JP4344305B2 - Unknown system estimation method and apparatus for implementing the same - Google Patents

Description

  The present invention relates to an unknown system estimation method and an apparatus for performing the method, and in particular, an FIR that simulates an unknown system by inputting an input signal given to the unknown system such as acoustic transfer characteristics and an output signal obtained from the unknown system. The present invention relates to an unknown system estimation method that estimates a filter or realizes output prediction and simulation from an unknown system, and an apparatus that implements the method.

Referring to FIG. 3, an input signal x (k) is given to an unknown system h characterized by a vector L _* of length L having the impulse response of the system as an element, and obtained from this unknown system. There is known an unknown system estimation apparatus 1 that gives an output signal y (k) to estimate the characteristics of an unknown system h. However, k represents discrete time. The vector h is expressed as h _* . Here, assuming that the input signal x (k) for the unknown system h is a voice signal transmitted via a telephone line, a receiver present at the input end of the unknown system h and a transmitter present at the output end. And the acoustic transfer characteristics of all the environments existing between the handset and the handset are expressed as an unknown system h.

In the learning identification method shown in [Non-Patent Document 1], the estimation filter h _* ′ (k) of the unknown system h is sequentially updated and estimated as follows. Hereinafter, the vector x is expressed as x _* .
_{h * '(k + 1)} = h *' (k) + μ (e (k) / ‖x * (k) || ²⁾ x (k) (Equation 1)
Here, x _* (k) = [x (k), x (k−1),..., X (k−L + 1)] ^T , T is a vector transposition, and ‖x _* (k) ‖ is a vector x _*. Norm of (k), μ is an update adjustment coefficient that takes a value between 0 and 2, e (k) = y (k) −y ′ (k), y ′ (k) = h _* ′ (k) ^T x _* (k).

This learning identification method has a problem that when the input signal x (k) is a colored signal like speech, the estimated speed of the unknown system becomes slow.
Here, an unknown system estimation apparatus based on the affine projection algorithm shown in [Non-Patent Document 2] will be described with reference to FIG. This unknown system estimation apparatus 100 includes an input signal vectorization unit 101 that samples and accumulates a finite number of input signals x (k) to an unknown system h _* , vectorizes them, and outputs them as input signal vectors x _* (k). , receives the input signal vector x _* (k), and unknown system estimation filter 102 which outputs an output test signal y simulating the unknown system h _* of the output signal y (k) '(k) , from the unknown system h _* An error calculation unit 103 that outputs an error signal e (k) by subtracting the output simulation signal y ′ (k) from the obtained output signal y (k), and an input signal vector x _* (k−1) of one step in the past. A delay unit 104 to obtain, a weighted delay unit 105 to obtain an error signal (1-μ) e (k−1) of one step past weighted by (1-μ), and x _* (k), x _* ( k-1), e (k), (1-μ) e (k-1) and ( According 2), constituted by the unknown system estimation filter h _* '(delayed input and the delay error reference types updating k) estimating filter updating unit 106.

但し、
ｒ₀₀＝‖ｘ_*（ｋ）‖²
ｒ₀₁＝ｘ^T（ｋ）ｘ_*（ｋ−１）
ｒ₁₀＝ｘ_* ^T（ｋ−１）ｘ_*（ｋ）＝ｒ₀₁
ｒ₁₁＝‖ｘ_*（ｋ−１）‖²
である。
J.Nagumo,A.noda;“A learning method for system identification”IEEE Trans.Automatic control,Vol.AC-12,No.3,June 1967． 尾関 和彦，梅田 哲夫：「アフィン部分空間への直行射影を用いた適応フィルタ・アルゴリズムとその諸性質」電子通信学会 論文誌（Ａ），Ｊ６７−Ａ，pp１２６−１３２，１９８４． The unknown system estimation apparatus based on this affine projection algorithm estimates the unknown system estimation filter h _* '(k) by updating it sequentially as follows (when the order is 2), and the estimation speed of the unknown system becomes slow. It overcomes the previous problem of learning identification method.

