KR102292091B1 - Sparse Frequency Analysis method for Passive SONAR System and System thereof - Google Patents

Abstract

A sparse frequency analysis method for a passive sonar system and a system thereof are disclosed. In this system, an observed variance calculation part calculates the observed variance of a prior probability using an acoustic signal received through an array sensor. An update part updates a frequency component magnitude and a noise variance using the observed variance calculated by the observed variance calculation part. A convergence determining part determines whether the magnitude of the frequency component updated by the update part converges. When the convergence determining part determines that the magnitude of the frequency component converges, a restored frequency calculation part calculates an estimated value of the restored frequency for the acoustic signal by using a probability statistical signal restoration technique.

Description

Sparse Frequency Analysis method for Passive SONAR System and System thereof

The present invention relates to a sparse frequency analysis method for a passive sonar system and a system therefor, and more particularly, to a sparse frequency analysis method for a passive sonar system capable of frequency analysis by applying a sparse Bayesian learning method based on a compressed sensing technique. It relates to a frequency analysis method and a system therefor.

Passive sonar systems receive acoustic signals emitted from marine objects (ships, submarines, marine life, etc.) and analyze the frequencies of the signals. Accurate identification of frequency components is very important for target object detection, and many studies are being conducted for this purpose.

Existing frequency analysis techniques such as Discrete Fourier Transformation (DFT) technology and Fast Fourier Transform (FFT) technology have limitations such as high computational amount and reduced resolution according to observation time. In order to do this, a compression sensing-based frequency analysis technology has been proposed.

This compression sensing technology is a technology that can accurately analyze the original signal with fewer observations than the existing frequency analysis technology by using the sparsity of the signal to restore the original signal in an optimization method. Atomic Norm Minimization (ANM) technology is a frequency analysis technology according to

However, in the case of the ANM technology, there is still a limitation in that the processing time is greatly increased when setting a regularization parameter according to a signal to noise ratio (SNR) and using multiple snapshots.

The technical problem to be solved by the present invention is to provide a sparse frequency analysis method and a system for a passive sonar system that can expect excellent signal restoration performance and can have a relatively accurate estimation value.

The characteristic configuration of the present invention for achieving the object of the present invention as described above and realizing the characteristic effects of the present invention to be described later is as follows.

According to one aspect of the present invention, a sparse frequency analysis system is provided, the system comprising:

A sparse frequency analysis system for a passive sonar system, comprising: an observed variance calculation unit for calculating an observed variance value of a prior probability using an acoustic signal received through an array sensor; the observed variance value calculated by the observed variance calculation unit An update unit for updating the frequency component magnitude and noise dispersion using When it is determined, a restoration frequency calculator for calculating an estimate value of a restoration frequency for the sound signal by a restoration technique of a probability statistical signal is included.

Here, the system further includes an initial value generator for generating an initial value of the magnitude of a frequency component used in the sparse frequency analysis system, an initial value of noise analysis, and a lowest convergence value.

The update unit may include a frequency component magnitude updater configured to update the frequency component size by calculating an update value for the frequency component size using the observed variance calculated by the observed variance calculation unit, and the observed variance and a noise variance updater configured to update the noise variance by calculating an update value for the noise variance using the observed variance calculated by the value calculator.

In addition, the convergence determining unit includes a convergence value calculator for calculating a convergence value of the frequency component size using the frequency component size before being updated by the update unit and the frequency component size after being updated by the update unit.

In addition, the convergence determining unit determines that the frequency component size converges when the convergence value of the frequency component magnitude calculated by the convergence value calculator is smaller than the lowest convergence value.

)은 다음의 관계식

에 따라 계산되며, 여기서 상기

은 잡음 분산이고,

은 N×N 단위 행렬이며,

및

는 주파수 성분의 특성을 나타내는 딕셔너리 행렬(dictionary matrix)이고,

는 주파수 성분 크기

의 대각 행렬이다. In addition, the observed variance (

) is the following relation

is calculated according to where

is the noise variance,

is an N×N identity matrix,

and

is a dictionary matrix indicating the characteristics of the frequency component,

is the magnitude of the frequency component

is a diagonal matrix of

)은 다음의 관계식

에 따라 계산되며, 여기서

은 m번째 주파수 성분 크기의 업데이트 값이고,

는 업데이트 전 주파수 성분의 크기이며,

는 상기 음향 신호에 대한 측정 벡터이고,

은 다중 스냅샷의 개수이며,

은 상기 관측 분산값의 역행렬이고,

은 딕셔너리 행렬 A의 m번째 열벡터이다.In addition, the update value (

) is the following relation

is calculated according to where

is the update value of the magnitude of the m-th frequency component,

is the magnitude of the frequency component before the update,

is a measurement vector for the acoustic signal,

is the number of multiple snapshots,

is the inverse matrix of the observed variance,

is the mth column vector of the dictionary matrix A.

