JP4582680B2 - Coefficient calculation support device, coefficient calculation device, program for realizing the coefficient calculation support device or coefficient calculation device, and recording medium storing the program - Google Patents

Description

ところで、上記の不等式(7) は、その不等式(7) に含まれる係数ベクトルｈ^ が時系列ｋにおいて先行して適応フィルタ５２に係数として与えられた係数ベクトルｈ^_kに等しい場合には、下記の不等式(10)で代替される。
【００４３】
gι(ｈ^_k)≦０ ・・・(10)
さらに、上述した距離射影ＰＨι^-(ｈ^) が時系列ｋに後続する時系列(ｋ＋１)において適応フィルタ５２に係数として与えられるべき係数ベクトルｈ^_k+1に該当する場合には、上式(8)、(9)はそれぞれ下記の漸化式(11)、(12)に変形可能である。
【数２】

係数更新部３１は、適応フィルタ５２の係数が更新されるべき所定の周期（時系列ｋの昇順に与えられる。）で下記の処理(1)〜(4)を反復する。
(1) 係数ベクトルｈ^_k（始動時には所定の初期値として与えられる。）に応じて上式(5) で示される算術演算を行うことによって、凸関数gι(ｈ^_k) の値を求める（図５(1))。
【００４４】
(2) その値に基づいて上記の不等式(10)が成立するか否かの判別を行う（図５(2 ))。
(3) この判別の結果が真である場合には、「先行して求められた係数ベクトルｈ ^_kがベクトル空間上において既述の閉半空間に位置すること」を意味するので、上式(11)に基づいてその係数ベクトルｈ^_kを何ら更新することなく後続して適応フィルタ５２に与えられるべき係数を示す係数ベクトルｈ^_k+1として確定する（図５(3))。
【００４５】
(4) しかし、上述した判別の結果が偽である場合には、「先行して求められた係数ベクトルｈ^_kがベクトル空間上において既述の閉半空間に位置しないこと」を意味するので、下記の一連の処理を行う。
・ 上式(5) に示す算術演算を行うことによって、必要に応じて係数ベクトルｈ ^_kに対する凸関数gι(ｈ^_k)の値を算出する（図５(4))。
【００４６】
・ 上式(6) に示す算術演算を行うことによって、係数ベクトルｈ^_kに対する法線ベクトルsι(ｈ^_k)を算出する（図５(5))。
・ 上式(12)に示す算術演算を行うことによって、後続して適応フィルタ５２に与えられるべき係数を示す係数ベクトルｈ^_k+1を算出する（図５(6))。
・ その係数ベクトルｈ^_k+1で示される新たな係数を適応フィルタ５２に与える（図５(7))。
【００４７】
すなわち、既述の線形多様体Ｖ_k に代えて、その線形多様体Ｖ_k を内包する実行可能集合Ｃ_k(ρ) が適用され、かつこのような係数ベクトルｈ^_k+1は、 ベクトル空間上においてこの実行可能集合Ｃ_k(ρ) と、先行して得られた係数ベクトルｈ^_kとの間に介在する分離超平面に対するその係数ベクトルｈ^_kの距離射影として順次更新される。
【００４８】
このように本実施形態によれば、出力信号に含まれる雑音のレベルが大きい場合であっても、係数ベクトルｈ^_kは、既述の数ρがその雑音の統計的な性質に整合する値に設定される限り、線形連立方程式の解法が行われることなく時系列ｋの順に精度よくかつ速やかに求められ、さらに、無用に変動することなく好適な値に収束する。
【００４９】
図６は、本発明の第二および第三の実施形態を示す図である。
図において、図３に示す実施形態との構成の主要な相違点は、係数更新部３１に代えて係数更新部４０が備えられた点にある。
係数更新部４０は、下記の要素から構成される。
・ 未知系５１および適応フィルタ５２の入力と共に、既述の入力信号ｕ_k が与えられるｑ(≧２)段のシフトレジスタ４１
・ 入力に未知系５１の出力が直結されたｑ(≧２)段のシフトレジスタ４２
・ 一方の入力に上述した入力信号ｕ_k が与えられ、かつ他方の入力が未知系５１の出力に直結された分散演算部４３-0
・ シフトレジスタ４１、４２の初段ないし第ｑ(≧２)段の出力にそれぞれ直結された２つの入力を有する分散演算部４３-1〜４３-q
・ これらの分散演算部４３-0〜４３-qの出力にそれぞれ直結された(ｑ＋１) 個の入力を有し、かつ出力が適応フィルタ５２の係数入力に直結された係数算出部４４
以下、図６を参照して本発明の第二の実施形態の動作を説明する。
【００５０】
シフトレジスタ４１は、既述の入力信号ｕ_kに所定の周期の整数ｉ(１≦ｉ≦ｑ）倍の時間に亘る遅延を時系列ｋの順に与えることによって、ｑ個の入力信号ｕ_kiを並行して出力する。
シフトレジスタ４２は、既述の未知系出力信号ｄ_k に所定の周期の整数ｉ（１≦ｉ≦ｑ）倍の時間に亘る遅延を時系列ｋの順に与えることによって、ｑ個の未知系出力信号ｄ_kiを並行して出力する。
【００５１】
なお、以下では、分散演算部４３-0〜４３-qに共通の事項については、添え番号「０」〜「ｑ」に代えて、これらの添え番号「０」〜「ｑ」の何れにも該当し得ることを示す添え文字「ｉ」を用いて記述する。
また、シフトレジスタ４１、４２の入力端にそれぞれ与えられる入力信号および未知系出力信号については、以下では、上述した整数ｉの値が「０」であることを前提してそれぞれ入力信号Ｕ_kiおよび未知系出力信号ｄ_kiと表記する。
【００５２】
分散演算部４３-iは、上述した入力信号ｕ_kiおよび未知系出力信号ｄ_kiとに応じて既述の第一の実施形態に備えられた係数更新部３１によって行われる演算と同じ演算を並行して行うことによって、添え文字「ｉ」が末尾に付加された係数ベクトルｈ^_ki を時系列の順に並行して求める。
係数算出部４４は、このようにして並行して求められた係数ベクトルｈ^_k0 〜ｈ^_kq と、先行して適応フィルタ５２に係数として与えられた係数ベクトルｈ^_kと、総和が「１」である（ｑ＋１）個の重みｗ₀〜ｗ_qと、規定の緩和係数μ_k(ここでは、簡単のため、「０」以上であり、かつ「２」以下である定数に予め設定されると仮定する。）とに対して下記の漸化式(13)で示される算術演算を行うことによって、その係数ベクトルｈ^_kを更新する。
【数３】

さらに、係数算出部４４は、このように更新された最新の係数ベクトルｈ^_k+1で示される係数を適応フィルタ５２に設定する。
すなわち、「ベクトル空間上において好適な係数ベクトルｈ^^* _k を含む実行可能集合Ｃ_ki(ρ)と、先行して求められた係数ベクトルｈ^_kとの間に介在する分離超平面」に対する係数ベクトルｈ^_ki の距離射影が分散演算部４３-0〜４３-qによって並行して求められ、かつ係数ベクトルｈ^_kはこれらの距離射影の重み付きベクトル和の誤差の単調な減少を図る適応アルゴリズムに基づいて順次更新される。
【００５３】
したがって、本実施形態によれば、「ベクトル空間上において単一の実行可能集合Ｃ_k(ρ) と、先行して求められた係数ベクトルｈ^_kとの間に介在する分離超平面」に対するこの係数ベクトルｈ^_kの距離射影として、その係数ベクトルｈ^_kが順次更新される既述の第一の実施形態に比べて、好適な係数ベクトルｈ^^* _k に対する収束の確度と速度とが平均的に高められる。
【００５４】
したがって、本実施形態にかかわるシステム同定系では、例えば、既述の値ρが大きい場合には、始動時における係数ベクトルｈ^_kの収束に時間を要する（図７(a)(1)) が、その値ρが適正な値に設定される限り、既述の好適な係数ベクトルｈ^^* _k に対する相対的な誤差（同定誤差）は、入力信号の相関性と値ｒとの如何にかかわらず、未知系５１で入力信号に重畳される雑音のレベルが大きい場合であっても、第一および第二の従来例に比べて大幅に改善され（図７(a)(2)、(3)、(b)(1)〜(3)、図８(a)(1)〜(3)、(b)(1)〜(3))、かつ応答性が高められる。
【００５５】
なお、本実施形態では、重みｗ₀〜ｗ_qの値が具体的に示されていないが、これらの重みｗ₀〜ｗ_qの値は、例えば、下記の何れの値に設定されてもよい。
・ 共通の値(＝１／(ｑ＋１))…未知系５１の伝送特性や出力信号に含まれる雑音のレベルの変動に起因する精度や応答性の低下が許容される場合には好適である。
【００５６】
・ 下記の不等式で示されるように時系列の降順に小さな値…未知系５１の伝送特性の変化に起因する精度や応答性の低下が軽減されるべき場合に好適である。
ｗ₀≧ｗ₁≧…≧ｗ_q ・・・(14)
・ 出力信号に含まれる雑音のレベル（例えば、既述の式(2) に基づいて分算演算部４３-iによって個別に求められた誤差ベクトルｅ^_ki の絶対値）の降順に大きな値…雑音のレベルの変動に起因する精度や応答性の低下が軽減されるべき場合に好適である。
【００５７】
以下、図６を参照して本発明の第三の実施形態について説明する。
本実施形態と既述の第二の実施形態との構成の相違点は、図６に点線で示すように、係数算出部４４の出力が分散演算部４３-0〜４３-qの対応する入力に接続された点にある。
以下、本実施形態の動作を説明する。
【００５８】
本実施形態の特徴は、既述の緩和係数μ_k が下記の手順に基づいて適宜更新される点にある。
分散演算部４３-iは、ベクトル空間において既述の実行可能集合Ｃ_ki(ρ)を内包し、かつ先行して係数算出部４４によって適応フィルタ５２に係数として与えられた係数ベクトルｈ^_kが含まれない仮想的な集合（以下、「包含凸集合」という。）Ｓ_kiを適宜特定し、かつ係数算出部４４にその包含凸集合Ｓ_kiを通知する。
【００５９】
係数算出部４４は、このようにして通知された(ｑ＋１)個の包含凸集合Ｓ_k0〜Ｓ_kqの何れにも、適応フィルタ５２に先行して係数として与えられた係数ベクトルｈ^_kが含まれないか否かの判別を行う。
