JP6892111B2 - Direct inverse identification method and device for multi-input multi-output system, program and storage medium, multi-input multi-output reverse filter device and method - Google Patents

Description

The present invention relates to a direct inverse identification method and apparatus for a multi-input multi-output system, a program and a storage medium, and a multi-input multi-output inverse filter apparatus and method.

Examples of reverse system identification include automated equalizers in the field of communications and transoral systems in the field of acoustics. The equalizer that compensates for the signal distortion that occurs during transmission is the reverse system of the 1-input 1-output system, and the reverse filter used in the transoral system that reproduces the binoral recorded sound source with a stereo speaker is the 2-input 2-output system. Corresponds to the reverse system.
As a method of acoustically reproducing the sense of presence, there are methods such as a volume difference that reproduces sound image localization due to the attenuation of volume due to distance and a difference in sound intensity between both ears, and a time difference that reproduces sound image localization due to the difference in the time that sound waves reach. In addition, there is a method of reproducing by changing the frequency characteristics, phase, and reverberation, but there is also a binaural recording that includes the actual presence by recording as if it were actually heard by the human ear.

FIG. 1 shows an explanatory diagram of binaural recording using a dummy head.
In binaural recording, for example, microphones are embedded in both ears of a doll called a dummy head that imitates the shape of a human head. When this sound source is listened to by headphones or earphones, the information at the time of recording is reproduced as it is, so that a high sense of presence can be obtained.

Haruo Hamada, "Binaural Sound Field Reproduction System", Journal of Acoustical Society of Japan, Vol. 48, No. 4, pp. 250-257, 1992. S. Uto, H. et al. Hamada, T.M. Miura, P.M. A. Nelson, S.M. J. Elliot, "AUDIO EQUALIZER USING MULTI-CHANNEL ADAPTIVE DIGITAL FILTER", ASJ Symposium 91 International Symposium on April 1 421-426, 1991. P. A. Nelson, H. et al. Hamada, S.A. J. Elliot, "Adaptive Inverse Filters for Stereophonic Sound Reproduction", IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 40, No. 7, pp. 1621-1632, JULY 1992.

Japanese Unexamined Patent Publication No. 2012-151529 Japanese Unexamined Patent Publication No. 2012-151530 Japanese Unexamined Patent Publication No. 6-165298

However, wearing earphones and headphones is a burden on the user and gives a feeling of blockage. Transoral reproduction is a method of reproducing this binaural sound source at the ear using two left and right speakers.

FIG. 2 shows an explanatory diagram of the transoral system.
In order to realize transoral reproduction, an unknown 2-input 2-output system (H) reverse system is required to cancel the crosstalk component from the speaker to the ear [Non-Patent Document 1]. The estimated value of this inverse system is the inverse filter G ^ of FIG. At this time, it is desired that the transfer function matrix G ^ of the inverse filter satisfies the following relational expression. In addition, "^" attached on the symbol means an estimated value, and it is described in the upper right corner of the character for convenience of input, but as shown in the mathematical formula, it is the same as the one described directly above the character. Is.

式（２）は音源のオールパス特性を表し、式（３）はクロストークのキャンセルを表す。上式を満たす逆フィルタＧ＾を実現できれば、耳元でバイノーラル音源が再現される。つまり、録音時の信号を耳元で再現できるので、３次元の高臨場感が実現される。トランスオーラルシステムによる３次元高臨場感再生において、未知の２入力２出力系の逆システムを正確に同定することが重要であり、その精度が聴取時に得られる臨場感に大きく影響を与える。
従来法［非特許文献２、非特許文献３等］では、まず未知の２入力２出力系を同定し、その結果を用いて逆フィルタ、すなわち逆システムを求めると云った２段階方式をとっていた。そのため、誤差が２重に蓄積すると共に系の変動の影響を受け易いことが想定される。

Equation (2) represents the all-pass characteristic of the sound source, and equation (3) represents the cancellation of crosstalk. If the inverse filter G ^ that satisfies the above equation can be realized, the binaural sound source can be reproduced at the ear. That is, since the signal at the time of recording can be reproduced at the ear, a three-dimensional high presence feeling is realized. In the three-dimensional high-realism reproduction by the transoral system, it is important to accurately identify the reverse system of the unknown 2-input 2-output system, and the accuracy greatly affects the realism obtained at the time of listening.
In the conventional method [Non-Patent Document 2, Non-Patent Document 3, etc.], an unknown 2-input 2-output system is first identified, and the result is used to obtain an inverse filter, that is, an inverse system. It was. Therefore, it is assumed that the error is double accumulated and it is easily affected by the fluctuation of the system.

To solve this problem, a binaural audio reproduction method of a 2-input 2-output system has been proposed [Patent Document 1, Patent Document 2], but it has not been able to support a multi-input multi-output system.
Further, although a 4-input 4-output system sound reproduction device has been devised [Patent Document 3], the same two steps as the conventional method in which forward identification is performed and then inverse identification is performed using the result. It was a method. Therefore, it has the same problems as the conventional transoral system. Further, since the inverse filter of this device uses a fixed infinite impulse response digital filter or a fixed IIR (Infinite Impulse Response) digital filter, it is expected that daily use in a living space may be difficult.
Therefore, transoral reproduction that allows a plurality of listeners to experience the same sense of presence cannot be realized at a practical level, and has not been commercialized until now. In addition, the development of MIMO communication, vibration reproduction of earthquakes, reverse kinematics of robots, etc. has not progressed.

As described above, conventionally, the inverse filter G ^ has been obtained after obtaining the transfer function matrix H in the forward direction (see FIG. 6 described later). Therefore, it is a two-step process, and it is assumed that errors due to system fluctuations and accumulation of numerical errors cannot be ignored.
Further, conventionally, there has been no method for obtaining a practical inverse filter G ^ when the input / output is 3 channels or more, an inverse system using such an inverse filter G ^, a trans-aurus system, or the like. ..

