Now, it is assumed that m (m is an integer of 2 or more) signals are simultaneously incident on an array of n (n is an integer of 2 or more) antenna elements. This state can be expressed by the following equation (15).
[0062]
(Equation 21)

Here, X1 to n are time series data observed by each antenna, and A = [a (θ1),... A (θm)] is a matrix of signal mixing of n rows × m columns determined by antenna arrangement and characteristics. , S1 to m (t) are m incident signals, and N1 to n (t) are noise in each antenna.
[0063]
In general, in azimuth measurement by super resolution or null steering, information corresponding to “A” in the above equation (15) is directly or indirectly estimated.
[0064]
Here, [A] is assumed to be a steering vector a. The steering vector a is generated by the steering vector generation unit 27. The steering vector a is a matrix representing the phase response of a plurality of incident signals at each of the antennas 11 to 14, and is represented by a matrix of [4 × 360], that is, the following equation (16).
[0065]
(Equation 22)

The steering vector a may be measured by, for example, a simulation. This steering vector a determines the direction of the main lobe of the antenna.
[0066]
The correlation amount calculation unit 28 calculates a complex conjugate transpose matrix of the steering vector based on the steering vector generated by the vector generation unit 27, and calculates the self-internal correlation amount of the steering vector by calculating the complex conjugate transpose matrix and the steering vector. Find P.
[0067]
The autocorrelation amount P is represented by the following equation (17).
[0068]
[Equation 23]

Here, the superscript H represents a complex conjugate transpose. Then, the autocorrelation amount P is a matrix of [360 × 360] as shown in the following equation (18).
[0069]
(Equation 24)

The diagonal component of this matrix is the autocorrelation part, and the other components are the cross-correlation part. Then, a cross-correlation amount is extracted from the auto-correlation amount. The correlation between the steering vectors a is obtained from the cross-correlation amount. For example, the cross-correlation amount p40 · 2 represents a correlation value of a component between 40 deg and 2 deg of the steering vector a. When the correlation is strong, the value of the cross-correlation amount p40 · 2 increases, and when the correlation is weak, the value of the cross-correlation amount p40 · 2 decreases.
[0070]
When the cross-correlation amount p40 · 2 shows a large value, when the arriving wave arrives from 40 deg, it also arrives from 2 deg other than 40 deg. Ambiguity) occurs.
[0071]
The arrival azimuth calculation unit 47 uses an algorithm such as MUSIC based on the signals from the first to fourth A / D converters 41 to 44 and the self-correlation amount calculated by the correlation amount calculation unit 28 to use an incident signal. The arrival direction of is measured. The processing of the arrival direction calculator 47 will be described in detail with reference to FIG.
[0072]
The MUSIC method is an estimation method using eigenvalues and eigenvectors of a correlation matrix. As shown in FIG. 6, K plane waves arrive at the M element equally spaced linear array with antenna spacing d, and the signal waveform and the arrival angle of each arriving wave are Fk (t), θk (k = 1, 2,..., K ), The direction vector a (θk) representing the phase response of each arriving wave at each antenna is given by the following equation (19).
[0073]
(Equation 25)

Here, the superscript T indicates transposition. Therefore, the input vector is represented by the following equations (20) to (24).
[0074]
(Equation 26)

In the above equation, N (t) is a thermal noise vector, and its component has a mean of 0 and a variance (power) of σ ² Is an independent complex Gaussian process. At this time, a correlation matrix representing a correlation characteristic between antennas is given by the following equations (25) and (26).
[0075]
[Equation 27]

Here, the superscript H represents a complex conjugate transpose. If the incoming waves are unrelated, the rank of the signal correlation matrix S is K. The rank of the direction matrix A is also K. Therefore, the correlation matrix Rxx in this case is a non-negative definite Hermitian matrix of rank K. The eigenvalues λi (i = 1, 2,..., M) of this matrix are real numbers and have the relationship of the following equation (27).
[0076]
[Equation 28]

Therefore, the eigenvalue of the correlation matrix is obtained, and the thermal noise power σ ² The number K of incoming waves can be estimated from the number of larger eigenvalues. If the eigenvector corresponding to the eigenvalue λi (i = 1, 2,..., M) is ei (i = 1, 2,..., M), the eigenvector is treated as an orthonormal base vector in an M-dimensional Hermitian space. This space can be divided into two subspaces, a signal space span {e1,... EK} and a noise space span {eK + 1,... EM}, and the signal space and the noise space have a mutually complementary space relationship.
[0077]
.., eK} is a space spanned by vectors ei (i = 1, 2,..., M). Also, the signal space can be expressed as span {a (θ1),..., A (θk)} using the direction vector. Therefore, all eigenvectors corresponding to eigenvalues equal to the thermal noise power are orthogonal to the direction vector of the incoming wave. Therefore, an evaluation function such as the following equation (28) is defined.
[0078]
(Equation 29)