)은 다음의 관계식

에 따라 계산되며, 여기서

은 관측 신호의 길이이며,

는 유의미한(0이 아님) 주파수 성분의 개수이고,

은 활성화된 딕셔너리 행렬로서

이다.In addition, the update value (

) is the following relation

is calculated according to where

is the length of the observed signal,

is the number of significant (non-zero) frequency components,

is the active dictionary matrix,

am.

)은 다음의 관계식

에 따라 계산되며, 여기서

는 주파수 성분 크기의 업데이트 값이고,

는 업데이트되기 전의 주파수 성분 크기이다.In addition, the convergence value (

) is the following relation

is calculated according to where

is the update value of the magnitude of the frequency component,

is the magnitude of the frequency component before being updated.

According to another aspect of the present invention, there is provided a sparse frequency analysis method, the method comprising:

A sparse frequency analysis method for a passive sonar system, comprising the steps of generating an initial value for sparse frequency analysis when an acoustic signal is received through an array sensor, wherein the initial value includes an initial value of frequency component magnitude, an initial value of noise analysis, and including a lowest convergence value, calculating an observed variance of the prior probability using the initial value, using the observed variance to update a frequency component magnitude and a noise variance, and the frequency component magnitude converges. , calculating a restored frequency estimate for the acoustic signal by a probabilistic statistical signal restoration technique. , and updating the frequency component magnitude and noise variance are repeatedly performed.

Here, whether the magnitude of the frequency component converges is performed by determining whether a convergence value between a value before and after the update of the magnitude of the frequency component is smaller than the lowest convergence value, and the convergence value is the lowest convergence value If smaller, it is determined that the magnitude of the frequency component converges.

According to the present invention, excellent signal restoration performance can be expected, and excellent signal restoration performance can be expected by allowing the probability distribution of the frequency to be restored to be approached from a complete probability point of view by assuming that the before/after and noise are normal probability distributions. By optimizing assuming noise, a relatively accurate estimate can be obtained.

In addition, even if multiple snapshots are used, there is no significant change in processing speed compared to the case of using a single snapshot, and there is no need to set normalization variables.

When the present invention is applied to a passive sonar system, it can have higher resolution and resolution than the conventional frequency analysis technique even in an actual marine environment having a low signal to noise ratio.

1 is a diagram illustrating an underwater environment to which a sparse frequency analysis method for a passive sonar system according to an embodiment of the present invention is applied.
2 is a schematic block diagram of a sparse frequency analysis system for a passive sonar system according to an embodiment of the present invention.
3 is a schematic flowchart of a sparse frequency analysis method for a passive sonar system according to an embodiment of the present invention.
4 is a diagram comparing the processing speed of the ANM method according to the use of multiple snapshots and the sparse Bayesian learning method according to an embodiment of the present invention.
5 is a diagram illustrating a frequency analysis result using a fast Fourier transform, ANM, and a sparse Bayesian learning method according to an embodiment of the present invention when a single snapshot is used in an SNR 0dB environment.
6 is a comparison diagram of frequency analysis results when single snapshot and multiple snapshots are used in an SNR -13dB environment.
7 is a diagram showing results of frequency analysis of actual resolution data received from 120 buried horizontal array sensors using fast Fourier transform and sparse Bayesian learning method according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those of ordinary skill in the art to which the present invention pertains can easily implement them. The present invention may be embodied in many different forms and is not limited to the embodiments described herein.

In order to clearly explain the present invention, parts irrelevant to the description are omitted, and the same reference numerals are given to the same or similar elements throughout the specification.

In addition, throughout the specification, when a part "includes" a certain component, this means that other components may be further included, rather than excluding other components, unless otherwise stated.

Hereinafter, a sparse frequency analysis method for a passive sonar system and a system thereof according to an embodiment of the present invention will be described with reference to the drawings.

The compression sensing technique used in the embodiment of the present invention is a technique for recovering a signal through optimization after assuming the sparsity of the received signal. Since the acoustic frequency received in water is a prime number within the observable range, it is scarce. Since it can be regarded as a signal with

In an embodiment of the present invention, a frequency analysis method using a compressed sensing-based sparse Bayesian learning method with improved frequency analysis performance by estimating ocean factors and ambient noise using a reconstruction technique of a probabilistic statistical signal is applied.

1 is a diagram illustrating an underwater environment to which a sparse frequency analysis method for a passive sonar system according to an embodiment of the present invention is applied.

Referring to FIG. 1 , the sparse frequency analysis system 100 according to an embodiment of the present invention receives an acoustic signal of a marine entity 200 (ship, submersible, etc.) using a horizontal array sensor or a vertical array sensor in water. . Here, the horizontal array sensor may be, for example, a tow-type horizontal array sensor 101 or a buried horizontal array sensor 102 , but the embodiment of the present invention is not limited thereto. In addition, the sparse frequency analysis system 100 assumes that the horizontal array sensors 101 and 102 (hereinafter, referred to as 'array sensors') are connected by wire or wireless and are mounted on a ship (submersible, etc.) 300 . .

는 다음의 [수학식 1]과 같이 표현될 수 있다.In this case, the radiation noise signal of the marine object 200 received by the array sensors 101 and 102 .

can be expressed as the following [Equation 1].

