KR101024123B1 - Method for radar imaging autofocus based on entropy of eigenvectors - Google Patents

Abstract

개의 고유값에 대응되는

개의 고유벡터들을 이용하여 신규 고유벡터행렬을 계산한 후 푸리에 또는 역푸리에 변환하여, 아이젠 프로파일(Eigen Profile)들을 포함한 영상행렬을 생성하는 단계; (f) 영상행렬의 엔트로피를 최소화하는 위상오차를 추정하는 단계; 및 (g) 추정된 위상오차를 초기행렬에 적용한 후 푸리에 또는 역푸리에 변환하여, 위상오차가 제거된 레이더 영상을 생성하는 단계;를 포함하는, 고유벡터 엔트로피에 기초한 레이더 영상 자동초점 방법을 제공한다.The present invention comprises the steps of: (a) receiving a radar signal comprising a plurality of pulses reflected from the target after being transmitted to the moving target side; (b) compressing the plurality of received pulses in a distance direction to generate a plurality of range profiles, which are one-dimensional radar images, and distance-aligning the range profiles, respectively; (c) calculating a covariance matrix from an initial matrix obtained from the radar signal on which the distance alignment is performed; (d) eigenvalue decomposition of the covariance matrix to compute an eigenvector matrix including eigenvectors and an eigenvalue matrix including eigenvalues, respectively; (e) the larger of the eigenvalues

Corresponding to eigenvalues

Calculating a new eigenvector matrix using the four eigenvectors and then performing Fourier or inverse Fourier transform to generate an image matrix including Eigen Profiles; (f) estimating a phase error that minimizes entropy of the image matrix; And (g) applying the estimated phase error to an initial matrix and then performing Fourier or inverse Fourier transform to generate a radar image from which phase error has been removed. .

According to the radar image autofocus method, the phase error is estimated by using the eigenvector entropy of the radar signal, which shortens the calculation time and is robust to noise.

Description

Method for radar imaging autofocus based on entropy of eigenvectors}

The present invention relates to a radar image autofocus method based on eigenvector entropy. More particularly, the present invention relates to an eigenvector entropy for correcting a phase error according to the movement of a target with respect to an acquired radar image to obtain a clearer radar image. A radar image autofocus method is based.

The classical concept of radar was to receive the signal reflected from the target and to estimate information such as the presence, distance, orientation, and speed of the target. In recent years, advances in electronics technology have made it possible to coherently transmit and receive radar signals. That is, the phase difference between the transmission signal and the reflected signal can be measured. In addition, due to the development of ultra-high frequency component technology, a radar having a wide frequency band has been developed. In addition, recent advances in computer technology have made it possible to process large amounts of data, and computation speed has increased dramatically. The development of these various technologies has improved the function of radar, and recently, it has been possible to produce two-dimensional and three-dimensional radar images of targets.

In general, two-dimensional radar images of a target include synthetic aperture radar (SAR) images and inverse synthetic aperture radar (ISAR) images. Referring to FIG. 1, SAR is a concept of obtaining a radar image of a fixed target while the radar platform moves. Most SAR systems attach a radar to an aircraft or satellite and then use the radar to obtain a two-dimensional radar image of the ground as the aircraft or satellite moves.

Contrary to the concept of the SAR system, the radar platform is called ISAR, a system that obtains radar imagery for fixed and moving targets. Referring to FIG. 2, in the ISAR system, a target may move arbitrarily, and a radar image is generated by using a relative movement between the radar and the target.

In the case of the ISAR image, the reflection signal is obtained from the target signal according to the change of the relative angle between the target and the radar. However, the ISAR image is blurred or distorted due to the phase error of the received signal caused by the random movement of the target. The phenomenon in which the frequency of the received signal changes due to the speed at which the target moves is called a Doppler effect, which causes a phase error in the received signal.

In the case of SAR images, a radar image is generated assuming that an aircraft or satellite is flying a predetermined linear trajectory. Normally, however, aircraft do not fly the desired trajectory due to changes in airflow, which causes phase error, which causes distortion and blur in the SAR image.

A signal processing technique for removing the phase error to improve distortion and blur of a SAR image or an ISAR image is called an autofocus technique or a motion compensation technique.