また、係数算出部４４は、その判別の結果に応じて下式(15)で示される変数Ｍ_k の値を求める。
【数４】

上述した判別の結果が真である場合における上式(15)の分子は、「先行して求められた係数ベクトルｈ^_kに対する既述の距離射影ｈ^_k0〜ｈ^_kq（分散演算部４３-0〜４３-qによって並行して求められる。）の誤差のエネルギーの重み付き総和」に該当し、かつ同式の分母は「その係数ベクトルｈ^_kに対するこれらの距離射影ｈ^_k0〜ｈ^_kqの誤差のエネルギーの加重平均」に該当する。
【００６０】
すなわち、変数Ｍ_k は、既述の「先行して求められた係数ベクトルｈ^_kに対する距離射影ｈ^_k0〜ｈ^_kqの誤差のエネルギーの重み付き総和」に対して単調に増加し、かつ既述の緩和係数μ_k が「２」を上回ることが許容されるべる限度に相当する「１」以上の値となる。
【００６１】
係数算出部４４は、規定の定数ｍ(０≦ｍ≦２)と上述した変数Ｍ_k とに対して下式(16)で示される緩和係数μ_k を求め、その緩和係数μ_k が適用される点を除いて既述の第二の実施形態と同じ演算を行うことによって、係数ベクトルｈ^_kを順次更新する。
μ_k ＝ｍ・Ｍ_k ・・・(16)
したがって、本実施形態によれば、既述の第二の実施形態に比べて精度が低下することなく係数ベクトルｈ^_kが高速に更新される。
【００６２】
なお、本実施形態では、上式(15)に示す算術演算は、既述の係数ベクトルｈ^_kに対する距離射影ｈ^_k0〜ｈ^_kqの分散（偏差の分布）に応じて増加する適正な値として変数Ｍ_k が算出される限り、如何なる算術演算で代替されてもよい。
また、上述した各実施形態では、値ρの値が具体的に示されていない。
このような値ρは、例えば、出力信号に含まれる雑音（ここでは、簡単のため「白色雑音」であると仮定する。）の電力σ² が既知である場合には、図１０に示すχ² 分布の平均ｍξ(＝ｒσ²)、分散σξ²(＝２ｒσ⁴）、極大値ξ(＝(ｒ−２)σ²) に対して、下記の通りに一義的に定まる値ρ₁〜ρ₄の何れに設定されてもよい。
【００６３】
・ ρ₁＝ｍξ＋σξ＝(ｒ＋√２)σ²
・ ρ₂＝ｍξ＝ｒσξ²
・ ρ₃＝max[(ｒ−２)σ²,０]
・ ρ₄＝ρ₃＋ασξ （α＞０）
さらに、上述した各実施形態では、図３および図６に示すシステム同定系に本発明が適用されている。
【００６４】
しかし、本発明は、このようなシステム同定系に限定されず、例えば、下記の多様な装置に適用可能であり、これらの装置の性能および信頼性は、従来例が適用された場合に比べてコストの増加や信頼性の低下を伴うことなく大幅に、かつ確度高く高められる。
【００６５】
・ 伝送路や通信路の伝送特性の変動に高速に、かつ柔軟に適応し、その伝送路や通信路で生じた伝送歪みの影響を抑圧する適応等化器
・ 伝送路や通信路の伝送特性の変動に高速に、かつ柔軟に適応し、その伝送路や通信路で生じたエコーを除去するエコーキャンセラ
・ スピーカからマイクロフォンに至る帰還路を介して音響領域で行われる正帰還に起因するハウリングを回避するハウリングキャンセラ
・ エンジン（車両、航空機、船舶等に搭載される。）、空調装置その他の装置によって発生した騒音を能動的に音響領域で抑圧するアクティブノイズキャンセラ
また、上述した各実施形態では、各部が専用のハードウエアとして構成されている。
【００６６】
しかし、本発明はこのような構成に限定されず、例えば、構成要素の全てが単一のプロセッサやＤＳＰによって実行されるソフトウエア（蓄積論理）として実現され、あるいは構成要素の全てまたは一部が如何なる形態で負荷分散や機能分散が図られてもよい。
さらに、上述した各実施形態では、更新された係数ベクトルｈ^_k+1で示される係数が適応フィルタ５２に直接与えられている。
【００６７】
しかし、本発明はこのような構成に限定されず、例えば、更新された係数ベクトルｈ^_k+1に何らかの付加処理を施すことによって新たな係数を求め、さらにその係数を適応フィルタ５２に与える手段が別途備えられてもよい。
また、本発明は、上述した実施形態に限定されるものではなく、本発明の範囲において、多様な形態による実施形態の実現が可能であり、かつ構成装置の一部もしくは全てに如何なる改良が施されてもよい。
【００６８】
【発明の効果】
上述したように請求項１に記載の発明では、好適なあるいは真の係数ベクトルｈ^^* _kを高い確率で含む凸集合Ｃ_k(ρ) が時系列の順に特定され、その凸集合Ｃ_k(ρ) を包含する包含凸集合に対する距離射影として係数ベクトルｈ^_kが更新されることによって、この係数ベクトルｈ^_kに含まれる誤差の単調性が確度高く保証される。
【００６９】
したがって、ＮＬＭＳ法やアフィン射影法が適用された従来例に比べて、多様な機器やシステムに対する適合が可能となり、かつ安価に応答性と性能との双方が高められる。
また、請求項２および請求項３に記載の発明では、処理量の削減が図られる。
さらに、請求項４に記載の発明では、性能および応答性が向上し、かつ多様な機器やシステムに対する適用が可能となる。
【００７０】
また、請求項５および請求項６に記載の発明では、未知系の特性と、出力信号に含まれる雑音のレベルや性質との何れかが急激に変化し得る場合であっても、ＦＩＲフィルタの濾波特性が安定に好適な特性に維持される。
さらに、請求項７に記載の発明では、ステップサイズが単に「２」以下の定数に設定される場合に比べて、性能が劣化することなく応答性が高められる。
【００７１】
また、請求項８に記載の発明にかかわるプログラムを実行するコンピュータは、請求項１ないし請求項３の何れか１項に記載の係数算出支援装置の構成要素となる。
さらに、請求項９に記載の発明にかかわるプログラムを実行するコンピュータは、請求項４ないし請求項７の何れか１項に記載の係数算出装置の構成要素となる。
【００７２】
また、請求項１０に記載の記録媒体からプログラムを読み取って実行するコンピュータは、請求項１ないし請求項３の何れか１項に記載の係数算出支援装置の構成要素となる。
【００７３】
さらに、請求項１１に記載の記録媒体からプログラムを読み取って実行するコンピュータは、請求項４ないし請求項７の何れか１項に記載の係数算出装置の構成要素となる。
すなわち、上述したＦＩＲフィルタに係数として与えられるべき係数ベクトルは、コストが増加し、あるいは構成が著しく複雑化することなく、入力信号の統計的な性質の如何にかかわらず的確な基準に基づいて安定に、かつ速やかに更新される。
【００７４】
したがって、これらの発明が適用された機器や信号処理系では、例えば、入力信号の相関性が高く、あるいはその入力信号の統計的な性質が刻々と変化し得る場合にも、柔軟に、かつ精度よく所望の伝達特性や濾波特性が達成される。
【図面の簡単な説明】
【図１】本発明にかかわる係数算出支援装置の原理ブロック図である。
【図２】本発明にかかわる係数算出装置の原理ブロック図である。
【図３】本発明の第一の実施形態を示す図である。
【図４】本発明の第一の実施形態の動作を説明する図である。
【図５】本発明の第一の実施形態の動作フローチャートである。
【図６】本発明の第二および第三の実施形態を示す図である。
【図７】本発明の第二の実施形態における同定誤差を示す図(1) である。
【図８】本発明の第二の実施形態における同定誤差を示す図(2) である。
【図９】適応フィルタが適用されたシステム同定系の構成例を示す図である。
【図１０】従来例の課題を説明する図である。
【符号の説明】
１０，５１ 未知系
１１ ＦＩＲフィルタ
１２ 凸集合特定手段
１３ 係数算出手段
２１ 信号分離手段
２２ 係数算出支援装置
２３ 係数適正化手段
２４ 外乱監視手段
２５ 包含凸集合特定手段
３１，４０，５３ 係数更新部
４１，４２ シフトレジスタ
４３ 分散演算部
４４ 係数算出部
５２ 適応フィルタ
５４ 減算器[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a coefficient calculation support device and a coefficient calculation device that update the coefficient of the adaptive filter according to the response or state of the adaptive filter, a program that implements these coefficient calculation support device or coefficient calculation device, and And a stored recording medium.
[0002]
[Prior art]
In recent years, DSPs and other hardware that realize advanced signal processing in the digital domain have been reduced in price, and such hardware is a major device that constitutes an adaptive equalizer, an echo canceller, and the like that reduce transmission distortion. As described above, it is often applied to mobile communication systems and other various transmission systems.
[0003]
  FIG. 9 is a diagram illustrating a configuration example of a system identification system to which an adaptive filter is applied.
