JP3572594B2 - Signal source search method and apparatus - Google Patents

Description

【００１５】
フーリエ変換は有限長データに対して次式のように定義する。
【００１６】
【数２】

【００１７】
そこで、次式で定義されるクロススペクトルマトリックスに着目する。
【００１８】
【数３】

【００１９】
ここで、Ｈはｃｏｎｊｕｇａｔｅ ｔｒａｎｓｐｏｓｅ を表し、また、Ｅ｛｝は期待値オペレータを表すものとする（厳密には、このオペレータはデータレコードのアンサンブル平均によってクロススペクトルを推定するプロセスを表している）。
従って、
【００２０】
【数４】

【００２１】
Ｓ _ａａをクロスパワースペクトルマトリックスとして、改めてつぎのように表す。
【００２２】
【数５】

【００２３】
ここで、それぞれ要素のクロスパワースペクトルは、例えば
【００２４】
【数６】

【００２５】
であるとする。
問題は、音場に設置されたマイクロホンアレイ位置で観測された音圧の時間的な履歴から、上述のマトリックスＳ _ａａを最適推定することである。
マイクロホン出力も、それぞれの出力もフーリエ変換を用いて、つぎのような複素ベクトルで表す。
【００２６】
【数７】

【００２７】
対応するクロスパワースペクトルマトリックスＳ _ｙｙは次式で与えられる。
【００２８】
【数８】

【００２９】
従って、これもつぎのように簡単に表現できる。
【００３０】
【数９】

【００３１】
本解析では、モデル音源からモデルマイクロホンまでの伝達関数マトリックスを仮定し、解析モデルは次式の関係が成り立つ線形システムとする（図６参照）。すなわち、
【００３２】
【数１０】

【００３３】
たとえばポイントモノポール音源モデルの場合、伝達関数Ｈ_１２ （ω） は音源２からマイクロホン１間の伝達関数を表現し、簡単に次式のように表現できる。
【００３４】
【数１１】

【００３５】
ここで、ｒ_１２は音源２ からマイクロホン１の間の距離、ρ_ｏ は空気の密度、κは波数である。ここまでの議論から、音源モデルはｐｏｉｎｔ ｄｉｐｏｌｅ（双極子）、あるいはｐｏｉｎｔ ｑｕａｄｒｕｐｏｌｅ（四極子）、また、それらの分布している任意の形態としてもよいことは自明である。さらに、モデル音源からモデルマイクロホンまでの伝達関数についても先見情報から導出されたものや、実測値であっていもよい。とりわけ、積分方程式を基礎としたシミューレーション技術によって得られた伝達関数などは、大変有用であるものと思われる。そこで、式（１０）の関係をコンパクトにつぎのように書く。
【００３６】
【数１２】

【００３７】
これにより、モデル音源はマイクロホン位置においてつぎのようなクロスパワースペクトルマトリックスＳ _ｙｙ’ を呈することになる。
【００３８】
【数１３】

【００３９】
従って、我々の最適化問題は、実測されたクロスパワースペクトルマトリックスＳ _ｙｙに最も近似するモデル・クロスパワースペクトルマトリックスＳ _ｙｙ’ を与えるという意味で最良の、音源の強さのベクトルａを求める問題として帰着される。そこで、次に誤差マトリックスに対するＦｒｏｂｅｎｉｕｓ （フロベニウス）ノルムを最小とする最適解を考える。はじめに、誤差マトリックス、
【００４０】
【数１４】

【００４１】
Ｅ＝Ｓ _ｙｙ−Ｓ _ｙｙ’
を定義する。上式を展開し、次式を得る。
【００４２】
【数１５】

【００４３】
一方、誤差マトリックスのＦｒｏｂｅｎｉｕｓ ノルムは次式で定義される。
【００４４】
【数１６】

【００４５】
厳密にはこのｓｑｕａｒｅ ｒｏｏｔ であるが、ここでは上式をもってＦｒｏｂｅｎｉｕｓ ノルムと定義する。従って、Ｆｒｏｂｅｎｉｕｓ ノルムは式（１５）からつぎのように表されることになる。
【００４６】
【数１７】

【００４７】
Ｆｒｏｂｅｎｉｕｓ ノルムを最小とする音源の強さのベクトルａ、あるいはそのクロススペクトルマトリックスＳ _ａａは、実測されたクロスパワースペクトルと、モデル・クロスパワースペクトルとの差の二乗和を最小とすることが分かる。従って、このＦｒｏｂｅｎｉｕｓ ノルム規範は我々の目的に適していると考えられる。
Ａｎｃｉａｎｔ ^（１） らは、一般の非線形最小二乗問題の解を、その数値計算手法とともに検討しているが、上述の問題に対するＦｒｏｂｅｎｉｕｓ ノルム規範の最適解は次式で与えられるとしている。
【００４８】
【数１８】

【００４９】
式（１８）が求める解であり、Ｈに対するモデルを仮定することで、音源の強さのクロススペクトルマトリックスＳ _ａａの最良推定が実測値Ｓ _ｙｙを用いて計算できることを示している。
また、クロススペクトルマトリックスＳ _ａａの解が与えられると、モデル・クロスパワースペクトルマトリックスＳ _ｙｙ’ は次式
【００５０】
【数１９】

【００５１】
から計算され、この式（１９）を式（１４）に代入すれば、このときのＦｒｏｂｅｎｉｕｓ ノルムが計算できる。尚、Ｆｒｏｂｅｎｉｕｓ ノルムはクロススペクトルマトリックスＳ _ａａの解に対して次式で与えられる。
【００５２】
【数２０】