Autofocus technique is divided into range bin alignment process and phase adjustment process. The distance alignment process is a process of aligning the distance between the radar and the target to the same value, using a correlation between the range profile, which is a one-dimensional radar image, and using a spectral domain phase difference. Etc. The phase correction process eliminates uncompensated phase errors in the distance alignment process. Phase correction techniques include Doppler centroid tracking, phase gradient autofocus (PGA), and prominent point processing (PPP). These methods extract the model variables after mathematically modeling the phase error, so if there is an error between the actual physical model and the mathematical model of the phase error, it does not work well.

To overcome this, there is a method of directly estimating the phase error of each range profile without mathematically modeling the phase error. It is a method of estimating phase error to minimize this by using contrast and entropy, which are numerical indicators related to radar image quality, as a cost function. These methods have the advantage of obtaining a high quality radar image, but there is a problem that the calculation time required to minimize the cost function is increased.

SUMMARY OF THE INVENTION An object of the present invention is to provide a radar image autofocus method capable of shortening a calculation time and improving robustness against noise by estimating a phase error using an eigenvector entropy of a radar signal.

개의 고유값에 대응되는

개의 고유벡터들을 이용하여 신규 고유벡터행렬을 계산한 후 푸리에 또는 역푸리에 변환하여, 아이젠 프로파일(Eigen Profile)들을 포함한 영상행렬을 생성하는 단계; (f) 상기 영상행렬의 엔트로피(Entropy)를 최소화하는 위상오차를 추정하는 단계; 및 (g) 상기 추정된 위상오차를 상기 초기행렬에 적용한 후 푸리에 또는 역푸리에 변환하여, 위상오차가 제거된 레이더 영상을 생성하는 단계;를 포함하는, 고유벡터 엔트로피에 기초한 레이더 영상 자동초점 방법을 제공한다.The present invention comprises the steps of: (a) receiving a radar signal comprising a plurality of pulses reflected from the target after being transmitted to a moving target side; (b) compressing the received plurality of pulses in a distance direction to generate a plurality of range profiles, which are one-dimensional radar images, and distance-aligning the range profiles, respectively; (c) calculating a covariance matrix from an initial matrix obtained from the radar signal on which the distance alignment is performed; (d) calculating eigenvalue decomposition of the covariance matrix, and computing eigenvector matrices including eigenvectors and eigenvalue matrices including eigenvalues, respectively; (e) the larger of the eigenvalues

Corresponding to eigenvalues

Calculating a new eigenvector matrix using the four eigenvectors and then performing Fourier or inverse Fourier transform to generate an image matrix including Eigen Profiles; (f) estimating a phase error that minimizes entropy of the image matrix; And (g) generating a radar image from which the phase error is removed by applying the estimated phase error to the initial matrix and performing Fourier or inverse Fourier transform. to provide.

According to the radar image autofocus method based on the eigenvector entropy according to the present invention, after calculating the eigenvector of the covariance matrix of the radar signal received for the target, it is calculated by estimating the phase error using the entropy of the eigenvector as a cost function It can save time and has the advantage of being robust against noise.

4 is a flowchart of a radar image autofocus method based on eigenvector entropy according to an embodiment of the present invention. Prior to the detailed description, it is apparent that a series of processes (S100 to S190) of the autofocus method may be performed by a general radar apparatus (not shown) subject that receives a radar signal from a target and generates a radar image corresponding thereto. Do. Hereinafter, an image autofocus method based on the eigenvector entropy will be described in more detail with reference to FIG. 4.

First, a radar signal including a plurality of pulses reflected from the target after being transmitted to the moving target side is received (S100). More specifically, after transmitting the radar signal including a plurality of pulses to the moving target side, and receives the radar signal reflected from the target again.

Next, the received plurality of pulses are compressed in a down-range to generate a plurality of range profiles, which are one-dimensional radar images (S110), and the range profiles are respectively distance aligned. (S120).

In the step S110, by matching the filtering radar signal using a chirp (Chirp) waveform (Matching filtering), in the case of a radar signal using a stepped frequency waveform (Stepped frequency) by performing an inverse Fourier transform, The distance direction is compressed and the range profile is obtained accordingly.

In general, a received signal of a radar using chirp pulses uses matched filtering to generate a range profile, which is a time domain 1D radar image. However, since the target moves while the radar device transmits and receives a pulse, the distance between the radar device and the target changes. Thus, the position where the range profile for the target appears in the distance direction is constantly changing. In order to obtain a radar image of a target, the distance change between the radar device and the target must be removed, and this signal processing process is called the distance alignment process (S120).