  In the figure, the input of the unknown system 51 and the adaptive filter 52Person in chargeOne input of the number updating unit 53 is an instantaneous value u that takes discrete values in the order of time series k._k An input signal is given as a sequence of the output of the unknown system 51 and the output of the unknown system 51 is connected to one input of the subtractor 54. The output of the subtractor 54 is connected to the other input of the coefficient updating unit 53, and the output of the coefficient updating unit 53 is connected to the coefficient input of the adaptive filter 52. An output signal is obtained at the output of the adaptive filter 52, and the output signal is given to the other input of the subtractor 54.
[0004]
In the following description, it is assumed that the configuration of the adaptive filter 52 is configured as an N (≧ 2) stage FIR filter for simplicity.
In the system identification system having such a configuration, the unknown system output signal d obtained at the output of the unknown system 51 in the order of the time series k._k Is a vector d ^ shown in the following equation (1) for the specifications listed below._kAs given.
[0005]
d ^_k= U ^^t _kh ^^*+ N ^_k  ... (1)
A sequence u of N instantaneous values that are consecutive in the time-series order of the input signal described above._ki, U_ki-1, ..., u_{ki-N + 1}The vector u ^ defined as_ki
・ The vector u ^_kiAre arranged with a predetermined number r (≠ 0) of input signals (size r × N) U ^_k(= [U ^_{k-r + 1}, ..., u ^_k])
A vector h ^ indicating the impulse response of the unknown system 51 when the unknown system 51 is regarded as an N-stage FIR filter similar to the adaptive filter 52^*(= [H^* ₀... h^* _N-1])
-Instantaneous value n of noise (disturbance) included in the output signal_k Is a noise vector n ^ in which r (≠ 0) are arranged in the order of time series k_k(= [N_k..., n_{k-r + 1}]^t)
The instantaneous value d of the output signal of the unknown system 51 observed with noise superimposed_k Output vector d ^ of the unknown system 51 in which r (≠ 0) are arranged in the order of time series k._k(= [D_k, ..., d_{k-r + 1}]^t)
Here, the symbol “^” means a vector (or matrix), and in the following, this symbol “^” is attached to all vectors (or matrices) in order to distinguish them from scalar quantities.
[0006]
In the following (including all embodiments described later), the noise described above is collectively superimposed at the output end of the (ideal) unknown system 51 that is the target of system identification for the sake of simplicity. Assume that
Here, the time series k and the vector d ^ described above_kAnd the input signal matrix U ^_kAnd an arbitrary coefficient vector h ^ (= [h₀... h_N-1] Indicating the output signal output from the adaptive filter 52 in accordance with^t _kh ^_k) And the error vector e ^ shown in the following equation (2)_kDefine (h ^).
[0007]
e ^_k(h ^) = U ^^t _kh ^ -d ^_k  ... (2)
The coefficient updating unit 53 repeats the following series of processes with a period of time series k.
・ "Error vector e ^ in vector space_k(h ^) length (norm) (= ‖U ^^t _kh ^ -d ^_kLinear manifold V defined as a set of coefficient vectors h ^_kIs specified.
[0008]
Linear manifold V_k Is the input signal matrix U ^_kAnd the vector d ^_kTherefore, the information of r output instantaneous values of unknown system is reflected. In general, N is set to a value sufficiently larger than r, so e ^_kThe minimum value of (h ^) can be considered to be “0”.
"Linear manifold V_k The latest coefficient vector h ^ obtained in advance in the order of time series k_kThe vector closest to the "coefficient vector h ^"_kThis linear manifold V_k Is called "distance projection (convex projection)" to P ^ v_k(h ^_k).
[0009]
・ Relaxation coefficient λ set according to time series k_k(0 ≦ λ_k≦ 2) and the coefficient vector h ^_kAnd the projection vector P ^ v_k(h ^_kThe coefficient vector indicating the coefficient to be given to the adaptive filter 52 is subsequently updated by performing a vector operation represented by the following recurrence formula.
h ^_{k + 1}= H ^_k+ Λ_k(P ^ v_k(h ^_k) −h ^_k(3)
Hereinafter, the processing procedure for realizing the above-described distance projection is referred to as “affine projection method”.