【００５３】
以上の理論的背景から、想定したモデル音源の位置において誤差（Ｆｒｏｂｅｎｉｕｓ ノルム）を最小にするクロススペクトルマトリックスＳ _ａａを算出することができる。即ち、想定した数と位置のモデル音源において最も測定値と適応する各周波数成分の音源の強さを求めることができる。
また、クロススペクトルマトリックスＳ _ａａが最適解のときの誤差（Ｆｒｏｂｅｎｉｕｓ ノルム）はその想定したモデル音源が実際の音源に対して適応する度合いを示しており、誤差が小さい程適合度が高いといえる。即ち、適合度が高いモデル音源ほど実際の音源を再現しているといえる。
【００５４】
そこで以下、この適応度を誤差の逆数で具体的に表現し、想定したモデル音源の良否を評価する。尚、以下誤差の逆数をＦｉｔｎｅｓｓ という。また、適応度の表現方法はこれに限ったものではない。
尚、上記では誤差をＦｒｏｂｅｎｉｕｓ ノルムで評価したが、誤差の評価にはさまざまな方法があり、これに限ったものではない。
【００５５】
また、上記では音源から出力される信号を単一周波数として説明したが、音源から出力される信号がある周波数帯域を持つ場合には周波数成分毎に上記誤差を求めて、例えばこれらの誤差の総和、或いは、これらの誤差の総和の対数をとったものを総合的な誤差として評価する。但し、この場合でもある周波数に着目して上記のように誤差を評価し、これに基づいて音源の位置を探査してもよい。
【００５６】
次に、モデル音源の想定方法について説明する。
上記では、与えられたモデル音源の数、位置に対して、音源の強さのクロススペクトルマトリックスＳ _ａａの最良推定を議論した。しかしながら、モデル音源の数、位置について推定を行なうためには、何らかの音源位置探査アルゴリズムが必要となる。例えば、３次元空間のメッシュ上の点として音源位置を与えて、モデル音源の数との組み合わせで、すべての組み合わせについて評価を行うことができるが、実用上困難な場合もある。たとえば、空間の３２点のみを対象として、８つのモデル音源を想定した大変小規模の探査の場合でも、その組み合わせは、１０^７ のオーダーとなる。そこで本実施例では、遺伝子アルゴリズムを音源探査に適用する。以下、遺伝子アルゴリズムについて説明する。
【００５７】
ここでの探索問題は、図３に示すように、可能なモデル音源の組み合わせ（変数ｘ）に対して、評価関数が複雑な形状を呈し、その全体像が既知でないという特徴がある。また、変数ｘの取りうるオーダーも実際の応用では、１０００ｂｉｔ程度は必要であるため、探索点は、およそ１０^３００ 個となり、全探索による解法は事実上不可能で、いわゆるＮＰ完全な問題である。探索空間を効率よく探索し、実用上の最適解をすみやかに発見する探索アルゴリズムとして遺伝的アルゴリズム（ＧＡ）が有効であるとされて、現在、様々な工学的な応用で用いられつつある。ＧＡでは、探索問題を、生物の進化の過程を模倣した方法によって解く。さらにＧＡでは、探索空間の探索点を、１点づつ順番に探索するのではなく、複数個の探索点を同時に用いる。また、各探索点が、遺伝子（ｇｅｎｅ）をもつ仮想的な生物であるとみなす。各個体に対して、それぞれの環境との適応度（ｆｉｔｎｅｓｓ） が計算される。本実施例では、前述のＦｒｏｂｅｎｉｕｓ ノルムを用いて適応度を評価するものとする。低い適応度をもつ個体を淘汰（ｓｅｌｅｃｔｉｏｎ） して消滅させ、高い適応度を有する個体を増殖（ｍｕｌｔｉｐｌｉｃａｔｉｏｎ）させ、親の形質を継承した遺伝子をもつ子孫の個体を生成する世代交代シミュレーションによって、進化すなわち、よりよい探索が進んでいく。
世代交代では、遺伝子の交差（ｃｒｏｓｓｏｖｅｒ） 、突然変異（ｍｕｔａｔｉｏｎ）と呼ばれる操作が行われる。
【００５８】
図４は、遺伝子アルゴリズムを用いた音源探査アルゴリズムを説明したフローチャートである。
まず、初期世代の個体（ｉｎｄｉｖｉｄｕａｌ）と染色体（ｃｈｒｏｍｏｓｏｍｅ）を決定する（ステップＳ１０）。染色体は複数の遺伝子（ｇｅｎｅ）から構成される。また、それぞれの遺伝子の位置は、遺伝子座（ｌｏｃｕｓ） と呼ばれる一種の座標によって規定される。個々の個体の染色体の内部表現を遺伝子型（ｇｅｎｏｔｙｐｅ）と称する。本実施例の音源探査アルゴリズムに適用する場合、音場における検索点の数（メッシュ上の点の数）を遺伝子の数として所定の配列でこれらの検索点を配列して染色体を構成する。そして、各検索点においてモデル音源が存在する場合の遺伝子を１、存在しない場合の遺伝子を０としてモデル音源の１配置形態を１つの個体として図５で示すようにビットコードで表現する。即ち、音場のメッシュ上の各点に各ビットを対応させてモデル音源を想定するビットを１とする。
【００５９】
初期世代の個体を決定する場合、まず個体数と１個体におけるモデル音源の数を決定する。尚、以下の説明において、個体数を４０、１個体におけるモデル音源の数を４とする。個体数とモデル音源の数を決定した後、モデル音源を配置する位置をランダムに決定して初期世代の個体を生成する。
次に、上記のようにして生成した４０個の各個体のＦｉｔｎｅｓｓ を計算する（ステップＳ１２）。そして、４０個の個体の中からＦｉｔｎｅｓｓ が最大となる個体と、その個体と合わせて合計２０個となるように残りの個体を選出する（淘汰と増殖）（ステップＳ１４）。この残りの個体を選出する際には、Ｆｉｔｎｅｓｓ が大きい個体程高い確立で選出されるようにする。
【００６０】
次に、淘汰と増殖によって選出された２０個の個体からランダムに２個の個体を抽出して組み合わせ、１０個の組を作る。そして、それぞれの組毎に遺伝子を組かえて２個の個体を新たに増殖させる（遺伝子の交差）（ステップＳ１６）。即ち、淘汰と増殖によって選出された個体から遺伝子の交差によって新たに２０個の個体を生成し、合計４０個の個体を生成する。尚、遺伝子を交差する際にどのビットから交差するかはランダムに決定する。
【００６１】
次に、上記のように増殖した２０個の個体に対して突然変異を発生させる（ステップ１８）。突然変異は音源の数を変化させずに音源の位置をある確立で変化させる操作で、例えば、０．０２％の確立で発生させる。
以上のようにして新しい世代の個体を生成し、生成した２０個の個体に対してＦｉｔｎｅｓｓ を計算する（ステップＳ２０）。そして、４０個の個体の中でＦｉｔｎｅｓｓ が最大となる個体を検索し、その値が所定の閾値以上か否かを判断する（ステップＳ２２）。この閾値は、実際の音源に対して想定したモデル音源（個体）が十分適応すると経験的に判断されるＦｉｔｎｅｓｓ の値を示している。もし、Ｆｉｔｎｅｓｓ の最大値が閾値以上の場合には、以上の処理を終了し、その個体のモデル音源の位置を実際の音源の位置とする。
【００６２】
逆にＦｉｔｎｅｓｓ の最大値が閾値より小さい場合には、ステップＳ１４に戻り、上記処理を繰り返す。
以上のようにして、Ｆｉｔｎｅｓｓ が所定の閾値を越える個体を遺伝子アルゴリズムを用いて検出し、実際の音源の位置を探査する。但し、上記で想定したモデル音源の数が実際の音源の数より少ない場合には上記処理を繰り返してもＦｉｔｎｅｓｓ が閾値を越える個体を検出することはできないため、上記処理をある程度繰り返し行ってもＦｉｔｎｅｓｓ が閾値を越える個体を検出することができない場合には、モデル音源の数を増やして同様の処理を行う。
【００６３】
以上、上述した音源探査アルゴリズムをまとめると基本的にはつぎのように要約される。
（１）音源探査の対象なるフィールドにおいて、マイクロホンアレイを用いて、音場をサンプルし、マトリックスＳ_ｙｙを得る。
（２）モデル音源からモデルマイクロホンまでの伝達関数マトリックスＨを設定する。通常、音源の先験的な情報から、シミュレーションあるいは実測データ（インパルス応答など）を用いて構築する。
（３）モデル音源の数を設定する。
（４）与えられたモデル音源の数に対し、遺伝子アルゴリズムを用いて、音源位置を探索していく。その際、Ｆｒｏｂｅｎｉｕｓ ノルムに基づく音源の強さのクロススペクトルマトリックスＳ _ａａの最良推定を行い、この最適解によってもたらされるＦｒｏｂｅｎｉｕｓ ノルムを用いて適応度を評価する。
（５）（３）〜（４）をモデル音源の数を増やしながら繰り返す。
（６）適応度が、十分な適応度に達するか、あるいは飽和するかを観測し、モデル音源の数、また、最良の適応度を示す空間位置をもって音源位置を推定する。また、応用によっては、（２）の伝達関数マトリックスを変更して再度、音源探査を実行することで、重要な情報を得る場合もあるものと思われる。
【００６４】
【実施例】
上記音源探査装置の実行例として、無響室においてラウドスピーカを音源として、５つのマイクロホンにより構成されるマイクロホンアレイで空間をサンプルし、音源探査を実行した簡単な例を示す。音源位置推定の軌跡を世代ごとにプロットしたものを図７に示す。実験では、ラウドスピーカ１，２，３がランダムノイズで駆動されており、図７はラウドスピーカ１についての探査結果である。サンプリング周波数４８ＫＨｚ、平均加算数３２回で、ＦＦＴ処理を施し、１ＫＨｚオクターブバンドの周波数成分に対して、クロススペクトルマトリックスＳ_ａａの最良推定を行っている。また、モデル音源は、ポイントモノポールを仮定し、仮想生物の個体数は５０、モデル音源を位置させるメッシュは初期値を１０×１０からスタートさせ、適応度によりメッシュ間隔をつめて実行するように設定した。ＧＡの各種パラメータにも依存するが、この簡単な設定では、ほぼ１００回程度の世代交代で現実の音源位置をほぼ正確に推定可能であった。
【００６５】
【発明の効果】
