KR101839236B1 - Subbottom profiler and subbottom profiling method - Google Patents

Abstract

The present invention relates to a shallow stratum detecting apparatus and a method thereof which can be applied to surface and shallow stratum detection. The shallow stratum detecting apparatus of the present invention, which transmits an acoustic signal and detects the shallow stratum on a basis of a received signal reflected through the shallow stratum, comprises: a matched filter which performs matched filtering on a received signal using signals of the entire frequency band and the entire time band used when transmitting an acoustic signal; a frequency convert unit for converting the matched filtered signal into a frequency domain signal; a subspace estimate unit for estimating a subspace including a signal subspace (E_s) and a noise subspace (E_n) of the frequency domain signal; and a time estimate unit estimating a delay time by applying a high-precision delay time estimation algorithm to the noise subspace (E_n).

Description

TECHNICAL FIELD [0001] The present invention relates to a sub-

The present invention relates to an apparatus and method for detecting a ground layer capable of being applied to surface and ground layer detection, and more particularly to a high precision ground layer detection apparatus and method based on statistical signal processing.

Geological exploration technology is applied to underground resource exploration, stratum media analysis, and hidden target detection. Undersea geophysical exploration technology is a technique for visualizing seafloor subsurface cross sections using received sound signals that are reflected according to various types and configurations of transmitted sound wave signals and sediments of seawater and seafloor. Generally, a short pulse width signal such as Burst or Ricker Pulse is used for seafloor exploration, or a chirp signal for receiving signal compression is used. In order to obtain high resolution signal quality, the coherent signal is a frequency swept signal according to time, and the bandwidth is maintained even after being reflected and transmitted by the deposition layer, so that it provides a constant distance resolution. And it has been applied in various fields such as seabed topography, burial detection and sediment characterization.

The performance of the subsea ground surveying system is determined by the vertical / horizontal resolution. The horizontal resolution is calculated by the relationship between the transmission beam width and the measurement depth, and the beam width is determined by the driving frequency and the transducer diameter or transducer arrangement shape. Also, the vertical resolution is determined by the pulse width or the bandwidth depending on the type of the transmission signal, and the bandwidth of the signal is limited to the bandwidth region of the transmission transducer. Also, in a device using an acoustic signal, the distance between the transducer and the target is measured by measuring the time of the received signal where the radiated signal reflects back to the target and obtains the distance. The position accuracy of the target is determined by the vertical resolution.

When such a coherent signal is used as a transmission signal, the vertical resolution (? _R ) is calculated by the relationship between the sound speed (c ₀ ) and the bandwidth (B) of the radiated signal, -null is placed at 1 / B. This situation is due to the limitation of the vertical resolution of the probe using a coherent signal, and various studies (such as layer peeling and Schur's algorithm) have been carried out to overcome the limitation of the vertical resolution depending on the pulse width or bandwidth And a detection technique with high precision is required.

Korean Registered Patent No. 0552931 (Name: Acoustic detection device and method of land mines and other burials)

An object of the present invention is to provide an apparatus and method for detecting a stratum corneum layer with high precision.

According to an aspect of the present invention, there is provided an apparatus for detecting a ground layer on the basis of a received signal reflected through a ground layer, A matched filter that performs matched filtering on a received signal using a signal of the entire time band; A frequency converter for converting the matched filtered signal into a frequency domain signal; Unit for estimating the sub-space that contains the signal subspace of a frequency-domain signal (E _s) and the noise subspace (E _n) area estimation unit; And estimating noise sub-space delay estimating a delay time by applying a high-precision delay estimation algorithm to (E _n) is characterized by comprising: a.

Also, the subspace estimator may estimate the subspace of the frequency domain signal using Eigen Value Decomposition (EVD) or Singular Value Decomposition (SVD).

Also, the subspace estimating unit obtains an autocorrelation matrix R _x for subspace estimation, and the autocorrelation matrix R _x is a signal subspace E _s and a noise subspace E _n , And the autocorrelation matrix R _x is divided into

(Equation)

은 신호 부공간(E_s)를 나타내고, L-L_p-1개의 고유벡터로 이루어진

은 잡음 부공간(E_n)을 나타낼 수 있다.And a matrix of L _p eigenvectors

Represents the signal subspace (E _s ), and LL _p -1 eigenvectors

Can represent the noise subspace (E _n ).

In addition, the delay time estimating unit estimates a delay time, but by obtaining the vector (d) representing the noise subspace (E _n), the vector (d),

(Equation)

And E ^H _s can represent a vector representing the signal subspace.

