JP5115952B2 - Noise suppression device and noise suppression method - Google Patents

Description

  The present invention relates to a noise suppression device and a noise suppression method based on a Kalman filter.

  It is necessary to remove unnecessary information from received information (information damaged due to additional noise, etc.) that contains unnecessary information in desired information, and to extract only desired information, such as voice, wireless communication, image, attitude control, etc. It is an important technology in the field and has been actively researched and developed in recent years.

  For example, as a known noise suppression method in the voice field, a method using a single microphone or a method using a microphone array composed of a plurality of microphones has been proposed.

  However, in the method using the microphone array, when the number of noise signals increases, the number of microphones inevitably increases in proportion to the cost, and the cost increases. Therefore, at present, development of noise suppression methods using a single microphone has become the mainstream.

  The following are known as algorithms of a conventional noise suppression method that uses only a single microphone.

  The ANC (adaptive noise canceller) algorithm described in Non-Patent Document 1 uses a periodicity of an audio signal to reduce a noise signal.

  Non-Patent Document 2 describes a noise suppression algorithm based on linear prediction. This algorithm does not require prior knowledge of pitch estimation, noise power spectrum, and noise average direction.

  In addition to the above algorithm, Non-Patent Document 3 proposes a noise suppression algorithm based on a Kalman filter. This algorithm models an audio signal in an autoregressive (AR) process. Further, this algorithm estimates a coefficient of an autoregressive model (hereinafter referred to as “AR coefficient”), and performs noise suppression based on a Kalman filter using the estimated AR coefficient. This algorithm is essentially different from the other algorithms described above because it needs to estimate the AR coefficient.

Many algorithms based on the Kalman filter usually operate in two stages. That is, such an algorithm first estimates an AR coefficient, and then performs noise suppression based on a Kalman filter using the estimated AR coefficient.
JR Deller, JG Proakis, JHL Hansen, "Discrete-Time Processing of Speech Signals," Macmillan Press, 1993 A. Kawamura, K. Fujii, Y. Itoh and Y. Fukui, “A Noise Reduction Method Based on Linear Prediction Analysis,” IEICE Trans. Fundamentals, vol.J85-A, no.4, pp.415-423, May 2002 W. Kim and H. Ko, "Noise Variance Estimation for Kalman Filtering of Noise Speech," IEICE Trans. Inf. & Syst., Vol.E84-D, no.1, pp.155-160, Jan 2001

  However, the known algorithm described in Non-Patent Document 1 requires accurate estimation of the pitch period of the audio signal. Therefore, this algorithm has a problem that its noise suppression capability is deteriorated by additional noise.

  In this regard, the algorithm described in Non-Patent Document 2 can suppress noise without requiring accurate estimation of the pitch period of the audio signal. Further, this algorithm has the advantages that the principle is simple and the amount of calculation can be reduced. However, the noise suppression capability of this algorithm depends on characteristics such as periodicity and linearity of the input speech signal. In other words, this algorithm has a certain limit in its practical use because there exists a parameter depending on an audio signal in the noise suppression capability.

  The algorithm described in Non-Patent Document 3 has a strong noise suppression capability, and is a technique suitable for application to the acoustic field in which high sound quality is particularly desired.

  However, since this algorithm requires an AR coefficient, it has a problem that noise suppression performance (that is, the performance of the Kalman filter algorithm) greatly depends on the estimation accuracy of the AR coefficient. That is, if the AR coefficient is not accurately estimated, not only the noise cannot be completely removed, but also the voice signal may be removed in addition to the noise. These can be a cause of deterioration of the sound quality of the sound signal from which noise is removed.

  In this respect, generally, it is difficult to accurately estimate the AR coefficient. This is because accurate estimation of the AR coefficient depends on a clear audio signal in the case of noise removal, for example. This means that the audio signal must be known, so real-time processing becomes difficult. Even if it becomes possible to accurately estimate the AR coefficient in real time by any method, the problem of computational complexity is inevitable because the processing increases.

  The present invention has been made in view of the above points, and an object thereof is to provide a noise suppression device and a noise suppression method based on a Kalman filter that do not require estimation of an AR coefficient and have a high noise suppression capability.

  The noise suppression apparatus according to the present invention removes the unnecessary information from the acquired information by using only an acquisition unit that acquires information in which unnecessary information is mixed in desired information and a Kalman filter. And the Kalman filter adopts a configuration in which the coefficient of the autoregressive model is not used in the observation equation of the state space model.

  The noise suppression method of the present invention includes an acquisition step of acquiring information in which unnecessary information is mixed with desired information, and removing the unnecessary information from the acquired information by using only a Kalman filter. The Kalman filter is configured not to use the coefficient of the autoregressive model in the observation equation of the state space model.

  According to the present invention, it is possible to improve the noise suppression capability with a simple configuration without using an AR coefficient estimation while using a Kalman filter.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

(Embodiment 1)
FIG. 1 is a block diagram showing a configuration of a noise suppression apparatus according to Embodiment 1 of the present invention.

  A noise suppression apparatus 100 illustrated in FIG. 1 includes an input unit 110, a sampling unit 120, an A / D conversion unit 130, a buffer 140, a noise suppression processing unit 150, and an output unit 160.

  The input unit 110 inputs an observation signal. The observation signal is a signal in which the clear signal from the signal source and the additional noise signal are combined. For example, the input unit 110 performs an input process on the input analog observation signal and outputs it to the sampling unit 120. The input process is, for example, a band limiting process or an automatic gain control process.

  The sampling unit 120 samples the input analog observation signal at a predetermined sampling frequency (for example, 16 kHz) and outputs the sampled analog observation signal to the A / D conversion unit 130. The A / D conversion unit 130 performs A / D conversion processing on the amplitude value of the sampled observation signal with a predetermined resolution (for example, 8 bits), and sends the result to the buffer 140. The buffer 140 outputs a signal frame (block) having a predetermined sampling number N to the noise suppression processing unit 150.

  The noise suppression processing unit 140 is a characteristic component of the present invention, and includes a Kalman filter that does not use an AR coefficient. That is, in the conventional noise suppression method based on the Kalman filter (see Non-Patent Document 3) (hereinafter referred to as “conventional method”), after estimating the AR coefficient using linear prediction, the Kalman filter is executed using the result. In contrast to noise suppression, the noise suppression method of the present invention (hereinafter referred to as “the present method”) realizes noise suppression using only a Kalman filter. Therefore, in this method, the state equation is constructed using only the clear signal from the signal source, and the observation equation is constructed using the clear signal and the additional noise signal. Hereinafter, the noise suppression processing operation based on the Kalman filter performed by the noise suppression processing unit 140 will be described in detail.

