JP4344306B2 - Unknown system estimation method and apparatus for carrying out this method - Google Patents

Description

  The present invention relates to an unknown system estimation method and an apparatus for performing the method, and in particular, simulates an unknown system by inputting an input signal given to the unknown system such as acoustic transfer characteristics and an output signal obtained by giving the input signal. The present invention relates to an unknown system estimation method for estimating an FIR filter to be performed, or realizing prediction and simulation of an output from an unknown system, and an apparatus for implementing this method.

Referring to FIG. 3, an input signal x (k) is given to an unknown system characterized by a vector L _* of length L having an impulse response as an element, and the resulting output signal y (k) And the input signal x (k) and the unknown system estimation apparatus 1 that estimates the characteristics of the unknown system are known. 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 is sequentially updated and estimated as follows. Hereinafter, the vector x is written as x _*, and the vector z is written as z _* .
_{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 _*. (K) norm, μ is an update adjustment coefficient that takes a value between 0 and 2, error signal e (k) = y (k) −y ′ (k), output simulation signal y ′ (k) = h _* '(K) ^T x _* (k). This method has a problem that the estimated speed of the unknown system becomes slow when the input signal x (k) is a colored signal like speech.

であり、更新調整係数は、固定、時変の場合も含め、μ（ｋ）と表記している。ここで、（式２）の場合は、（式１）の場合と比較して、未知系推定フィルタｈ_*’（ｋ）に２つベクトルを加えて更新するので、更新に要する計算量は、（式１）の場合の約２倍に増加する。この問題を克服する［非特許文献３］による更新方法は、未知系推定フィルタｈ_*’（ｋ）をｚ_*（ｋ）で置き換え、以下の様に更新する。 On the other hand, the affine projection algorithm shown in [Non-Patent Document 2] overcomes this problem, and estimates the estimation filter h _* '(k) of the unknown system by updating it as follows (order). Is 2).
h _* ′ (k + 1) = h _* ′ (k) + D (k) α (k) x _* (k) + D (k) β (k) x _* (k−1) (Formula 2)
However,

The update adjustment coefficient is expressed as μ (k), including fixed and time-varying cases. Here, in the case of (Expression 2), compared to the case of (Expression 1), two vectors are added to the unknown system estimation filter h _* ′ (k) and updated. It increases about twice as much as in the case of (Formula 1). In the update method according to [Non-Patent Document 3] that overcomes this problem, the unknown system estimation filter h _* ′ (k) is replaced with z _* (k) and updated as follows.

z _* (k + 1) = z _* (k) + {D (k-1) [alpha] (k-1) + D (k) [beta] (k)} x _* (k-1) (Formula 4)
here,
h _* ′ (k) = z _* (k) + D (k−1) α (k−1) x _* (k−1) (formula 4.1)
Therefore, the output simulation signal y˜ (k) = z _* (k) ^T x _* (k), which is the output of the unknown system estimation filter z _* (k), is obtained from the unknown system estimation filter h _* ′ ( The output simulation signal y ′ (k) = h _* ′ (k) ^T x _* (k) by k) does not match, but from (Equation 4.1),
y ′ (k) = y˜ (k) + D (k−1) α (k−1) r ₁ (k) (Formula 5)
It can be seen that it can be corrected. Therefore, the update method of [Non-Patent Document 3] can obtain a processing result that completely matches the affine projection algorithm, and (Equation 4) updates the unknown system estimation filter by one vector. It is possible to realize the update with a smaller amount of calculation than Expression (2). Hereinafter, this unknown system estimation apparatus will be described in detail 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). , a power calculation unit 102 for calculating the input power r ₀ (k) as the sum of the squares of each element of the input signal vector x _* (k), a delay unit to obtain a one-step past input signal vector x _* (k-1) 103, a correlation calculation unit 104 that calculates an input correlation r ₁ (k) as an inner product of the input signal vector x _* (k) and x _* (k−1) in the past by one step, and the input signal vector x _* (k) , And an unknown system estimation filter z _* (k) that outputs an output simulation signal y˜ (k) = z _* (k) ^T x _* (k) that simulates the output signal y (k) from the unknown system h _*. ) 105 and the output simulation signals y to (k) according to (Equation 5). Y as a correction output simulation signal 'and the output correction unit 106 for outputting (k), the unknown system h _* correction from the output signal y (k) from the output simulation signal y' (k) by subtracting the error signal e (k) , An error calculation unit 107 that outputs a weighted delay error signal eμ (k−1) = (1−μ (k−1)) e (k−1), and a time-varying or It has a fixed update adjustment coefficient μ (k), inputs an input power r ₀ (k), an input correlation r ₁ (k), an error signal e (k), and a weighted delay error signal eμ (k−1), Based on (Expression 3), a vector multiplier calculation unit 109 that calculates [D (k−1) α (k−1) + D (k) β (k)] in (Expression 4) as a vector multiplier v (k). If, as the product of one step past input signal vector x _* (k-1) and the vector multipliers v (k), the estimated filter update vector Le v give _{(k) x * (k-} 1), by adding the _* unknown system estimation filter z (k), the unknown system to generate a _* unknown system estimation filter z (k + 1) for use in the next step estimates A filter update unit 110.
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. Yusuke Maruyama: “Fast Algorithm of Projection Algorithm” 1990 IEICE Spring National Convention, B-744, 1990.