However,
r ₀₀ = ‖x _* (k) || ²
r ₀₁ = x ^T (k) x _* (k−1)
r ₁₀ = x _* ^T (k−1) x _* (k) = r ₀₁
r ₁₁ = ‖x _* (k−1) ‖ ²
It is.
J. Nagumo, A. noda; “A learning method for system identification” IEEE Trans. Automatic control, Vol. AC-12, No. 3, June 1967. Kazuhiko Ozeki, Tetsuo Umeda: "Adaptive filter algorithm using direct projection to affine subspace and its properties" IEICE Transactions (A), J67-A, pp126-132, 1984.

The unknown system estimation apparatus 100 illustrated in FIG. 4 has the advantage that the speed of unknown system estimation is fast even if the input signal x (k) is colored, but the delay input and delay error reference type estimation filter update unit Since 106 performs the operation according to (Equation 2), there is a problem that the operation becomes more complicated than in the case of the learning identification method that performs the operation according to (Equation 1).
The present invention provides an unknown system estimation method and an apparatus that implements the unknown system estimation filter that can easily update the unknown system estimation filter while achieving an unknown system estimation speed equivalent to that of the unknown system estimation apparatus 100 shown in FIG. To do.

Claim 1: In an unknown system estimation method for inputting an input signal x (k) to an unknown system in a discrete time k region and an output signal y (k) from the unknown system, and estimating transfer characteristics of the unknown system, the input signal x (k) and accumulates the finite number samples, and vectorized outputs the input signal vector x _* (k), receives the input signal vector x _* (k) to the unknown system estimation filter 102, the unknown system An output simulation signal y ′ (k) that simulates the output signal y (k) from the output signal y (k) is generated, and the error simulation signal y (k) is subtracted from the output simulation signal y ′ (k) of the unknown system. generate, based on the input signal vector x _* (k) to generate a one-step past input signal vector x _* (k-1), has an update adjustment factor varying or fixed time, the input signal vector, 1 Step Based on past input signal vector and error signal , To obtain a correlation-reduced input signal vector obtained by subtracting a vector component correlated with an input signal vector in the past of one step from the input signal vector multiplied by the update adjustment coefficient used in the past of one step. The update value of the unknown system estimation filter is given to the unknown system estimation filter 102 by dividing the correlation reduction input signal vector by the inner product of the input signal vector and the correlation reduction input signal vector, multiplying by the error signal, and multiplying by the update adjustment coefficient. An unknown system estimation method was constructed.

Claim 2: In an unknown system estimation device for inputting an input signal x (k) to an unknown system in a discrete time k region and an output signal y (k) from the unknown system, and estimating the transfer characteristics of the unknown system, An input signal vectorization unit 101 that samples and accumulates a finite number of input signals x (k), vectorizes them and outputs an input signal vector x _* (k), and an input signal vector vectorized by the input signal vectorization unit 101 An unknown system estimation filter 102 that inputs x _* (k) and outputs an output simulation signal y ′ (k) that simulates an output signal y (k) from the unknown system, and an unknown system estimation filter h _* ′ (k) An error calculation unit 103 that subtracts an output simulation signal y ′ (k) output from the output signal y (k) from the unknown system and outputs an error signal e (k), and vectorization from the input signal vectorization unit 101 Input signal And torr x _* (k) delay unit 104 for generating an input to one step past input signal vector x _* (k-1) to have an update adjustment factor varying or fixed time, the input signal vector, one step The past input signal vector and the error signal are input, and the update adjustment coefficient used one step in the past from the input signal vector to the vector component correlated with the input signal vector in the previous step of the input signal vector. The correlation reduced input signal vector obtained by subtracting the value obtained by multiplying by, and the unknown signal is obtained by dividing the correlation reduced input signal vector by the inner product of the input signal vector and the correlation reduced input signal vector, multiplying by the error signal, and multiplying by the update adjustment coefficient. An unknown system estimation device having a delay input reference type estimation filter update unit 201 that supplies an updated value of the system estimation filter to the unknown system estimation filter 102 is configured.