以上説明したように、本発明の信号源探査方法及び装置によれば、センサアレイによってサンプリングした信号からクロスパワースペクトルマトリックスＳ _ｙｙと、信号源位置を仮定することによって理論的に算出されるモデルクロスパワースペクトルマトリックスＳ _ｙｙ′との差を示す誤差マトリックスＥに基づいて、仮定した信号源の数及び信号源位置の適応度を評価し、これに基づいて信号源位置及び特性を探査するようにしたため、センサアレイを予想される信号源の位置に配置することなく、信号源の位置及び特性を検出することができるようになる。
【図面の簡単な説明】
【図１】図１は音源探査装置の一実施例を示した構成図である。
【図２】図２はマイクロホン１０Ａ、１０Ｂ、１０Ｃ、１０Ｄの配置を示した図である。
【図３】図３は可能なモデル音源の組み合わせ（変数ｘ）に対して、評価関数の形状を示した図である。
【図４】図４は遺伝子アルゴリズムを用いた音源探査アルゴリズムを説明したフローチャートである。
【図５】図５はモデル音源を遺伝子として表現したビットコードの一例を示した図である。
【図６】図６はモデル音源、マイクロホン及び伝達関数の関係を説明した図である。
【図７】図７は音源探査装置を実行結果を示した図である。
【符号の説明】
１０…マイクロホンアレイ
１２…サンプリング部
１４…ＦＦＴ演算部
１６…音源探査演算部
１８…結果表示部[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a signal source searching method and apparatus, and more particularly to a signal source for detecting a signal output from a signal source such as a noise source or a vibration source with a plurality of sensors, and searching the position and characteristics of the signal source from the detection result. The present invention relates to an exploration method and apparatus.
[0002]
[Prior art]
Estimating the characteristics of a sound source from a result of a field measurement and searching for a sound source position provide important information in a wide range of applications in the acoustic field. It is obvious that identification and exploration of sound sources is important in noise control, but it is also important in building acoustics and sound field control. In particular, in recent acoustic technology, the border from measurement to control is disappearing, and accurate understanding of the characteristics and spatial position of the sound source is an essential condition for efficient realization of continuous advanced control. Often.
[0003]
Conventionally, when detecting characteristics of generated vibration of a signal source such as a sound source, a sensor such as a microphone or a vibration pickup is installed near the signal source.
[0004]
[Problems to be solved by the invention]
However, when the position of the signal source cannot be specified, when there are a plurality of signal sources, or when the position of the signal source changes with time, the sensor is moved to various places by the conventional exploration method. In addition, there is a problem that it takes a lot of time and money to install many sansa in various places. Further, some signal sources do not allow a sensor to be mounted in the vicinity thereof, and in some cases, it is impossible to specify the characteristics and position of the signal source.
[0005]
The present invention has been made in view of such a problem, and provides a signal source searching method and apparatus capable of detecting the position and characteristics of a signal source without disposing a sensor at a position of an expected signal source. The purpose is to do.
[0006]
[Means for solving the problem]
The present invention provides a sensor array which is provided at a predetermined interval in advance and samples signals propagated from a signal source, and calculates a cross power spectrum matrix S _yy from a plurality of observation signals sampled by the sensor array. The arithmetic means and the number of the signal sources are assumed, and a region to be searched by the signal source is subdivided, and a position indicating each divided region is set as a signal source position, and a signal of each of the assumed signal sources is set. A second calculating means for assuming a source position and calculating a transfer function matrix H from the signal source at the assumed signal source position to the sensor array by actual measurement or simulation, and a cross power spectrum calculated by the first calculating means a matrix S _yy, based on the transfer function matrix H calculated by the second arithmetic means, Shin Source of strength following equation cross spectrum matrix S _aa of
^{_{S aa = [[H H H}} ] -1 H H] S yy [[H H H] -1 H H] H
And a model cross power spectrum matrix S _yy ′ is calculated based on the calculated cross spectrum matrix S _aa and the transfer function matrix H by the following equation:
S _yy ′ = H S _aa H ^H