In the case of a SAR image, a radar apparatus generally estimates actual position information of an aircraft from a sensor such as a global positioning system (GPS) or an inertial measurement unit (IMU), and then uses the same to perform distance alignment. In the case of ISAR images, the radar device is fixed and the target moves randomly, so various sensor data cannot be used as in SAR. Therefore, distance alignment must be performed using only a given radar received signal. As mentioned above, algorithms developed in relation to distance alignment include a method using correlation and a method using a spectral domain phase difference.

Figure 3 shows the change in the range profile for the target before and after performing such distance alignment (S120). Each horizontal axis is a range bin, and the vertical axis is a pulse number over time.

3 (a) is obtained after performing the matching filtering process S110 on the radar signal received from a target consisting of a plurality of point scatterers, before performing the distance alignment process S120. Represents one range profile. Referring to this, it can be seen that the position at which the target appears as the distance between the radar device and the target changes.

3B illustrates a change in the range profile after performing the distance alignment process S120. By the distance alignment process, it can be seen that the distance between the radar device and the target is kept constant.

However, even after the above-described distance alignment process, a phase error exists. That is, due to such a phase error, a high quality radar image cannot be obtained only by the above-described distance alignment process, and then a phase correction process should be performed.

)로부터 공분산행렬(

)을 연산한다(S130). To do this, follow the steps below. First, an initial matrix obtained from the radar signal after the distance alignment is performed (

From the covariance matrix (

) Is calculated (S130).

)은 거리정렬이 수행된 이후의 레이더 신호를 행렬로 나타낸 것으로서,

개의 수신 신호를 포함한 행렬이다. 이러한 초기행렬(

)은 하기의 수학식 1로 정의된다. The initial matrix (

) Is a matrix of radar signals after distance alignment is performed.

Matrix containing two received signals. This initial matrix (

) Is defined by Equation 1 below.

[Equation 1]

: 상기 거리 방향에 대한 레인지 빈(Range bin)의 개수,

: 상기 수신된 펄스들의 개수,

: 상기 표적의 이동에 의한 도플러 효과로 인하여 실제로 발생된 위상오차,

: 상기 위상오차(

)가 포함된 상기 레이더 신호,

: 상기 위상오차(

)가 포함되지 않은 것으로 가정한 경우의 상기 레이더 신호,

,

)(

: Number of range bins for the distance direction,

= Number of received pulses,

: Phase error actually generated due to the Doppler effect due to the movement of the target,

= Phase error (

The radar signal,

= Phase error (

The radar signal, assuming that is not included,

,

)

개의 펄스들을 얻었다고 가정한 것이다.Here, the column direction (Down-Range) of the initial matrix is the distance direction. In addition, the cross-range corresponds to a time axis and represents each pulse number received according to the movement of the target. Here

It is assumed that two pulses were obtained.

) 때문에 상기 생성된 영상에 흐려짐 또는 왜곡이 발생된다. 이러한 문제를 해결하기 위해서는 추정된 위상오차(

)를 이용하여

를 재정의(

) 한 후, 재정의된

를 상기 초기행렬에 적용하여 위상오차를 제거한 다음, 푸리에 변환을 수행해야 한다. Here, if the Fourier transform is performed in the row direction of the initial matrix, a two-dimensional radar image may be generated, but a phase error caused by the movement of the target (

), Blurring or distortion occurs in the generated image. To solve this problem, the estimated phase error (

)

Override

), Then overridden

Is applied to the initial matrix to remove the phase error, and then Fourier transform is performed.

를 추정하기 위해, 기존에는 레이더 영상의 엔트로피를 직접 계산하는 방식을 이용하였으며 이에 따르면 계산 시간이 다소 오래 소요되는 단점이 있다. 그러나, 제안한 자동초점 방법에서는 레이더 영상에 대한 고유벡터의 엔트로피로부터 상기

를 추정함으로써 계산 시간을 단축시킬 수 있다. By the way,

In order to estimate, conventionally, a method of directly calculating entropy of a radar image has been used, and accordingly, a calculation time is somewhat longer. In the proposed autofocus method, however, the entropy of the eigenvectors for the radar image

By estimating, the calculation time can be shortened.

)로부터 공분산행렬(

;Covariance Matrix)을 연산한다. 상기 공분산행렬(

)은, 각각의 레인지 빈(Range-bin)에 해당되는 초기행렬(

)의 열 벡터(Column Vector)를 이용하여 아래의 수학식 2로 정의 가능하다.That is, for this purpose, the initial matrix (

From the covariance matrix (

; Covariance Matrix). The covariance matrix (

) Is the initial matrix corresponding to each range-bin (

) Can be defined by Equation 2 below using a column vector.