  The unknown system estimation apparatus shown in FIG. 4 can efficiently update the affine projection algorithm defined by (Equation 2) and the processing result while completely matching. By the way, the present invention removes the constraint that the processing result and the affine projection algorithm defined by (Equation 2) are completely coincident, and the processing result is only approximate coincidence, so that the unknown system estimation illustrated in FIG. It is an object of the present invention to provide an unknown system estimation apparatus that requires a smaller amount of calculation than the apparatus.

In the affine projection algorithm shown in (Expression 2), there is a method based on (Expression 4) and (Expression 5) as a high-speed algorithm (an algorithm with a small amount of calculation) that exactly matches the processing result of (Expression 2). In the present invention, (Equation 2) is approximated by (Equation 9), and further, by reducing the amount of calculation based on (Equation 11) and (Equation 12), (Equation 4), (Equation 5) The unknown system estimation can be achieved with a smaller amount of calculation than the method based on.
Claim 1: In an unknown system estimation method for inputting an input signal to an unknown system in the discrete time domain and an output signal from the unknown system and estimating the transfer characteristics of the unknown system, the input signal to the unknown system Are sampled and stored, vectorized and output as an input signal vector, input power is calculated as the sum of squares of each element of the input signal vector, an input signal vector of one step in the past is obtained, and an input signal vector and one step are calculated Calculates input correlation as inner product of past input signal vectors, inputs input signal vector to unknown system estimation filter, outputs output simulation signal to simulate output signal from unknown system, and outputs output signal to input correlation value And output a corrected output simulation signal, subtract the corrected output simulation signal from the output signal from the unknown system, output an error signal, and change the time-varying or fixed update adjustment coefficient That is, the input power, the input correlation, and the error signal are input, the weighted input correlation is calculated as the product of the input correlation and the update adjustment coefficient used in the previous step, and the input power and the input power in the previous step The product of the weighted input correlation and the input correlation is subtracted from the product of to calculate a correlation reduced power product, and the product of the error signal divided by the correlation reduced power product and the update adjustment coefficient is obtained as a weighted normalized error signal, A vector multiplier is obtained by subtracting the product of the weighted normalized error signal and the weighted input correlation from the product of the weighted normalized error signal calculated in the past one step and the input power in the past two steps. The estimated filter update vector is obtained as the product of the input signal vector and the vector multiplier, and is added to the unknown system estimation filter. Generating a filter constituted the unknown system estimation method of.