This is called a MUSIC spectrum, and K peaks of the spectrum with respect to the angle of arrival θ are the arrival directions θk (k = 1, 2,... K). As can be seen from the above equation (27), since at least one minimum eigenvalue equal to the thermal noise power is required, the number of sensors in the array must be M ≧ K + 1.
[0079]
Here, the numerator of the equation (28) is the autocorrelation amount P in the equation (17). Therefore, the direction-of-arrival calculating unit 47 obtains the MUSIC spectrum shown in the above equation (28) using the self-correlation amount P calculated by the correlation amount calculating unit 28, and calculates a plurality of incident signals based on the MUSIC spectrum. Find the direction of arrival.
[0080]
That is, by using the first to fourth antennas 11 to 14 optimally arranged so that the degree of occurrence of a false image is minimized, the cross-correlation amount among the auto-correlation amounts P is set to a predetermined value or less. Therefore, as shown in FIG. 7, a false image on the MUSIC spectrum is minimized, and only a peak P1 of a desired signal (a plurality of incident signals) appears on the spectrum. Therefore, the azimuth at the peak P1 is the arrival azimuth of the plurality of incident signals, and the azimuths of the plurality of incident signals can be accurately estimated.
[0081]
【The invention's effect】
As described above in detail, according to the sensor arrangement optimizing method and the apparatus thereof according to the present invention, the azimuth and omnidirectional angle and the omnidirectional angle of the sensor For the elevation angle, the degree of occurrence of false images due to frequencies below the maximum frequency band is automatically determined, so that the quality of the sensor arrangement does not depend on the subjectivity of the judge, and the degree of occurrence of false images can be objectively determined. . Further, since the degree of occurrence of a false image is obtained for all azimuth angles and all elevation angles of the sensor position pattern, it is not necessary for the sensors to be on the same horizontal plane, and the degree of freedom of sensor arrangement increases.
[0082]
Further, according to the direction-of-arrival measurement apparatus according to the present invention, the direction of arrival of the incident signal is measured using the sensor element arranged so that the degree of occurrence of the false image is minimized. As a result, the arrival direction of the incident signal is not erroneously determined, and the arrival direction of the input signal can be reliably measured.
[Brief description of the drawings]
FIG. 1 is a diagram for explaining a position vector of an antenna element in a sensor arrangement optimizing method according to a first embodiment of the present invention.
FIG. 2 is a diagram illustrating an example of a false image pattern obtained by the sensor arrangement optimizing method according to the first embodiment of the present invention.
FIG. 3 is a flowchart showing a procedure for obtaining a sensor position pattern in the sensor arrangement optimizing method according to the first embodiment of the present invention.
FIG. 4 is a block diagram showing a configuration of a sensor arrangement optimizing device for realizing the sensor arrangement optimizing method according to the first embodiment of the present invention.
FIG. 5 is a block diagram showing a configuration of an arrival direction measuring device according to a second embodiment of the present invention.
FIG. 6 is a diagram for explaining arrival direction estimation by MUSIC in an arrival direction measurement device according to a second embodiment of the present invention.
FIG. 7 is a diagram showing a MUSIC spectrum with respect to an angle of arrival in a direction-of-arrival measuring apparatus according to a second embodiment of the present invention.
[Explanation of symbols]
1 computer
2 Input section
3 Calculation section
4 memory
5 Sensor arrangement determination unit
11 to 14 first to fourth antennas
21 to 24 first to fourth band-limited filters
25 Band limit controller
27 Vector Generator
28 Correlation amount calculator
31 to 34 First to fourth intermediate frequency converters
35 Local oscillator
41 to 44 first to fourth A / D converters
45 oscillator
47 Arrival direction calculation unit
60 Output processing unit
61-64 1st-4th D / A converter

Claims (8)

An input step of inputting a sensor position pattern representing a position of a plurality of sensor elements constituting the sensor array and a wavelength of a maximum frequency of a desired frequency band,
By determining whether or not a false image occurs based on the arrival direction of the incident wave and the phase difference between the steering vectors for all the sensor element positions of the sensor position pattern input in the input step, a predetermined value of the incident wave is obtained. A first calculation step of calculating a degree of occurrence of a false image up to the maximum frequency in an arrival direction and an elevation angle;
A second calculation step of calculating the degree of occurrence of the false image in the sensor position pattern by integrating the calculated degree of occurrence of the false image with respect to all azimuths and all elevation angles. . In the first calculation step, α is the arrival azimuth angle of the incident wave, ε is the arrival angle of the incident wave, α ₀ is the azimuth angle at which a false image is generated, ε ₀ is the elevation angle at which a false image is generated, and n is the sensor element. When the number and Φ _k are the phase difference between the direction of arrival of the incident wave and the steering vector, the degree of occurrence F (α, α ₀ , ε, ε ₀ ) of the false image is calculated according to the following equation (10):

In the second calculation step, the following equation (14) is used.