[0010]
Further, the detailed procedure of the calculation to be performed for obtaining the above-described distance projection is well known and is not a feature of the present invention, and therefore the description thereof is omitted here.
Such a coefficient vector h ^_kThe direction and length of is the linear manifold V described above_kIt is updated appropriately based on the distance projection for (determined based on r output instantaneous values of the unknown system).
[0011]
Accordingly, the coefficient updating unit 53 performs coefficient vector h ^_kIs updated based on the “affine projection method” (hereinafter, referred to as “first conventional example”), the response of the unknown system 51 observed multiple times in the order of the time series k. Is effectively applied to the efficient update of the coefficients of the adaptive filter 52, and the accuracy of system identification is kept high.
[0012]
Further, the coefficient updating unit 53 performs the above-described processing even when “1” is applied instead of the above-described plurality of r, so that an NLMS (Normalized LMS) which is a subordinate algorithm of the “affine projection method” ) Method (learning identification method) coefficient vector h ^_kCan be updated.
In such a system identification system to which the NLMS method is applied (hereinafter referred to as “second conventional example”), the required processing amount is significantly smaller than in the case where the “affine projection method” is applied, and Since the convergence speed is higher than when the LMS method is applied, a high-speed response to a change in transfer characteristics of the unknown system 51 can be achieved at a low cost.
[0013]
[Problems to be solved by the invention]
By the way, in the first conventional example described above, the coefficient vector generally converges at a high speed in the initial stage at the time of starting, but when the output signal contains noise, the vector calculation represented by the above equation (3) is performed. Coefficient vector h ^_kHave not necessarily converged to a suitable speed with a desired speed and accuracy for the reasons listed below.
[0014]
・ The previously described linear manifold V_k Is a “closed convex set in vector space” obtained without taking into account any noise included in the output signal. Therefore, the coefficient vector h ^_kPreferred or true coefficient vector h ^^* _k Is this linear manifold V in vector space_kIt is not always located inside the (closed convex set).
[0015]
Therefore, in the conventional example in which the coefficient vector is updated based on the above equation (3), the monotonicity of the error expressed by the following equation is not guaranteed, and the convergence speed is often deteriorated.
‖H ^_{k + 1}-H ^^* _k‖ ≦ ‖h ^_k-H ^^* _k‖
・ The relaxation factor λ described above_k Is not necessarily set to a suitable value, and the relaxation coefficient λ_k A systematic standard and calculation procedure necessary for sequentially updating the value of to an appropriate value has not been established.
[0016]
Here, the following inequality (4) is satisfied for a predetermined number ρ (≧ 0) on the vector space (the linear manifold V described above)._k Is included. ) Set the coefficient vector h ^ to C_kIt is defined as (ρ).
‖D ^_k-U ^^t _kh ^ ‖²−ρ ≦ 0 (4)
“Such a set C_k(ρ) is a coefficient vector h ^ indicating a suitable coefficient to be given to the adaptive filter 52.^* _kThe probability density function that gives the probability of "include" is generally the noise vector n ^_kThe square value of the length of (= ‖n ^_k‖²) For a random variable defined as² As shown in FIG. 10, the distribution is different, and the value varies depending on the number r described above. That is, the set C_k(ρ) is the coefficient vector h ^^* _kIs a value obtained by integrating the probability density function shown in FIG. 10 from “0” to “ρ”.
[0017]
Linear manifold V_k For e ^_kSince the minimum value of (h ^) can be regarded as “0” as described above, C_kCorresponds to (0).
In addition, the above noise n_k Is assumed to be Gaussian noise with an average value of “0” and the set C described above_kHereinafter, (ρ) is simply referred to as an “executable set”.
[0018]
Therefore, when the value r is set to a value of “3” or more, a suitable coefficient vector h ^^* _kThe amount of processing required to calculate is significantly increased (linear manifold V_k Is a set of solutions of simultaneous equations with the number of scalars equal to the number r described above. )^* _k∈V_k Hardly holds (coefficient vector h ^^* _kIs a linear manifold V_k The probability of being included in is substantially “0”. Therefore, the convergence speed in the first conventional example is not always improved.
[0019]
In the second conventional example, the processing amount required for calculating the coefficient vector is significantly smaller than that in the first conventional example. However, when the correlation of the input signal is high, the value of the coefficient vector is preferable. The speed of convergence to the value was remarkably reduced, and sufficient response was not always obtained.
The present invention provides a coefficient calculation support apparatus and coefficient calculation apparatus capable of obtaining a suitable coefficient at high speed and with high accuracy regardless of the statistical properties of the input signal even when the SN ratio is extremely small, and calculation of these coefficients. It is an object of the present invention to provide a program for realizing a support device and a coefficient calculation device, and a recording medium storing the program.
[0020]
[Means for Solving the Problems]
FIG. 1 is a block diagram showing the principle of a coefficient calculation support apparatus according to the present invention.
In the coefficient calculation support apparatus according to claim 1, the convex set specifying unit 12 receives the input signal u input to the unknown system 10 in the order of time series k._k Represents an input signal matrix U ^ ι in which r (≠ 0) column vectors composed of N instantaneous values are arranged, and a column of r instantaneous values of the output signal dι output by the unknown system 10. Vector d ^_kAnd this input signal u for a predetermined number ρ (≧ 0)_k In a vector space indicating a coefficient vector h ^ to be given as a coefficient to the FIR filter 11 that filters the inequality ‖d ^ ι-U ^ ι^t h ^ ‖²A convex set which is a set of coefficient vectors h ^ satisfying −ρ ≦ 0 is specified. The coefficient calculation means 13 is a coefficient vector h ^ given as a coefficient preceding each stage of the FIR filter 11 in the order of time series k in the vector space described above._kFrom the coefficient vector h ^_kAnd a distance projection to a separation hyperplane interposed between the convex set specified by the convex set specifying means 12 and the distance projection to be given subsequent to the FIR filter 11 is a coefficient vector h ^._{k + 1}And
[0021]
That is, even if the level of the noise included in the output signal dι is large, the coefficient vector h ^ as long as the above-mentioned number ρ matches the statistical properties of the noise._kAre successively updated with high accuracy over an appropriate direction and distance in the vector space without a significant increase in the processing amount.
Therefore, compared to the conventional example to which the NLMS method or the affine projection method is applied, it is possible to adapt to various devices and systems, and the responsiveness and performance can be improved at a low cost.
[0022]
In the coefficient calculation support apparatus according to claim 2, in the coefficient calculation support apparatus according to claim 1, the convex set specifying means 12 is arranged so that the column vector u ^ with respect to the number N of stages of the FIR filter 11._k-ι₁, ..., u ^_k-ι_rAn input signal matrix U ^ ι in which is arranged is applied to the above-described convex set specification.
That is, the convex set specified by the convex set specifying means 12 is not necessarily updated every unit time of the time series k.
[0023]
Therefore, a coefficient vector h ^ with a desired accuracy for the statistical properties of the noise contained in the output signal dι._kAs long as this update is achieved, the amount of processing can be reduced.
In the coefficient calculation support apparatus according to claim 3, in the coefficient calculation support apparatus according to claim 1 or 2, the convex set specifying unit 12 has the convexity with a frequency equal to or less than the reciprocal of the unit time giving the time series k. Identify the set.
[0024]
That is, the convex set specified by the convex set specifying means 12 is not necessarily updated every unit time of the time series k.
Therefore, a coefficient vector h ^ with a desired accuracy for the statistical properties of the noise contained in the output signal dι._kAs long as this update is achieved, the amount of processing can be reduced.
FIG. 2 is a block diagram showing the principle of the coefficient calculation apparatus according to the present invention.