[Equation 1]

는 측정 벡터이고,

는 주파수 성분의 특성을 나타내는 딕셔너리 행렬(dictionary matrix)이며,

는 복원하고자 하는 주파수 성분 벡터이고,

은 주변 잡음을 의미하며,

은 다중 스냅샷의 개수이다. 여기서, 단일 스냅샷은 하나의 수동 소나에서 수신한 일정 길이의 신호를 의미하고, 복수의 단일 스냅샷

들을 이용한 다중 측정 벡터를 다중 스냅샷이라고 한다. here,

is the measurement vector,

is a dictionary matrix indicating the characteristics of the frequency component,

is the frequency component vector to be restored,

stands for ambient noise,

is the number of multiple snapshots. Here, a single snapshot means a signal of a certain length received from one passive sonar, and a plurality of single snapshots

Multiple measurement vectors using these are called multiple snapshots.

가 주어졌을 때 주파수 성분 벡터

와 주파수 성분의 크기

그리고 잡음 분산

을 최대화하는

를 찾는 문제로 생각할 수 있으며, 이는 다음의 [수학식 2]와 같이 표현될 수 있다. On the other hand, when the restoration technique of the probabilistic statistical signal is used for [Equation 1], the received signal measurement vector

frequency component vector given

and the magnitude of the frequency component

and noise dispersion

to maximize

It can be thought of as a problem of finding , which can be expressed as the following [Equation 2].

[Equation 2]

는 확률 통계적 신호의 복원 기법을 이용해 구하는 주파수 추정값, 즉 복원 주파수를 의미한다. here

denotes a frequency estimation value obtained by using a probabilistic statistical signal restoration technique, that is, a restoration frequency.

는 체인룰(Chain Rule)을 이용하여 다음의 [수학식 3]과 같이 분해될 수 있다.On the other hand, in [Equation 2],

can be decomposed as in the following [Equation 3] using a chain rule.

[Equation 3]

은 측정 벡터

가 주어졌을 때 측정 벡터를 가장 잘 설명할 수 있는 복원 주파수를 의미하며, 구체적으로는 [수학식 3]과 같이 변환될 때, 측정 벡터

를 사용하여 업데이트한 주파수 성분의 크기

와 잡음 분산

을 이용한 확률 통계적 신호의 복원 기법에 의한 복원 주파수를 의미한다.In the above-mentioned [Equation 2] and [Equation 3]

silver measurement vector

It means the restoration frequency that can best explain the measurement vector when given, and specifically, when transformed as in [Equation 3], the measurement vector

magnitude of the frequency component updated using

and noise dispersion

It means the restoration frequency by the restoration technique of the probabilistic statistical signal using

의 사후 함수(posterior function)

는 베이즈 정리(Baye's Theorem)에 따라 사전 함수

와 가능도 함수

를 이용하여 다음의 [수학식 4]와 같이 표현될 수 있다.In [Equation 3], the measurement vector

posterior function of

is a dictionary function according to Baye's Theorem

and the likelihood function

It can be expressed as the following [Equation 4] using

[Equation 4]

는 주변 함수를 의미한다.here,

is the surrounding function.

는 계측값에 대한 확률값으로 하나의 데이터 집합에 대하여 정의되었기 때문에 정규화시킬 수 없다. 따라서, 사후 함수에 따른 사후 확률 분포는 직접적으로 계산할 수 없으며, 사후 확률 분포를 분해하여 각각의 요소들을 계산하여 다음의 [수학식 5]와 같이 수식적으로 표현한다. On the other hand, the peripheral function

Since is defined for one data set as a probability value for the measured value, it cannot be normalized. Therefore, the posterior probability distribution according to the posterior function cannot be calculated directly, and each element is calculated by decomposing the posterior probability distribution and expressed mathematically as in the following [Equation 5].

[Equation 5]

에 대한 가능도 함수는 다음의 [수학식 6]과 같이 잡음 분산

을 갖는 조건부 확률 밀도 함수(probability density function)로 표현될 수 있다.In [Equation 5], assuming that the noise of the likelihood function is a complex Gaussian with an average of 0, the measurement vector

The likelihood function for is the noise variance as shown in Equation 6 below.

It can be expressed as a conditional probability density function having

[Equation 6]

은 관측 신호의 길이를 나타낸다. here

is the length of the observed signal.

에서 음원은 스냅샷과 주파수에 대해 독립이며 주파수에 종속인 분산을 갖는 평균이 0인 복소 가우시안 분포를 갖는다고 가정하면, 사전 함수에 대한 희소 신호 모델은 다음의 [수학식 7]과 같다.On the other hand, the dictionary function

Assuming that the sound source has a complex Gaussian distribution with an average of 0 and a variance independent of the snapshot and frequency, the sparse signal model for the prior function is as follows [Equation 7].

[Equation 7]

는

의 대각 행렬을 의미한다.here,

Is

means the diagonal matrix of

Therefore, the above-mentioned [Equation 5] can be arranged as follows [Equation 8] by multiplying [Equation 6] and [Equation 7].