And an error matrix E indicating a difference between the cross power spectrum matrix S _yy and the model cross power spectrum matrix S _yy ′, and an error matrix E calculated by the third arithmetic means. A fourth calculating means for calculating the fitness of the assumed number of signal sources and the signal source position based on the error matrix E; and changing the combination of the assumed number of signal sources and the signal source position by changing the fourth number. And exploring means for estimating the number of signal sources and the signal source position by the number of signal sources and the position of the signal source when the best fitness is obtained from these fitness values. , Characterized by comprising.
[0007]
According to the present invention, sampled by a pre arranged at a predetermined interval the sensor array signals propagating from the signal source, calculates the cross power spectrum matrix S _yy from the observed signal sampling. Then, while assuming the number of signal sources, the area to be searched for the signal source is subdivided, and the position indicating each divided area is set as the signal source position, and the assumed signal source position of each signal source is assumed. The transfer function matrix H from the signal source at the assumed signal source position to the sensor array is obtained by actual measurement or simulation. Next, based on the cross power spectrum matrix S _yy calculated in this way and the transfer function matrix H , a model calculated from the cross power spectrum matrix S _yy , the transfer function matrix H and the cross power spectrum matrix S _yy An error matrix E indicating a difference from the cross power spectrum matrix S _yy ′ is calculated, and based on this, the assumed number of signal sources and the fitness of the signal source position are calculated. The above process is repeated by changing the combination of the number of signal sources and the position of the signal source assuming the above processing, and by the number of signal sources and the position of the signal source when the best fitness is obtained from the fitness obtained by this repetition. , The number of signal sources and the source position. Thus, the position and characteristics of the signal source can be detected without disposing the sensor at the expected position of the signal source.
[0008]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, preferred embodiments of a signal source searching method and apparatus according to the present invention will be described in detail with reference to the accompanying drawings.
In the following embodiments, a method and an apparatus for searching for a signal source in the case where the signal source to be searched is a sound source will be described. However, the present invention is not limited to this, and the present invention is not limited to this. The present invention can be applied to any signal source whose characteristics can be analyzed. Hereinafter, a sound source searching method and apparatus when a signal source is used as a sound source will be described in detail.
[0009]
The sound source detection device of this embodiment observes sound with a plurality of microphones (microphone arrays) arranged at predetermined positions, and analyzes various characteristics including spatial information of a sound source present in a sound field from observation signals observed by these microphones. It is a device to do. First, the configuration will be described.
FIG. 1 is a configuration diagram showing an embodiment of a sound source detection device.
[0010]
As shown in FIG. 1, the sound source detection device includes microphones 10A, 10B, 10C, and 10D (hereinafter, these microphones are collectively referred to as a microphone array), a sampling unit 12, an FFT operation unit 14, a sound source. It comprises a search operation unit 16 and a result display unit 18.