In view of the above points, it is an object of the present invention to directly identify an unknown multi-input multi-output system inverse system / inverse filter from input / output data.

According to the first solution of the present invention
A direct inverse identification method for multi-input multi-output systems for multi-input multi-output inverse filter devices.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
An output unit _U 1 ~U _M first to M,
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The output unit U _i outputs the added value of the outputs of the inverse filters G ^ _{i 1} , ..., G ^ _{iM, and outputs the added value.}

The processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system.
^{The processing unit directly reverse-identifies the estimated value g ^ ij} _k of each filter coefficient of the inverse filter G ^ _ij (i, j = 1, ..., M) according to the following equations (6) to (11). Perform processing by the method and identify directly from the input / output measured values of the multi-input multi-output system.
A direct inverse identification method for a multi-input multi-output system is provided.

ここで、
ｇ＾^ｉｊ _ｋ：Ｎ次元ベクトル；ｊ番目のソースからｉ番目の伝達系の入力又は出力部への逆フィルタのフィルタ係数の推定値。
Ｋ^ｊ _ｓ，ｋ：Ｎ×１行列；ｊ番目のソースを処理する逆フィルタを求めるためのフィルタゲイン。
Ｙ^ｊ _ｋ：１×Ｎ行列；ｊ番目の伝達系の出力又は入力部の出力系列。
ｅ^〜ｉ _ｋ：ｉ番目の時間領域の誤差
ｋ：時間のインデックス

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
^e ~i _k: error of the i-th time domain k: index of the time

According to the second solution of the present invention
A direct inverse identification device for a multi-input multi-output system for a multi-input multi-output reverse filter device.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
An output unit _U 1 ~U _M first to M,
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The output unit U _i outputs the added value of the outputs of the inverse filters G ^ _{i 1} , ..., G ^ _{iM, and outputs the added value.}
The direct inverse identification device of the multi-input multi-output system is
Processing unit and
Memory and
With
The processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system.
^{The processing unit directly reverses the estimated value g ^ ij} _k of each filter coefficient of the inverse filter G ^ _ij (i, j = 1, ..., M) according to the following equations (6) to (11). Perform processing by the identification method to identify directly from the input / output measured values of the multi-input multi-output system.
A direct inverse identification device for a multi-input multi-output system is provided.

ここで、
ｇ＾^ｉｊ _ｋ：Ｎ次元ベクトル；ｊ番目のソースからｉ番目の伝達系の入力又は出力部への逆フィルタのフィルタ係数の推定値。
Ｋ^ｊ _ｓ，ｋ：Ｎ×１行列；ｊ番目のソースを処理する逆フィルタを求めるためのフィルタゲイン。
Ｙ^ｊ _ｋ：１×Ｎ行列；ｊ番目の伝達系の出力又は入力部の出力系列。
ｅ^〜ｉ _ｋ：ｉ番目の時間領域の誤差

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain

According to the third solution of the present invention
A direct inverse identification program for multi-input multi-output systems for multi-input multi-output inverse filter devices.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
An output unit _U 1 ~U _M first to M,
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The output unit U _i outputs the added value of the outputs of the inverse filters G ^ _{i 1} , ..., G ^ _{iM, and outputs the added value.}

A step in which the processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system, and
^{The processing unit directly reverse-identifies the estimated value g ^ ij} _k of each filter coefficient of the inverse filter G ^ _ij (i, j = 1, ..., M) according to the following equations (6) to (11). The step of executing the processing by the method and identifying directly from the input / output measured values of the multi-input multi-output system,
And storing said processing unit, an estimate g ^ ^ij _k of each filter coefficients identified in the storage unit,
A direct inverse identification program for a multi-input, multi-output system is provided to allow a computer to execute.

ここで、
ｇ＾^ｉｊ _ｋ：Ｎ次元ベクトル；ｊ番目のソースからｉ番目の伝達系の入力又は出力部への逆フィルタのフィルタ係数の推定値。
Ｋ^ｊ _ｓ，ｋ：Ｎ×１行列；ｊ番目のソースを処理する逆フィルタを求めるためのフィルタゲイン。
Ｙ^ｊ _ｋ：１×Ｎ行列；ｊ番目の伝達系の出力又は入力部の出力系列。
ｅ^〜ｉ _ｋ：ｉ番目の時間領域の誤差

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain

According to the fourth solution of the present invention
A computer-readable recording medium that records a direct inverse identification program for a multi-input, multi-output system for a multi-input, multi-output reverse filter device.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
An output unit _U 1 ~U _M first to M,
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The output unit U _i outputs the added value of the outputs of the inverse filters G ^ _{i 1} , ..., G ^ _{iM, and outputs the added value.}

A step in which the processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system, and
^{The processing unit directly reverse-identifies the estimated value g ^ ij} _k of each filter coefficient of the inverse filter G ^ _ij (i, j = 1, ..., M) according to the following equations (6) to (11). The step of executing the processing by the method and identifying directly from the input / output measured values of the multi-input multi-output system,
And storing said processing unit, an estimate g ^ ^ij _k of each filter coefficients identified in the storage unit,
A computer-readable recording medium is provided that records a direct inverse identification program for a multi-input, multi-output system for causing a computer to execute.

ここで、
ｇ＾^ｉｊ _ｋ：Ｎ次元ベクトル；ｊ番目のソースからｉ番目の伝達系の入力又は出力部への逆フィルタのフィルタ係数の推定値。
Ｋ^ｊ _ｓ，ｋ：Ｎ×１行列；ｊ番目のソースを処理する逆フィルタを求めるためのフィルタゲイン。
Ｙ^ｊ _ｋ：１×Ｎ行列；ｊ番目の伝達系の出力又は入力部の出力系列。
ｅ^〜ｉ _ｋ：ｉ番目の時間領域の誤差

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain

According to the fifth solution of the present invention
It is a multi-input multi-output inverse filter device that uses a multi-input multi-output system as a transmission system.
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
An output unit _U 1 ~U _M first to M,
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The output unit U _i outputs the added value of the outputs of the inverse filters G ^ _{i 1} , ..., G ^ _{iM, and outputs the added value.}

The processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system, executes processing by the direct inverse identification method according to the following equations (6) to (11), and executes the multi-input multi-output system. ^{Multi-input multi-output in which the estimated value g ^ ij} _{k of} each filter coefficient directly identified from the input / output measurement values of the output system is set in the inverse filter G ^ _ij (i, j = 1, ..., M). An inverse filter device is provided.