[Equation 8]

와 사전 함수

가 가우시안 함수이기 때문에 가능도 함수와 사전 함수의 곱인 [수학식 8]은 사후 확률의 평균값(

), 사후 확률의 분산값(

) 그리고 사전 확률의 분산값, 즉 관측 분산값(

)이 다음의 [수학식 9]와 같은 가우시안 함수이다.Here, the likelihood function

and dictionary functions

Since is a Gaussian function, [Equation 8], which is the product of the likelihood function and the prior function, is the average value of the posterior probability (

), the variance of the posterior probability (

) and the variance of the prior probabilities, i.e. the observed variance (

) is a Gaussian function like the following [Equation 9].

[Equation 9]

는 딕셔너리 행렬로서 각각의 주파수 성분의 특징을 나타내는 행렬이며,

은 N×N 단위 행렬을 나타낸다.here,

is a dictionary matrix indicating the characteristics of each frequency component,

denotes an N×N unitary matrix.

)와 잡음 분산(

)을 안다면 MAP 추정(Maximum a posteriori estimation)에 따른 주파수 추정값은 다음의 [수학식 10]에 나타낸 바와 같이 사후 확률의 평균값(

)과 같음을 알 수 있다.In this way, the mathematically developed posterior probability value can be inferred through the optimization technique, in which case the size of the frequency component that maximizes the posterior probability distribution (

) and the noise variance (

), the frequency estimation value according to the MAP estimation (Maximum a posterior estimation) is the average value of the posterior probability (

) can be found to be the same as

[Equation 10]

를 상수 취급하여 전술한 [수학식 5]와 같이 나타내었으므로, 여기에서는 주변 함수를 최대화하는 초매개변수(hyperparameter)인 주파수 성분의 크기(

)와 잡음 분산(

)을 구하기 위해 유형∥최대 가능도 방법(type ∥ maximum likelihood estimation)을 이용한다. On the other hand, in the above-mentioned [Equation 4], the marginal function that is the denominator

Since it is expressed as in [Equation 5] above by treating as a constant, here, the magnitude of the frequency component (hyperparameter) that maximizes the

) and the noise variance (

), the type │ maximum likelihood estimation method is used.

와 사전 함수

의 곱을 복소 신호인 주파수 성분 벡터

로 적분한 값으로, 다음의 [수학식 11]과 같이 나타낼 수 있다.In [Equation 4], the marginal function, which is the denominator term, is a likelihood function

and dictionary functions

The product of a frequency component vector that is a complex signal

As a value integrated with , it can be expressed as the following [Equation 11].

[Equation 11]

개의 다중 스냅샷을 갖는 [수학식 11]에 한계 로그 우도(marginal log-likelihood) 형태를 취하면 다음의 [수학식 12]와 같이 표현할 수 있으며, [수학식 12]를 최대화하는 초매개변수 주파수 성분의 크기(

)와 잡음 분산(

)을 구한다.

If [Equation 11] having multiple snapshots takes the form of marginal log-likelihood, it can be expressed as the following [Equation 12], and the hyperparameter frequency that maximizes [Equation 12] the size of the component (

) and the noise variance (

) to find

[Equation 12]

)와 잡음 분산(

)의 두 가지 변수에 의하여 목적 함수의 공간이 변화하기 때문에 직접적인 최적화 적용에 어려움이 있으므로, 주파수 성분의 크기(

)는 기댓값 최대화 기법(expectation maximization method) 그리고 잡음 분산(

)은 통계적 최대 우도 추정(stochastic maximum likelihood estimation) 기법을 이용하여 업데이트된다.[Equation 12] is the magnitude of the frequency component, which is a hyperparameter (

) and the noise variance (

), since the space of the objective function is changed by two variables, it is difficult to apply direct optimization,

) is the expectation maximization method and the noise variance (

) is updated using a statistical maximum likelihood estimation technique.

)를 업데이트하기 위해서 [수학식 12]를

으로 미분하여

이 되는

을 찾는다. 여기서

은 m번째 주파수의 크기를 의미한다.　 the magnitude of the frequency component (

) to update [Equation 12]

by differentiating

becoming

look for here

denotes the magnitude of the m-th frequency.

으로 미분한 값이며,

이 되는 값을 반복 인자(iterative factor)를 이용하면, 다음의 [수학식 14]와 같이 업데이트 값

을 찾을 수 있다.The following [Equation 13] is [Equation 12]

is the value differentiated by

If this value is used as an iterative factor, the update value as shown in the following [Equation 14]

can be found

[Equation 13]

[Equation 14]

은 업데이트된 주파수 성분의 크기를 나타내고,

는 업데이트 전 주파수 성분의 크기를 나타내며,

은 관측 분산값의 역행렬이고,

은 딕셔너리 행렬 A의 m번째 열벡터를 의미한다. here

represents the magnitude of the updated frequency component,

represents the magnitude of the frequency component before the update,

is the inverse matrix of the observed variance,

denotes the m-th column vector of the dictionary matrix A.