The microphones 10 </ b> A to 10 </ b> D are installed in a sound field in a predetermined arrangement, detect sound propagating in the sound field, convert the detected sound into an electric signal as a detection signal, and output the signal to the sampling unit 12. The microphones 10A to 10D are arranged such that the microphones 10B, 10C, and 10D are mounted on support rods extending in the x, y, and z directions with respect to the microphone 10A, as shown in FIG. These microphones are arranged at an interval equal to or less than half the wavelength of the signal to be detected. Further, in this embodiment, four microphones are used, but the number of microphones does not need to be particularly four.
[0011]
The detection signals output from the microphones 10A to 10D are sampled by the sampling unit 12 at a predetermined sampling cycle, and output to the FFT operation unit 14. The sampled detection signal is Fourier-transformed by the FFT operation unit 14 and output to the sound source search operation unit 16 as a frequency spectrum.
The sound source search calculation unit 16 calculates the position of the sound source and the intensity of the sound source (frequency spectrum of the generated sound) from the frequency spectrum of the detection signal detected by each microphone, and displays these results in the result display unit 18. Output to
[0012]
Next, the processing performed by the sound source search calculation unit 16 will be described in detail.
In calculating the position of the sound source and the strength of the sound source from the frequency spectrum of the sound detected by the microphone array as described above, the problem is first divided into two major steps. In the first step, a sound field model in which a plurality of discrete sound sources exist in the measured sound field is considered, and the number of sound sources and their positions in space are arbitrarily given. Next, the strength of each model sound source that optimally approximates the measured microphone array output is determined by an optimization technique. This problem is generally regarded as an inverse problem by nonlinear least-squares approximation. By introducing an appropriate norm, the problem is formulated as a linear least-squares problem, and an optimal solution to the inverse problem is given. At this stage, since the model error with respect to the assumed number and positions of the sound sources can be evaluated using the optimal solution of the inverse problem, this is adopted as the evaluation function. Therefore, in the next step, the number and the position of the model sound source are searched by the genetic algorithm (Genetic Algorithm; GA) using the above evaluation function as the fitness of the biological population. Therefore, the sound source identification and search method according to the present invention can be regarded as one hybrid solution to the inverse problem of sound field estimation, which combines the solution of the multi-channel linear least squares problem and the solution of the search problem of the genetic algorithm. .
[0013]
Therefore, a procedure for calculating the position of the sound source and the strength of the sound source will be described below, while sequentially explaining the theoretical background of the solution of the multi-channel linear least squares problem and the solution of the search problem of the genetic algorithm.
This theory assumes that the sound source in the sound field is a plurality of discrete sound sources, expressed as the source strength of the distributed sound source. In general, it should be assumed that the sources are correlated with each other. By the way, in the actual analysis and application, it is often necessary to know the auto spectrum and cross spectrum information of the sound source. Therefore, all the analysis is performed in the frequency domain. Therefore, consider the problem of estimating the cross spectrum between all sound sources. In the following description, for convenience, the number of sound sources is two, and the number of microphones in a microphone array is three. Finally, a general expression is given so that this does not lose generality. The Fourier transform of the time history of the intensity of the sound source can be expressed as a complex vector as follows.
[0014]
(Equation 1)