Further, the delay time estimating unit may calculate the delay time using the following equation:

(Equation)

The vector d can be obtained so that the constraint Q is minimized

Further, the delay time estimator may set a value at which the pseudo spectrum P _MN becomes the maximum in the following equation as the delay time?

(Equation)

Also, the delay time estimator may estimate the delay time through the Minimum-Norm algorithm.

In addition, the apparatus for detecting a ground layer according to an embodiment of the present invention may further include an imaging unit for imaging an estimated delay time through a delay time estimator.

A method for detecting a stratum corneum based on a received signal reflected from a heavily layered stratum, the method comprising the steps of: detecting a total frequency Performing matched filtering on a received signal using signals in a band and a full time band; Converting the matched filtered signal into a frequency domain signal by a frequency converter; Estimating a unit space, which unit space by the estimator, a signal subspace of a frequency-domain signal (E _s) and the noise subspace (E _n); And a delay is characterized in that it comprises the step of estimating a delay time by applying a high-precision delay estimation algorithm in the noise subspace (E _n), by the estimation unit.

In addition, the step of estimating the subspace may be performed using eigenvalue decomposition (EVD) or singular value decomposition (SVD).

Further, the sub-step of estimating the space comprises the step to obtain the auto-correlation matrix (R _x) for the subspace estimation, and the auto-correlation matrix (R _x) is a signal subspace (E _s) and the noise subspace (E _n ), And the autocovariance matrix R _x is divided into two orthogonal sub-

(Equation)

은 신호 부공간(E_s)를 나타내고, L-L_p-1개의 고유벡터로 이루어진

은 잡음 부공간(E_n)을 나타낼 수 있다. And a matrix of L _p eigenvectors

Represents the signal subspace (E _s ), and LL _p -1 eigenvectors

Can represent the noise subspace (E _n ).

The step of estimating the delay time may include the step of obtaining a vector d representative of the noise subspace E _n ,

(Equation)

And E ^H _s can represent a vector representing the signal subspace.

Also, the step of estimating the delay time may calculate the vector d such that the constraint condition Q is minimized in the following equation

(Equation)

.

.

Further, the step of estimating the delay time can be performed by setting a value at which the pseudo spectrum becomes maximum in the following equation to the delay time?

(Equation)

.

.

In addition, the step of estimating the delay time can be performed through the Minimum-Norm algorithm.

In addition, the method for detecting a ground layer according to an exemplary embodiment of the present invention may further include imaging the estimated delay time through a step of estimating a delay time by the imaging unit.

According to the apparatus and method for detecting a ground layer in accordance with an embodiment of the present invention, various input signal processing is possible, and various high-precision estimation techniques can be used.

In addition, according to the apparatus and method for detecting a ground layer in accordance with an embodiment of the present invention, since various high-speed signal processing techniques can be applied, it is possible to implement a system relatively easily through modification of software, and if beam steering and formation are applied It is expected to play an important role in system performance improvement because it can get improved performance.

1 is a block diagram of an apparatus for detecting a ground layer according to an embodiment of the present invention.
FIG. 2 is a view showing an example of a result screen output through an imaging unit included in the apparatus for detecting a ground layer according to an exemplary embodiment of the present invention. Referring to FIG.
FIG. 3 is a graph illustrating a result of delay time estimation that is detected by a delay time estimator included in the apparatus for detecting a ground layer according to an embodiment of the present invention.
FIGS. 4A through 4F are graphs illustrating a process of detecting a ground layer through a ground layer detection apparatus according to an exemplary embodiment of the present invention.
5 is a flowchart illustrating a method for detecting a ground layer according to an exemplary embodiment of the present invention.

The present invention will now be described in detail with reference to the accompanying drawings. Hereinafter, a repeated description, a known function that may obscure the gist of the present invention, and a detailed description of the configuration will be omitted. Embodiments of the present invention are provided to more fully describe the present invention to those skilled in the art. Accordingly, the shapes and sizes of the elements in the drawings and the like can be exaggerated for clarity.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an apparatus and method for detecting a ground layer according to an embodiment of the present invention will be described.

FIG. 1 is a block diagram of a conventional ground layer detection apparatus 100 according to an embodiment of the present invention. The apparatus for detecting a ground layer 100 according to an embodiment of the present invention is characterized in that it detects a ground layer by transmitting an acoustic signal and processing a received signal reflected through the ground layer. In detail, the ground layer detection apparatus 100 according to an embodiment of the present invention performs processing on a received signal using signals of the entire frequency band and the entire time band used when transmitting acoustic signals, The delay time can be estimated with high precision by applying a high-precision delay time algorithm to the delay time.