)은 통계적 최대 우도 추정법을 사용하여 업데이트되며

개의 활성화된 주파수가 주어졌을 때 다음의 [수학식 15]와 같이 업데이트된다. 이 때, 잡음 분산(

)은 각 주파수별로 동일하다.Next, the noise variance (

) is updated using statistical maximum likelihood estimation,

When n activated frequencies are given, they are updated as in the following [Equation 15]. In this case, the noise dispersion (

) is the same for each frequency.

[Equation 15]

은 활성화된 딕셔너리 행렬(dictionary matrix)이고,

이며,

은 관측 신호의 길이를 나타내고,

는 유의미한(0이 아님) 주파수 성분의 개수를 나타낸다.here

is the active dictionary matrix,

is,

represents the length of the observed signal,

represents the number of significant (non-zero) frequency components.

Hereinafter, a sparse frequency analysis system for a passive sonar system according to an embodiment of the present invention will be described in detail with reference to the above description.

2 is a schematic block diagram of a sparse frequency analysis system for a passive sonar system according to an embodiment of the present invention.

As shown in FIG. 2 , the sparse frequency analysis system 100 for a passive sonar system according to an embodiment of the present invention includes an array sensor 110 , a signal receiver 120 , an initial value generator 130 , and observation variance. It includes a value calculation unit 140 , an update unit 150 , a convergence determination unit 160 , and a restoration frequency calculation unit 170 .

The array sensor 110 refers to a sensor in which a plurality of sensors are arranged one-dimensionally or two-dimensionally, and in the present embodiment, it may be the towing-type horizontal array sensor 101 or the buried-type horizontal array sensor 102 as described above.

로서, 전술한 [수학식 1]과 같이 표현될 수 있다.The signal receiver 120 receives the acoustic signal generated from the external marine entity 200 through the array sensor 110 . For example, the signal received by the signal receiving unit 120 through the array sensor 110 is a measurement vector

As, it can be expressed as in [Equation 1] described above.

)의 초기값인

, 잡음 분산(

)의 초기값인

, 유의미한 주파수 성분의 개수를 나타내는 K 값 및 최저 수렴값(

)을 생성하며, 여기서 K값은 일반적으로 수동 소나 시스템에서 관심을 갖는 주파수 성분이 희소성을 갖기 때문에 신호 길이보다 작은 값으로 설정된다. 이 때, 각각의 초기값 또는 최저 수렴값은 사용자에 의해 설정될 수 있다.The initial value generator 130 generates an initial value for each parameter used in an embodiment of the present invention. For example, the magnitude of the frequency component (

) is the initial value of

, the noise variance (

) is the initial value of

, the K value representing the number of significant frequency components and the lowest convergence value (

), where K is generally set to a value smaller than the signal length because frequency components of interest in passive sonar systems have sparseness. In this case, each initial value or the lowest convergence value may be set by a user.

)을 계산한다. The observed variance calculation unit 140 uses the initial value generated by the initial value generation unit 130 and the signal received by the signal receiving unit 120 to obtain the observed variance value (

) is calculated.

)와 잡음 분산(

)을 새로운 값으로 각각 업데이트한다. The update unit 150 uses the signal received by the signal receiving unit 120 and the observed variance calculated by the observed variance calculation unit 140 to increase the frequency component (

) and the noise variance (

) with the new value, respectively.

More specifically, the update unit 150 includes a frequency component magnitude update unit 151 and a noise dispersion update unit 152 .

The frequency component magnitude update unit 151 uses the signal received by the signal receiving unit 120 and the observed variance calculated by the observed variance calculation unit 140 to determine the magnitude of the frequency component according to [Equation 14] above. Find the update value for , and update the magnitude of the frequency component.

The noise variance update unit 152 uses the signal received by the signal receiving unit 120 and the observed variance calculated by the observed variance calculation unit 140 to update the noise variance according to Equation 15 above. to find and update the magnitude of the frequency component.

The convergence determination unit 160 determines whether the magnitude of the frequency component updated by the frequency component magnitude updater 151 converges. To this end, the convergence determination unit 160 includes a convergence value calculation unit 161 for calculating a convergence value of the magnitude of the frequency component.

)와 업데이트될 때의 주파수 성분 크기(

)를 사용하여 주파수 성분 크기의 수렴값을 계산한다. 구체적으로, 수렴값 계산부(161)는 다음의 [수학식 16]에 따라 주파수 성분 크기의 수렴값(

)을 계산한다.The convergence value calculator 161 determines the frequency component size (

) and the magnitude of the frequency component when updated (

) to calculate the convergence value of the frequency component magnitude. Specifically, the convergence value calculation unit 161 calculates the convergence value (

) is calculated.

[Equation 16]

)과 초기값 생성부(130)에서 생성된 최저 수렴값(

)을 비교하여 주파수 성분 크기의 수렴 여부를 판단한다.Therefore, the convergence determination unit 160 is a convergence value calculated by the convergence value calculation unit 161 (

) and the lowest convergence value (

) to determine whether the frequency component magnitudes converge.