[0015]
The Fourier transform is defined as follows for finite-length data.
[0016]
(Equation 2)

[0017]
Therefore, attention is paid to a cross spectrum matrix defined by the following equation.
[0018]
(Equation 3)

[0019]
Here, H represents the conjugate transport, and E ｛｝ represents the expected value operator (strictly, this operator represents the process of estimating the cross spectrum by ensemble averaging of data records).
Therefore,
[0020]
(Equation 4)

[0021]
S _aa is represented as a cross power spectrum matrix again as follows.
[0022]
(Equation 5)

[0023]
Here, the cross power spectrum of each element is, for example,
(Equation 6)

[0025]
And
The problem is to optimally estimate the above-mentioned matrix S _aa from the temporal history of sound pressure observed at the position of the microphone array installed in the sound field.
Both the microphone output and each output are represented by the following complex vector using the Fourier transform.
[0026]
(Equation 7)

[0027]
The corresponding cross power spectrum matrix S _yy is given by:
[0028]
(Equation 8)

[0029]
Therefore, this can also be easily expressed as follows.
[0030]
(Equation 9)

[0031]
In this analysis, a transfer function matrix from the model sound source to the model microphone is assumed, and the analysis model is a linear system that satisfies the following relationship (see FIG. 6). That is,
[0032]
(Equation 10)

[0033]
For example, in the case of a point monopole sound source model, the transfer function H ₁₂ (ω) represents a transfer function between the sound source 2 and the microphone 1 and can be easily expressed as the following equation.
[0034]
(Equation 11)

[0035]
Here, r ₁₂ is the distance between the sound source 2 and the microphone 1, ρ _o is the density of air, and κ is the wave number. From the above discussion, it is obvious that the sound source model may be a point dipole (dipole) or a point quadrupole (quadrupole), or any form in which these are distributed. Further, the transfer function from the model sound source to the model microphone may be derived from foresight information or may be an actually measured value. In particular, transfer functions obtained by simulation techniques based on integral equations are considered to be very useful. Therefore, the relationship of equation (10) is compactly written as follows.
[0036]
(Equation 12)

[0037]
Accordingly, the model sound source presents the following cross power spectrum matrix S _yy ′ at the microphone position.
[0038]
(Equation 13)

[0039]
Therefore, our optimization problem is to find the best sound source intensity vector a in the sense of giving the model cross power spectrum matrix S _yy ′ that is closest to the actually measured cross power spectrum matrix S _yy. Will be returned. Therefore, next, an optimal solution for minimizing the Frobenius norm for the error matrix is considered. First, the error matrix,
[0040]
[Equation 14]

[0041]
E = S _yy - S _yy '
Is defined. By expanding the above equation, the following equation is obtained.
[0042]
(Equation 15)

[0043]
On the other hand, the Frobenius norm of the error matrix is defined by the following equation.
[0044]
(Equation 16)

[0045]
Strictly speaking, the square root is used, but here, the above equation is used to define the Frobenius norm. Accordingly, the Frobenius norm is expressed as follows from Expression (15).
[0046]
[Equation 17]

[0047]
It can be seen that the sound source intensity vector a or the cross spectrum matrix S _aa that minimizes the Frobenius norm minimizes the sum of squares of the difference between the actually measured cross power spectrum and the model cross power spectrum. Therefore, this Frobenius norm norm is considered suitable for our purpose.
Anciant ⁽¹⁾ and others study the solution of a general nonlinear least-squares problem together with its numerical calculation method. The optimum solution of the Frobenius norm criterion for the above problem is given by the following equation.
[0048]
(Equation 18)

[0049]
Equation (18) is a solution to be found, and shows that by assuming a model for H , the best estimation of the cross-spectral matrix S _aa of the intensity of the sound source can be calculated using the measured value S _yy .
Also, given the solution of the cross spectrum matrix S _aa , the model cross power spectrum matrix S _yy ′ is given by the following equation:
[Equation 19]

[0051]
By substituting equation (19) into equation (14), the Frobenius norm at this time can be calculated. The Frobenius norm is given by the following equation with respect to the solution of the cross spectrum matrix S _aa .
[0052]
(Equation 20)