ここで、ｎとは、装置の時刻ｎである。時刻ｎは、サンプリング部１２０で生成された離散的な時間系列において、処理開始時刻を時刻０と仮定したときに、そこからｎ番目の時刻のことを意味する。 The observation signal r (n) input to the noise suppression processing unit 140 includes an additional noise signal v (n) in addition to a clear signal (for example, an audio signal) d (n) from the signal source. (1) is satisfied.

Here, n is the time n of the apparatus. The time n means the nth time when the processing start time is assumed to be time 0 in the discrete time series generated by the sampling unit 120.

ここで、α_ｋ（ｎ）は時刻ｎでのＡＲ係数、ＫはＡＲ係数の次数、ｅ（ｎ）は信号ｄ（ｎ）が、式（２）に示すＫ次のＡＲ過程でモデル化されるとした場合の予測誤差（モデルリング誤差）である。 In the conventional modeling method based on the AR process (conventional method), it is assumed that the signal d (n) is modeled by the following equation (2) using the AR coefficient.

Here, α _k (n) is the AR coefficient at time n, K is the order of the AR coefficient, e (n) is the signal d (n), and is modeled in the K-order AR process shown in Equation (2). This is a prediction error (modeling error).

ここで、Ｅ［・］はアンサンブル平均を示す。 As is well known, in the conventional method, it is a precondition that the additional noise signal v (n) is zero average and white noise. In other words, in the conventional method, the signal d (n) and the additional noise signal v (n) are uncorrelated, that is, the following equation (3) is satisfied.

Here, E [•] indicates an ensemble average.

  The AR coefficient is estimated by an AR coefficient estimation algorithm. The most important point in the conventional method is that accurate estimation of the AR coefficient is required to achieve high-performance noise suppression using the Kalman filter. From this, it can be easily imagined that the noise suppression capability of the Kalman filter greatly deteriorates because the noise suppression capability greatly depends on the estimation accuracy of the AR coefficient.

  In this method, the state equation of the Kalman filter without using the AR coefficient, that is, the state equation using only the clear signal from the sound source signal, and the observation equation using the clear signal and the additional noise signal are constructed. Yes.

Hereinafter, a configuration method of the state space model in this method will be described. In order to facilitate the notation, first, a K × first order signal vector x _p (n) is defined by the following equation (4). The subscript “p” indicates an expression devised by the present invention.

Next, a model of the signal d (n) is constructed in the same manner as the equation (2). Here, even if the AR coefficient is not used, an unknown K × K-order state transition matrix Φ _p (n + 1) and a K × first-order drive noise vector δ _p (n + 1) are introduced as in the conventional method. . As a result, the following equation (5) is determined as the form of the state equation of the state space model (described by the signal vector) of the present embodiment.

In order for Equation (5) to hold without using the AR coefficient as an equation, the K × K-order state transition matrix Φ _p (n + 1) and the K × first-order drive noise vector δ _p (n + 1) are It is calculated | required that Formula (6) and Formula (7) of these are satisfy | filled.

Therefore, equation (5) can be rewritten into the following equation (8).

The matrix elements of the K × K-order state transition matrix Φ _p (n + 1) represented by Expression (6) are only 0 and 1, and in particular, all the first rows are 0. This is one of the features of the state space model of this method. Further, as is clear from the above, it should be noted that no precondition is given to the drive noise vector δ _p (n + 1) in the derivation of the equations (5), (6), and (7). is there. That is, the driving noise vector δ _p (n + 1) may be colored. The reason for this will be described later.

In the Kalman filter algorithm of this method, in order to avoid singular value decomposition, a K × first-order observation vector y _p (n + 1) is defined by the following equation (9).

ここで、Ｍ_ｐはＫ×Ｋ次の状態遷移行列、ε_ｐはＫ×１次の付加雑音ベクトルであり、それぞれ次の式（１１）および式（１２）で定義される。

Therefore, the following equation (10) is derived from the equations (1) and (9) as an observation equation of the state space model of the present method.

Here, M _p is a K × K-order state transition matrix, and ε _p is a K × first-order additional noise vector, which are defined by the following equations (11) and (12), respectively.

  From the above, Equation (5) and Equation (10) were obtained as the state equation and the observation equation of the state space model used in the Kalman filter algorithm of the present method, respectively.

  FIG. 2 is a block diagram illustrating a state space model of the noise suppression device according to the present embodiment.

In FIG. 2, 500 is a signal vector x _p (n) at time n, 501 is a signal vector x _p (n + 1) at time n + 1, 502 is an observation vector y _p (n) at time n, and 503 is an additional noise at time n. Vectors ε _p (n) and 504 are driving noise vectors δ _p (n + 1) at time n + 1, 505 is a state transition matrix Φ _p , and 506 is a state transition matrix M _p .

  As can be understood from FIG. 2, the Kalman filter algorithm of the present method can be executed in the same procedure as the conventional Kalman filter algorithm even though the driving noise is colored (the reason will be described later). Signal estimation based on the Kalman filter algorithm of this method is performed according to a flowchart described later.

  FIG. 3 is a flowchart for explaining a signal estimation procedure based on the Kalman filter algorithm of the noise suppression apparatus according to the present embodiment.

First, the initial value x _e (0 | 0) of the estimated signal vector, the initial value P (0 | 0) of the estimation error covariance matrix, and the covariance Rε _p (n) [i, j] is set as shown in the following equation (13) (ST100).

ここで、Ｎは所定のサンプル数である。 Here, I is a unit matrix. Also, σ _v ² is the noise variance of the additional noise signal v (n), and is assumed to be known. If the additional noise signal v (n) is white noise and is zero average, σ _v ² is given by the following equation (14).

Here, N is a predetermined number of samples.

  Next, the Kalman filter algorithm is executed (ST101). The processing procedure of the Kalman filter algorithm will be described in detail later.

  Next, it is determined whether or not the time n has reached a predetermined number of samples N (ST102). If the predetermined number of samples N has not been reached (ST102: NO), the process returns to step ST101 to perform the Kalman filter algorithm. If the predetermined number N of samples is reached repeatedly (ST102: YES), the above series of processing ends.

  In this method, the state space model is set without using the AR coefficient. Therefore, it is possible to reduce the step of estimating the AR coefficient that is necessary in the conventional method, and it is possible to perform signal estimation by one-stage processing. This is one of the major features of the present invention.

  FIG. 4 is a flowchart showing the processing contents of the Kalman filter algorithm of FIG.