The apparatus for detecting a ground layer according to an embodiment of the present invention includes a data receiving unit 110, a matched filter 120, a frequency converting unit 130, a subspace estimating unit 140, A display unit 150, and a imaging unit 160. In order to facilitate the understanding of the present invention, the above-described configurations divide the respective components into functional units. MPU, and GPU. Referring now to FIG. 1, a description will be given of each configuration included in the apparatus for detecting ground layer 100 according to an embodiment of the present invention.

The data receiving unit 110 functions to receive a reception signal reflected through a sheer layer. Here, the acoustic signal may be generated and transmitted by a sound signal generator (not shown), for example, a transducer, and the acoustic signal may be reflected back at the interface of the seafloor, The reflected signal (i.e., the received signal) can be received.

The matched filter 120 performs a pre-filtering process, and performs matched filtering on a received signal input through the data receiving unit 110. Specifically, the matched filter 120 performs matched filtering on the received signal using the entire frequency band and the entire time band signals used in the transmission of the acoustic signal. That is, since the perineural stratum detection apparatus 100 according to an exemplary embodiment of the present invention receives signals transmitted in multiple bands and multiple time zones, the matched filter 120 can detect the reception signals The characteristics of the signals transmitted in the multi-band and multi-time zones described above must be considered. Accordingly, when the matched filter 120 performs the matched filtering process, the matched filter 120 performs matched filtering on the received signal using the entire frequency band and the entire time band signals used in the transmission process of the acoustic signal.

Here, it is assumed that the matched filtered signal h (t) filtered through the matched filter 120 faithfully includes the impulse response of the channel, and the channel response at this time is a finite number of time delayed It can be defined as the sum of the impulses.

와

는 각각 k번째 진폭과 이의 도달 시간을 나타낸다.In Equation (1), Lp represents the number of impulses due to reflection of the deep ground layer,

Wow

Represents the kth amplitude and its arrival time, respectively.

The frequency conversion unit 130 converts the matched filtered signal through the matched filter 120 into a frequency domain signal. Specifically, the frequency converter 130 applies Fourier transform of the matched filtered signal through the matched filter 120. When the equation (1) is Fourier transformed, the frequency domain signal H (f) can be expressed by the following equation (2).

Here, define the frequency division unit as f _d and l = 0,1, ..., given the L frequency represented by L-1, including white noise amplitude w (l) for the l-th discrete frequency is The discrete frequency domain channel response can be expressed as follows and the signal model x (l) can be obtained using this.

Expressing Equation (3) as a matrix, a vector signal model as shown in Equation (4) below can be obtained.

In Equation (4), a represents a vector of impulse amplitudes (a _k ) and can be defined as Equation (5) below.

In Equation (4), the matrix V represents a matrix of L _p vectors (v) and can be defined as Equation (6) below.

로 이루어진 벡터로서, 아래의 수학식 7과 같이 표현될 수 있다.In Equation (6), the vector (v) includes L

And can be expressed by the following Equation (7).

In Equation (4), w is a vector of white noise amplitudes corresponding to the l-th discrete frequency, and can be expressed as Equation (8) below.

Using the vector signal model described above with reference to equations (4) to (8) above, subspace based signal processing for high precision arrival time estimation is enabled.

The subspace estimator 140 estimates the subspace of the frequency domain signal transformed through the frequency transformer 130. Specifically, the sub-spatial estimator 140 may estimate an autocorrelation matrix R _x for subspace estimation and a subspace of the signal using eigenvalue decomposition (EVD). Here, the autocorrelation matrix Rx for subspace estimation can be expressed by Equation (9) below.

In equation (9), A = [q ₀ q ₁ ... q _{L -1} ], where S = E {aa ^H } and q _l is the lth eigenvector. Also, σ ² represents the variance of the noise, and the subscript H represents the Hermitian conjugate. From equation (9), the autocorrelation matrix R _x can be divided into two orthogonal subspaces: signal subspace E _s and noise subspace E _n . Accordingly, the autocorrelation matrix R _{x obtained} by dividing the two orthogonal sub-spaces described above can be expressed by Equation (10) below.