[Equation 2]

는 행렬에 대한 켤레전치(Conjugate Transpose) 연산을 의미한다. 또한, 공분산행렬

는

의 행렬을 갖는다. Of course, in equation (2)

Denotes a conjugate transpose operation on the matrix. Also, covariance matrix

Is

Has a matrix

)을 연산한 이후에는, 수학식 2의 공분산행렬(

)을 고유값 분해(Eigen-Decomposition)하여, 고유벡터들(

;Eigenvector)을 포함한 고유벡터행렬(

)과 고유값들(

;Eigenvalue)을 포함한 고유값행렬(

)을 각각 수학식 3과 같이 연산한다(S140).As above, the covariance matrix (

After calculating), the covariance matrix (2)

) Are eigen-decomposition, so that the eigenvectors (

Eigenvector matrix (including; Eigenvector)

) And eigenvalues (

Eigenvalue matrix (; Eigenvalue)

) Are respectively calculated as in Equation 3 (S140).

&Quot; (3) "

,

,

,

,

: 상기 고유벡터행렬로서 상기 공분산행렬(

)의

고유벡터들인

를 열벡터로 갖는 정방행렬,

: 상기 고유값행렬로서 공분산행렬(

)의 고유값들인

를 대각성분으로 갖고 나머지 원소는 모두 0인 대각행렬(),

)(

Is the eigenvector matrix,

)of

Eigenvectors

Square matrix with,

= Covariance matrix as the eigenvalue matrix

Eigenvalues

Is a diagonal component with the rest of the elements being zero.

)

)은 하기의 수학식 4와 같이 크기가 큰 순서대로 정렬되고, 상기 고유벡터들(

)은 상기 고유값들(

)의 크기에 대응되도록 정렬되어 있다고 가정한다. 즉, 고유값들은 아래의 부등식을 만족한다.Where the eigenvalues (

) Are arranged in order of increasing magnitude as shown in Equation 4 below, and the eigenvectors (

Is the eigenvalues (

Assume that they are aligned to correspond to the size of). In other words, the eigenvalues satisfy the following inequality:

&Quot; (4) "

) 중에서 크기가 큰

개(

＜

)의 고유값에 대응되는

개의 고유벡터들을 이용하여, 새로운

행렬인 신규 고유벡터행렬(

)을 수학식 5로 계산한다(S150). 물론, 상기

개는 별도의 추정 과정을 통해 획득 가능하며 이는 추후에 설명하기로 한다. On the other hand, after that, the eigenvalues (

) Large in size

dog(

<

Corresponding to the eigenvalue of

New eigenvectors,

New eigenvector matrix that is a matrix (

) Is calculated by the equation (5) (S150). Of course, the above

Dogs can be obtained through a separate estimation process, which will be explained later.

[Equation 5]

)의 고유값(

)은, 행렬

의 각 고유벡터(

) 방향으로의 분산(Variance) 값을 나타내며, 이 분산값은 레이더 펄스들 사이의 정보의 양을 표현한다. 따라서, 수학식 5의 행렬

는 주어진 레이더 수신 펄스의 고유벡터로 이루어진 벡터공간 상에서 정보가 가장 많은

개의 방향을 의미한다. 즉, 제안하는 레이더 영상 자동초점 방법에서는 수신된 레이더 신호에 해당되는 초기행렬(

)의 엔트로피를 계산하는 대신, 상기 신규 고유벡터행렬(

)을 이용하여 엔트로피를 계산하고 이로부터 위상오차를 추정한다.The covariance matrix (

Eigenvalues of

) Is a matrix

Each eigenvector of

Represents a variance value in the () direction, which represents the amount of information between radar pulses. Therefore, the matrix of Equation 5

Is the most information in vector space consisting of the eigenvectors of a given radar received pulse.

Direction of the dog. That is, in the proposed radar image autofocus method, the initial matrix corresponding to the received radar signal (

Instead of computing the entropy of, the new eigenvector matrix (

Calculate the entropy and estimate the phase error from it.