ここで、
ｇ＾^ｉｊ _ｋ：Ｎ次元ベクトル；ｊ番目のソースからｉ番目の伝達系の入力又は出力部への逆フィルタのフィルタ係数の推定値。
Ｋ^ｊ _ｓ，ｋ：Ｎ×１行列；ｊ番目のソースを処理する逆フィルタを求めるためのフィルタゲイン。
Ｙ^ｊ _ｋ：１×Ｎ行列；ｊ番目の伝達系の出力又は入力部の出力系列。
ｅ^〜ｉ _ｋ：ｉ番目の時間領域の誤差

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain

According to the sixth solution of the present invention
This is a multi-input multi-output reverse filter method using a multi-input multi-output reverse filter device that uses a multi-input multi-output system as a transmission system.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
An output unit _U 1 ~U _M first to M,
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The output unit U _i outputs the added value of the outputs of the inverse filters G ^ _{i 1} , ..., G ^ _{iM, and outputs the added value.}

The processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system, executes processing by the direct inverse identification method according to the following equations (6) to (11), and executes the multi-input multi-output system. ^{Multi-input multi-output in which the estimated value g ^ ij} _{k of} each filter coefficient directly identified from the input / output measurement values of the output system is set in the inverse filter G ^ _ij (i, j = 1, ..., M). A multi-input multi-output inverse filter method using an inverse filter device is provided.

ここで、
ｇ＾^ｉｊ _ｋ：Ｎ次元ベクトル；ｊ番目のソースからｉ番目の伝達系の入力又は出力部への逆フィルタのフィルタ係数の推定値。
Ｋ^ｊ _ｓ，ｋ：Ｎ×１行列；ｊ番目のソースを処理する逆フィルタを求めるためのフィルタゲイン。
Ｙ^ｊ _ｋ：１×Ｎ行列；ｊ番目の伝達系の出力又は入力部の出力系列。
ｅ^〜ｉ _ｋ：ｉ番目の時間領域の誤差

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain

According to the present invention, an unknown multi-input multi-output system inverse system / inverse filter can be identified directly from input / output data.

Explanatory drawing of binaural recording using a dummy head. Explanatory drawing of the transoral system. The block diagram of the inverse identification apparatus. Another block diagram of the inverse identification device. The figure of the transmission characteristic from the speaker SP1, SP2, SP3, SP4 to the microphone Mic1. Explanatory drawing which shows the difference between the present invention and / or the present embodiment and a conventional method. Explanatory drawing of direct inverse identification method of M input M output system. It is explanatory drawing of the input reproduction and the reverse filter apparatus of M input M output system. Flow chart of M × M transoral reproduction using direct inverse identification method. The same sound source _{(S L,} S _R) in two listen's illustration of 4x4 transaural system that can be enjoyed by sharing the sense of realism. Explanatory drawing of an example of a direct inverse identification method of a 3-input 3-output system and a verification experiment of a 3 × 3 transoral system. The figure which shows the transmission signal from the left speaker to the left microphone. The figure which shows the transmission signal of the left microphone from the right or the center speaker. The figure which shows the transmission signal of a central microphone from a central speaker. The figure which shows the transmission signal of a central microphone from a right or left speaker. The figure which shows the transmission signal from the right speaker to the right microphone. The figure which shows the transmission signal of the right microphone from the left or the center speaker. Explanatory drawing of an example of a direct inverse identification method of a 4-input 4-output system and a verification experiment of a 4 × 4 transoral system.

A. Overview According to the present invention and / or the present embodiment, for example, the following methods or devices can be provided.
1) A method / device for identifying the reverse system of a multi-input multi-output system directly from input / output data in real time.
2) A method / device for constructing a multi-input multi-output equalizer using the inverse filter obtained above.
3) A sound field reproduction method / device that allows multiple people to share a high sense of presence using the above inverse filter.
4) A method / apparatus for generating a system input that gives a desired output using the above inverse filter.

The transfer functions of the M × M paths of the unknown M input M output system H are set to H _ij , i, j = 1, ···, M, respectively, and the inputs of the z-transformed system are U ₁ , ···. , U _M , If the output of the system is Y ₁ , ..., Y _M , it can be expressed as follows. Here, M is a predetermined integer of 2 or more, and the present invention and / or the present embodiment can be applied particularly to a multi-input multi-output system in which M is an integer of 3 or more. ..

ここで、｛Ｕ_ｉ｝と｛Ｙ_ｉ｝は測定より既知となるが、伝達関数｛Ｈ_ｉｊ｝は未知である。

本発明及び／又は本実施の形態の特徴のひとつとしては、例えば、事前にＨ_ｉｊ， ｉ，ｊ＝1，・・・，Ｍを求めることなく、直接、次式を満たす逆フィルタＧ＾_ｉｊ， ｉ，ｊ＝１，・・・，Ｍを求めることである。

Here, {U _i } and {Y _i } are known from the measurement, but the transfer function {H _ij } is unknown.

One of the features of the present invention and / or the present embodiment is, for example, _{an inverse filter G ^ ij that directly satisfies the following equation without obtaining} H ij, i, j = 1, ..., M in advance. , I, j = 1, ..., M.