  Claim 2: In an unknown system estimation device that inputs an input signal to an unknown system in the discrete time domain and an output signal from the unknown system, and estimates the transfer characteristics of the unknown system, the input signal to the unknown system is An input signal vectorization unit 101 that samples and accumulates a finite number of samples, vectorizes them, and outputs an input signal vector; a power calculation unit 102 that calculates input power as the sum of squares of each element of the input signal vector; A delay unit 103 that obtains a signal vector, a correlation calculation unit 104 that calculates an input correlation as an inner product of the input signal vector and the input signal vector of one step in the past, and an input signal vector are input to simulate an output signal from an unknown system The unknown system estimation filter 105 that outputs the output simulation signal and the output simulation signal are corrected according to the value of the input correlation to output the corrected output simulation signal. A correction unit 202; an error calculation unit 107 that outputs an error signal by subtracting a correction output simulation signal from an output signal from an unknown system; and a time-varying or fixed update adjustment coefficient, and includes input power, input correlation, and error signal. , And calculates the weighted input correlation as the product of the input correlation and the update adjustment coefficient used in the past by one step, and calculates the weighted input correlation and the input correlation from the product of the input power and the input power in the previous step. The product of the correlation reduction power product is calculated by subtracting the product of, and the product of the error signal divided by the correlation reduction power product and the update adjustment coefficient is obtained as a weighted normalization error signal, and the weighted normalization error calculated one step in the past A vector multiplier calculation unit 2 that obtains a vector multiplier by subtracting the product of the weighted normalized error signal and the weighted input correlation from the product of the signal and the input power of two steps in the past. An unknown system estimation generating an unknown system estimation filter used in the next step by obtaining an estimated filter update vector as a product of 1 and the input signal vector of the previous step and the vector multiplier and adding it to the unknown system estimation filter An unknown system estimation device including the filter update unit 110 is configured.

  In the affine projection algorithm shown in (Expression 2), there is a method based on (Expression 4) and (Expression 5) as a high-speed algorithm (an algorithm with a small amount of calculation) that exactly matches the processing result of (Expression 2). In the present invention, (Equation 2) is approximated by (Equation 9), and further, by reducing the amount of calculation based on (Equation 11) and (Equation 12), (Equation 4), (Equation 5) The unknown system estimation can be achieved with less computational complexity. Comparing the amount of calculation required for updating the unknown system estimation filter with the number of taps of the unknown system estimation filter as L, the method according to (Expression 4) and (Expression 5) is added: 2L + 9 times, multiplication: 2L + 15 times, and division: The method according to (Equation 11) and (Equation 12) according to the present invention can be executed at once: addition: 2L + 7 times, multiplication: 2L + 12 times, division: once. For example, the calculation amount can be reduced by about 20% in a portion that does not depend on the number of taps L of the filter. The estimation speed of the estimation filter of the present invention for a colored input signal is equivalent to the affine projection algorithm and is faster than the learning identification method.

これは以下の考えに基く。誤差信号ｅ（ｋ）を生成する入力信号ベクトルｘ_*（ｋ）を、以下の様に、

と表し、１ステップ過去の入力信号ベクトルｘ_*（ｋ−１）と直交する方向（式７右辺第一項）と、１ステップ過去の入力信号ベクトルｘ_*（ｋ−１）の方向（式７右辺第二項）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誤差信号ｅ（ｋ）を分配する際に、１ステップ過去の入力信号ベクトル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（ｋ−１））倍小さくなったとみなすことにより得られる。即ち、誤差信号ｅ（ｋ）は、

と分解され、この式の右辺第二項が、１ステップ過去の入力信号ベクトルｘ_*（ｋ−１）の方向のベクトル成分、即ち、
（ｒ₁(ｋ）／ｒ₀(ｋ−１））ｘ_*（ｋ−１）に起因すると、近似的に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（ｋ−１））ｅ（ｋ−１）に相当する誤差は、（式８）右辺第二項をｒ₀(ｋ−１）／ｒ₁(ｋ）倍することにより、（式６）の様に近似される。（式６）近似を（式２）に適用し、記号の標記を改めると、