[0025]
In the coefficient calculating apparatus according to claim 4, the signal separating means 21 is an input signal matrix U ^ input to the unknown system 10 at a plurality of times p different in order of the time series k._k1~ U ^_kpAnd the output signal d ^ ι output by the unknown system 10₁~ D ^ ι_pAnd in parallel. The coefficient calculation support devices 22-1 to 22-p receive the input signal matrix U ^ acquired in this way._k1~ U ^_kpAnd output signal d ^ ι₁~ D ^ ι_pAccordingly, by performing the same operation as that of the first to third aspects of the invention, a plurality of p coefficient vectors h ^ that can be given to the FIR filter 11 as individual subsequent coefficients._k1~ H ^_kpIn parallel. The coefficient optimizing means 23 uses these plural p coefficient vectors h ^._k1~ H ^_kpAnd a plurality of p predetermined weights W₁~ W_pAnd a coefficient vector h ^ given as a coefficient preceding the FIR filter 11 in the order of the time series k._kA coefficient vector h ^ to be given as a coefficient following the FIR filter 11 based on an adaptive algorithm that reduces the difference between_{k + 1}Ask for.
[0026]
That is, a single convex set in the vector space described above and the coefficient vector h ^ obtained in advance._kThis coefficient vector h ^ for the separating hyperplane interposed between_kAs the distance projection of the coefficient vector h ^_kCompared to the case where is sequentially updated, the preferred coefficient vector h ^^* _k The accuracy and speed of convergence with respect to is increased on average.
Therefore, performance and responsiveness are improved under distributed processing by the coefficient calculation support devices 22-1 to 22-p, and further, application to various devices and systems is possible.
[0027]
In the coefficient calculation apparatus according to claim 5, in the coefficient calculation apparatus according to claim 4, the coefficient optimization unit 23 includes a plurality of coefficient vectors h ^._k1~ H ^_kpThe weight W used for the individual weighting of₁ ~ W_p These weights W₁~ W_pA small value is applied in ascending order of the suffix numbers “1” to “p”.
That is, a coefficient vector h ^ of plural p_k1~ H ^_kpIs weighted more as the time elapsed from the time point at which it is obtained is shorter.
[0028]
  Therefore, the characteristics of the unknown system 10 and the output signal d_k Even when any one of the noise levels and characteristics included in the filter can change abruptly, the filtering characteristics of the FIR filter 11 are stably maintained at suitable characteristics.
  In the coefficient calculation apparatus according to claim 6,4In the coefficient calculation device described in the above, the disturbance monitoring unit 24 is configured to output the output signal d._k1~ D_kpLevel n of noise individually contained in_k1~ N_kpAsk for. The coefficient optimizing means 23 uses a plurality of p coefficient vectors h ^_k1~ H ^_kpThe weight W used for the individual weighting of₁ ~ W_p Level n determined in this way_k1~ N_kpApply large values in descending order.
[0029]
That is, a coefficient vector h ^ of plural p_k1~ H ^_kpAre respectively output signals d_k1~ D_kpNoise level n individually included_k1~ N_kpThe coefficient vector obtained according to the output signal having a low (high SN ratio) is weighted more.
Therefore, the characteristics of the unknown system 10 and the output signal d_k1~ D_kpEven when any one of the noise levels and characteristics included in the filter can change abruptly, the filtering characteristics of the FIR filter 11 are stably maintained at suitable characteristics.
[0030]
In the coefficient calculation apparatus according to claim 7, in the coefficient calculation apparatus according to any one of claims 4 to 6, the inclusion convex set specifying means 25 is a coefficient vector to be given to the FIR filter 11 as a coefficient. In the vector space indicating h ^, the first to pth convex sets specified by the convex set specifying means 12-1 to 12-p individually included in the plurality of p coefficient calculation support devices 22-1 to 22-p And a coefficient vector h ^ obtained in advance by the coefficient optimization means 23_kConvex convex set S that does not contain_k1~ S_kpIs identified. The coefficient optimizing means 23 includes the inclusive convex set S specified in this way._k1~ S_kpThe coefficient vector h ^ given as a coefficient prior to the FIR filter 11_kWhether or not is included is determined. Further, the coefficient optimizing means 23, when the result of this determination is false, is a coefficient vector h ^ indicating the coefficient given prior to the FIR filter 11._kCoefficient vectors h ^ obtained by coefficient calculation support devices 22-1 to 22-p for_k1~ H ^_kpWhen the product of the value (≧ 1) that increases according to the variance of the value and the specified constant m (0 ≦ m ≦ 2) is applied as the step size of the adaptive algorithm described above, and the result of the determination is true The constant m is applied as the step size.
[0031]
Such a step size is obtained by calculating a coefficient vector h ^ of plural p obtained by the coefficient calculation support devices 22-1 to 22-p._k1~ H ^_kpThe larger the error included in the record is, the larger the value can be set.
Therefore, as compared with the case where the step size is simply set to a constant equal to or smaller than “2”, the above-described error can be quickly compressed without deterioration in performance, and the responsiveness can be further improved.
[0032]
The program according to claim 8 is provided as the convex set specifying means 12 and the coefficient calculation means 13 constituting the coefficient calculation support apparatus according to any one of claims 1 to 3, Make the computer work.
[0033]
Therefore, the computer that executes the program according to the present invention is a component of the coefficient calculation support apparatus according to any one of claims 1 to 3.
A program according to a ninth aspect includes a signal separation unit 21 that constitutes the coefficient calculation device according to any one of the fourth to seventh aspects, a plurality of coefficient calculation support devices 22-1 to 22-p, The computer is caused to function as all or part of the coefficient optimization unit 23, the disturbance monitoring unit 24, and the inclusive convex set specifying unit 25.
[0034]
Therefore, the computer that executes the program according to the present invention is a component of the coefficient calculation apparatus according to any one of claims 4 to 7.
A recording medium according to a tenth aspect of the present invention is a recording medium according to any one of the first to third aspects, wherein the convex set specifying means 12 and the coefficient calculating means 13 constituting the coefficient calculation supporting apparatus according to any one of the first to third aspects are used. The computer-readable program on which a program for causing the computer to function is recorded.
[0035]
Such a program is configured as software to be executed by the above-described computer or a microprogram incorporated in the computer, and is distributed by being recorded on a removable recording medium separate from such a computer. Can do.
Therefore, a computer that reads and executes such a program from the recording medium according to the present invention is a component of the coefficient calculation support apparatus according to any one of claims 1 to 3.
[0036]
A recording medium according to an eleventh aspect includes a signal separating unit 21 constituting the coefficient calculating apparatus according to any one of the fourth to seventh aspects, and a plurality of coefficient calculating support apparatuses 22-1 to 22-p. As a whole or a part of the coefficient optimizing means 23, the disturbance monitoring means 24, and the inclusive convex set specifying means 25, a computer-readable program in which a program for causing the computer to function is recorded can be read.
[0037]
Such a program is configured as software to be executed by the above-described computer or a microprogram incorporated in the computer, and is distributed by being recorded on a removable recording medium separate from such a computer. Can do.
Therefore, a computer that reads and executes such a program from the recording medium according to the present invention is a component of the coefficient calculation apparatus according to any one of claims 4 to 7.
[0038]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 3 is a diagram showing a first embodiment of the present invention.
The main difference between the present embodiment and the conventional example shown in FIG. 9 is that the subtracter 54 is not provided, the coefficient update unit 31 is provided instead of the coefficient update unit 53, and the output of the unknown system 51 is provided. Is directly connected to the corresponding input of the coefficient updating unit 31.
[0039]
FIG. 4 is a diagram for explaining the operation of the first embodiment of the present invention.
FIG. 5 is an operation flowchart of the first embodiment of the present invention.
The operation of the first embodiment of the present invention will be described below with reference to FIGS.
The feature of this embodiment is the following calculation procedure performed by the coefficient updating unit 31.
[0040]
The linear manifold V described above_k Is the executable set C described above in vector space, as shown by the thick dotted line in FIG._kincluded in (ρ).
In addition, the vector d ^, the input signal matrix U ^, and the coefficient vector h ^ obtained in advance in the order of the time series k are single or plural common time series ι For the vectors d ^ ι, U ^ ι and the coefficient vector h ^ ι respectively corresponding to the set of time series k of_kThe outer edge of the feasible set Cι (ρ) representing (ρ) is defined as a set of h ^ in which the convex function gι (h ^) represented by the following expression is “0”, for example.