  The affine projection algorithm uses an input signal vector of one step past and an error signal of one step past in addition to the input signal and error signal of the current step for updating the unknown system estimation filter. By replacing the error signal of the step past with an approximate value based on the error signal of the current step, the unknown system estimation filter can be updated by simple calculation compared with the affine projection algorithm. The estimation speed of the unknown system estimation filter of the present invention is equivalent to the affine projection algorithm for colored input signals and is faster than the learning identification method.

を満足する様に、更新ベクトルΔｈ_*’（ｋ）を求め、
ｈ_*’（ｋ＋１）＝ｈ_*’（ｋ）＋μΔｈ_*’（ｋ）
とすることにより与えられている。 The unknown system estimation filter is updated by (Equation 2). The updated unknown system estimation filter h _* ′ (k + 1) is represented by the following simultaneous equations:

To obtain an update vector Δh _* ′ (k) so that
h _* ′ (k + 1) = h _* ′ (k) + μΔh _* ′ (k)
And is given by.

の最小ノルム解に相当する。
ここで、（式２）が（式１）より複雑な原因となっているのは、ｘ_*（ｋ）とｅ（ｋ）に加え、１ステップ過去の入力信号ベクトルｘ_*（ｋ−１）と誤差信号ｅ（ｋ−１）が導入されているためとみることができる。いま、（式２）の右辺第２項

とを比較すると、ｘ_*（ｋ）とｘ_*（ｋ−１）、或いはｅ（ｋ）とｅ（ｋ−１）とが統計的に同じ程度の大きさをとるとすれば、その絶対値が１より小さい（１−μ）により重み付けられている（式２）の右辺第３項の方が、更新に小さく影響しているとみることができる。そこで、（式２）の右辺第３項にのみ現れるｅ（ｋ−１）を正確に適用する変わりに、（式２）の右辺第２項にあるｅ（ｋ）に基づいて、以下の様に近似することを考える。 That is, in the affine projection algorithm, Δh ′ (k) is

Corresponds to the minimum norm solution of.
Here, the reason why (Equation 2) is more complicated than (Equation 1) is that x _* (k) and e (k), in addition to the input signal vector x _* (k−1) of one step in the past. And the error signal e (k−1) is introduced. Now, the second term on the right side of (Equation 2)

If x _* (k) and x _* (k-1) or e (k) and e (k-1) are statistically the same size, the absolute value It can be considered that the third term on the right side of (Expression 2) weighted by (1-μ) smaller than 1 has a smaller influence on the update. Therefore, instead of correctly applying e (k−1) that appears only in the third term on the right side of (Expression 2), the following is obtained based on e (k) in the second term on the right side of (Expression 2). Consider approximating to.

と表し、ｘ_*（ｋ−１）と直交する方向（式４右辺第１項）と、ｘ_*（ｋ−１）の方向（式４右辺第２項）との２つのベクトルに直交展開し、それぞれのベクトル成分のノルムの二乗に応じてｅ（ｋ）を分配する際に、ｘ_*（ｋ−１）の方向のベクトル成分に起因する誤差は、１ステップ過去の推定フィルタ更新によって、（１−μ）倍小さくなったとみなすことにより得られる。即ち、ｅ（ｋ）は、

と分解され、この式の右辺第２項が、ｘ_*（ｋ−１）の方向のベクトル成分、即ち（ｒ₀₁／ｒ₁₁）ｘ_*（ｋ−１）に起因するとみなされる誤差信号である。そこで、ｘ_*（ｋ−１）に起因する誤差（１−μ）ｅ（ｋ−１）に相当する誤差は、（式５）右辺第２項をｒ₁₁／ｒ₀₁倍することにより、（式３）の様に近似される。