ただし、ｚ^−１は遅延演算子と呼ばれサンプルが1つ遅れることを表し、ｚ^−ＤＵ_ｉの逆ｚ変換はｕ^ｉ _ｋ−Ｄとなる。
また、Ｇ＾_ｉｊ、Ｕ_ｉ、Ｙ_ｊは、それぞれ、ｇ＾^ｉｊ _ｋ、ｕ^ｉ _ｋ、ｙ^ｊ _ｋのｚ変換である。

なお、記号の上に付される”＾”は、推定値の意味である。また、”〜”、”Ｕ”等は、便宜上付加した記号である。これらの記号は、入力の都合上、文字の右上に記載するが、数式で示すように、文字の真上に記載されたものと同一である。また、数式中太字で標記される記号、Ｙ、Ｈ、Ｕ、Ｇ、ｇ、Ｌ、Ｃ、Ｉ，Ｋ、Ｒ等は行列であり、本来数式で示すように太文字で記されるものであるが、出願形式の制約上、普通の文字で記載する。

^{However, z -1} represents that delayed one sample is called a delay ^operator, the inverse z transform of ^z -D _{U i} becomes ^u _{i k-D.}
Further, G ^ _ij , U _i , and Y _j are z-transforms of g ^ ^ij _k , u ⁱ _k , and y ^j _{k, respectively.}

The "^" attached above the symbol means an estimated value. Further, "~", "U" and the like are symbols added for convenience. These symbols are written in the upper right corner of the letters for convenience of input, but as shown in the mathematical formula, they are the same as those written directly above the letters. In addition, the symbols marked in bold in the mathematical formula, Y, H, U, G, g, L, C, I, K, R, etc. are matrices, and are originally written in bold as shown in the mathematical formula. However, due to restrictions on the application format, it will be written in ordinary characters.

B. Direct inverse identification method

FIG. 7 shows an explanatory diagram of the direct inverse identification method of the M input M output system.
Here, the acoustic system will be described as an example of the M input M output system, but the present invention and / or the present embodiment can be applied to a communication system, a vibration system, a control system, and the like. For example, in the case of a communication system, a vibration system, a control system, etc., a speaker and a microphone are used as an output unit such as a corresponding transmitter / transmitter / transmitter and a corresponding receiver / receiver / receiver / measurement unit. -The sound source may be replaced with an input unit such as a detection unit, or the sound source may be replaced with a source such as a corresponding signal source, transmission source, or information source. However, for example, the sources (eg, sound sources) X _{i of each input U i} to the transmission system are uncorrelated with each other. In this embodiment, U _1, ..., using a de-correlation of the U _M, running equalization and crosstalk cancellation passage area parallel distributed manner. U ₁ +. .. .. Even if it overlaps with + U _{M , U 1} ,. .. .. If ， _UM are uncorrelated, they can be processed separately.
In the forward identification (forward identification), U ₁ , ... .. .. _{If UM} is uncorrelated, the correlation matrix of the input signal is a block diagonal matrix and can be executed in parallel and distributed. In this embodiment (reverse identification), U ₁ , ... .. .. Even uncorrelated _{U M,} the input signal _Y 1 for general reverse system. .. .. , There is no guarantee that the Y _M correlation matrix will be a block diagonal matrix.

The direct inverse identification method is a block diagonalization of the correlation matrix based on the difference in signal arrival time from the input to the transmission system / unknown system H such as a speaker to the output of the transmission system / unknown system H such as a microphone.

を利用した並列分散適応フィルタ｛Ｇ＾_ｉｊ｝となる。各適応フィルタＧ＾_ｉｊのフィルタ係数（有限インパルス応答）ｇ＾^ｉｊ _ｋ＝［ｇ＾^ｉｊ _ｋ（０），・・・，ｇ＾^ｉｊ _ｋ（Ｎ−１）］^Ｔを求めるフィルタ方程式は次のように表される。

It becomes a parallel distribution adaptive filter {G ^ _ij } using. Filter coefficient of each adaptive filter G ^ _ij (finite impulse response) g ^ ^ij _k = [g ^ ^ij _k (0), ···, g ^ ^ij _k (N-1)] The filter equation for obtaining ^{T is as follows.} It is expressed as.

ただし、フィルタゲインＫ^ｊ _ｓ、ｋは、一例として後述のような、適応アルゴリズムによって計算される。また、伝達系・未知系Ｈの入力{ｕ^ｉ _ｋ−Ｄ｝（例えば、スピーカへの入力等）と伝達系・未知系Ｈの出力｛Ｙ^ｉ _ｋ｝（例えば、マイクの出力等）は測定により既知となり、ｋ−Ｎ＋１＜０のときｙ^ｉ _{ｋ−Ｎ＋１}＝０である。

However, the filter gains K ^js _{and k} are calculated by an adaptive algorithm as described later as an example. The input of the transmission system, the unknown system _{^{H {u i k-D}}} ( e.g., input or the like to the speaker) output of the transmission system, the unknown system H {Y i ^k} _(e.g., output, etc. of the microphone) is measured When k-N + 1 <0, y ⁱ _{k-N + 1} = 0.

[Explanation of symbols]
g ^ ^ij _k : N-dimensional vector; estimated value of the filter coefficient of the inverse filter from the j-th source (eg, sound source) to the input to the i-th transmission system / unknown system H (eg, output part of a speaker, etc.) ..
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source (eg, sound source).
Y j ^k: ₁ × N matrix; j-th output from the transmission system, the unknown system H (eg, the output sequence of the input unit such as a microphone).
N: Number of taps (impulse response length)
k: time of the index ^E _{~ i:} z conversion of error ^{e ~i} _k of time domain

Here, the filter gain ^K ₁ s of the formula directly opposite identification method (6) ~ (7), k ~K M s, k is the filter gain ^K _{1 s} of formula (9) ~ (10), k ~K M _{It is shown that it is equal to s and k} , that is, there are M × M filter coefficients, but only M filter gains are required.