[0041]
gι (h ^) ＝ ‖d ^ ι−U ^^tιh ^ ‖²−ρ (5)
Furthermore, since such a convex function gι (h ^) is differentiable in all regions, the convex function gι (h ^) in time series k_k) Gradient (normal vector) sι (h ^_k) Is given by:
sι (h ^_k) ＝ ∇gι (h ^_k) =-2U ^^t(d ^ ι-U ^^tιh ^_k(6)
Also, an executable set C in time series k on the vector space_k(ρ) and coefficient vector h ^_kThis feasible set C out of two regions formed with a virtual plane (hereinafter simply referred to as “separation hyperplane”) interposed between_kOne region including (ρ) (hereinafter referred to as “closed half space”) Hι^- Is defined as a region where the following inequality holds.
[0042]
(h ^ −h ^_k)^tsι (h ^_k) ＋ gι (h ^_k) ≦ 0 (7)
Therefore, the coefficient vector h ^ for such a closed half space in vector space_kDistance projection PHι^-(h ^) is expressed by the following equation.
[Expression 1]

By the way, the above inequality (7) is obtained when the coefficient vector h ^ included in the inequality (7) is given in advance to the adaptive filter 52 as a coefficient in the time series k._kIs replaced by the following inequality (10).
[0043]
gι (h ^_k) ≦ 0 (10)
Furthermore, the distance projection PHι mentioned above^-A coefficient vector h ^ to be given as a coefficient to the adaptive filter 52 in the time series (k + 1) where (h ^) follows the time series k_{k + 1}When this is true, the above equations (8) and (9) can be transformed into the following recurrence equations (11) and (12), respectively.
[Expression 2]

The coefficient updating unit 31 repeats the following processes (1) to (4) in a predetermined cycle (given in ascending order of time series k) in which the coefficient of the adaptive filter 52 is to be updated.
(1) Coefficient vector h ^_k(It is given as a predetermined initial value at the time of start-up), and the convex function gι (h ^_k) Is obtained (FIG. 5 (1)).
[0044]
(2) Based on the value, it is determined whether or not the inequality (10) is established (FIG. 5 (2)).
(3) If the result of this discrimination is true, “coefficient vector h ^_kMeans that the coefficient vector h ^ is based on the above equation (11)._kIs a coefficient vector h ^ indicating the coefficient to be subsequently applied to the adaptive filter 52 without updating any_{k + 1}(Fig. 5 (3)).
[0045]
(4) However, if the result of the above discrimination is false, “coefficient vector h ^ obtained in advance”_kIs not located in the above-described closed half space on the vector space ", the following series of processing is performed.
・ By performing the arithmetic operation shown in the above equation (5), the coefficient vector h ^_kConvex function gι (h ^_k) Is calculated (FIG. 5 (4)).
[0046]
・ By performing the arithmetic operation shown in equation (6) above, the coefficient vector h ^_kNormal vector to sι (h ^_k) Is calculated (FIG. 5 (5)).
A coefficient vector h ^ indicating a coefficient to be subsequently given to the adaptive filter 52 by performing the arithmetic operation shown in the above equation (12)_{k + 1}Is calculated (FIG. 5 (6)).
・ The coefficient vector h ^_{k + 1}Is given to the adaptive filter 52 (FIG. 5 (7)).
[0047]
That is, the linear manifold V described above_k Instead of its linear manifold V_k An executable set C containing_k(ρ) is applied, and such a coefficient vector h ^_{k + 1}Is the feasible set C in vector space_k(ρ) and the previously obtained coefficient vector h ^_kIts coefficient vector h ^ for the separating hyperplane interposed between_kIt is updated sequentially as the distance projection.
[0048]
As described above, according to the present embodiment, even when the level of noise included in the output signal is large, the coefficient vector h ^_kIs determined accurately and promptly in the order of time series k without solving the linear simultaneous equations, as long as the above-mentioned number ρ is set to a value that matches the statistical properties of the noise. It converges to a suitable value without unnecessarily fluctuating.
[0049]
FIG. 6 is a diagram showing the second and third embodiments of the present invention.
In the figure, the main difference from the configuration shown in FIG. 3 is that a coefficient updating unit 40 is provided instead of the coefficient updating unit 31.
The coefficient update unit 40 includes the following elements.
Along with the input of the unknown system 51 and the adaptive filter 52, the input signal u described above_k Q (≧ 2) stages of shift register 41
A q (≧ 2) stage shift register 42 in which the output of the unknown system 51 is directly connected to the input
・ Input signal u mentioned above at one input_k And the other input is directly connected to the output of the unknown system 51.
The distributed arithmetic units 43-1 to 43-q each having two inputs directly connected to the outputs of the first to qth (≧ 2) stages of the shift registers 41 and 42, respectively.
A coefficient calculation unit 44 having (q + 1) inputs that are directly connected to the outputs of the variance calculation units 43-0 to 43-q and whose output is directly connected to the coefficient input of the adaptive filter 52.
The operation of the second embodiment of the present invention will be described below with reference to FIG.
[0050]
The shift register 41 receives the input signal u described above._kBy giving a delay over an integer i (1 ≦ i ≦ q) times of a predetermined period in the order of time series k to q input signals u_kiAre output in parallel.
The shift register 42 outputs the above-mentioned unknown output signal d._k By giving a delay over an integer i (1 ≦ i ≦ q) times of a predetermined period in the order of time series k, q unknown output signals d_kiAre output in parallel.
[0051]
In the following, items common to the distributed arithmetic units 43-0 to 43-q are replaced with any of these suffix numbers “0” to “q” instead of suffix numbers “0” to “q”. It is described using a subscript “i” indicating that it is applicable.
In addition, regarding the input signal and the unknown system output signal respectively applied to the input terminals of the shift registers 41 and 42, the input signal U is assumed on the assumption that the value of the integer i described above is “0”._kiAnd unknown system output signal d_kiIs written.
[0052]
The variance calculation unit 43-i receives the input signal u described above._kiAnd unknown system output signal d_kiIn accordance with the above, by performing the same operation as the operation performed by the coefficient updating unit 31 provided in the first embodiment described above in parallel, the coefficient vector h ^ with the suffix “i” added to the end_ki Are obtained in parallel in the order of time series.
The coefficient calculator 44 calculates the coefficient vector h ^ obtained in parallel in this way._k0 ~ H ^_kq And a coefficient vector h ^ given as a coefficient to the adaptive filter 52 in advance._kAnd (q + 1) weights w of which the sum is “1”₀~ W_qAnd the specified relaxation coefficient μ_k(Here, for the sake of simplicity, it is assumed that a constant that is greater than or equal to “0” and less than or equal to “2” is preset.) The arithmetic operation represented by the following recurrence formula (13) The coefficient vector h ^_kUpdate.
[Equation 3]

Further, the coefficient calculation unit 44 updates the latest coefficient vector h ^ updated in this way._{k + 1}Are set in the adaptive filter 52.
That is, “a suitable coefficient vector h ^ on the vector space.^* _k An executable set C containing_ki(ρ) and the previously obtained coefficient vector h ^_kThe coefficient vector for the separated hyperplane between_ki Is calculated in parallel by the variance calculation units 43-0 to 43-q, and the coefficient vector h ^_kAre updated sequentially based on an adaptive algorithm that monotonically reduces the error of the weighted vector sum of these distance projections.
[0053]
Therefore, according to the present embodiment, “a single executable set C in the vector space”_k(ρ) and the previously obtained coefficient vector h ^_kThis coefficient vector h ^ for the separated hyperplane between_kAs the distance projection of the coefficient vector h ^_kCompared with the first embodiment described above in which the values are sequentially updated, a suitable coefficient vector h ^^* _k The accuracy and speed of convergence with respect to is increased on average.