)이 초기값 생성부(130)에서 생성된 최저 수렴값(

)보다 작을 때 주파수 성분 크기가 수렴하는 것으로 판단한다.More specifically, the convergence determination unit 160 calculates the convergence value (

) is the lowest convergence value (

), it is judged that the magnitude of the frequency component converges.

[Equation 17]

If it is determined by the convergence determination unit 160 that the frequency component magnitudes do not converge, the observed variance calculation unit 140, the update unit 150, and the convergence determination unit 160 repeat until the frequency component sizes converge. it works by

)와 이 때의 잡음 분산(

)을 사용하여 전술한 [수학식 10]에 따라 확률 통계적 신호의 복원 기법에 의한 복원 주파수 추정값을 계산한다.When it is determined that the frequency component size converges in the convergence determination unit 160 , the restored frequency calculation unit 170 determines the size of the converged frequency component (

) and the noise variance at this time (

) to calculate the estimated value of the restoration frequency by the restoration technique of the probabilistic statistical signal according to [Equation 10] described above.

Hereinafter, a sparse frequency analysis method for a passive sonar system according to an embodiment of the present invention will be described. The sparse frequency analysis method for the passive sonar system may be performed by the sparse frequency analysis system 100 for the passive sonar system described above with reference to FIG. 2 .

3 is a schematic flowchart of a sparse frequency analysis method for a passive sonar system according to an embodiment of the present invention.

로서, 전술한 [수학식 1]과 같이 표현될 수 있다.Referring to FIG. 3 , an acoustic signal is received by a passive sonar system (not shown) equipped with the sparse frequency analysis system 100 according to an embodiment of the present invention. That is, each of the array sensors 110 receives an acoustic signal ( S100 ). At this time, the acoustic signal received through the array sensor 110 is a measurement vector

As, it can be expressed as in [Equation 1] described above.

)의 초기값인

, 잡음 분산(

)의 초기값인

, 유의미한 주파수 성분의 개수를 나타내는 K값 및 최저 수렴값(

)을 생성한다. 이 때, 각각의 초기값 또는 최저 수렴값은 사용자에 의해 설정될 수 있다.Next, when an external sound signal is received, an initial value for each parameter used in the embodiment of the present invention is generated (S110). For example, the magnitude of the frequency component (

) is the initial value of

, the noise variance (

) is the initial value of

, the K value representing the number of significant frequency components and the lowest convergence value (

) is created. In this case, each initial value or the lowest convergence value may be set by a user.

)을 계산한다. Thereafter, the observed variance is calculated using the initial value ( S120 ). Specifically, the observed variance (

) is calculated.

)이 계산되면, 계산된 관측 분산값(

)과 상기 단계(S100)에서 수신된 음향 신호를 사용하여 주파수 성분의 크기에 대한 업데이트를 수행한다(S130).As such, the observed variance (

) is calculated, the calculated observed variance (

) and the sound signal received in step S100 is used to update the magnitude of the frequency component (S130).

)와 관측 분산값(

)을 사용하여 전술한 [수학식 14]에 따라 주파수 성분의 크기(

)에 대한 업데이트 값을 찾아서 주파수 성분의 크기(

)에 대한 업데이트를 수행한다. Specifically, the received acoustic signal (

) and the observed variance (

) using the above-mentioned [Equation 14], the magnitude of the frequency component (

) by finding the update value for the magnitude of the frequency component (

) is updated.

)과 상기 단계(S100)에서 수신된 음향 신호를 사용하여 잡음 분산에 대한 업데이트를 수행한다(S140).Also, the calculated observed variance (

) and the sound signal received in step S100 is used to update the noise distribution (S140).

)와 관측 분산값(

)을 사용하여 전술한 [수학식 15]에 따라 잡음 분산(

)에 대한 업데이트 값을 찾아서 잡음 분산(

)에 대한 업데이트를 수행한다.Specifically, the received acoustic signal (

) and the observed variance (

) using the above-mentioned [Equation 15], the noise dispersion (

) by finding the update value for the noise variance (

) is updated.

)와 잡음 분산(

)에 대한 업데이트가 수행된 후에, 주파수 성분 크기에 대한 수렴 여부를 판단하기 위해 먼저 주파수 성분 크기의 수렴값을 계산한다(S150).As such, the magnitude of the frequency component, which is a hyperparameter (

) and the noise variance (

), in order to determine whether the magnitude of the frequency component converges or not, a convergence value of the magnitude of the frequency component is first calculated (S150).

)은 전술한 [수학식 16]에 따라 계산될 수 있다.Specifically, the convergence value (

) can be calculated according to [Equation 16] described above.

Thereafter, it is determined whether the magnitude of the frequency component is converged by using the calculated convergence value for the magnitude of the frequency component (S160).

)이 상기 단계(S110)에서 생성된 최저 수렴값(

)보다 작은지 여부를 판단하여 주파수 성분 크기의 수렴 여부를 판단한다. 즉, 계산된 주파수 성분 크기에 대한 수렴값(

)이 최저 수렴값(

)보다 작은 경우 주파수 성분 크기가 수렴하는 것으로 판단된다.Specifically, according to the above-mentioned [Equation 17], the convergence value (

) is the lowest convergence value (

) to determine whether the magnitude of the frequency component is convergence or not. That is, the convergence value (

) is the lowest convergence value (

), it is judged that the magnitude of the frequency component converges.