となる。更に、（式９）に対して、未知系推定フィルタｈ_*’（ｋ）を以下の様に、ｚ_*（ｋ）で置き換える。
ｚ_*(k+1)＝ｚ_*’(ｋ)＋｛Ｅ(ｋ−１）ｒ₀(ｋ−２）−Ｅ(ｋ）ｒμ(ｋ)｝ｘ_*(ｋ−1)
（式１１）
ここで、
ｈ_*’（ｋ）＝ｚ_*(ｋ)＋Ｅ(ｋ−１）ｒ₀(ｋ−２）ｘ_*(ｋ−１) （式１１．１）
の関係があるため、未知系推定フィルタｚ_*（ｋ）の出力である出力模擬信号
ｙ〜(ｋ）＝ｚ_*（ｋ）^Tｘ_*（ｋ）は、未知系推定フィルタｈ_*’（ｋ）による出力模擬信号ｙ’（ｋ）＝ｈ_*’（ｋ）^Tｘ_*（ｋ）とは一致しないが、（式１１．１）より、
ｙ’(ｋ)＝ｙ〜(ｋ)＋Ｅ(ｋ−１）ｒ₀(ｋ−２）ｒ₁(ｋ) （式１２）
と補正できることがわかる。 In the present invention, the weighted delay error signal eμ (k−1) = (1−μ (k−1)) e (k−) used in the calculation of α (k) and β (k) in (Equation 2). Consider replacing 1) with the following approximate values:

This is based on the following idea. An input signal vector x _* (k) that generates an error signal e (k) is expressed as follows:

And it represents one step of the past input signal vector x _* (k-1) orthogonal to the direction (7 first term on the right side), one step past input signal vector x _* (k-1) direction (Equation 7 When the error signal e (k) is distributed orthogonally to the two vectors in the second term on the right side) and the error signal e (k) is distributed according to the square of the norm of each vector component, the input signal vector x _* (k−1) The error due to the vector component in the direction) is obtained by assuming that the estimation filter has been reduced by (1−μ (k−1)) times by updating the estimation filter in one step. That is, the error signal e (k) is

And the second term on the right side of the equation is a vector component in the direction of the input signal vector x _* (k−1) in the past of one step, that is,
(R ₁ (k) / r ₀ (k−1)) x _* (k−1) is an error signal that can be regarded approximately. Therefore, the error corresponding to the error (1-μ (k−1)) e (k−1) due to x _* (k−1) is expressed by (Equation 8) where the second term on the right side is represented by r ₀ (k−1). ) / R ₁ (k) times, it is approximated as (Equation 6). (Equation 6) Applying the approximation to (Equation 2) and revising the symbol,

It becomes. Further, for (Equation 9), the unknown system estimation filter h _* ′ (k) is replaced with z _* (k) as follows.
z _* (k + 1) = z _* ′ (k) + {E (k−1) r ₀ (k−2) −E (k) rμ (k)} x _* (k−1)
(Formula 11)
here,
h _* ′ (k) = z _* (k) + E (k−1) r ₀ (k−2) x _* (k−1) (Formula 11.1)
Therefore, the output simulation signal y to (k) = z _* (k) ^T x _* (k), which is the output of the unknown system estimation filter z _* (k), is represented by the unknown system estimation filter h _* ′ (k ) Output simulation signal y ′ (k) = h _* ′ (k) ^T x _* (k) does not match, but from (Equation 11.1),
y ′ (k) = y˜ (k) + E (k−1) r ₀ (k−2) r ₁ (k) (Formula 12)
It can be seen that it can be corrected.