Here, the start time is n + 1, and in the following flow, the observation signal r (n + 1) and the observation vector y _p (n + 1) at time n + 1 and the covariance matrix P (n of the estimation error at time n) | N), the estimated signal vector x _pe (n + 1 | n) at time n + 1 is estimated, and at the same time, the covariance matrix P (n + 1 | n + 1) of the estimation error is updated.

First, the value of the covariance Rδ _p (n) [i, j] of the drive noise vector is calculated using the following equation (15) (ST200).

Next, the estimation error covariance matrix P (n + 1 | n) is calculated and updated (ST201). Here, the update equation of the estimation error covariance matrix P (n + 1 | n) is the following equation (16). Hereafter, the subscripts “pe” and “e” indicate estimated values.

When this equation (16) is expanded, the following equation (17) is obtained.

Here, attention is focused on the third and fourth terms of Equation (16). The third and fourth terms include an ensemble average of the estimated signal vector x _pe (n | n) and the drive noise vector δ _p (n | n), and therefore the estimated signal vector x _pe (n | n). And the driving noise vector δ _p (n | n) are not uncorrelated, in other words, when the driving noise vector δ _p (n | n) is colored, the third and fourth terms do not become zero. That is, whether or not the Kalman filter algorithm of the present method can be applied by the same Kalman filter algorithm procedure as in the past when the driving noise signal is a colored signal is expressed by the equation (15). It depends on how much it affects the update of the covariance matrix P (n + 1 | n) of the estimation error.

と書き表せる。 Therefore, attention is focused on the third term of Expression (17). The third term is expressed by the following equation (18):

Can be written.

とすれば、次の式（２０）となる。

Here, as in the following equation (19),

Then, the following equation (20) is obtained.

を考慮すれば、式（１８）は、次の式（２２）のように書き直すことができる。

ただし、次の式（２３）である。

ここで、ｄ_ｅ（ｎ）は時刻ｎでの推定信号である。 Formula (5) and the following formula (21)

(18) can be rewritten as the following equation (22).

However, it is the following formula (23).

_{Here, d} e (n) is the estimated signal at time n.

In Equation (23), the first term represents an ensemble average of true values, and the second term represents an ensemble average of estimated values. Therefore, the difference is small and e (l + 1) is a negligible value. Therefore, the update equation (15) of the estimation error covariance matrix P (n + 1 | n) is rewritten as the following equation (24). From this, even if the driving noise is colored, if it is a state space model (state equation and observation equation) composed of Equation (5) and Equation (9) of this method, the same Kalman filter algorithm as in the conventional method The procedure becomes applicable.

Next, Kalman gain K _p (n + 1) is calculated (ST202). Here, the Kalman gain K _p (n + 1) is given by the following equation (25).

Then, first, an estimated signal vector x _pe (n + 1 | n) is calculated from these values (ST203). Here, the estimated signal vector x _pe (n + 1 | n) is given by the following equation (26).

Then, an estimated signal vector x _pe (n + 1 | n + 1) is calculated (ST204). Here, the estimated signal vector x _pe (n + 1 | n + 1) is given by the following equation (27).

Finally, the estimation error covariance matrix P (n + 1 | n + 1) is calculated and updated (ST205), and the flow ends. Here, the estimation error covariance matrix P (n + 1 | n + 1) is given by the following equation (28).

  The noise suppression processing unit 140 outputs an estimation signal estimated by the above-described procedure and algorithm to the output unit 150. The output unit 150 includes, for example, a speaker, a display, a communication unit, a storage device, and the like.

  A problem of the conventional Kalman filter that requires estimation of the AR coefficient is that the ability of the Kalman filter algorithm depends on the estimation accuracy of the AR coefficient. On the other hand, since this method is executed only by the Kalman filter algorithm, it does not depend on the estimation accuracy of the AR coefficient.

  The Kalman algorithm of this method can also be executed by a further improved method (hereinafter referred to as “improved method”) described below. Hereinafter, this improved technique will be described.

ここで、ｙ’_ｐ（ｎ＋１）、ｍ^Ｔ _ｐ、ε’_ｐ（ｎ＋１）は、それぞれ改良手法における観測信号、雑音信号、状態遷移ベクトルであり、次の式（３０）を満たす。

The state equation of the improved Kalman algorithm is the same as the above equation (5). However, the observation equation is rewritten as the following equation (29). The observation equation (29) of the improved method is a partial extraction of the observation equation (10) of the present method.

Here, y ′ _p (n + 1), m ^T _p , and ε ′ _p (n + 1) are an observation signal, a noise signal, and a state transition vector in the improved method, respectively, and satisfy the following equation (30).

One of the major features of the improved method is that the observation vector y _p (n + 1) in the method before the improvement (this method), as can be seen from the comparison between the observation equation (10) of this method and the observation equation (30) of the improved method. ), The noise vector ε _p (n + 1), and the state transition matrix m _p are changed to a scalar and a vector, respectively. Therefore, it is clear that the improved method can be executed with a smaller amount of computation. Further, as is apparent from the above, it should be noted that the improved method does not give a precondition to the drive noise vector δ _p (n + 1) as in the present method. That is, even in the improved method, the driving noise vector δ _p (n + 1) may be colored.

ここで、また以下の式で、行列式中、斜線網掛け部分で示される部分は駆動雑音が有色であるときに影響を受ける部分である。 That is, when the covariance matrix P (n + 1 | n) of the estimation error given by Expression (17) is written down again in matrix form, the following Expression (31) is obtained.

Here, in the following equation, the portion indicated by the hatched portion in the determinant is a portion that is affected when the driving noise is colored.

The Kalman filter algorithm using the improved method is different from the Kalman filter algorithm of the present method shown in FIG. 4 in the calculation of the Kalman gain K _p (n + 1) (ST202) and the calculation of the estimated signal vector x _pe (n + 1 | n + 1) (ST204). The calculation formula is different.

となる。ただし、雑音信号ε’_ｐ（ｎ＋１）の共分散をσ^２ _ｖとしたときに、次の式（３３）が成り立つ。

That is, the Kalman gain K _p (n + 1) is calculated by the following equation (32), that is,

It becomes. However, when the covariance of the noise signal ε ′ _p (n + 1) is σ ² _v , the following equation (33) is established.

となる The calculation formula of the estimated signal vector x _pe (n + 1 | n + 1) is the following formula (34).