)에는 상기 초기행렬(

) 내의 위상오 차(

)가 포함됨에 따라 상기 수학식 5가 수학식 6으로 재정의된다.Where the new eigenvector matrix (

) Is the initial matrix (

Phase error within

Equation 5 is redefined as Equation 6 as

&Quot; (6) &quot;

,

, 그리고

: 위상오차(

)가 포함된 레이더 신호로부터 얻어진 공분산행렬의 고유벡터들,

: 위상오차(

)가 포함되지 않은 것으로 가정한 경우의 레이더 신호로부터 얻어진 공분산행렬의 고유벡터들)(At this time,

,

, And

= Phase error (

Eigenvectors of the covariance matrix obtained from the radar signal containing

= Phase error (

Eigenvectors of the covariance matrix from the radar signal, assuming no)

)을 행방향으로 푸리에 또는 역푸리에 변환하여, 아이젠 프로파일들(Eigen Profile;

)을 포함한 새로운

의 상기 영상행렬(

)을 생성한다.After that, the new eigenvector matrix (6)

) Is Fourier or inverse Fourier transformed in the row direction, and thus Egen profiles;

New including)

The image matrix of

).

[Equation 7]

,

,

When actually implementing the Fourier transform and the Inverse Fourier transform, Fast Fourier Transform (FFT) or Inverse Fast Fourier Transform (IFFT) is used.

)의 생성(S160) 이후의 단계 설명에 앞서, 차후의 엔트로피 계산과 위상오차 추정 단계(S170~180)를 보다 효과적으로 수행하기 위해서는, 상기

를 적절히 결정하여야 한다. On the other hand, the image matrix (

In order to more efficiently perform subsequent entropy calculations and phase error estimation steps S170 to 180, before the step description after the generation of the step S160,

Should be appropriately determined.

값이 큰 경우는 위상오차 추정에 사용되는 정보의 양이 증가하기 때문에 보다 정확한 위상오차를 추정할 수 있는 반면,

및

의 크기가 증가함으로써 위상오차 추정을 위한 최적화 알고리즘의 계산 시간이 증가하는 문제점이 있다. 이와 반대 개념으로, 상기

값이 너무 작으면 위상오차 추정에 필요한 계산 시간을 줄일 수는 있으나, 정확한 위상오차 추정이 불가능할 수 있다. E.g,

If the value is large, more accurate phase error can be estimated because the amount of information used for estimating the phase error increases.

And

As the size of P increases, the computation time of the optimization algorithm for estimating the phase error increases. In contrast to this, the above

If the value is too small, the calculation time required for the phase error estimation may be reduced, but accurate phase error estimation may not be possible.

를 결정하기 위하여 아래의 방법을 사용한다. 즉, 상기 S150단계에서는, 수학식 3의 고유벡터들(

) 중 최적화에 필요한 고유벡터들의 개수인 상기 개를 수학식 8을 이용하여 적절히 추정하여 수행 가능하다.While solving these problems,

Use the following method to determine. That is, in step S150, the eigenvectors of Equation 3 (

Is the number of eigenvectors required for optimization The dog can be estimated by using Equation 8.

[Equation 8]

,

,

의 분모: 상기 공분산행렬(

)로부터 얻어진

개의 고유값들(

)의 합으로서

개의 펄스 신호에 포함된 정보의 총합,

의 분자: 상기 공분산행렬(

)로부터 얻어진

개의 고유값들(

)의 합으로서

개의 펄스 신호에 포함된 정보의 총합,

)(

Denominator of: the covariance matrix (

Obtained from

Eigenvalues (

As the sum of

Total information contained in pulse signals,

Molecular: The covariance matrix (

Obtained from

Eigenvalues (

As the sum of

Total information contained in pulse signals,

)

는 상기 고유값들(

)을 크기가 큰 순서대로 정렬할 경우, 전체

개의 고유벡터들(

)로 형성된 벡터 공간 전체(분모값) 내에서

개의 특정 고유벡터들로 이루어진 공간(분자값)이 포함하고 있는 양을 의미한다.That is

Is the eigenvalues (

), If you sort them in larger order,

Eigenvectors

Within the whole vector space (denominator) formed by

Mean amount of space (molecular value) of specific eigenvectors.

값이 1에 근접할수록

개의 고유벡터로 이루어진 공간에 포함되어 있는 레이더 신호의 정보의 양이 증가한다고 볼 수 있다.

는 사용자 또는 레이더장치에서 정해주는 값으로서, 연구 결과 상기

는 0.9~0.95 정도로 션택되 는 것이 적당한 것으로 파악되었다. 즉, 레이더 신호에 저장되어 있는 표적에 대한 정보의 90~95%를 이용하여 최적화를 수행하는 것이 계산시간 측면에서나 추정된 위상오차의 정확도 측면에서 타당한 결과를 얻는다고 볼 수 있다.therefore,

As the value approaches 1

It can be said that the amount of information of the radar signal included in the space consisting of two eigenvectors increases.