Next, the inverse filter G ^ obtained by the direct inverse identification methods of equations (6) to (11) becomes the inverse system of the unknown multi-input multi-output system H (that is, the synthesis system G ^ H = HG). Proof that ^ has all-pass characteristics) is shown.
If attention is paid to _{U 1} in FIG. 7, _{it can be seen that G ^ 11} , ..., G ^ _1M satisfies the following equation.

この両辺に右からＵ_１を掛け、期待値をとれば次式を得る。

_{Multiply these two sides by U 1} from the right, and take the expected value to obtain the following equation.

ここで、Ｕ_１とＵ_ｊ，ｊ＝２，・・・，Ｍの無相関性（Ｅ｛Ｕ_ｊＵ_１｝＝０）と推定誤差Ｅ^〜 _１とＵ_１の直交性（Ｅ｛Ｅ^〜 _１Ｕ_１｝＝０）を用いれば次のように整理できる。なお、Ｕ_１とＵ_ｊの無相関とは、Ｕ_１とＵ_ｊの掛けたものの期待値が０、すなわちＥ｛Ｕ_ｊＵ_１｝＝０を意味する。また、Ｅ^〜 _１とＵ_１の直交性は、Ｅ｛Ｅ^〜 _１Ｕ_１｝＝０を意味する。

Here, the _{uncorrelatedness of U 1} and U _j , j = 2, ..., M (E {U _j U ₁ } = 0) and the orthogonality of the ^{estimation error E ~} ₁ and U ₁ ^{(E {E ~).} _{If 1} U ₁ } = 0) is used, it can be arranged as follows. Note that the uncorrelated _{U 1} and _{U j,} an expected value despite multiplied of _{U 1} and _{U j} is 0, that means the _{E {U j U 1} =} 0. Further, ^{the orthogonality between E ~} ₁ and U ₁ means E {E ^~ ₁ U ₁ } = 0.

これを式（１２）に代入すれば次のように整理できる。

By substituting this into equation (12), it can be organized as follows.

以上により、直接逆同定法が平均収束すれば（Ｅ｛ｇ＾^ｉｊ _ｋ｝＝Ｅ｛ｇ＾^ｉｊ _ｋ−１｝）、

From the above, if the direct inverse identification method converges on average (E {g ^ ^ij _k } = E {g ^ ^ij _k-1 }),

を満たす逆フィルタＧ＾が得られることがわかる。よって、未知系Ｈを事前に同定することなく、逆システムを実現する逆フィルタＧ＾を直接求めることができる。ここで、システムＧ＾Ｈがｚ^−ＤＩとなるから、その出力は入力のＤサンプル遅れであることがわかる。ただし、Ｉは単位行列を表す。

特に、直接逆同定法では適応フィルタとしてＪ₋高速Ｈ_∞フィルタを用いると効果的である。Ｊ₋高速Ｈ_∞フィルタをベースにした直接逆同定法の場合、各フィルタゲインＫ^ｉ _ｓ，ｋ， ｉ＝1，・・・，Ｍ は次の再帰式で更新される。なお、Ｋ^ｉ _ｓ，ｋは、他にも適宜の適応フィルタ等のアルゴリズム・処理により求めても良い（例えば、特許第４０６７２６９号公報、特許第４４４４９１９号公報、特許第５１９６６５３号公報、等参照）。

It can be seen that an inverse filter G ^ that satisfies the condition is obtained. Therefore, the inverse filter G ^ that realizes the inverse system can be directly obtained without identifying the unknown system H in advance. Here, since the system G ^ H becomes z- ^DI , it can be seen that the output is delayed by the D sample of the input. However, I represents an identity matrix.

In particular, in the direct inverse identification method, it is effective to use a _J- fast H _{∞ filter as an adaptive filter.} When the J _- fast H _∞ reverse identification method directly that is based on the filter, the filter gain _{^{K i s, k, i =}} 1, ···, M is updated by the following recursive equation. ^{Incidentally,} _{K i s, k} is may be obtained by also algorithmic process such as a suitable adaptive filter to another (e.g., Japanese Patent No. 4067269, Japanese Patent No. 4444919, Japanese Patent No. 5196653 discloses, referring etc) ..

と定義され、再帰式は次のように初期化される。

The recursive expression is initialized as follows.

また、χ（γ_ｆ）はχ（１）＝１，χ（∞）＝０を満たすγ_ｆの単調減衰関数であり、γ_ｆはＨ_∞フィルタの最大エネルギーゲインの上限を与えるパラメータである。

Further, χ (γ _f ) is a monotonous decay function of _{γ f} that satisfies χ (1) = 1, χ (∞) = 0 _{, and γ f} is a parameter that gives an upper limit of the maximum energy gain of the _{H ∞ filter.}

FIG. 8 shows an explanatory diagram of an input reproduction and inverse filter device of the M input M output system.
Multiple-input multiple-output inverse filter device 200 to a multi-input multi-output system and the transmission system, inverse filter _{G ^} 11 ~G ^ _MM, and an output section (see U ₁ ~U _M), inverse filter _{G ^} i1, · · · comprises adder i to be output to the output unit adds inputs an output from the _{G ^ iM (i = 1,} ···, M) and, the. The inverse filter G ^ _1i , ..., G ^ _Mi inputs the source S _i (i = 1, ..., M), and the output unit ( see U _i ) outputs the adders 1 to M. Output.

_{At the time of reproduction, the source (eg, sound source) S 1} , ... To the M × M system HG ^ such as the M × M transoral system constructed by using the inverse filter G ^ obtained in FIG. 7 as shown in FIG. , _SM is input, and from the relational expression of G ^ H = HG ^ = z- ^DI _{, Y 1} ≒ z ^-DS ₁ ,, ..., Y at the position of each input unit (eg, microphone), respectively. _M ≈ z ^-DS _M appears. In this _{case, S 1, ···,} S _M need not be mutually uncorrelated.
The signal (e.g., sound) from _{S 1} is transmitted to only _{Y 1,} similarly _S 2, · · ·, signals (e.g., sound) from _{S M,} each _Y 2, ···, _{Y M} only Transoral reproduction is the process of transmitting to the sound. Signal source if the output from the output unit after processing (for example, sound source sound) in the inverse filter G ^ (e.g., a speaker) (see _U 1 ~U _M), the signal from _{S 1} (e.g., sound) is not transmitted to the Y ₂ ~Y _M. This is called crosstalk cancellation.