Become

Here, paying attention to the first element of x _pe (n + 1 | n + 1) in Expression (34), since it is not hatched (that is, not affected by the colored noise), even if the driving noise is colored, A clear estimated signal can be obtained. Therefore, the improved method can be executed by the conventional Kalman filter algorithm as in the present method. As described above, the improved method can reduce the amount of calculation compared to the present method. However, while this method uses the observation vector y _p (n + 1), the improved method uses the observation signal y ′ _p (n + 1) that is a scalar quantity. From the difference in size, it is clear that this method, which can use past observations more actively, has higher noise suppression capability.

In summary, the above two methods in the present invention (the present method and the improved method) can greatly reduce the amount of calculation by changing the observation equation of the state space model necessary for the Kalman filter. More specifically, the above two methods in the present invention do not require estimation of the AR coefficient, and therefore the amount of calculation is less than that of the conventional method. Further, in the improved method, the size of the variable used for the calculation is smaller than that of the present method, so that the amount of calculation is smaller than that of the present method. That is, regarding the amount of calculation,
Improved method <this method <conventional method.

  In addition, the above-described two methods in the present invention may be implemented, for example, when implemented as hardware such as a semiconductor integrated circuit or a semiconductor circuit, or as software that can be executed by a personal computer or the like. Is simpler than the conventional method. Therefore, it is clear that the circuit scale and the program amount can be greatly reduced by using the two methods in the present invention.

In addition, the above two methods in the present invention can greatly improve the noise suppression capability by changing the observation equation of the state space model necessary for the Kalman filter. More specifically, since the above two methods in the present invention do not require estimation of AR coefficients, the noise suppression capability is higher than the conventional methods in which the noise suppression capability depends on the estimation accuracy of the AR coefficient. In the improved method, since the size of the variable used for the calculation is smaller than that of the present method, the past observation amount is not actively used. Therefore, its noise suppression capability is low compared to this method. That is, regarding noise suppression capability,
Conventional method <improved method <this method.

  For example, in the acoustic field, the improved technique is effective when it is desired to increase the calculation speed even if the sound quality is slightly reduced (but higher than the conventional technique).

  The above two methods in the present invention that do not use the AR coefficient are contrary to the assumption of the conventional Kalman filter, that is, the driving noise is a white signal, because the driving noise of the state equation is a colored signal. However, due to the structural nature of the state equation and the observation equation in the state space model of the present invention, it can be executed with the same algorithm as the conventional Kalman filter algorithm in which the driving noise is a white signal, for the reason described above. . In addition, it is clear from the above that the improved technique of the present invention can be similarly implemented.

  In the above two methods in the present invention, the Kalman filter is configured not to use the AR coefficient. In other words, since it is a noise suppression method that can be executed only by the Kalman filter, it is clear that the conventional problem of noise suppression capability is solved.

(Embodiment 2)
The second embodiment is a case where the noise suppression apparatus shown in the first embodiment is applied to speech.

  FIG. 5 is a block diagram showing the configuration of the noise suppression apparatus according to Embodiment 2 of the present invention.

  A noise suppression apparatus 200 illustrated in FIG. 5 includes a personal computer 210, a microphone 220, a sampling unit 120, and an A / D conversion unit 130 that can execute the noise suppression processing of the present embodiment.

  The personal computer 210 includes an operation device 211, a display 212, a bus interface 213, a recording device 214, a main storage memory 215, and a central processing unit 216. The operation device 211 is typically a keyboard or a mouse, but a voice recognition device or the like may be used. The user can operate the computer while confirming on the display 212 using the operation device 211.

  Program software for causing the personal computer 210 to execute the noise suppression processing of the present embodiment may be stored in the recording device 214 or downloaded from the outside via the bus interface 213. The recording device 214 is typically a hard disk device, but may be a portable device such as a CD-ROM device, a DVD device, or a flash memory. Moreover, those combinations may be sufficient.

  The sampling unit 120 and the A / D conversion unit 130 may be an internal card (board) stored in the personal computer 210 or may be an externally installed device connected via the bus interface 213. Good.

  The observation audio signal from the microphone 220 is input to the sampling unit 120. The sampling unit 120 performs sampling processing on the input analog observation voice signal at a predetermined sampling frequency (for example, 16 kHz), and outputs it to the A / D conversion unit 130. The A / D conversion unit 130 performs A / D conversion processing on the amplitude value of the sampled observation audio signal with a predetermined resolution (for example, 8 bits), and temporarily stores it. The A / D conversion unit 130 outputs the digitized observation audio signal to the bus interface 213 of the personal computer 210 in units of a predetermined sampling number N of audio frames.

  The personal computer 210 temporarily stores the observed audio signal output to the bus interface 213 in the main memory 215, and after performing noise suppression processing in a predetermined audio frame (sampling number) unit, the main computer again Store in the memory 215. The noise suppression process is performed by calling and executing software stored in the main memory 215 or the recording device 214 to the central processing unit 216 via the bus interface 213.

  The personal computer 210 executes, interrupts, or terminates processing according to the user's operation. Moreover, you may output the estimated estimated audio | voice signal outside by operation of a user.

  Next, speech noise suppression processing in the present embodiment will be described with reference to the drawings.

  For the purpose of evaluating the performance of speech noise suppression in this embodiment, a numerical simulation of speech waveforms was performed.

  FIG. 6 is a diagram illustrating a result of the first example of the speech waveform simulation in the present embodiment, and FIG. 7 is a diagram illustrating a result of the second example of the speech waveform simulation in the present embodiment. FIG. 8 is a diagram showing a result of the third example of the speech waveform simulation in the present embodiment, and FIG. 9 is a diagram showing a result of the fourth example of the speech waveform simulation in the present embodiment. is there.

  Original audio signals (clear audio signals) of Japanese adult men and women were sampled and digitized in an anechoic chamber at a sampling rate of 16 kHz. In this example, two audio signal samples were considered. The two audio signal samples are (A-1) a clear audio signal without an unvoiced section shown in FIG. 6 (A), and (A-2) a clear audio signal with an unvoiced section shown in FIG. 7 (A). . Each audio signal sample is hereinafter referred to as audio (A-1) and audio (A-2).

  The noise signal is an artificial additional noise signal. In this example, two noise signal samples were examined. The two noise signal samples are (B-1) the added white Gaussian noise shown in FIGS. 6 (B) and 7 (B), (B-2) the added colored colors shown in FIG. 8 (B) and FIG. 9 (B). Bubble noise. Each noise signal sample is hereinafter referred to as noise (B-1) and noise (B-2).

である。ここで、Ｌは全音声信号サンプル数である。 The noise variance σ _v ² of the noise signal is assumed to be expressed by the following equation (35). That is,

It is. Here, L is the total number of audio signal samples.

Further, the signal to noise ratio SNR _in is defined by Expression (36).