The method according to the present invention based on (Expression 11) and (Expression 12) can realize unknown system estimation with a smaller amount of calculation than the methods based on (Expression 4) and (Expression 5).
An embodiment of the unknown system estimation apparatus according to the present invention will be specifically described with reference to FIG.
Compared with the conventional example of the unknown system estimation apparatus illustrated and described with reference to FIG. 4, this embodiment has an input signal vectorization unit 101, a power calculation unit 102, a delay unit 103, a correlation calculation unit 104, an unknown system estimation filter 105, The error calculation unit 107 and the unknown system estimation filter update unit 110 are shared. However, this embodiment eliminates the need for the weighted delay unit 108 for obtaining the error signal (1-μ) e (k−1) of one step past weighted by (1-μ). Instead, the input power r ₀ (k), the input correlation r ₁ (k), and the error signal e (k) are input, and the weighted input correlation rμ (k) according to (Equation 10) and (Equation 11). = Μ (k−1) r ₁ (k) is calculated and divided by [r ₀ (k) r ₀ (k−1) −rμ (k) r ₁ (k)] calculated as a correlation reduction power product. The product of the error signal e (k) and the update adjustment coefficient μ (k) is obtained as a weighted normalized error signal E (k), and the vector multiplier v (k) is v (k) = E (k−1) r. _The vector multiplier calculation unit 201 obtained as ₀ (k−2) −E (k) rμ (k), and according to (Equation 12), the output simulation signals y to (k) are input to the input correlation r ₁ (k) and one step past. and a correction by adding the product of the weighted normalized error signal E (k-1) and two steps past input power r ₀ (k-2), to output the y '(k) as a corrected output simulation signal An output correction unit 202, a is independently a.

[Example 2]
A non-negative parameter δ is introduced, and the weighted normalized error signal E (k) shown in (Equation 10) is expressed as E (k) = μ (k) e (k) / {r ₀ (k) r ₀ (k− 1) −rμ (k) r ₁ (k) + δ}
If this is replaced, it is possible to prevent the numerical value from becoming unstable due to division by zero while maintaining the effect of the present invention, although it involves an increase of one addition. Here, it is obvious that [r ₀ (k) r ₀ (k−1) −rμ (k) r ₁ (k)] > 0 always holds in the range of 0 <μ (k) <2.

[Example 3]
As another embodiment for preventing the division by zero of the weighted normalized error signal E (k) shown in (Expression 10), [r ₀ (k) r ₀ (k−1) −rμ (k) r _{When 1} (k)] = 0, r ₀ (k) = 0, or r ₀ (k−1) = 0, μ (k) = 0 is set, and updating of (Equation 11) is stopped. Good. Further, the condition for setting μ (k) = 0 is [r ₀ (k) r ₀ (k−1) −rμ (k) r ₁ (k)] <ε or r ₀ (k) <ε or As r ₀ (k−1) <ε, etc., μ (k) = 0 may be set in the vicinity of 0 as well as when it completely matches 0.

  The present invention is as described above. In the affine projection algorithm shown in (Expression 2), (Expression 4), (Expression 4), (Expression 4), There is a method based on (Equation 5), but (Equation 4) is approximated by (Equation 9), and further, by reducing the amount of calculation based on (Equation 11) and (Equation 12), (Equation 4) The unknown system estimation can be achieved with a smaller amount of calculation than (Equation 5). Comparing the amount of calculation required for updating the unknown system estimation filter with the number of taps of the unknown system estimation filter as L, the method according to (Expression 4) and (Expression 5) is added: 2L + 9 times, multiplication: 2L + 15 times, and division: The method according to (Equation 11) and (Equation 12) according to the present invention can be executed at once: addition: 2L + 7 times, multiplication: 2L + 12 times, division: once. For example, the calculation amount can be reduced by about 20% in a portion that does not depend on the number of taps L of the filter.

  As shown in FIG. 2, the estimation speed of the estimation filter of the present invention is the same as that of the affine projection algorithm for the colored input signal, 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 defined as “filter coefficient error”. , DB plotted for each estimation step. The comparison estimation methods are the present invention, the affine projection algorithm, and the learning identification method. In addition, white noise is added to the output of the unknown system, and the update adjustment coefficient μ is set to 0.65 in the present invention, and the affine projection algorithm is set to 0.22 so that the “filter coefficient error” becomes equal in the steady state. The learning identification method was set to 1.0.