The procedure from the above reverse identification to transoral regeneration is shown in the flowchart of FIG. 9 described later.

C. Devices and methods for direct identification of multi-input, multi-output systems

FIG. 3 is a block diagram of the inverse identification device.
The inverse identification device 100 includes a processing unit 101, an input unit 102, an output unit 103, a display unit 104, and a storage unit 105, which are central processing units (CPUs). Further, the processing unit 101, the input unit 102, the output unit 103, the display unit 104, and the storage unit 105 are connected by an appropriate connecting means such as a star or a bus. The storage unit 105 stores measured values, predetermined values, unknown / known data, data related to the inverse filter (filter coefficient, etc.), various data calculated by the processing unit 101, and the like, and is stored by the processing unit 101. Each of the data and the like is written to and / or read from the unit 105 as needed.

FIG. 4 is another configuration diagram of the inverse identification device.
In the inverse identification device 100', the measurement unit 107 measures the input and output, and the measured values are input to the storage unit 105 via the input unit 102 or the I / F 106, mainly in FIG. It is different from the inverse identification device 100. The storage unit 105 may include an appropriate file such as an inverse filter data file 151 for storing data related to the inverse filter, an input / output measurement value file 152 for storing input / output data, and the like (also in FIG. 3). Similarly). Further, for the file such as the input / output measurement value file 152, for example, a ring buffer may be used.

FIG. 9 shows a flowchart of M × M transoral reproduction using the direct inverse identification method. The processing of each step will be described below.
(S1) The processing section 101, the filter gain ^K _{i s,} initializes the recursion variable _k. In Tatoee, processing unit 101 reads the initial conditions as shown in equation (29) from the storage unit 105, or inputs the initial condition from the input unit _{^{102, R i e, -1,}} R, ρ, γ f _{^{, ε 0, K ~i -1,}} P ^ 0 | -1, L ~i -1, R i r, substitutes an initial value ₁ and the like (equation (29)) to. It should be noted that k = 0.
(S2) processing unit 101, input and output of the system _^{u i k}, to measure ^{y _{i k}.} As for the input / output of the system, the processing unit 101 may measure the data for a plurality of k in advance and store the data in the storage unit 105, and read the data each time the data is processed according to k.
(S3) processing unit 101 calculates the filter gain ^K _{i s,} the _k from equation (23) by equation (28).
(S4) The processing unit 101 ^{obtains g ^ ij} _k by the formulas (6) to (11) by the direct inverse identification method.
(S5) When the estimated values of the filter coefficients have converged (|| g ^ ^ij _{k −} g ^ ^ij _k-1 || ≈ 0), the processing unit 101 shifts to the transoral reproduction process (S7). On the other hand, when the estimated values of the filter coefficients do not converge, the process proceeds to step S6.
(S6) The processing unit 101 adds 1 to the time index k, and returns to step S2.

(S7) After shifting to the transoral reproduction process (S7), _{the characteristics of the inverse filter G ^ ij} of the M input M output system shown in FIG. 8 were obtained by g ^ ^ij _k = [g ^ ^ij _k (0)). , ..., g ^ ^ij _k (N-1)] ^{By setting to T} , a multi-input multi-output system inverse filter device is constructed. The constructed inverse filter device _{inputs a large number of each source {S i} } (sound source, etc.).
(S8) The inverse filter device calculates and outputs G ^ S for M × M transoral reproduction.
(S9) inverse filter apparatus multiple output the calculated G ^ S from each of the output section {See _{U i}} (speaker etc.).

The processing unit 101 appropriately stores the appropriate intermediate value, final value, measured value, / or calculated value, etc. obtained in each step in the storage unit 105 as necessary, and reads them out from the storage unit 105. You may.

In the transoral system, G ^ has ^{a z-transform of {g ^ ij} _k }, and S has a z-transform of {s _ik } for each component. The inverse z-transform of the over ones G ^ S is the convolution ^g _^ ij k _{* s ik} of ^{g ^ ij} _k and _{s ik.} When a signal {s _ik } is input to a system having an impulse response {g ^ ^ij _k }, the output of the linear system is g ^ ^ij _k * s _ik . For example, if the sound source S is processed (G ^ S) by the inverse filter G ^ obtained in advance and then output to the speaker, the sound of the right sound source reaches only the right microphone and the sound of the left sound source reaches only the left microphone. You can avoid it. This utilizes the fact that the synthesis system HG ^ = G ^ H becomes a system that outputs the input as it is. Therefore, G ^ S preprocesses the sound source S before outputting it to the speaker.

Figure 10 represents the same sound source _{(S L,} S _R) illustration of 4x4 transaural system that can be enjoyed by sharing realism at two listening person.
Similarly, if the number of channels is increased, in principle, three people, four people, and so on can share the same sense of presence of the sound source.
For example, the left side of the sound source _{(S L,} S _R) in FIG. 10 the Japanese broadcast, the right side of the sound source _{(S L,} S _R) if the English broadcast, the left and right of television viewers in the same space in each language You can also watch TV.

D. Experimental example

(1) 3 × 3 Transoral System FIG. 11 shows an explanatory diagram of an example of a direct inverse identification method of a 3-input 3-output system and a verification experiment of a 3 × 3 transoral system.
Further, FIGS. 12 to 17 show explanatory diagrams of signals of each microphone from each speaker at that time.
FIG. 12 is a diagram showing a transmission signal from the left speaker to the left microphone, FIG. 13 is a diagram showing a transmission signal from the right or center speaker to the left microphone, and FIG. 14 is a diagram showing a transmission signal from the center speaker to the center microphone. FIG. 15 is a diagram showing the transmission signal of the central microphone from the right or left speaker, FIG. 16 is a diagram showing the transmission signal of the right microphone from the right speaker, and FIG. 17 is a diagram showing the transmission signal of the right microphone from the left or center speaker. It is a figure showing.
From this, it was confirmed that the crosstalk cancellation is satisfactorily performed even in the 3-input 3-output system according to the present invention and / or the present embodiment.