  The results of noise suppression by the conventional method and the method of the present invention (the present method) are expressed as speech (A-1), speech (A-2) and noise (B-1), and speech (A-1) and Comparison was made from the signal waveform of the observed voice signal consisting of a combination of voice (A-2) and noise (B-2).

  FIGS. 6C and 7C show observed sound signal waveforms composed of sound (A-1) and noise (B-1), and sound (A-2) and noise (B-1), respectively.

  FIGS. 6D and 7D show a conventional method for a synthesized waveform of speech (A-1) and noise (B-1), speech (A-2) and noise (B-1), respectively. It is an estimated speech signal waveform after noise suppression.

  On the other hand, FIG. 6E and FIG. 7E show the conventional waveforms for speech (A-1) and noise (B-1) and speech (A-2) and noise (B-1), respectively. It is an estimated speech signal waveform after performing noise suppression by the technique.

  Referring to FIG. 6 (A) and FIG. 7 (A) with respect to FIG. 6 (D) and FIG. 7 (D), referring to FIG. 6 (D) and FIG. Comparing the clear speech signal shown in FIG. 6A and FIG. 7A, in the noise suppression by the conventional method, the amplitude of the estimated speech signal is reduced after the noise suppression, and the clear speech signal is suppressed. You can see that In addition, in the noise suppression by the conventional method, as the number of samplings increases, the waveform of the estimated speech signal after noise suppression is transformed from the clear speech signal waveform shown in FIGS. 6 (A) and 7 (A). Go.

  Furthermore, in the noise suppression of the conventional method, not only the estimated speech signal is suppressed but also noise different from the original noise signal is observed in the unvoiced section for the voice (A-2) having the unvoiced section. This is because in the conventional method, although the signal d (n) is zero in the unvoiced interval, the AR coefficient is obtained by the equation (2), and therefore the AR coefficient value diverges and is unstable. Is presumed to be given.

  From this, it can be easily estimated that application of the conventional method will be difficult when the noise signal is colored.

  In contrast to the conventional method, in the noise suppression of the present invention shown in FIGS. 6 (E) and 7 (E), the waveform of the estimated speech signal after noise suppression is shown in FIGS. 6 (A) and 7 (A). It is very similar to the waveform of a clear audio signal shown in

  Next, when the clear audio signal shown in FIG. 8A and FIG. 9A is compared with FIG. 8D and FIG. 9D, noise (B− It can be seen that the inferior result is given to the observed speech signal including 2). This is because it is difficult for the conventional method to accurately estimate the AR coefficient for the observed speech signal including the noise (B-2) that is colored noise.

  On the other hand, in the noise suppression method of the present invention, the same level of noise suppression is achieved in the case of noise (B-2) as in the case of noise (B-1).

  That is, as described above, the noise suppression method of the present invention is effective regardless of the presence or absence of white, colored noise, and unvoiced intervals. This is one of the major features of the noise suppression method of the present invention.

  The fact that the noise suppression method of the present invention can also be applied to colored additive noise is obvious from the process of deriving the update equation (23) of the covariance matrix P (n + 1 | n) of the estimation error in the Kalman algorithm described above. The numerical simulation of the present embodiment described above supports this.

ここで、ｄ_ｅｉ（ｎ）は推定音声信号を表す。 Next, in order to numerically compare the noise suppression performance, the noise suppression performance SNR _out was defined by Expression (37), and the numerical simulation was performed.

Here, d _ei (n) represents the estimated speech signal.

Table 1 is a table showing a result of an example of numerical simulation of noise suppression performance in the present embodiment, and shows several SNR _in , K ( _in a combination of speech (A-1) and noise (B-1). In the conventional method, the noise suppression performance SNR _out of the conventional method and the method of the present invention in the value of the order of the AR coefficient in Expression (2), the value of the state transition matrix Φ _{p in} the present invention) is shown in comparison.

Table 2 is a table showing the results of another example of the numerical simulation of the noise suppression performance in the present embodiment. Several SNR _in in the combination of speech (A-1) and noise (B-1) The noise suppression performance SNR _out of the conventional method and the method of the present invention in the value of K is compared and shown.

Referring to Tables 1 and 2, it can be seen that the method of the present invention improves the noise suppression capability compared to the conventional method at all SNR _in and K values.

  In particular, in the case of the colored noise shown in Table 2, the method of the present invention gives the same result as that of the white noise shown in Table 1, although the conventional method gives a very inferior result. Show. That is, it can be said that the noise suppression method of the present invention is a noise suppression method that is effective for both white noise and colored noise and is robust in noise characteristics.

Further, as seen in Tables 1 and 2, in the method of the present invention, the noise suppression performance SNR _out is stable with respect to the value of K, and tends to increase as the value of K increases. In contrast, in the conventional method, as shown in Table 1, the noise suppression performance SNR _out is unstable with respect to the value of K. This means that it is difficult to determine the optimum value of K, that is, the order of the AR coefficient, in the conventional method.

  What is most problematic in the conventional method that requires AR coefficient estimation is that accurate estimation of the order of the AR coefficient is generally difficult. This is because accurate estimation of the order of the AR coefficient depends on a clear speech signal if, for example, noise removal is performed.

  This means that a clear audio signal must be known, making real-time processing difficult. If the order of the AR coefficient is not accurate, it can be easily imagined that the performance of the Kalman filter algorithm deteriorates. Even if it becomes possible to estimate in real time by some method, it is impossible to avoid problems such as the amount of computation due to the increase in processing.

  Next, in order to evaluate the voice quality of the estimated voice signal according to the present embodiment, a subjective evaluation by a listening test was performed.

The original voice signal and the original noise signal used for the voice quality evaluation are the same as those in the second embodiment, and a description thereof will be omitted. The noise signal was added to the audio signal at different SNR _in (0, 5, and 10 [dB]).

  The voice quality evaluation was performed by a listening test using a 5-step MOS (average opinion value) based on ACR (absolute category evaluation). Fifty listeners evaluated some of the estimated speech signals obtained by noise suppression. Each listener determines points 1 to 5. Point 5 is the best.

  FIG. 10 is a diagram illustrating an example of a subjective evaluation result of speech quality after noise suppression according to the present embodiment, and shows a conventional method in a combination of speech (A-1) and noise (B-1). The results of the method of the present invention and the listening test are shown in comparison.

  FIG. 11 is a diagram showing another example of the subjective evaluation result of the speech quality after noise suppression in the present embodiment, in the conventional combination of speech (A-1) and noise (B-2). The method, the method of the present invention, and the result of the listening test are shown in comparison.