And represents, x _* (k-1) orthogonal to the direction (Expression 4 the first term of the right side), x _* (k-1) orthogonal expanded into two vectors and the direction (Equation 4 the second term on the right side) of the When e (k) is distributed according to the square of the norm of each vector component, the error caused by the vector component in the direction of x _* (k−1) It can be obtained by assuming that 1−μ) times smaller. That is, e (k) is

The second term on the right side of this equation is an error signal that is considered to be caused by a vector component in the direction of x _* (k−1), that is, (r ₀₁ / r ₁₁ ) x _* (k−1). . Therefore, the error corresponding to the error (1-μ) e (k−1) due to x _* (k−1) is expressed by (Expression 5) by multiplying the second term on the right side by r ₁₁ / r ₀₁ ( It is approximated as shown in Equation 3).

（式６）は、この発明の課題を解決する未知系推定フィルタの更新式である。また、この発明において、未知系推定フィルタの更新に用いる更新調整係数が、各ステップｋに対して、変化してもよく、その場合、（式６）は、

となる。
この発明においては、（式６）、或いは、より一般化された（式７）により、未知系の推定フィルタの更新を行う。これらの式は、（式２）と比較して、ｅ（ｋ−１）を含まず、簡易に更新を実現することができる。
この発明の実施例を図１を参照して具体的に説明する。 When the approximation of (Expression 3) is applied to (Expression 2), a new update expression for updating the unknown system estimation filter is obtained.

(Expression 6) is an update expression of the unknown system estimation filter that solves the problem of the present invention. In the present invention, the update adjustment coefficient used for updating the unknown system estimation filter may change with respect to each step k.

It becomes.
In the present invention, the unknown system estimation filter is updated according to (Expression 6) or more generalized (Expression 7). These equations do not include e (k−1) compared to (Equation 2), and can be easily updated.
An embodiment of the present invention will be specifically described with reference to FIG.

The embodiment of FIG. 1 inputs an unknown system output signal y (k) and the unknown system input signal x (k) obtained by giving an input signal x (k) to the unknown system, This is an unknown system estimation device that estimates the transfer characteristics of the system or realizes output prediction and simulation from an unknown system.
Reference numeral 101 denotes an input signal vectorization unit, which is a part that samples and accumulates a finite number of input signals x (k), vectorizes them, and outputs an input signal vector x _* (k).
An unknown system estimation filter 102 receives the input signal vector x _* (k) vectorized by the input signal vectorization unit 101 and simulates the output signal y (k) from the unknown system. k) is a part to output.

An error calculation unit 103 subtracts the simulated output signal y ′ (k) output from the unknown system estimation filter h _* ′ (k) 102 from the unknown system output signal y (k) to generate an error signal e (k). Is a part that outputs.
Reference numeral 104 denotes a delay unit, which is a part that inputs the input signal vector x _* (k) vectorized from the input signal vectorization unit 101 and generates the input signal vector x _* (k−1) of one step in the past.
Reference numeral 201 denotes a delay input reference type estimation filter update unit which inputs the input signal vector x _* (k) from the input signal vectorization unit 101 and inputs the input signal vector x _* (k−1) from the delay unit 104 one step in the past. Further, an error signal obtained by subtracting the output simulation signal y ′ (k) from the output signal y (k) of the unknown system is input from the error calculation unit 103. The delayed input reference type estimation filter update unit 201 has a time-varying or fixed update adjustment coefficient, inputs an input signal vector, an input signal vector of one step past, and an error signal, and from the input signal vector, A correlation-reduced input signal vector is obtained by subtracting a vector component correlated with an input signal vector in the past of one step from the input signal vector multiplied by the update adjustment coefficient used in the past of one step. Is an area where the update value of the unknown system estimation filter is given to the unknown system estimation filter 102 by dividing by the inner product of the input signal vector and the correlation reduced input signal vector, multiplying by the error signal, and multiplying by the update adjustment coefficient.