(2) 4 × 4 Transoral System FIG. 18 shows an explanatory diagram of an example of a direct inverse identification method of a 4-input 4-output system and a verification experiment of a 4 × 4 transoral system.
Further, FIG. 5 shows a diagram of transmission characteristics from the speakers SP1, SP2, SP3, and SP4 to the microphone Mic1.
In this example, the transfer characteristics from SP1 to Mic1 are almost flat above 200 Hz, showing good passage characteristics. On the other hand, the transmission characteristics from SP2, SP3, and SP4 to the microphone Mic1 are such that the gain of about 10 to 20 dB is attenuated at 200 Hz or higher, and it can be seen that the crosstalk is cancelled.

E. Effects of embodiments, applications of the present invention / embodiments, etc.

FIG. 6 is an explanatory diagram showing a difference between the present invention and / or the present embodiment and the conventional method.

According to this embodiment, an unknown multi-input multi-output reverse system can be enabled with a single real-time identification. Further, according to the present embodiment, it is possible to construct an equalizer of a multi-input multi-output system and generate an input of a system that gives a desired output by using the inverse filter obtained by the inverse identification. .. In particular, according to the present embodiment, it is possible to realize sound field reproduction in which a plurality of people can share a high sense of presence.

As described above, according to the present invention and / or the present embodiment, for example, a method for identifying an unknown reverse system of a multi-input multi-output system directly from input / output data in real time is provided. According to the present invention and / or the present embodiment, for example, it is possible to put into practical use a sound field reproducing device in which a plurality of people enjoy a common sound source or different sound sources with a high sense of presence. Further, in the above description, the acoustic system has been mainly described as an example of the multi-input multi-output system, but the present invention and / or the present embodiment may be applied to, for example, a communication system, a vibration system, a control system, and the like. Can be done. According to the present invention and / or the present embodiment, for example, the result greatly contributes to solving problems such as an equalizer of optical communication, spatial multiplexing in a MIMO communication system, reproduction of an earthquake, and control of a robot.

The direct reverse identification method or the direct reverse identification device / system of the present invention and / or the present embodiment is a computer-readable record of a direct reverse identification program and a direct reverse identification program for causing a computer to execute each procedure. It can be provided by a medium, a program product that includes a direct inverse identification program and can be loaded into the internal memory of the computer, a computer such as a server that includes the program, and the like.

100 Inverse identification device 101 Processing unit 102 Input unit 103 Output unit 104 Display unit 105 Storage unit 200 Inverse filter device

Claims (15)

A direct inverse identification method for multi-input multi-output systems for multi-input multi-output inverse filter devices.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
The first to third output units and
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The i-th output unit outputs the added value of the outputs of the inverse filters G ^ _i1 , ..., G ^ _{iM, and outputs the added value.}

The processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system.
The ^{processing unit directly reverses the estimated value g ^ ij} _k of each filter coefficient of the inverse filter G ^ _ij (i, j = 1, ..., M) according to the following equations (6) to (11). Perform processing by the identification method to identify directly from the input / output measured values of the multi-input multi-output system.
Direct inverse identification method for multi-input multi-output systems.

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
^e ~i _k: error of the i-th time domain k: index of the time
u ⁱ _k-D: ^i-th input of the transmission system (D represents a sample delay.)
In the direct inverse identification method of the multi-input multi-output system according to claim 1,
Wherein the processing unit comprises the steps of filter gain K ^{i _s,} the _k recursive variable is initialized,
A step in which the processing unit inputs input and output measurement values of the multi-input multi-output system, and
Wherein the processing unit includes a calculating filter gain ^K _{i s,} the _k,
Wherein the processing unit is performing a process by direct inverse identification method determined by the estimate of the filter coefficients g ^ ^ij _k of the equation (6) to (11),
The processing unit repeats the step of adding 1 to the time index k, the step of calculating, and the step of executing the processing until the estimated value g ^ ^ij _{k of each filter coefficient converges, and converges.} The step of storing the estimated value g ^ ^ij _k in the storage unit,
A method for direct inverse identification of a multi-input multi-output system, which comprises.
In the direct inverse identification method of the multi-input multi-output system according to claim 2.
Wherein the processing unit is, in the step of calculating, updating the filter gain _{^{K i s, k, i =}} 1, ···, from the following equation M (23) by a recursive formula of Equation (28) A direct inverse identification method for a multi-input, multi-output system.

In the direct inverse identification method of the multi-input multi-output system according to claim 3.
Wherein the processing unit, the multi-input multi-output system directly opposite identification method, characterized in that determined by the equation (29) below the initial value.