Is a value determined by the user or radar device.

It was found that it is appropriate to select the range between 0.9 and 0.95. In other words, it can be said that performing optimization using 90-95% of the information on the target stored in the radar signal has a valid result in terms of calculation time and accuracy of the estimated phase error.

개의 고유값에 대응되는

개의 고유벡터들을 이용하여 신규 고유벡터행렬(

)을 계산한 후 , 상기 신규 고유벡터행렬(

)을 행방향으로 푸리에 또는 역푸리에 변환하여, 아이젠 프로파일(

)들을 포함한 영상행렬(

)을 생성한다.In summary, the steps S150 to S160, the estimated

Corresponding to eigenvalues

New eigenvectors matrix using two eigenvectors

After calculating the new eigenvector matrix (

) By Fourier or Inverse Fourier transformation in the row direction,

Image matrix including

).

)의 엔트로피를 최소화하는 위상오차(

)를 추정한다(S170~S180). 이를 위해, 먼저 영상행렬(

)의 엔트로피(

)를 계산(S170)하며, 이는 아래의 수학식 9로 정의된다.After that, the image matrix (

Phase error to minimize entropy of

) Is estimated (S170 to S180). To do this, first, the image matrix (

Entropy ()

(S170), which is defined by Equation 9 below.

[Equation 9]

: 상기 추정된 위상오차(

)를 포함한 영상행렬(

),

: 상기

을 영상의 파워로 정규화한 값)(

= Estimated phase error (

), Including image matrix

),

: remind

Is normalized to the power of the image)

)를 최소화하기 위해 추정된 위상오차(

)는 수학식 10으로 정의된다. And, the entropy (

Estimated phase error () to minimize

) Is defined by Equation 10.

[Equation 10]

값 추정의 알고리즘으로는 SSA(Stage-by-Stage Approaching) 기법, MEPA(Minimum Entropy Phase Adjustment) 기법 등의 다양한 방식들이 이용 가능한데, SSA 기법에 비해 MEPA 기법 경우 계산 시간이 더욱 빠르다. Where to minimize entropy

As a value estimation algorithm, various methods such as a stage-by-stage approach (SSA) technique and a minimum entropy phase adjustment (MEPA) technique are available. The calculation time is faster in the MEPA technique than the SSA technique.

값 추정을 거치지 않는 경우, 상기 두 기법(SSA, MEPA) 모두 미지수

개를 추정하여야 하며

차원 공간에서 탐색을 수행하여야 하므로 많은 계산 시간을 요구한다. 따라서, 계산 시간을 효과적으로 줄이기 위하여

영상을 모두 이용하는 것이 아니라 상기

값을 추정하여 일부분인

영상만을 이용하여 엔트로피를 최소화하고 그 위상오차를 추정 함으로써, 계산에 소요되는 시간을 전체적으로 줄일 수 있다.Of course, using Equation 8

If no values are estimated, both techniques (SSA, MEPA) are unknown

Must be estimated

Since the search must be performed in the dimensional space, it requires a lot of computation time. Thus, to reduce the computation time effectively

Not all of the video

To estimate the value

By minimizing entropy and estimating the phase error using only the image, the computation time can be reduced as a whole.

)를 상기 초기행렬(

)에 적용한 후 이를 푸리에 또는 역푸리에 변환하여, 위상오차가 제거된 고품질의 레이더 영상을 최종적으로 생성할 수 있다(S190). On the other hand, after the estimation of the phase error (S180), the estimated phase error (

) Is the initial matrix (

) And then Fourier or inverse Fourier transform to finally generate a high quality radar image from which phase error is removed (S190).

)를 이용하여 상기 초기행렬 내의

를 재정의하고, 상기 재정의된

를 초기행렬(

)에 적용한 후 이를 행방향으로 푸리에 또는 역푸리에 변환하여, 상기 위상오차(

)가 제거된 초점이 맞춰진 고품질의 2차원 레이더 영상을 생성할 수 있게 된다. 여기서, 상기 재정의된

는 수학식 11로 표현 가능하다.More specifically, the phase error (Equation 10)

In the initial matrix using

Overridden and redefined

Is the initial matrix (

) And then Fourier or inverse Fourier transform in the row direction,

) To create a focused, high-quality, two-dimensional radar image. Where the overridden

Can be expressed by Equation (11).