)이 최저 수렴값(

)보다 크거나 같은 경우, 주파수 성분 크기가 수렴할 때까지 상기 단계(S130)에서 업데이트된 주파수 성분 크기(

)와 상기 단계(S140)에서 업데이트된 잡음 분산(

)을 사용하여 상기 단계(S120, S130, S140, S150, S160)을 반복 수행한다.If it is determined that the magnitude of the frequency component does not converge in step S160, that is, the convergence value (

) is the lowest convergence value (

), the updated frequency component size ( S130 ) until the frequency component size converges.

) and the noise variance updated in step S140 (

) to repeat the above steps (S120, S130, S140, S150, S160).

)이 최저 수렴값(

)보다 작은 경우, 수렴한 주파수 성분의 크기(

)와 이 때의 잡음 분산(

)을 사용하여 전술한 [수학식 10]에 따라 확률 통계적 신호의 복원 기법에 의한 복원 주파수 추정값을 계산한다(S170).However, when it is determined that the magnitude of the frequency component converges in step S160, that is, the convergence value (

) is the lowest convergence value (

), the magnitude of the converged frequency component (

) and the noise variance at this time (

) to calculate a restoration frequency estimate by the restoration technique of a probability statistical signal according to [Equation 10] described above (S170).

As described above, according to the embodiment of the present invention, excellent signal restoration performance can be expected by allowing the probability distribution of the frequency to be restored to be approached from a perfect probability point of view, assuming the pre/post and noise are normal probability distributions. , it is possible to have a relatively accurate estimate by optimizing assuming a noise having a normal probability distribution.

In addition, even if multiple snapshots are used, there is no significant change in processing speed compared to the case of using a single snapshot, and there is no need to set normalization variables.

When the present invention is applied to a passive sonar system, it can have higher resolution and resolution than the conventional frequency analysis technique even in an actual marine environment having a low signal to noise ratio.

4 is a diagram comparing the processing speed of an atomic norm minimization (ANM) method according to the use of multiple snapshots and a sparse Bayesian learning method according to an embodiment of the present invention.

Referring to FIG. 4 , it is assumed that a single sensor, 5 frequency signals, and an SNR of 10 dB are used. In the case of ANM, the processing time increases as the number of snapshots increases, but in the case of the sparse Bayesian learning method according to the embodiment of the present invention, it can be seen that the processing time does not change even if the number of snapshots increases.

5 is a diagram of frequency analysis results using Fast Fourier Transform (FFT), ANM, and a sparse Bayesian learning method according to an embodiment of the present invention when a single snapshot is used in an SNR 0dB environment.

Referring to FIG. 5 , the black dotted line is the frequency estimation result using the fast Fourier transform, the blue solid line and circle are the frequency estimation results using the ANM, and the red solid line is the frequency using the sparse Bayesian learning method according to the embodiment of the present invention. It is an estimation result, and the green box and dotted line mean the actual positions of five frequencies (100Hz, 110Hz, 230Hz, 290Hz, 370Hz).

In the case of ANM and sparse Bayesian learning method, five frequencies are accurately restored, but in the case of fast Fourier transform, 100Hz and 110Hz cannot be distinguished, and it can be seen that it has a relatively low resolution compared to compression sensing-based frequency estimation techniques. .

6 is a comparison diagram of frequency analysis results when single snapshot and multiple snapshots are used in an SNR -13dB environment.

Referring to FIG. 6 , the black dotted line is the frequency analysis result using the fast Fourier transform, the blue solid line and the circle are the frequency analysis results using the ANM, and the red solid line is the sparse Bayesian learning method according to the embodiment of the present invention. This is the frequency analysis result, and the green solid line and the square box indicate the actual positions of the five frequencies (100Hz, 110Hz, 230Hz, 290, 370Hz).

Referring to (a) of FIG. 6 , it can be seen that all techniques fail to restore the frequency when using a single snapshot. Referring to FIG. 6B , it can be seen that when multiple snapshots (L=50) are used, frequency estimation performance of all techniques is improved in the same SNR environment. However, in the case of ANM, 4 frequencies are restored in addition to 5 frequencies, and in the case of the fast Fourier transform, it can be seen that 100 Hz and 110 Hz are still not distinguished and the resolution is low. On the other hand, in the case of the sparse Bayesian learning method according to the embodiment of the present invention, it can be seen that five frequencies are accurately restored.

7 is a diagram showing results of frequency analysis of actual resolution data received from 120 buried horizontal array sensors using fast Fourier transform and sparse Bayesian learning method according to an embodiment of the present invention.