2. The sensor arrangement optimizing method according to claim 1, wherein a degree J of occurrence of a false image in the sensor position pattern is calculated according to the following formula. The input step inputs a plurality of sensor position patterns,
A determining step of determining, as a final sensor position pattern, a smallest one of a plurality of false image occurrence degrees obtained by performing the calculation in the second calculation step based on the plurality of sensor position patterns; 3. The method according to claim 1, wherein the sensor arrangement is optimized. An input unit for inputting a sensor position pattern representing a position of a plurality of sensor elements constituting the sensor array and a wavelength of a maximum frequency of a desired frequency band,
By determining whether or not a false image is generated based on the phase difference between the arrival direction of the incident wave and the steering vector with respect to the positions of all the sensor elements of the sensor position pattern input by the input unit, a predetermined value of the incident wave is determined. A first calculation unit that calculates a degree of occurrence of a false image up to the maximum frequency in an arrival direction and an elevation angle;
A second calculating unit that calculates the degree of occurrence of the false image in the sensor position pattern by integrating the calculated degree of occurrence of the false image with respect to all azimuths and all elevation angles. . The first calculation unit calculates α as the azimuth of arrival of the incident wave, ε as the arrival angle of the incident wave, α ₀ as the azimuth at which a false image occurs, ε ₀ as the elevation angle at which a false image occurs, and n as the sensor element. When the number and Φ _k are the phase difference between the direction of arrival of the incident wave and the steering vector, the degree of occurrence F (α, α ₀ , ε, ε ₀ ) of the false image is calculated according to the following equation (10):

The second calculation unit calculates the following equation (14).

5. The sensor arrangement optimizing device according to claim 4, wherein a false image occurrence degree J in the sensor position pattern is calculated according to the following formula. The input unit inputs a plurality of sensor position patterns,
The image processing apparatus further includes a determining unit that determines a smallest one of a plurality of false image occurrence degrees obtained by performing the calculation in the second calculating unit based on the plurality of sensor position patterns as a final sensor position pattern. The sensor arrangement optimizing device according to claim 4 or 5, wherein: An input unit for inputting a sensor position pattern representing a position of a plurality of sensor elements constituting the sensor array and a wavelength of a maximum frequency of a desired frequency band,
By determining whether or not a false image is generated based on the phase difference between the arrival direction of the incident wave and the steering vector with respect to the positions of all the sensor elements of the sensor position pattern input by the input unit, a predetermined value of the incident wave is determined. A first calculation unit that calculates a degree of occurrence of a false image up to the maximum frequency in an arrival direction and an elevation angle;
A second calculation unit that calculates the degree of occurrence of a false image in the sensor position pattern by integrating the calculated degree of occurrence of the false image with respect to all azimuth angles and all elevation angles;
Based on the plurality of sensor position patterns input by the input unit, the smallest one of a plurality of false image occurrence degrees obtained by calculation by the second calculation unit is determined as a final sensor position pattern. A decision unit to
A vector generation unit that generates a steering vector based on signals from the plurality of sensor elements arranged in the sensor position pattern determined by the determination unit,
A correlation amount calculation unit that calculates an autocorrelation amount based on the steering vector from the vector generation unit,
Arrival azimuth calculation unit for determining the azimuth of arrival of the incident signal based on the signals from the plurality of sensor elements and the self-internal correlation amount from the correlation amount calculation unit,
An arrival direction measuring device, comprising: The first calculation unit calculates α as the azimuth of arrival of the incident wave, ε as the arrival angle of the incident wave, α ₀ as the azimuth at which a false image occurs, ε ₀ as the elevation angle at which a false image occurs, and n as the sensor element. When the number and Φ _k are the phase difference between the direction of arrival of the incident wave and the steering vector, the degree of occurrence F (α, α ₀ , ε, ε ₀ ) of the false image is calculated according to the following equation (10):

The second calculation unit calculates the following equation (14).

The direction-of-arrival measuring apparatus according to claim 7, wherein a false image occurrence degree J in the sensor position pattern is calculated according to the following equation:

Images