を得、未知系推定フィルタを更新する遅延入力参照型推定フィルタ更新部２０１を独自に有している。 The embodiment of the present invention includes the input signal vectorization unit 101, the unknown system estimation filter 102, the error calculation unit 103, and the delay unit 104 of the conventional example illustrated and described with reference to FIG. However, the embodiment of the present invention does not require the weighted delay unit 105 of the conventional example that obtains the error signal (1-μ) e (k−1) of one step past weighted by (1-μ). Further, the input signal vector x _* (k), the input signal vector x _* (k−1) in the past of one step, and the error signal e (k) are input, and the input signal vector x _* (k) according to (Equation 7). from used one step past x _* 1 step past input signal of the _{(k) x * (k-} 1) and a correlation vector component _{(r 10 / r 11) x} * (k-1) The correlation-reduced input signal vector [x _* (k) −μ (k−1) (r ₁₀ / r ₁₁ ) x _* (k−1)] obtained by subtracting the product of the update adjustment coefficient μ (k−1). Is divided by the inner product [r ₀₀ −μ (k−1) (r ₀₁ r ₁₀ / r ₁₁ )] of the input signal vector and the correlation-reduced input signal vector, and the error signal e (k) , The update value of the unknown system estimation filter by multiplying by the update adjustment coefficient μ (k)

And has a delay input reference type estimation filter update unit 201 for updating the unknown system estimation filter.

の様に拡張することにより、この発明の効果を維持しながら、更に、零除算による数値の不安定化を防ぐことができる。この場合、相関低減入力信号ベクトルは、
[ｘ_*（ｋ）−μ（ｋ−１）（ｒ₁₀／（ｒ₁₁＋δ₁））ｘ_*（ｋ−１）]に相当し、入力信号ベクトルと相関低減入力信号ベクトルの内積は、[ｒ₀₀−μ（ｋ−１）（ｒ₀₁ｒ₁₀／（ｒ₁₁＋δ₁））+δ₂]に相当する。また、（式６）についても同様な拡張をすることができる。 [Example 2]
Introducing non-negative parameters δ ₁ and δ ₂ ,

By extending like this, it is possible to further prevent the numerical value from becoming unstable due to division by zero while maintaining the effect of the present invention. In this case, the correlation-reduced input signal vector is
[x _* (k) −μ (k−1) (r ₁₀ / (r ₁₁ + δ ₁ )) x _* (k−1)], and the inner product of the input signal vector and the correlation-reduced input signal vector is [ r ₀₀ −μ (k−1) (r ₀₁ r ₁₀ / (r ₁₁ + δ ₁ )) + δ ₂ ]. Further, the same extension can be applied to (Equation 6).

[Example 3]
When the update adjustment coefficient μ may be changed with respect to step k, as an alternative for preventing division by zero described in [Embodiment 2], r ₁₁ = 0 or [r ₀₀ −μ ( (k-1) When (r ₀₁ r ₁₀ / r ₁₁₁ )] = 0, it is also possible to update (Equation 7) by setting μ (k) = 0. Also, the condition for setting μ (k) = 0 is only when it completely matches 0 as r ₁₁ <ε, r ₀₀ −μ (k−1) (r ₀₁ r ₁₀ / r ₁₁₁ ) <ε. Alternatively, μ (k) = 0 may be set in the vicinity of 0.

  The present invention is as described above, and the affine projection algorithm uses the input signal vector of the previous step and the error signal of the previous step for updating the unknown system estimation filter in addition to the input signal and the error signal of the current step. In contrast, instead of using the error signal of one step in the past, this is replaced with an approximate value based on the error signal of the current step, so that the unknown system estimation filter is updated by a simple calculation compared to the affine projection algorithm. be able to. The estimation speed of the unknown system estimation filter of the present invention is equivalent to the affine projection algorithm for colored input signals and is faster than the learning identification method. In FIG. 2, a stationary signal having an average spectrum of speech as a frequency characteristic is given as an input signal, and the norm of the difference between the 512-tap unknown filter coefficient vectors as well as the 512-tap estimated filter coefficient vector is “filter coefficient error”. Are plotted for each estimation step in dB. The comparison estimation methods are the present invention, the affine projection algorithm, and the learning identification method. Further, white noise is added to the output of the unknown system, and the update adjustment coefficient μ is set so that the “filter coefficient error” becomes equal in the steady state, μ = 0.65 in the present invention, and μ = 0 in the affine projection algorithm. .22, the learning identification method was set to μ = 1.0.