[0053]
From the above theoretical background, it is possible to calculate the cross spectrum matrix S _aa that minimizes the error (Frobenius norm) at the assumed model sound source position. That is, it is possible to obtain the intensity of the sound source of each frequency component that most adapts to the measured value among the model sound sources of the assumed number and positions.
The error (Frobenius norm) when the optimal solution cross-spectral matrix S _aa is indicates the degree of adaptation to the assumed model tone the actual sound sources, it can be said that a high fitness as the error is small. In other words, it can be said that a model sound source having a higher degree of matching reproduces an actual sound source.
[0054]
Therefore, hereinafter, this fitness is specifically expressed by the reciprocal of the error, and the quality of the assumed model sound source is evaluated. Hereinafter, the reciprocal of the error is referred to as “Fitness”. The method of expressing the fitness is not limited to this.
In the above description, the error was evaluated using the Frobenius norm, but there are various methods for evaluating the error, and the method is not limited to this.
[0055]
In the above description, the signal output from the sound source is described as a single frequency. However, when the signal output from the sound source has a certain frequency band, the above error is obtained for each frequency component, and for example, the sum of these errors is calculated. Alternatively, a logarithm of the sum of these errors is evaluated as a total error. However, in this case, the error may be evaluated as described above by focusing on a certain frequency, and the position of the sound source may be searched based on the error.
[0056]
Next, a method of assuming a model sound source will be described.
In the above, the best estimation of the cross-spectral matrix S _aa of the intensity of the sound source for a given number and position of model sound sources has been discussed. However, in order to estimate the number and position of the model sound sources, some sound source position search algorithm is required. For example, a sound source position is given as a point on a mesh in a three-dimensional space, and all combinations can be evaluated in combination with the number of model sound sources. However, it may be practically difficult. For example, targeting only the 32-point space, even in the case of eight very small exploration model sound source is assumed, the combination becomes 10 ⁷ order. Therefore, in the present embodiment, the genetic algorithm is applied to sound source search. Hereinafter, the genetic algorithm will be described.
[0057]
As shown in FIG. 3, the search problem here is characterized in that the evaluation function has a complicated shape for a possible combination of model sound sources (variable x), and the entire image is not known. Further, in the Possible order also practical applications of variable x, for about 1000bit is required, the search point becomes approximately 10 ^300, solution by full search is practically impossible, so-called NP-complete problems . Genetic algorithms (GA) are considered to be effective as a search algorithm for efficiently searching a search space and quickly finding a practical optimum solution, and are currently being used in various engineering applications. In GA, the search problem is solved by a method that mimics the evolutionary process of living things. Further, in the GA, a plurality of search points are simultaneously used instead of searching for search points in a search space one by one in order. Also, each search point is regarded as a virtual creature having a gene. For each individual, the fitness for each environment is calculated. In this embodiment, the fitness is evaluated using the above-mentioned Frobenius norm. Evolution is carried out by generational alteration simulations in which individuals with low fitness are eliminated by selection (selection), individuals with high fitness are multiplied, and individuals of offspring having genes that inherit the characteristics of the parent are generated. That is, a better search proceeds.
In alternation of generation, operations called crossover and mutation are performed.
[0058]
FIG. 4 is a flowchart illustrating a sound source search algorithm using a genetic algorithm.
First, an initial generation individual and a chromosome are determined (step S10). A chromosome is composed of a plurality of genes. In addition, the position of each gene is defined by a kind of coordinates called a locus. The internal representation of the chromosome of an individual individual is referred to as genotype. When applied to the sound source search algorithm of this embodiment, the number of search points (the number of points on the mesh) in the sound field is used as the number of genes, and these search points are arranged in a predetermined array to form a chromosome. At each search point, the gene when the model sound source is present is 1 and the gene when the model sound source is not present is 0, and one arrangement form of the model sound source is represented by a bit code as one individual as shown in FIG. That is, each bit is made to correspond to each point on the mesh of the sound field, and the bit assumed to be a model sound source is set to 1.
[0059]
When determining the individuals of the initial generation, first, the number of individuals and the number of model sound sources in one individual are determined. In the following description, it is assumed that the number of individuals is 40 and the number of model sound sources in one individual is 4. After determining the number of individuals and the number of model sound sources, the position where the model sound sources are arranged is determined at random to generate individuals of the initial generation.
Next, the Fitness of each of the forty individuals generated as described above is calculated (step S12). Then, out of the forty individuals, the remaining individuals are selected (selection and multiplication) so that the total fitness becomes 20 in total, together with the individual having the highest Fitness (step S14). When selecting the remaining individuals, individuals having larger Fitness are selected with higher probability.
[0060]
Next, two individuals are randomly extracted from the twenty individuals selected by selection and multiplication and combined to form a set of ten individuals. Then, the genes are recombined for each pair, and two individuals are newly proliferated (intersection of the genes) (step S16). That is, 20 new individuals are generated by crossing genes from individuals selected by selection and propagation, and a total of 40 individuals are generated. When crossing genes, the bit from which to cross is determined at random.
[0061]
Next, mutations are generated in the 20 individuals that have proliferated as described above (step 18). Mutation is an operation in which the position of a sound source is changed at a certain probability without changing the number of sound sources, and is generated, for example, at a probability of 0.02%.
The individuals of the new generation are generated as described above, and the Fitness is calculated for the generated 20 individuals (step S20). Then, an individual having the largest Fitness is searched from among the forty individuals, and it is determined whether or not the value is equal to or greater than a predetermined threshold (step S22). This threshold value indicates a Fitness value that is empirically determined that the model sound source (individual) assumed to the actual sound source is sufficiently adapted. If the maximum value of Fitness is equal to or larger than the threshold, the above processing is terminated, and the position of the model sound source of the individual is set as the actual position of the sound source.
[0062]
Conversely, if the maximum value of Fitness is smaller than the threshold, the process returns to step S14, and the above processing is repeated.
As described above, individuals whose Fitness exceeds a predetermined threshold are detected by using the genetic algorithm, and the actual position of the sound source is searched. However, if the number of model sound sources assumed above is smaller than the actual number of sound sources, it is not possible to detect individuals whose Fitness exceeds the threshold value even if the above processing is repeated. If it is not possible to detect an individual exceeding the threshold, the same processing is performed by increasing the number of model sound sources.
[0063]
As described above, the sound source search algorithm described above is basically summarized as follows.
(1) In a field to be searched for a sound source, a sound field is sampled using a microphone array to obtain a matrix S _yy .
(2) Set a transfer function matrix H from the model sound source to the model microphone. Usually, it is constructed using simulation or actual measurement data (such as impulse response) from a priori information of a sound source.
(3) Set the number of model sound sources.
(4) For a given number of model sound sources, a sound source position is searched using a genetic algorithm. At this time, the best estimation of the cross-spectral matrix S _aa of the intensity of the sound source based on the Frobenius norm is performed, and the fitness is evaluated using the Frobenius norm obtained by this optimal solution.
(5) Repeat (3) to (4) while increasing the number of model sound sources.
(6) Observe whether the fitness reaches a sufficient fitness or saturate, and estimate the sound source position based on the number of model sound sources and the spatial position showing the best fitness. Depending on the application, it is considered that important information may be obtained by changing the transfer function matrix of (2) and executing the sound source search again.
[0064]
【Example】
As an execution example of the sound source searching device, a simple example in which a loudspeaker is used as a sound source in a anechoic room, a space is sampled by a microphone array composed of five microphones, and a sound source search is executed. FIG. 7 shows a locus of sound source position estimation plotted for each generation. In the experiment, the loudspeakers 1, 2, and 3 were driven by random noise, and FIG. 7 shows a search result for the loudspeaker 1. FFT processing is performed at a sampling frequency of 48 KHz and an average number of additions of 32, and the best estimation of the cross spectrum matrix S _aa is performed for the frequency component of the 1 KHz octave band. Also, assuming that the model sound source is a point monopole, the number of virtual creatures is 50, the mesh for locating the model sound source is started from an initial value of 10 × 10, and the mesh interval is reduced according to the fitness and executed. Set. Although it depends on various parameters of the GA, with this simple setting, the actual sound source position can be estimated almost exactly in about 100 generation changes.
[0065]
【The invention's effect】
As described above, according to the signal source searching method and apparatus of the present invention, the cross power spectrum matrix S _yy and the model cross calculated theoretically by assuming the signal source position from the signal sampled by the sensor array are used. Based on the error matrix E indicating the difference from the power spectrum matrix S _yy ′, the number of assumed signal sources and the fitness of the signal source position are evaluated, and based on this, the signal source position and characteristics are searched. , The position and characteristics of the signal source can be detected without placing the sensor array at the expected signal source position.
[Brief description of the drawings]
FIG. 1 is a configuration diagram showing an embodiment of a sound source detection device.
FIG. 2 is a diagram showing an arrangement of microphones 10A, 10B, 10C, and 10D.
FIG. 3 is a diagram showing the shape of an evaluation function for a possible combination of model sound sources (variable x).
FIG. 4 is a flowchart illustrating a sound source search algorithm using a genetic algorithm.
FIG. 5 is a diagram showing an example of a bit code expressing a model sound source as a gene.
FIG. 6 is a diagram illustrating the relationship between a model sound source, a microphone, and a transfer function.
FIG. 7 is a diagram showing an execution result of the sound source detection device.
[Explanation of symbols]
Reference Signs List 10 microphone array 12 sampling unit 14 FFT calculation unit 16 sound source search calculation unit 18 result display unit