[Equation 11]

As described above, the above-described radar image autofocus method can reduce the calculation time by calculating the eigenvector of the covariance matrix of the radar signal received for the target, and then estimating the phase error using the entropy of the eigenvector as the cost function. have.

값 결정을 위한

의 분포를 나타낸다. 그리고, 도 8은 상기 SSA 기법을 이용한 레이더 영상의 비교, 도 9는 상기 MEPA 기법을 이용한 레이더 영상의 비교를 나타낸다.Hereinafter, the experimental results for the performance evaluation of the proposed autofocus technique will be described in detail with reference to FIGS. 5 to 9. 5 is a three-dimensional CAD model and a three-dimensional scatter scatter model of the B737, Figure 6 is a target movement scenario, Figure 7

For value determination

Indicates the distribution of. 8 shows a comparison of radar images using the SSA technique, and FIG. 9 shows a comparison of radar images using the MEPA technique.

km 떨어진 위치에서 출발하여,

방향으로 속도

와 가속도

를 가지고 이동한다고 가정하였다. 실험을 위해 사용된 처프(chirp) 레이더 변수는 아래의 표 1을 참조한다.In order to evaluate the performance, a radar image fabrication experiment was performed on a target composed of a plurality of point scatterers of FIG. 5. In this experiment, the target consisting of the point scatterer of FIG. 5 is moved from the radar at the origin of FIG.

starting from km away,

Speed in direction

And acceleration

Assume that we move with. See Table 1 below for the chirp radar parameters used for the experiments.

[Table 1]: Radar and Target Movement Related Parameters

First, as an experiment related to the SSA technique, the performance of the SSA technique using the conventional radar image entropy and the SSA technique using the proposed eigenvector entropy will be discussed.

For the experiment, first, a radar signal was generated for a target composed of the scatterers of FIG. 5. Noise was added to the generated signal so that the signal-to-noise ratio (SNR) was 0 dB. After applying the same distance alignment process to the noise-added data, phase correction was performed using the conventional SSA technique using radar image entropy and the SSA technique using proposed eigenvector entropy. .

이다. 제안된 방법은 수학식 8을 이용하여

값을 결정하였으며

를 사용하였다. 즉, 레이더 신호에 포함되어 있는 표적의 에너지 중 적어도 95% 이상을 이용하여 최적화를 수행한다고 생각할 수 있다. 비교를 위하여 기존의 방법 또한 최적화에 참여하는 레인지 빈(range bin)의 개수

를 다음의 수학식 12를 통해 결정하였다. In order to implement this phase correction process, one of the important variables is the number of range bins or eigenvalues required for the optimization algorithm to perform the phase correction process.

to be. The proposed method using Equation 8

Determined the value

Was used. That is, it can be considered that the optimization is performed using at least 95% or more of the energy of the target included in the radar signal. For comparison purposes, the existing method also counts the range bins involved in the optimization.

Was determined by the following equation (12).

[Equation 12]

는 정합필터링 및 거리정렬 과정을 끝낸 수신신호를 거리방향에 투영한 1차원 영상이다. 비교를 위해

를 사용함으로써

값을 결정하였다. 상기 표 1에서 펄스의 개수

이며, 표적 주변의 190개의 레인지 빈(range bin)만을 추출하여 사용하였으므로

이다. 이러한 기존의 방법에서도 상기

를 크기가 큰 순서대로 정렬한 후 상기

개 중에서

값이 가장 큰

개의 레인지 빈(range bin)을 선택하여

수신신호만을 사용하여 위상오차를 추정할 수 있다. In equation (12)

Is a 1-dimensional image projecting the received signal after the matching filtering and distance alignment process in the distance direction. for comparison

By using

The value was determined. Number of pulses in Table 1 above

Since only 190 range bins around the target were extracted and used,

to be. Even in these conventional methods

Sort them in order of size

Out of

The largest value

Select range bins

The phase error can be estimated using only the received signal.

값을 결정하기 위하여 필요한

값의 분포를 보여준다. 사각형(□)은 기존의 레이더 영상의 엔트로피를 사용하는 SSA의 결과 얻어진

분포이고, 원(○)은 제안된 고유벡터 엔트로피를 사용하는 SSA의 결과 얻 어진

분포이다. 7 is used for optimization

Necessary to determine the value

Show the distribution of values. Squares are obtained as a result of SSA using entropy of existing radar images.

The circle (○) is the result of the SSA using the proposed eigenvector entropy.

Distribution.