은 신호 부공간, L-L_p-1개의 고유벡터로 이루어진

은 잡음 부공간을 나타낸다. 이때, i번째 고유벡터는

로 나타낼 수 있다.Here,? _I represents the i-th eigenvalue. A matrix of L _p eigenvectors

Consists of a signal subspace, LL _p -1 eigenvectors

Represents the noise subspace. At this time, the i-th eigenvector is

.

Also, the subspace estimator 140 may perform subspace estimation of a signal using singular value decomposition (SVD) instead of eigenvalue decomposition (EVD).

The delay time estimator 150 estimates the delay time by applying a high-precision delay time estimation algorithm to the signal having been subjected to the subspace estimation. Here, the Minimum-Norm algorithm can be used for the high precision delay time estimation algorithm. Here, the delay time estimating unit 150 may use a MUSIC (MULTIPLE SIGNAL CLASSIFICATION) algorithm in addition to the above algorithm among the high precision delay time estimation algorithms. However, the MUSIC algorithm has a large deviation and low resolution, Due to this great point, it is difficult to detect the above-mentioned ground layer. Therefore, it is desirable to adopt the Minimum-Norm algorithm instead of the MUSIC algorithm for the high-resolution layer search.

Also, the MUSIC algorithm estimates the arrival time of the signal using all the eigenvectors existing in the noise subspace, while the Minimum-Norm algorithm estimates the arrival time of the signal by obtaining a new vector d representing the noise subspace . Let d be a vector orthogonal to the signal space.

In Equation (11), E ^H _s represents a vector representing a signal subspace. The vector (d) can be interpreted as an L-order linear prediction error filter for q ^* _i . Therefore, the vector d satisfying Equation (11) can have infinitely many values, but it is possible to minimize the following constraint (Q) among the various solutions of the vector (d) . This is a constraint condition (Q) satisfying the minimum norm of the vector (d), and the constraint condition (Q) can be expressed by the following equation (12).

In view of the filter analysis using the Z transform, the extraneous zero of LL _p among the L zeros of the polynomial D (z) defined as shown in Equation (13) is uniformly distributed in the unit circle Effect. This results in the stability of the L-th order linear prediction error filter of Equation (11).

Where z represents the time-shifting element of the Z transform. The solution of Equation (11) that satisfies the minimum norm condition of Equation (12), that is, the vector (d), can be given by Equation (14) below.

In Equation 14, g is a vector composed of the first elements of the signal eigenvectors, and E ' _s is a matrix obtained by removing the first row of E _s , that is, g. Finally, the pseudo spectrum (P _MN ) obtained by the Minimum-Norm algorithm can be defined by the following equation (15).

According to Equation (15), if the pseudo spectrum (P _MN ) is obtained according to the time delay (?), The spectrum according to the sound arrival time can be obtained. This means that the peak of the spectrum can be obtained at the arrival time of the shallow stratum since the inner product with the vector (d) near to the signal subspace is approximated to zero by the equation (11). In this manner, the pseudo spectrum P _MN has a high resolution due to the constraint added to the vector d, and the effect of the correlation signal is small.

The imaging unit 160 functions to image the estimated delay time through the delay time estimating unit 150. [ That is, the imaging unit 160 displays the result of the high precision delay time continuously according to time or distance, thereby informing the user of the result. For example, the imaging unit 160 may perform imaging using linear, log-scale, or other methods. An example of a ceiling stratum imaged through the imaging unit 160 according to an embodiment of the present invention is shown in Fig.

As shown in FIG. 2, the imaging unit 160 may output the final result through the process described with reference to FIG. 1 according to time. Of course, it is also possible to output this final result along the distance.

FIG. 3 is a graph illustrating a result of delay time estimation that is detected by the delay time estimator 150 included in the apparatus for detecting a ground layer 100 according to an embodiment of the present invention. In FIG. 3, the result of the time-domain de-juxtaposition process according to the prior art is denoted as Dechirp, the frequency domain process result according to the prior art is denoted by IFT, and the result is detected through a delay time estimator 150 according to an embodiment of the present invention. The estimated delay time is expressed as Minimum-Norm.

As shown in FIG. 3, according to the delay time estimation result detected through the delay time estimating unit 150 according to an embodiment of the present invention, it can be seen that delay time estimation can be performed with higher accuracy than the prior art , Indicating that it is possible to detect deep stratum with higher accuracy.