  The present invention can be used for estimation of transfer characteristics between a speaker and a microphone in an acoustic echo canceller, and can also be used for a line echo canceller.

The figure explaining the Example of an unknown system estimation apparatus. The figure which shows the comparison of the unknown system estimated speed between this invention and a prior art example. The figure explaining the concept of unknown system estimation. The figure explaining the prior art example of an unknown system estimation apparatus.

Explanation of symbols

DESCRIPTION OF SYMBOLS 101 Input signal vectorization part 102 Unknown system estimation filter 103 Error calculation part 104 Delay part 105 Weighted delay part 106 Delay input and delay error reference type estimation filter update part 201 Delay input reference type estimation filter update part

Claims (2)

In an unknown system estimation method for inputting an input signal x (k) to an unknown system in a discrete-time k domain and an output signal y (k) from the unknown system and estimating transfer characteristics of the unknown system,
Sample and store a finite number of input signals x (k), vectorize them, and output an input signal vector x _* (k),
An input signal vector x _* (k) is input to the unknown system estimation filter, and an output simulation signal y ′ (k) that simulates the output signal y (k) from the unknown system is generated.
An error signal e (k) is generated by subtracting the output simulation signal y ′ (k) from the output signal y (k) of the unknown system,
Based on the input signal vector x _* (k), an input signal vector x _* (k−1) of one step past is generated,
An input signal vector that has a time-varying or fixed update adjustment coefficient and that is one step past from the input signal vector based on the input signal vector, the input signal vector that is one step past, and the error signal. A correlation-reduced input signal vector is obtained by subtracting the vector component correlated with the update adjustment coefficient used in the previous step, and the correlation-reduced input signal vector is the inner product of the input signal vector and the correlation-reduced input signal vector. Dividing the error signal and multiplying by the update adjustment coefficient to give the update value of the unknown system estimation filter to the unknown system estimation filter.
An unknown system estimation method characterized by this. In an unknown system estimation apparatus that inputs an input signal x (k) to an unknown system in the discrete time k region and an output signal y (k) from the unknown system, and estimates the transfer characteristics of the unknown system,
An input signal vectorization unit that samples and accumulates a finite number of input signals x (k), vectorizes them, and outputs an input signal vector x _* (k);
An unknown system estimation filter h that receives an input signal vector x _* (k) vectorized by the input signal vectorization unit and outputs an output simulation signal y ′ (k) that simulates an output signal y (k) from the unknown system. _* '(K),
An error calculator that subtracts the output simulation signal y ′ (k) output from the unknown system estimation filter h _* ′ (k) from the output signal y (k) of the unknown system and outputs an error signal e (k);
A delay unit that inputs an input signal vector x _* (k) vectorized from the input signal vectorization unit to generate an input signal vector x _* (k−1) that is one step past;
It has a time-varying or fixed update adjustment coefficient, inputs an input signal vector, an input signal vector of one step past, and an error signal, and inputs an input signal of one step past of the input signal vector from the input signal vector A correlation-reduced input signal vector obtained by subtracting the vector component correlated with the vector multiplied by the update adjustment coefficient used in the previous step is obtained, and the inner product of the correlation-reduced input signal vector and the correlation-reduced input signal vector A delay input reference type estimation filter update unit that gives an update value of the unknown system estimation filter to the unknown system estimation filter 102 by multiplying by an error signal and multiplying by an update adjustment coefficient,
An unknown system estimation device characterized by that.

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