10 and 11, it can be seen that the score of the speech signal estimated by the method of the present invention is higher than the score of the conventional method _in all SNR _in values. In particular, the difference is large for the combination of speech (A-1) and noise (B-2).

  From the above, it can be said that the noise suppression method of the present invention is an excellent noise suppression method effective for white noise and colored noise without sacrificing the voice quality of the voice signal.

(Embodiment 3)
The noise suppression device according to the present invention can be applied to uses other than noise suppression. Hereinafter, one application example will be described.

  FIG. 12 is a block diagram showing a configuration of a multicarrier receiver to which the noise suppression method of the present invention, that is, a Kalman filter that does not require an AR coefficient is applied.

  12 mainly includes a detection unit 301, a GI (guard interval) removal unit 302, a channel equalization unit 303, a channel estimation unit 304, an FFT unit 305, a demodulation unit 306, and a decoding unit 307. Have

  In the present embodiment, the channel estimation unit 304 is configured to be able to execute channel estimation based on a Kalman filter using the state space model of the present invention. More specifically, the channel estimation unit 304 has a configuration including a sampling unit 120, an A / D conversion unit 130, a buffer 140, a noise suppression processing unit 150, and an output unit 160.

  The detector 301 performs quadrature detection of the received signal affected by frequency selective fading or the like on the transmission path at the intermediate frequency, and outputs it to the GI removal unit 402. GI removal section 302 removes the guard interval of the received signal and outputs a signal that is continuous in symbol units to channel equalization section 303 and channel estimation section 304.

  The signal input to the channel estimation unit 304 is output to the input unit 110. The input unit performs predetermined input signal processing on the signal and outputs the signal to the sampling unit 120. The sampling unit 120 samples the input analog reception signal at a predetermined sampling frequency (for example, 16 kHz) and outputs the sampled analog reception signal to the A / D conversion unit 130. The A / D converter 130 subjects the amplitude value of the sampled received signal to A / D conversion processing at a predetermined resolution (for example, 8 bits), and sends it to the buffer 140. The buffer 140 outputs a received signal frame (block) having a predetermined sampling number N to the noise suppression processing unit 150.

  The noise suppression processing unit 150 performs channel estimation based on the Kalman filter for the entire subcarrier or each subcarrier, and outputs the estimated (sub) channel gain to the output unit 160. The output unit 160 outputs the input estimated channel gain to the channel equalization unit 302. Details of the processing in the noise processing unit 150 will be described later.

  Channel equalization section 303 performs synchronous detection of the signal input from GI removal section 302 using the input estimated channel gain, and outputs the result to FFT section 305. FFT section 305 performs a Fourier transform process, separates the received signal into subcarrier signal components, and outputs the result to demodulation section 306. Demodulation section 306 performs signal demodulation processing and outputs the result to decoding section 307. The decoding unit 307 decodes the signal and outputs digital data.

となる。ここでｎは時刻、Ｎは総キャリア数、Ｓ_ｋ（ｔ）、Ｈ_ｋ（ｔ）は第ｋキャリアの送信信号、チャネルゲインである。 In this embodiment, first, the fading channel is expressed by the state space model described above. In multicarrier communication, when attention is focused only on the k-th subcarrier, the received signal y _k (t) is expressed by the following equation (38).

It becomes. Here, n is time, N is the total number of carriers, S _k (t) and H _k (t) are the transmission signal and channel gain of the k-th carrier.

ここで、Ｋは後述の状態遷移行列の次数である。 In order to facilitate the notation, the N × first-order channel gain vector h _p (n) is defined by the following equation (39).

Here, K is the order of a state transition matrix described later.

In the present embodiment, the estimated value of the channel gain is adaptively obtained based on the Kalman filter using the state space model of the present invention. The state vector x _p (n + 1) of the state space model is defined by the following equation (40).

また、観測方程式は、次の式（４２）で記述される。

ここで、δ_ｐ（ｎ＋１）は駆動雑音ベクトル、ε_ｐ（ｎ＋１）は雑音信号ベクトル、Ｃ_ｐ、Ｄ_ｐは状態遷移行列、Ｇは定数行列である。 The state equation representing the time variation of the transmission path characteristic is described by the following equation (41).

The observation equation is described by the following equation (42).

Here, δ _p (n + 1) is a drive noise vector, ε _p (n + 1) is a noise signal vector, C _p and D _p are state transition matrices, and G is a constant matrix.

ここで、Ｉ_Ｎ×Ｎ、０_Ｎ×ＮはＮ×Ｎの単位行列、零行列である。 The drive noise vector δ _p (n + 1), the noise signal vector ε _p (n + 1), the state transition matrices C _p and D _p , and the constant matrix G are defined by the following formulas (43) to (48).

Here, I _{N × N} and 0 _{N × N} are N × N unit matrices and zero matrices.

In the above formulation, the state space model of the present invention is applied to a channel gain estimation method conventionally called Vector Kerman. Since not only the correlation between fading channels but also the correlation between subchannels is used, it has a good estimation accuracy. However, for example, the size of the state vector x _p (n + 1) in Expression (38) is K × N, and there is a problem that the amount of calculation increases.

  What improved this problem is a technique conventionally called Per Subcarrier Kalman. In this method, the above method is divided into subcarriers for processing. When the state space model of the present invention is applied, a desired equation can be obtained by dividing Equation (40) to Equation (48) into subcarriers k.

Taking the state transition matrix C _p as an example, the subcarrier unit is divided into an N × N unit matrix and a zero matrix I _{N × N} , 0 _{N × N} as scalar quantities in the equation (42). This corresponds to the replacement with a certain 1,0. Therefore, the size of the matrix becomes 1 / N, and the amount of calculation can be reduced. In the case of wireless transmission, unlike the acoustic field, processing speed is required depending on the estimated signal quality. Therefore, this method is more practical.

  Next, an example of a comparison result of channel estimation accuracy in the present embodiment will be described with reference to the drawings.

  A comparative study of channel estimation accuracy was performed by numerical simulation. The numerical simulation conditions were set as follows. The transmission frame is composed of 64 symbols, of which 4 symbols are pilot symbols and 60 symbols are data symbols. The total number of transmission frames is 200, and the total number of transmission data symbols is 12000. The evaluation amount was NMSE (Normarized Mean Square Error).

FIG. 13 is a diagram illustrating a result of one example of the numerical simulation of channel estimation accuracy according to the present embodiment. NMSE with respect to the signal-to-noise ratio SNR at f _D T = 0.045 and (NT _s ) = 0.08 μs. The characteristics are shown. Where f _D is the maximum Doppler frequency, T is the OFDM symbol period, T _s is the sampling interval, and τ _max is the maximum delay spread. FIG. 13 shows that the estimation accuracy of the method of the present invention is improved as compared with the conventional method. This is presumably because the degradation of the channel estimation accuracy due to the AR coefficient estimation error can be reduced in the method of the present invention. Also, if f _D is greater than 180 Hz, the performance improvement of the method of the present invention becomes larger one is obvious.