[0054]
Therefore, in the system identification system according to the present embodiment, for example, when the aforementioned value ρ is large, the coefficient vector h ^_kTakes time to converge (FIG. 7 (a) (1)), but as long as the value ρ is set to an appropriate value, the preferred coefficient vector h ^^* _k The relative error (identification error) with respect to the first and the second even if the level of noise superimposed on the input signal in the unknown system 51 is large, regardless of the correlation of the input signal and the value r. Compared to the second conventional example, it is greatly improved (FIGS. 7 (a) (2), (3), (b) (1) to (3), FIGS. 8 (a) (1) to (3), (b) (1) to (3)) and responsiveness is improved.
[0055]
In this embodiment, the weight w₀~ W_qAlthough the value of is not specifically shown, these weights w₀~ W_qThe value of may be set to any of the following values, for example.
Common value (= 1 / (q + 1))... This is suitable when a decrease in accuracy and response due to fluctuations in the transmission characteristics of the unknown system 51 and the level of noise included in the output signal is allowed.
[0056]
A small value in descending order of time series as indicated by the following inequality: suitable for a case where a decrease in accuracy and responsiveness due to a change in transmission characteristics of the unknown system 51 should be reduced.
w₀≧ w₁≧… ≧ w_q  ···(14)
The level of noise included in the output signal (for example, the error vector e ^ obtained individually by the division operation unit 43-i based on the above-described equation (2)_ki Large value in descending order of (absolute value of...)... Suitable for a case where a decrease in accuracy and responsiveness due to fluctuations in noise level should be reduced
[0057]
  Hereinafter, a third embodiment of the present invention will be described with reference to FIG.
  The difference between the present embodiment and the second embodiment described above is that the output of the coefficient calculation unit 44 is distributed as shown by the dotted line in FIG.CalculationThe points 43-0 to 43-q are connected to the corresponding inputs.
  The operation of this embodiment will be described below.
[0058]
The feature of the present embodiment is that the above-described relaxation coefficient μ_k Is updated as appropriate based on the following procedure.
The distributed arithmetic unit 43-i is the executable set C described above in the vector space._ki(ρ) and a coefficient vector h ^ given as a coefficient to the adaptive filter 52 by the coefficient calculation unit 44 in advance._kA virtual set (hereinafter referred to as an “inclusive convex set”) S_kiIs appropriately specified, and the coefficient calculation unit 44 includes the inclusive convex set S._kiTo be notified.
[0059]
The coefficient calculation unit 44 (q + 1) inclusive convex sets S notified in this way._k0~ S_kqIn either case, a coefficient vector h ^ given as a coefficient in advance of the adaptive filter 52_kWhether or not is included is determined.
Further, the coefficient calculation unit 44 determines the variable M represented by the following equation (15) according to the determination result._k Find the value of.
[Expression 4]

The numerator of the above equation (15) when the above-described discrimination result is true is “coefficient vector h ^_kThe distance projection h ^_k0~ H ^_kq(Determined in parallel by the variance computing units 43-0 to 43-q) and the denominator of the equation is “the coefficient vector h ^”._kThese distance projections for h ^_k0~ H ^_kqCorresponds to the "weighted average of the error energy".
[0060]
That is, the variable M_k Is the previously described coefficient vector h ^_kDistance projection for h ^_k0~ H ^_kq, And the above-mentioned relaxation coefficient μ_k Is a value equal to or greater than “1” corresponding to a limit that should be allowed to exceed “2”.
[0061]
The coefficient calculation unit 44 uses the specified constant m (0 ≦ m ≦ 2) and the variable M described above_k And the relaxation coefficient μ shown by the following equation (16)_k And its relaxation coefficient μ_k By performing the same operation as in the second embodiment described above except that is applied, the coefficient vector h ^_kAre updated sequentially.
μ_k = M ・ M_k  ... (16)
Therefore, according to the present embodiment, the coefficient vector h ^ without reducing the accuracy as compared with the second embodiment described above._kIs updated at high speed.
[0062]
In the present embodiment, the arithmetic operation shown in the above equation (15) is the coefficient vector h ^ described above._kDistance projection for h ^_k0~ H ^_kqVariable M as an appropriate value that increases according to the variance (deviation distribution) of_k As long as is calculated, any arithmetic operation may be substituted.
Further, in each of the above-described embodiments, the value ρ is not specifically shown.
Such a value ρ is, for example, power σ of noise included in the output signal (here, it is assumed that it is “white noise” for simplicity).² Is known, χ shown in FIG.² Mean of distribution mξ (= rσ²), Variance σξ²(= 2rσ^Four), Maximum value ξ (= (r−2) σ²) For a value ρ that is uniquely determined as follows:₁~ Ρ_FourEither of these may be set.
[0063]
・ Ρ₁= Mξ + σξ = (r + √2) σ²
・ Ρ₂= Mξ = rσξ²
・ Ρ_Three= Max [(r-2) σ², 0]
・ Ρ_Four= Ρ_Three+ Ασξ (α> 0)
Furthermore, in each embodiment mentioned above, this invention is applied to the system identification system shown in FIG. 3 and FIG.
[0064]
However, the present invention is not limited to such a system identification system, and can be applied to, for example, the following various devices. The performance and reliability of these devices are compared to the case where the conventional example is applied. It is greatly and highly accurate without increasing costs or reducing reliability.
[0065]
・ An adaptive equalizer that adapts to changes in the transmission characteristics of a transmission line or communication path at high speed and flexibly and suppresses the effects of transmission distortion that occurs in the transmission line or communication path.
・ Echo canceller that adapts to transmission path and communication path fluctuation characteristics at high speed and flexibly and removes echo generated in the transmission path and communication path.
・ Howling canceller that avoids howling due to positive feedback in the acoustic domain via a feedback path from the speaker to the microphone.
Active noise canceller that actively suppresses noise generated by engines (mounted on vehicles, aircraft, ships, etc.), air conditioners and other devices in the acoustic range.
In each embodiment described above, each unit is configured as dedicated hardware.
[0066]
However, the present invention is not limited to such a configuration. For example, all of the constituent elements are realized as software (storage logic) executed by a single processor or DSP, or all or a part of the constituent elements are realized. Load distribution and function distribution may be achieved in any form.
Further, in each of the above-described embodiments, the updated coefficient vector h ^_{k + 1}The coefficient indicated by is directly given to the adaptive filter 52.
[0067]
However, the present invention is not limited to such a configuration. For example, the updated coefficient vector h ^_{k + 1}A means for obtaining a new coefficient by performing some kind of additional processing and further supplying the coefficient to the adaptive filter 52 may be provided.
In addition, the present invention is not limited to the above-described embodiments, and various embodiments can be realized within the scope of the present invention, and any improvements can be made to some or all of the constituent devices. May be.
[0068]
【The invention's effect】
As described above, in the first aspect of the invention, the preferred or true coefficient vector h ^^* _kConvex set C with high probability_k(ρ) is specified in order of time series, and its convex set C_kCoefficient vector h ^ as a distance projection for the inclusive convex set containing (ρ)_kIs updated so that this coefficient vector h ^_kThe accuracy of the monotonicity of the error contained in is guaranteed.
[0069]
Therefore, as compared with the conventional example to which the NLMS method or the affine projection method is applied, it is possible to adapt to various devices and systems, and both responsiveness and performance can be improved at low cost.
In the inventions according to claims 2 and 3, the amount of processing can be reduced.
Furthermore, the invention according to claim 4 improves the performance and responsiveness, and can be applied to various devices and systems.
[0070]
In the inventions according to claims 5 and 6, even if any of the characteristics of the unknown system and the level or nature of the noise included in the output signal can change abruptly, the FIR filter The filtering characteristics are stably maintained at suitable characteristics.
Furthermore, in the invention according to claim 7, the responsiveness is improved without degrading the performance as compared with the case where the step size is simply set to a constant equal to or smaller than “2”.