Claims (4)

A first step of sampling a signal propagating from a signal source at a predetermined interval in advance by a sensor array and calculating a cross power spectrum matrix S _yy from the sampled observation signal;
While assuming the number of the signal sources, the area to be searched by the signal source is subdivided, and the position indicating each divided area is set as the signal source position, and the assumed signal source position of each signal source is assumed. A second step of:
A third step of determining a transfer function matrix H from the signal source at the assumed signal source position to the sensor array by actual measurement or simulation;
Based on the cross power spectrum matrix S _yy calculated in the first step and the transfer function matrix H calculated in the third step, the cross spectrum matrix S _aa of the signal source strength is expressed by the following equation:
^{_{S aa = [[H H H}} ] -1 H H] S yy [[H H H] -1 H H] H
And a model cross power spectrum matrix S _yy ′ is calculated based on the calculated cross spectrum matrix S _aa and the transfer function matrix H by the following equation:
S _yy ′ = H S _aa H ^H
And a fourth step of calculating an error matrix E indicating a difference between the cross power spectrum matrix S _yy and the model cross power spectrum matrix S _yy ′.
A fifth step of calculating the fitness of the assumed number of signal sources and the signal source position based on the error matrix E calculated by the fourth step means;
In the second step, the combination of the assumed number of signal sources and the position of the signal source is changed to repeat the second to fifth steps, and the best adaptation is obtained from the fitness obtained by the repetition. A sixth step of estimating the number of signal sources and the position of the signal source by the number of signal sources and the position of the signal source when the degree is obtained;
A signal source searching method characterized by comprising: In the sixth step, one of the assumed combination of the number of signal sources and the position of the signal source is regarded as one individual, a plurality of preset individuals are created, and the fitness obtained corresponding to each individual is determined. By using a genetic algorithm on the basis of which the next generation is alternated until sufficient fitness is obtained or the fitness is saturated, and performing this operation with a different number of signal sources, the number of signal sources and the number of signal sources 2. The method according to claim 1, wherein the position is searched. A sensor array which is arranged at a predetermined interval in advance and samples a signal propagated from a signal source,
First calculating means for calculating a cross power spectrum matrix S _yy from a plurality of observation signals sampled by the sensor array;
While assuming the number of the signal sources, the area to be searched by the signal source is subdivided, and the position indicating each divided area is set as the signal source position, and the assumed signal source position of each signal source is assumed. A second calculating means for obtaining a transfer function matrix H from the signal source at the assumed signal source position to the sensor array by actual measurement or simulation;
On the basis of the cross power spectrum matrix S _yy calculated by the first calculation means and the transfer function matrix H calculated by the second calculation means, a cross spectrum matrix S _aa of the strength of the signal source is expressed by the following equation:
^{_{S aa = [[H H H}} ] -1 H H] S yy [[H H H] -1 H H] H
And a model cross power spectrum matrix S _yy ′ is calculated based on the calculated cross spectrum matrix S _aa and the transfer function matrix H by the following equation:
S _yy ′ = H S _aa H ^H
A third calculating means for calculating an error matrix E indicating the difference between the cross power spectrum matrix S _yy and the model cross power spectrum matrix S _yy ′.
Fourth calculating means for calculating the assumed number of signal sources and the fitness of the signal source position based on the error matrix E calculated by the third calculating means;
The combination of the assumed number of signal sources and the position of the signal source is changed to obtain fitness values from the fourth calculating means, respectively, and the number of signal sources when the best fitness value is obtained from these fitness values. Exploration means for estimating the number of signal sources and the position of the signal source, and
A signal source searching device, comprising: 4. The signal source search device according to claim 3, wherein the sensor array includes sensors arranged at an interval of one half or less of a wavelength of a signal to be observed by the signal source.

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