FIG. 14 is a diagram showing the results of another example of the channel estimation accuracy numerical simulation according to the present embodiment. NMSE with respect to the maximum Doppler frequency f _D when SNR = 20 dB and τ _max / (NT _s ) = 0.08 μs. The characteristics are shown. From this result, the method of the present invention, since the NMSE is not dependent on the maximum Doppler frequency f _D, it can be seen that the prior art technique has a good performance. That is, the effectiveness of the method of the present invention can be confirmed even in an environment where the fading fluctuation is severe where the influence of inter-channel interference becomes serious.

  The present invention is not limited to the above embodiments.

  The noise suppression device of the present invention can extract a clear audio signal (necessary information) from an audio signal containing noise (obtained information). As one embodiment thereof, a preprocessing noise removal device for a speech recognition device that is indispensable for a car navigation device or the like can be considered.

  In the image field, a clear image (necessary information) can be extracted from a blurred image (obtained information) that has been blurred for some reason, and can be used as an image processing apparatus. is there.

  Furthermore, it goes without saying that the present invention can be applied to communication and signal processing in general using a combination of modeling by an AR process and a Kalman filter algorithm.

  Further, in the medical field, conventionally, in order to inspect the condition of a pregnant woman's fetus, an expensive device that cannot be purchased by an individual and high expertise are required. It is possible to remove unnecessary sounds (information) from the heart sounds of the mother and the fetus and other sounds (obtained information), and only the heart sounds of the fetus (necessary information) can be taken out. The fetal health can be easily confirmed from the heart sound.

  Each functional element used in the description of the above embodiments is realized as an integrated circuit, for example. These may be individually made into one chip, or may be made into one chip so as to include a part or all of them. Further, an FPGA (Field Programmable Gate Array) that can be programmed after manufacturing the integrated circuit or a reconfigurable processor that can reconfigure the circuit may be used.

  Further, each of the above embodiments is not limited to hardware, and may be software. The reverse is also true. Moreover, those combinations may be sufficient.

  The noise suppression device and the noise suppression method according to the present invention are a noise suppression device and a noise suppression method that can improve the noise suppression capability with a simple configuration without using an AR coefficient estimation while using a Kalman filter. Useful as.

The block diagram which shows the structure of the noise suppression apparatus which concerns on Embodiment 1 of this invention. Block diagram for explaining a state space model of the noise suppression apparatus according to the present embodiment Flowchart for explaining a signal estimation procedure based on the Kalman filter algorithm of the noise suppression apparatus according to the present embodiment The flowchart which shows the processing content of the Kalman filter algorithm of FIG. The block diagram which shows the structure of the noise suppression apparatus which concerns on Embodiment 2 of this invention. The figure which shows the result of the 1st example of the speech waveform numerical simulation in this Embodiment. The figure which shows the result of the 2nd example of the speech waveform numerical simulation in this Embodiment. The figure which shows the result of the 3rd example of the speech waveform numerical simulation in this Embodiment. The figure which shows the result of the 4th example of the speech waveform numerical simulation in this Embodiment. The figure which shows an example of the subjective evaluation result of the speech quality after noise suppression in this Embodiment The figure which shows the other example of the subjective evaluation result of the speech quality after noise suppression in this Embodiment The block diagram which shows the structure of the multicarrier receiver to which the noise suppression method of this invention was applied The figure which shows the result of one example of the channel estimation precision numerical simulation in this Embodiment The figure which shows the result of the other example of the channel estimation accuracy numerical simulation in this Embodiment

Explanation of symbols

DESCRIPTION OF SYMBOLS 100,200 Noise suppression apparatus 110 Input part 120 Sampling part 130 A / D conversion part 140 Buffer 150 Noise suppression process part 160 Output part 210 Personal computer 211 Operation apparatus 212 Display 213 Bus interface 214 Recording apparatus 215 Main memory 216 Central processing unit DESCRIPTION OF SYMBOLS 220 Microphone 300 Multicarrier receiver 301 Detection part 302 GI removal part 303 Channel equalization part 304 Channel estimation part 305 FFT part 306 Demodulation part 307 Decoding part 500, 501 Signal vector 502 Observation vector 503 Additional noise signal vector 504 Drive noise vector 505 State transition matrix 506 State transition matrix

Claims (9)