Referring to FIG. 7 , signals radiated from 120 buried horizontal array sensors were received, the number of radiated signals was 8, and the distance between the sensor array and the sound source was about 700 m. 7(a) shows that, as a result of frequency analysis for a 1-second signal, noises other than the radiation frequency of the sparse Bayesian learning method are greatly reduced, and it can be confirmed that 7 frequency signals among the 8 radiated frequency signals are accurately restored. On the other hand, in the case of a fast Fourier change, a peak point can be confirmed at 7 points among 8 radiation signals, but it can be seen that there is a large amount of ambient noise.

7 (b) shows the result of performing frequency analysis 50 times with a 90% overlap rate. As in (a) of FIG. 7 , in the case of the fast Fourier transform, it can be seen that noises are large around the relatively radiated signal frequency. It can be seen that the radiated frequencies are accurately restored.

The drawings and detailed description of the described invention referenced so far are merely exemplary of the present invention, which are only used for the purpose of describing the present invention, and are used to limit the meaning or the scope of the present invention described in the claims. it is not Therefore, those skilled in the art will understand that various modifications and equivalent other embodiments are possible therefrom. Accordingly, the true technical protection scope of the present invention should be determined by the technical spirit of the appended claims.

Claims (11)

A sparse frequency analysis system for a passive sonar system, comprising:
An observed variance calculation unit for calculating the observed variance of the prior probability according to Baye's Theorem for the acoustic signal received through the array sensor;
an update unit for updating the frequency component magnitude and noise variance using the observed variance calculated by the observed variance calculation unit;
a convergence determination unit that determines whether the magnitudes of the frequency components updated by the update unit converge; and
When it is determined by the convergence determining unit that the size of the frequency component converges, the estimated value of the restored frequency for the sound signal by the reconstruction technique of the probabilistic statistical signal using the size of the frequency component and the noise variance updated by the update unit Restoration frequency calculator to calculate
A sparse frequency analysis system comprising a. According to claim 1,
An initial value generator for generating an initial value of the magnitude of a frequency component used in the sparse frequency analysis system, an initial value of noise analysis, and a lowest convergence value
A sparse frequency analysis system further comprising a. According to claim 1,
The update unit,
a frequency component size update unit that calculates an update value for the frequency component size using the observed variance value calculated by the observed variance value calculation unit and performs an update on the frequency component size; and
A noise variance update unit that performs an update on the noise variance by calculating an update value for the noise variance using the observed variance calculated by the observed variance calculation unit.
Including, sparse frequency analysis system. 3. The method of claim 2,
The convergence determining unit is a convergence value calculator for calculating a convergence value of the frequency component size using the frequency component size before being updated by the update unit and the frequency component size after being updated by the update unit
Including, sparse frequency analysis system. 5. The method of claim 4,
The convergence determining unit determines that the frequency component size converges when the convergence value of the frequency component size calculated by the convergence value calculation unit is smaller than the lowest convergence value,
Sparse Frequency Analysis System. 6. The method according to any one of claims 1 to 5,
The observed variance (

) is the following relation

is calculated according to
here above

is the noise variance,

is an N×N identity matrix,

and

is a dictionary matrix indicating the characteristics of the frequency component,

is the magnitude of the frequency component

is the diagonal matrix of
Sparse Frequency Analysis System. 7. The method of claim 6,
An update value for updating the magnitude of the frequency component (

) is the following relation

is calculated according to
here

is the update value of the magnitude of the m-th frequency component,

is the magnitude of the frequency component before the update,

is a measurement vector for the acoustic signal,

is the number of multiple snapshots,

is the inverse matrix of the observed variance,

is the mth column vector of the dictionary matrix A,
Sparse Frequency Analysis System. 8. The method of claim 7,
An update value for updating the noise variance (

) is the following relation

is calculated according to
here

is the length of the observed signal,

is the number of significant (non-zero) frequency components,

is the active dictionary matrix,

sign,
Sparse Frequency Analysis System. 9. The method of claim 8,
The convergence value (

) is the following relation

is calculated according to
here

is the update value of the magnitude of the frequency component,

is the magnitude of the frequency component before being updated,
Sparse Frequency Analysis System. A sparse frequency analysis method for a passive sonar system, comprising:
generating an initial value for sparse frequency analysis when an acoustic signal is received through the array sensor, wherein the initial value includes an initial value of frequency component magnitude, an initial value of noise analysis, and a lowest convergence value;
calculating an observed variance value of prior probabilities according to Bayes theorem for the acoustic signal using the initial value;
updating frequency component magnitude and noise variance using the observed variance; and
When the frequency component magnitude converges, calculating a restored frequency estimate value for the acoustic signal by a probability statistical signal reconstruction technique using the updated frequency component magnitude and noise variance;
includes,
If the frequency component magnitude does not converge, repeating the steps of calculating the observed variance and updating the frequency component magnitude and noise variance until the frequency component magnitude converges,
Sparse frequency analysis method. 11. The method of claim 10,
Whether the magnitude of the frequency component converges,
It is performed by determining whether the convergence value of the value before and after the update of the frequency component magnitude is smaller than the lowest convergence value,
When the convergence value is smaller than the lowest convergence value, it is determined that the frequency component magnitude converges,
Sparse frequency analysis method.

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