[0071]
A computer that executes a program according to the invention described in claim 8 is a constituent element of the coefficient calculation support apparatus according to any one of claims 1 to 3.
Furthermore, a computer that executes a program according to the invention described in claim 9 is a component of the coefficient calculation apparatus according to any one of claims 4 to 7.
[0072]
A computer that reads and executes a program from the recording medium according to claim 10 is a component of the coefficient calculation support apparatus according to any one of claims 1 to 3.
[0073]
Furthermore, a computer that reads and executes a program from the recording medium according to claim 11 is a component of the coefficient calculation device according to any one of claims 4 to 7.
That is, the coefficient vector to be given as a coefficient to the FIR filter described above is stable on the basis of an accurate standard regardless of the statistical properties of the input signal without increasing the cost or making the configuration significantly complicated. And will be updated promptly.
[0074]
Therefore, in the devices and signal processing systems to which these inventions are applied, for example, even when the correlation of the input signal is high or the statistical properties of the input signal can change from moment to moment, it is flexible and accurate. Well desired transfer characteristics and filtering characteristics are achieved.
[Brief description of the drawings]
FIG. 1 is a block diagram showing the principle of a coefficient calculation support apparatus according to the present invention.
FIG. 2 is a principle block diagram of a coefficient calculation apparatus according to the present invention.
FIG. 3 is a diagram showing a first embodiment of the present invention.
FIG. 4 is a diagram for explaining the operation of the first embodiment of the present invention.
FIG. 5 is an operation flowchart of the first embodiment of the present invention.
FIG. 6 is a diagram showing second and third embodiments of the present invention.
FIG. 7 is a diagram (1) showing an identification error in the second embodiment of the present invention.
FIG. 8 is a diagram (2) showing an identification error in the second embodiment of the present invention.
FIG. 9 is a diagram illustrating a configuration example of a system identification system to which an adaptive filter is applied.
FIG. 10 is a diagram illustrating a problem of a conventional example.
[Explanation of symbols]
10,51 Unknown system
11 FIR filter
12 Convex set identification means
13 Coefficient calculation means
21 Signal separation means
22 Coefficient calculation support device
23 Coefficient optimization means
24 Disturbance monitoring means
25 Inclusive convex set identification means
31, 40, 53 Coefficient update unit
41, 42 shift register
43 Distributed computing unit
44 Coefficient calculator
52 Adaptive filter
54 Subtractor

Claims (11)

N column vector of the instantaneous value of the input signal u _k is the r (≠ 0) pieces aligned and becomes the input signal matrix U ^ iota input to the unknown system in the order of time sequence k, outputted by the unknown system that the vector d ^ iota showing the sequence of the r instantaneous value of the output signal d _k, the coefficient to be given as a coefficient to the FIR filter for filtering the input signal u _k with respect to a predetermined number ρ (≧ 0) A convex set specifying means for specifying a convex set that is a set of coefficient vectors h ^ for which the inequality ‖d ^ ι-U ^ ι ^t h ^ ‖ ² −ρ ≦ 0 holds in the vector space representing the vector h ^;
In the vector space, the coefficient vector h ^ _k given as the coefficient preceding each stage of the FIR filter in the order of the time series k is specified by the coefficient vector h ^ _k and the convex set specifying means. Coefficient calculation means for obtaining a distance projection to a separation hyperplane interposed between the convex set and setting the distance projection to a coefficient vector h ^ _{k + 1} to be given subsequent to the FIR filter. A characteristic coefficient calculation support device. The coefficient calculation support device according to claim 1,
The convex set specifying means includes:
To the FIR filter stages N, the r number of different column vectors _{u ^ k- ι 1, ...,} u ^ k- ι r is the input signal matrix U ^ iota comprising arranged in particular the convex sets A coefficient calculation support apparatus characterized by being applied. In the coefficient calculation support device according to claim 1 or 2,
The convex set specifying means includes:
The coefficient calculation support apparatus, wherein the convex set is specified at a frequency equal to or less than a reciprocal of a unit time giving the time series k. The time of the plurality p of different order of time sequence k, an input signal matrix U ^ _k1 ~U ^ _kp respectively input to the unknown system, the output signal d ^ ι ₁ ~d ^ ι _p output by the unknown system A signal separation means for acquiring in parallel,
Described in any one of claims 1 to 3, and according to the acquired input signal matrix U ^ _k1 ~U ^ _kp output signal d ^ ι ₁ ~d ^ ι _p by the signal separating means A plurality of p coefficient calculation support devices for obtaining in parallel a plurality of p coefficient vectors h ^ _{k1 to} h ^ _kp that can be given as individual subsequent coefficients to the FIR filter;
Preceding the FIR filter and the product sum of the predetermined weight W ₁ to _W-p of the coefficient vector h ^ _k1 ~h ^ _kp and a plurality p of a plurality p obtained by the coefficient calculation support apparatus, in order of the time sequence k Coefficient optimization means for obtaining a coefficient vector h ^ _{k + 1} to be given to the FIR filter as the subsequent coefficient based on an adaptive algorithm for reducing the difference from the coefficient vector h ^ _k given as a coefficient. A coefficient calculation apparatus comprising: In the coefficient calculation apparatus according to claim 4,
The coefficient optimization means is:
As the weights W _{1 to} W _{p used} for individually weighting the coefficient vectors h ^ _{k1 to} h ^ _kp of the plurality p, ascending order of the suffix numbers “1” to “p” indicating these weights W _{1 to} W _p A coefficient calculation device characterized by applying a small value to the value. In the coefficient calculation apparatus according to claim 4 ,
Disturbance monitoring means for obtaining noise levels n _{k1 to} n _kp individually included in the output signals d _{k1 to} d _kp ;
The coefficient optimization means is:
As weights W _{1 to} W _{p used} for individually weighting the coefficient vectors h ^ _{k1 to} h ^ _kp of the plurality p, large values are applied in descending order of the levels n _{k1 to} n _kp obtained by the disturbance monitoring means. A coefficient calculation device characterized by: In the coefficient calculation device according to any one of claims 4 to 6,
In a vector space indicating a coefficient vector h ^ to be given as a coefficient to the FIR filter, the first to pth convex sets specified by the convex set specifying means individually included in the plurality of p coefficient calculation support devices are individually set. An inclusive convex set specifying means for specifying an inclusive convex set S _{k1 to} S _kp that is included and does not include the coefficient vector h ^ _k obtained in advance by the coefficient optimizing means;
The coefficient optimization means is:
It is determined whether any of the inclusion convex sets S _{k1 to} S _kp specified by the inclusion convex set specifying means includes a coefficient vector h ^ _k given as a coefficient prior to the FIR filter. If the result of the determination is false, the value (≧ 1, which increases with the variance of the coefficient vector h ^ _k1 ~h ^ _kp plurality p obtained by the coefficient calculation support device for the coefficient vector h ^ _k ) And a predetermined constant m (0 ≦ m ≦ 2) is applied as the step size of the adaptive algorithm, and when the result of this determination is true, the constant m is applied as the step size. The coefficient calculation apparatus characterized by the above-mentioned. A program for causing a computer to function as both or any one of the convex set specifying means and the coefficient calculating means constituting the coefficient calculation support apparatus according to any one of claims 1 to 3. A signal separation unit, a plurality of p coefficient calculation support devices, a coefficient optimization unit, a disturbance monitoring unit, an inclusive convex set specifying unit, which constitute the coefficient calculation device according to any one of claims 4 to 7. A program that causes a computer to function as a part. A program for causing a computer to function is recorded as both or any one of the convex set specifying means and the coefficient calculating means constituting the coefficient calculation support apparatus according to any one of claims 1 to 3. Computer-readable recording medium. A signal separation unit, a plurality of p coefficient calculation support devices, a coefficient optimization unit, a disturbance monitoring unit, an inclusive convex set specifying unit, which constitute the coefficient calculation device according to any one of claims 4 to 7. A computer-readable recording medium on which a program for causing a computer to function is recorded.

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