A noise suppression device that estimates the desired information only from observation information in which noise is mixed in the desired information,
Obtaining means for obtaining the observation information;
Using a Kalman filter using colored noise as a driving source , and extracting means for removing the noise from the acquired observation information and extracting the desired information,
The Kalman filter is
It is configured not to use autoregressive model coefficients in the state equation of the state space model,
Noise suppression device. The extraction means includes
A first correlation calculation unit that calculates a first correlation value matrix of an estimation error when the state quantity of the system at time n + 1 including the desired information is estimated from information up to time n with respect to observation information only at time n When,
For observation information only at time n, using the first correlation value matrix of the estimation error calculated by the first correlation calculation unit, optimal estimation of the state quantity at that time by information up to time n + 1 A weighting coefficient matrix for defining the relationship between the value vector, the optimum estimated value vector of the state quantity at time n + 1 based on the information up to time n, and the estimated error vector of the observed quantity including the observation information is calculated. A weighting factor calculation unit;
A first optimum estimated value calculating unit for calculating a first optimum estimated value vector of the state quantity at time n + 1 based on information up to time n with respect to observation information only at time n;
For the observation information only at time n, using the weighting coefficient matrix calculated by the weighting coefficient calculation unit, calculate a second optimal estimated value vector of the state quantity at the time based on information up to time n + 1. A second optimum estimated value calculation unit;
A second correlation calculation unit that calculates a second correlation value matrix of an estimation error when the state quantity at the time is estimated from information up to time n + 1 with respect to observation information only at time n;
The noise suppression device according to claim 1, comprising: The first correlation calculation unit includes:
Using a predetermined state transition matrix, an element value of covariance of a given drive source vector, and a second correlation value matrix of the estimation error given or previously calculated by the second correlation calculation unit, Calculate the first correlation value matrix of the estimation error,
The weight coefficient calculation unit includes:
Calculation of the weighting coefficient matrix using a first correlation value matrix of the estimation error calculated by the first correlation calculation unit, a given observation transition matrix, and a covariance element value of a given noise vector And
The first optimal estimated value calculation unit includes:
Using the state transition matrix and the second optimum estimated value vector of the state quantity given or previously calculated by the second optimum estimated value calculating unit, the first optimum estimated value vector of the state quantity Perform the calculation
The second optimum estimated value calculation unit includes:
The first optimal estimated value vector of the state quantity calculated by the first optimal estimated value calculating unit, the weighting coefficient matrix calculated by the weighting coefficient calculating unit, the observation transition matrix, and the observed amount only at time n + 1 To calculate a second optimum estimated value vector of the state quantity,
The second correlation calculation unit includes:
Using the weight coefficient matrix calculated by the weight coefficient calculation unit, the observation transition matrix, and the first correlation value matrix of the estimation error calculated by the first correlation calculation unit, the second estimation error is calculated. Calculate the correlation value matrix,
The noise suppression device according to claim 2. A noise suppression method for estimating the desired information only from observation information in which noise is mixed in the desired information,
An acquisition step of acquiring the observation information;
An extraction step of extracting the desired information by removing the noise from the acquired observation information using a Kalman filter using colored noise as a driving source , and
The Kalman filter is
It is configured not to use autoregressive model coefficients in the state equation of the state space model,
Noise suppression method. The extraction step includes
A first correlation calculation step of calculating a first correlation value matrix of an estimation error when the state quantity of the system at time n + 1 including the desired information is estimated from information up to time n with respect to observation information only at time n When,
For the observation information only at time n, using the first correlation value matrix of the estimation error calculated in the first correlation calculation step, the optimum estimated value of the state quantity at that time by the information up to time n + 1 A weight for calculating a weight coefficient matrix for defining a relationship between a vector, an optimal estimated value vector of the state quantity at time n + 1 based on information up to time n, and an estimated error vector of the observed quantity including the observation information Coefficient calculation step;
A first optimal estimated value calculating step of calculating a first optimal estimated value vector of the state quantity at time n + 1 based on information up to time n with respect to observation information only at time n;
For the observation information only at time n, the second optimal estimated value vector of the state quantity at the time according to the information up to time n + 1 is calculated using the weight coefficient matrix calculated in the weight coefficient calculation step. 2 optimal estimated value calculation steps;
A second correlation calculation step of calculating a second correlation value matrix of an estimation error when the state quantity at the time is estimated from information up to time n + 1 with respect to observation information only at time n;
The noise suppression method according to claim 4, comprising: The first correlation calculation step includes:
The estimation is performed using a predetermined state transition matrix, a covariance element value of a given drive source vector, and a second correlation value matrix of the estimation error given or previously calculated in the second correlation calculation step. Calculate the first correlation value matrix of error,
The weighting factor calculating step includes
The weighting coefficient matrix is calculated using the first correlation value matrix of the estimation error calculated in the first correlation calculation step, the given observation transition matrix, and the covariance element value of the given noise vector. Done
The first optimum estimated value calculating step includes:
Calculation of the first optimum estimated value vector of the state quantity using the state transition matrix and the second optimum estimated value vector of the state quantity given or previously calculated in the second optimum estimated value calculating step And
The second optimum estimated value calculating step includes:
The first optimal estimated value vector of the state quantity calculated in the first optimal estimated value calculating step, the weighting coefficient matrix calculated in the weighting coefficient calculating step, the observation transition matrix, and the observed amount only at time n + 1 are used. Calculating a second optimal estimated value vector of the state quantity,
The second correlation calculation step includes:
A second correlation value of the estimation error using the weighting coefficient matrix calculated in the weighting coefficient calculation step, the observation transition matrix, and a first correlation value matrix of the estimation error calculated in the first correlation calculation step. Calculate the matrix,
The noise suppression method according to claim 5. A noise suppression program for estimating the desired information only from observation information in which noise is mixed in the desired information,
On the computer,
An acquisition step of acquiring the observation information;
An extraction step of extracting the desired information by removing the noise from the acquired observation information using a Kalman filter using colored noise as a driving source; and the Kalman filter is a coefficient of an autoregressive model in a state equation of a state space model Configured to not use the
Noise suppression program for running. The extraction step includes
A first correlation calculation step of calculating a first correlation value matrix of an estimation error when the state quantity of the system at time n + 1 including the desired information is estimated from information up to time n with respect to observation information only at time n When,
For the observation information only at time n, using the first correlation value matrix of the estimation error calculated in the first correlation calculation step, the optimum estimated value of the state quantity at that time by the information up to time n + 1 A weight for calculating a weight coefficient matrix for defining a relationship between a vector, an optimal estimated value vector of the state quantity at time n + 1 based on information up to time n, and an estimated error vector of the observed quantity including the observation information Coefficient calculation step;
A first optimal estimated value calculating step of calculating a first optimal estimated value vector of the state quantity at time n + 1 based on information up to time n with respect to observation information only at time n;
For the observation information only at time n, the second optimal estimated value vector of the state quantity at the time according to the information up to time n + 1 is calculated using the weight coefficient matrix calculated in the weight coefficient calculation step. 2 optimal estimated value calculation steps;
A second correlation calculation step of calculating a second correlation value matrix of an estimation error when the state quantity at the time is estimated from information up to time n + 1 with respect to observation information only at time n;
The noise suppression program according to claim 7. The first correlation calculation step includes:
The estimation is performed using a predetermined state transition matrix, a covariance element value of a given drive source vector, and a second correlation value matrix of the estimation error given or previously calculated in the second correlation calculation step. Calculate the first correlation value matrix of error,
The weighting factor calculating step includes
The weighting coefficient matrix is calculated using the first correlation value matrix of the estimation error calculated in the first correlation calculation step, the given observation transition matrix, and the covariance element value of the given noise vector. Done
The first optimum estimated value calculating step includes:
Calculation of the first optimum estimated value vector of the state quantity using the state transition matrix and the second optimum estimated value vector of the state quantity given or previously calculated in the second optimum estimated value calculating step And
The second optimum estimated value calculating step includes:
The first optimal estimated value vector of the state quantity calculated in the first optimal estimated value calculating step, the weighting coefficient matrix calculated in the weighting coefficient calculating step, the observation transition matrix, and the observed amount only at time n + 1 are used. Calculating a second optimal estimated value vector of the state quantity,
The second correlation calculation step includes:
A second correlation value of the estimation error using the weighting coefficient matrix calculated in the weighting coefficient calculation step, the observation transition matrix, and a first correlation value matrix of the estimation error calculated in the first correlation calculation step. Calculate the matrix,
The noise suppression program according to claim 8.

Images