FIGS. 4A to 4F are graphs illustrating a process of detecting a ground layer through the ground layer detection apparatus 100 according to an embodiment of the present invention. In this example, the transmission signal is a coherent signal having a band of 3.5 kHz to 4.5 kHz, and the sampling frequency is 50 kHz. Specifically, FIGS. 4A and 4B are graphs showing a simulated generated reception signal (i.e., a simulated deep layer ground survey signal), and FIGS. 4C and 4D show results of matched filtering of the signals of FIGS. 4A and 4B, respectively . 4A shows a noiseless received signal, and FIG. 4B shows a simulated received signal including a Gaussian noise. 4A to 4F, the x-axis represents time and the y-axis represents amplitude.

4C to 4F, the surface reflection signal is indicated by a one-dot chain line at 0 second. The signal in the vicinity of the surface layer is originally divided into two layers. However, as shown in FIGS. 4C and 4D, the result of the matched filtering shows that the two layers are united and united. The results that are not included in the noise may seem somewhat different but not clear, and it is not easy to understand if the noise is included. In order to distinguish between the two layers described above, a coherent signal of a wider frequency band can be used. However, this is limited by the system specification.

Meanwhile, as in the present invention, after performing the matched filtering in consideration of the multi-band and the multi-time band, the subspace of the signal is estimated through EVD or SVD, and the delay-time is estimated by applying the Minimum- 4E and 4F can be derived. As shown in FIGS. 4E and 4F, when looking at the regions r ₁ and r ₂ , the two surface layer signals are clearly distinguished. As shown in FIG. 4F, even when noise is included, it can be seen that the configuration of the heavily layered layer is accurately shown as shown in the area r ₂ .

5 is a flowchart illustrating a method for detecting a ground layer according to an exemplary embodiment of the present invention. As described above, the method for detecting a ground layer according to an exemplary embodiment of the present invention is characterized in that the method detects a ground layer by transmitting an acoustic signal and processing a received signal reflected through the ground layer. Specifically, the method for detecting a ground layer according to an exemplary embodiment of the present invention performs processing on a received signal using signals of the entire frequency band and the entire time band used for transmitting an acoustic signal, By applying the algorithm, the delay time can be estimated with high precision. Now, referring to FIG. 5, a description will be given of a method for detecting a ground layer according to an embodiment of the present invention.

Step S110 is a step of receiving, by the data receiving unit, the reception signal reflected through the sheer layer. Here, the acoustic signal may be generated and transmitted by a sound signal generating device, for example, a transducer, and the acoustic signal may be reflected back at the interface of the seabed layer, Receiving signal).

In step S120, matched filtering is performed on the received signal using the entire frequency band and the entire time band signal used when the acoustic signal is transmitted by the matched filter. As described above, the step S110 is characterized in that it is possible to receive the signals transmitted in the multi-band and the multi-time band. Accordingly, in step S120, when processing the received signal input through step S110, characteristics of signals transmitted in the multi-band and multi-time periods described above should be considered. In order to consider the above-described characteristics, It is possible to perform matched filtering on the received signal using the entire frequency band and the entire time band signal used in the process. Here, the matching filtering method for the received signal has been described in detail with reference to FIG. 1, so that redundant description will be omitted.

Step S130 is a step of converting the matched filtered signal into a frequency domain signal by the frequency converter. Here, the step S130 may be performed by applying a Fourier transform to the matched filtered signal.

S140 is a step for estimating the space portion including a signal subspace of a frequency-domain signal (E _s) and the noise subspace (E _n) by the subspace estimation. Specifically, in operation S140, an autocorrelation matrix R _x may be obtained for subspace estimation, and eigenvalue decomposition (EVD) or singular value decomposition (SVD) may be used to estimate the subspace of the signal. Here, the auto-correlation matrix (R _x) described, and auto-correlation matrix (R _x) noise subspace (E _n) a description of how to extract mentioned in detail with reference to Equation (9) and equation (10) from above in about , So redundant explanations are omitted.

S150 is a step for estimating a delay time by applying a high-precision delay estimation algorithm in the noise subspace (E _n), by the delay estimator. Here, the high-precision delay time estimation algorithm may include a Minimum-Norm algorithm. In addition, step S150 may be performed by using the vector (d) representing the noise subspace (E _n) derived through the step S140. Here, the description of the vector (d) has been described in detail with reference to the equations (11) to (15) above, so that further explanation is omitted.

In addition, the step S150 may be performed by setting the value at which the pseudo spectrum becomes maximum in the above-described expression (15) to the delay time?.

Step S160 is a step of imaging the estimated delay time through the step of estimating the delay time by the imaging unit.