In the direct inverse identification method of the multi-input multi-output system according to any one of claims 1 to 4.
A direct inverse identification method for a multi-input multi-output system, wherein M is an integer of 3 or more.
In the direct inverse identification method of the multi-input multi-output system according to any one of claims 1 to 5.
Further, an equalizer can be constructed by the multi-input multi-output inverse filter device using the inverse filters G ^ _{11 to} G ^ _MM set by the estimated value g ^ ^ij _{k of each obtained filter coefficient.} A direct inverse identification method for a multi-input, multi-output system, characterized by spatial multiplexing in MIMO systems or other communication systems.
In the direct inverse identification method of the multi-input multi-output system according to any one of claims 1 to 5.
Further, the multi-input multi-output inverse filter device using the inverse filters G ^ _{11 to} G ^ _MM set by the estimated value g ^ ^ij _k of each obtained filter coefficient allows a plurality of people to share a high sense of presence. A direct inverse identification method for a multi-input multi-output system characterized by performing sound field reproduction.
In the direct inverse identification method of the multi-input multi-output system according to claim 7.
The source _Si is a sound source and
The output unit is a speaker.
The multiple-input multiple-output inverse filter device, crosstalk canceling sound from the output unit, the multi-input multi-output system directly opposite identification method, characterized in that to realize a transaural playback.
In the direct inverse identification method of the multi-input multi-output system according to any one of claims 1 to 5.
Further, the multi-input multi-output inverse filter device using the inverse filters G ^ _{11 to} G ^ _MM set by the estimated value g ^ ^ij _k of each obtained filter coefficient generates the input of the system that gives a desired output. A direct inverse identification method for a multi-input, multi-output system.
A direct inverse identification device for a multi-input multi-output system for a multi-input multi-output reverse filter device.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
The first to third output units and
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The i-th output unit outputs the added value of the outputs of the inverse filters G ^ _i1 , ..., G ^ _{iM, and outputs the added value.}
The direct inverse identification device of the multi-input multi-output system is
Processing unit and
Memory and
With
The processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system.
^{The processing unit directly reverses the estimated value g ^ ij} _k of each filter coefficient of the inverse filter G ^ _ij (i, j = 1, ..., M) according to the following equations (6) to (11). Perform processing by the identification method to identify directly from the input / output measured values of the multi-input multi-output system.
A direct inverse identification device for multi-input, multi-output systems.

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain
k: Time index
u ⁱ _k-D: ^i-th input of the transmission system (D represents a sample delay.)
A direct inverse identification program for multi-input multi-output systems for multi-input multi-output inverse filter devices.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
The first to third output units and
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The i-th output unit outputs the added value of the outputs of the inverse filters G ^ _i1 , ..., G ^ _{iM, and outputs the added value.}

A step in which the processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system, and
The ^{processing unit directly reverses the estimated value g ^ ij} _k of each filter coefficient of the inverse filter G ^ _ij (i, j = 1, ..., M) according to the following equations (6) to (11). A step of performing processing by the identification method and directly identifying from the input / output measured values of the multi-input multi-output system, and
And storing said processing unit, an estimate g ^ ^ij _k of each filter coefficients identified in the storage unit,
A direct inverse identification program for a multi-input, multi-output system that allows a computer to execute.

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain
k: Time index
u ⁱ _k-D: ^i-th input of the transmission system (D represents a sample delay.)
A computer-readable recording medium that records a direct inverse identification program for a multi-input, multi-output system for a multi-input, multi-output reverse filter device.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
The first to third output units and
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The i-th output unit outputs the added value of the outputs of the inverse filters G ^ _i1 , ..., G ^ _{iM, and outputs the added value.}

A step in which the processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system, and
The ^{processing unit directly reverses the estimated value g ^ ij} _k of each filter coefficient of the inverse filter G ^ _ij (i, j = 1, ..., M) according to the following equations (6) to (11). A step of performing processing by the identification method and directly identifying from the input / output measured values of the multi-input multi-output system, and
And storing said processing unit, an estimate g ^ ^ij _k of each filter coefficients identified in the storage unit,
A computer-readable recording medium that records a direct inverse identification program for a multi-input, multi-output system that allows a computer to execute.

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain
k: Time index
u ⁱ _k-D: ^i-th input of the transmission system (D represents a sample delay.)
It is a multi-input multi-output inverse filter device that uses a multi-input multi-output system as a transmission system.
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
The first to third output units and
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The i-th output unit outputs the added value of the outputs of the inverse filters G ^ _i1 , ..., G ^ _{iM, and outputs the added value.}

The processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system, executes processing by the direct inverse identification method according to the following equations (6) to (11), and executes the multi-input multi-output system. ^{Multi-input multi-output in which the estimated value g ^ ij} _{k of} each filter coefficient directly identified from the input / output measurement values of the output system is set in the inverse filter G ^ _ij (i, j = 1, ..., M). Inverse filter device.

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain
k: Time index
u ⁱ _k-D: ^i-th input of the transmission system (D represents a sample delay.)
In the multi-input multi-output inverse filter device according to claim 13.
Further, it is provided with an adder i (i = 1, ..., M) that inputs and adds the outputs from the inverse filters G ^ _i1 , ..., G ^ _{iM and outputs the added value to the output unit.} A multi-input, multi-output reverse filter device.
This is a multi-input multi-output reverse filter method using a multi-input multi-output reverse filter device that uses a multi-input multi-output system as a transmission system.
The multi-input multi-output reverse filter device is
First to first [M × M] inverse filters G ^ _{11 to} G ^ _MM
And (M is an integer greater than or equal to 2),
The first to third output units and
With
For the inverse filter G ^ _1i , ..., G ^ _{Mi , the source S i} (i = 1, ..., M) is input, and the source S i (i = 1, ..., M) is input.
The i-th output unit outputs the added value of the outputs of the inverse filters G ^ _i1 , ..., G ^ _{iM, and outputs the added value.}

The processing unit inputs input / output measurement values using the multi-input multi-output system as a transmission system, executes processing by the direct inverse identification method according to the following equations (6) to (11), and executes the multi-input multi-output system. ^{Multi-input multi-output in which the estimated value g ^ ij} _{k of} each filter coefficient directly identified from the input / output measurement values of the output system is set in the inverse filter G ^ _ij (i, j = 1, ..., M). Multi-input multi-output reverse filter method using a reverse filter device.

here,
g ^ ^ij _k : N-dimensional vector; an estimated value of the filter coefficient of the inverse filter from the j-th source to the input or output of the i-th transmission system.
K ^j _{s, k} : N × 1 matrix; filter gain for finding the inverse filter that processes the j-th source.
Y j ^k: ₁ × N matrix; j-th output or input of the output sequence of the transmission system.
e ~i _k: ^i-th error in the time domain
k: Time index
u ⁱ _k-D: ^i-th input of the transmission system (D represents a sample delay.)

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