  The present invention can be used to estimate the transfer characteristic between the speaker and the microphone in the acoustic echo canceller, and the same applies to the line echo canceller.

The figure explaining the Example of an unknown system estimation apparatus. The figure which compares this system and the unknown system estimated speed of a prior art example. The figure explaining the application concept of an unknown system estimation apparatus. 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 Power calculation part 103 Delay part 104 Correlation calculation part 105 Unknown system estimation filter 106 Output correction part 107 Error calculation part 108 Weighted delay part 109 Vector multiplier calculation part 110 Unknown system estimation filter update part 201 Vector multiplier Calculation unit 202 Output correction unit

Claims (2)

In the unknown system estimation method that inputs the input signal to the unknown system in the discrete time domain and the output signal from the unknown system and estimates the transfer characteristics of the unknown system,
Sample and store a finite number of input signals to the unknown system, vectorize and output the input signal vector,
Calculate the input power as the sum of squares of each element of the input signal vector,
Obtain the input signal vector of one step past,
Calculate the input correlation as the inner product of the input signal vector and the input signal vector of one step past,
Input the input signal vector to the unknown system estimation filter, and output the output simulation signal that simulates the output signal from the unknown system,
Correct the output simulation signal according to the input correlation value and output the corrected output simulation signal,
Subtract the correction output simulation signal from the output signal from the unknown system to output the error signal,
Has a time-varying or fixed update adjustment coefficient, inputs input power, input correlation, and error signal, calculates a weighted input correlation as the product of the input correlation and the update adjustment coefficient used in the previous step, and inputs Subtract the product of the weighted input correlation and the input correlation from the product of the power and the input power of one step in the past to calculate the correlation reduced power product, and calculate the product of the error signal divided by the correlation reduced power product and the update adjustment coefficient Obtained as a weighted normalized error signal, by subtracting the product of the weighted normalized error signal and the weighted input correlation from the product of the weighted normalized error signal calculated in the past one step and the input power in the past two steps. Get the vector multiplier,
An unknown filter estimation vector used in the next step is generated by obtaining an estimated filter update vector as a product of the input signal vector of the previous step and the vector multiplier and adding it to the unknown filter.
An unknown system estimation method characterized by this. In the unknown system estimation device that inputs the input signal to the unknown system in the discrete time domain and the output signal 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 to an unknown system, vectorizes them, and outputs an input signal vector;
A power calculator that calculates input power as the sum of squares of each element of the input signal vector;
A delay unit for obtaining an input signal vector of one step in the past;
A correlation calculation unit that calculates an input correlation as an inner product of the input signal vector and the input signal vector of one step in the past;
An unknown system estimation filter that inputs an input signal vector and outputs an output simulation signal that simulates an output signal from the unknown system;
An output correction unit that corrects the output simulation signal according to the value of the input correlation and outputs a corrected output simulation signal;
An error calculator that outputs an error signal by subtracting the corrected output simulation signal from the output signal from the unknown system;
Has a time-varying or fixed update adjustment coefficient, inputs input power, input correlation, and error signal, calculates a weighted input correlation as the product of the input correlation and the update adjustment coefficient used in the previous step, and inputs Subtract the product of the weighted input correlation and the input correlation from the product of the power and the input power of one step in the past to calculate the correlation reduced power product, and calculate the product of the error signal divided by the correlation reduced power product and the update adjustment coefficient Obtained as a weighted normalized error signal, by subtracting the product of the weighted normalized error signal and the weighted input correlation from the product of the weighted normalized error signal calculated in the past one step and the input power in the past two steps. A vector multiplier calculation unit for obtaining a vector multiplier;
An unknown system estimation filter update unit for generating an unknown system estimation filter to be used in the next step by obtaining an estimation filter update vector as a product of an input signal vector and a vector multiplier of one step in the past, and adding it to the unknown system estimation filter When,
An unknown system estimation device comprising:

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