As described above, an optimal embodiment has been disclosed in the drawings and specification. Although specific terms have been employed herein, they are used for purposes of illustration only and are not intended to limit the scope of the invention as defined in the claims or the claims. Therefore, those skilled in the art will appreciate that various modifications and equivalent embodiments are possible without departing from the scope of the present invention. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

100: underground stratum detector 110: data receiver
120: matched filter 130: frequency converter
140: subspace estimator 150: delay time estimator
160:

Claims (16)

CLAIMS: 1. A ground layer detection apparatus for transmitting acoustic signals and detecting a ground layer based on a received signal reflected through a ground layer,
A matched filter for performing matched filtering on the received signal using signals of the entire frequency band and the entire time band used when the acoustic signal is transmitted;
A frequency converter for converting the matched filtered signal into a frequency domain signal;
Subspace estimation unit for estimating the sub-space that contains the signal subspace (E _s) and the noise subspace (E _n) of the signal in the frequency domain; And
Superficial layers detection apparatus comprising the noise subspace (E _n) estimate the delay time for estimating a delay time by applying a high-precision delay estimation algorithm in part. The method according to claim 1,
Wherein the subspace estimating unit estimates the subspace of the frequency domain signal using Eigen Value Decomposition (EVD) or Singular Value Decomposition (SVD). The method according to claim 1,
The subspace estimation unit obtains a subspace auto-correlation matrix (R _x) for estimating the auto-correlation matrix (R _x) are the two orthogonal sub-space signal part space (E _s) and the noise subspace (E _n) , And the autocorrelation matrix (R _x )
(Equation)

And a matrix of L _p eigenvectors

Represents the signal subspace (E _s ), and LL _p -1 eigenvectors

(E _n ) is the noise subspace (E _n ). The method of claim 3,
Said delay time estimating unit estimates a delay time, but by obtaining the vector (d) representing the noise subspace (E _n), the vector (d),
(Equation)

And E ^H _s represents a vector representing the signal subspace. 5. The method of claim 4,
Wherein the delay time estimating unit obtains a vector d such that the constraint condition Q is minimized in the following equation.
(Equation)

6. The method of claim 5,
Wherein the delay time estimator sets a value at which the pseudo spectrum (P _MN ) becomes maximum in the following equation as a delay time (tau).
(Equation)

The method according to claim 1,
Wherein the delay time estimator estimates the delay time using a Minimum-Norm algorithm. The method according to claim 1,
And an imaging unit for imaging the estimated delay time through the delay time estimating unit. CLAIMS 1. A method for detecting a stratum corneum based on a received signal reflected from a heel stratum,
Performing matched filtering on the received signal by using a matched filter using signals of the entire frequency band and the entire time band used when transmitting the acoustic signal;
Converting the matched filtered signal into a frequency domain signal by a frequency converter;
Estimating a unit area comprising a portion of the space signal part space, the signal in the frequency domain by estimating (E _s) and the noise subspace (E _n); And
By the delay estimator, superficial layers detection method comprising the step of estimating a delay time by applying a high-precision delay estimation algorithm in the noise subspace (E _n). 10. The method of claim 9,
Wherein the step of estimating the subspace is performed using eigenvalue decomposition (EVD) or singular value decomposition (SVD). 10. The method of claim 9,
Estimating the subspace comprises:
Obtaining an autocorrelation matrix (R _x ) for subspace estimation,
The auto-correlation matrix (R _x) is a signal subspace (E _s) and the second part space is divided into orthogonal noise subspace (E _n), the autocorrelation matrix (R _x) is
(Equation)

And a matrix of L _p eigenvectors

Represents the signal subspace (E _s ), and LL _p -1 eigenvectors

(E _n ) is the noise floor space (En). 12. The method of claim 11,
Wherein estimating the delay time comprises obtaining a vector d representative of the noise subspace E _n ,
(Equation)

And E ^H _s represents a vector representing the signal subspace. 13. The method of claim 12,
Wherein the step of estimating the delay time comprises: obtaining a vector d such that a constraint (Q) is minimized in the following equation.
(Equation)

14. The method of claim 13,
Wherein the step of estimating the delay time is performed by setting a value at which the pseudo spectrum (P _MN ) becomes maximum in the following equation as a delay time (tau).
(Equation)

10. The method of claim 9,
Wherein the step of estimating the delay time is performed through a Minimum-Norm algorithm. 10. The method of claim 9,
Further comprising the step of imaging the estimated delay time through the step of estimating the delay time by the imaging unit.

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