Referring to FIG. 7, the distribution (b) using the proposed method (entropy of the inherent vector) is more skewed to the left side than the distribution (a) using the conventional method (entropy of the radar image). That is, in the conventional method, the amount of information included in the radar signal is spread evenly over 190 range bins. In the proposed method, the amount of information included in the radar signal is It means that it is contained in about 20 eigenvectors. As a result, the proposed method can efficiently represent the information contained in the radar signal with much less data.

로 선택하였으므로, 기존의 방법을 이용한 SSA의 경우 (a)는

이고, 제안된 방법을 이용한 SSA의 경우 (b)는

이다. 즉, 제안된 기법을 이용한 (b)의 경우는 기존의 방법인 (a)의 경우에 비해, 최적화에 필요한 데이터의 양을 9.4%(=(14／149)×100%)만 사용한다. 이렇게 적은 수의 데이터를 사용하여 최적화를 수행하므로, 최적화 내부에서 필요한 FFT의 횟수가 줄어들게 된다. 따라서 위상보정 과정에 필요한 계산 시간을 단축시킬 수 있다.Referring to Figure 7, in this experiment

In the case of SSA using the conventional method, (a)

In case of SSA using the proposed method, (b)

to be. That is, in case of (b) using the proposed method, only 9.4% (= (14/149) × 100%) of the data required for optimization is used, compared to the case of the conventional method (a). The optimization is performed using this small number of data, which reduces the number of FFTs needed inside the optimization. Therefore, the calculation time required for the phase correction process can be shortened.

In Figure 8 (a) is a radar image according to the SSA technique using a conventional radar image entropy, (b) is a radar image according to the SSA technique using the proposed eigenvector entropy. Both (a) and (b) well represent the spatial distribution of the point targets for the model of FIG. However, as a result of measuring the calculation time of the phase correction process required to produce these two radar images, it took about 22 seconds for the conventional SSA method and about 2.8 seconds for the SSA method according to the proposed method. In other words, it can be seen that the proposed SSA method using eigenvector entropy can be calculated about 8 times faster than the SSA method using entropy of radar image. Therefore, on the basis of various experimental results, the SSA method using the proposed eigenvector entropy is capable of generating radar images of almost the same quality as the SSA method using the conventional radar image entropy, and greatly increases the computation time. It can be shortened.

Secondly, as an experiment related to the MEPA method, we compare the performance of the MEPA method using the radar image entropy and the MEPA method using the proposed eigenvector entropy.

값을 결정하기 위하여

를 사용하였고, SNR=-10dB로 설정하여 첫 번째 실험보다 잡음의 양을 더욱 증가시켰다.The MEPA technique was developed to reduce the computation time of the aforementioned SSA technique. Both MEPA and SSA techniques estimate phase errors to minimize the entropy of radar images, but MEPA techniques can estimate phase errors much faster than SSA. In this experiment, we estimate the phase error by combining the MEPA method with the cost function of entropy based on the inherent vectors. The targets and variables used in the experiment are the same as in the first experiment. only

To determine the value

And SNR = -10dB to increase the amount of noise more than the first experiment.

 In FIG. 9, (a) shows a radar image according to the MEPA technique using the conventional radar image entropy, and (b) shows a radar image according to the MEPA technique using the proposed eigenvector entropy. However, the radar image of the conventional method of FIG. 9A does not properly represent the distribution of the point scatterer of FIG. 5. On the contrary, the radar image according to the proposed method shown in FIG. 9 (b) properly represents the distribution of the point scatterers. In other words, the MEPA method according to the conventional method fails to produce a radar image for a target under the influence of noise, but the MEPA method using the proposed eigenvector entropy succeeds in generating a high quality radar image for a target. It was. The calculation time required to produce the radar image of FIG. 9 is 0.12 seconds for the MEPA method according to the conventional method, 0.07 seconds for the MEPA method according to the proposed method, and the calculation time for the proposed method compared to the conventional method. This took less.

In summary, the proposed auto-focus method of the radar image generates an eigen profile by Fourier transforming the eigenvectors of the covariance matrix obtained from the radar signal, and focuses the radar image by using the entropy calculated from the eigen profile as a cost function. Apply the matching method. Using the proposed cost function, it is proved that the computation time can be further shortened and the noise is more robust compared to the conventional method using the entropy of the radar image directly.

In particular, when the SSA method and the proposed eigenvector entropy are combined, the performance of the radar image is almost similar to that of the conventional method, and the computation time can be greatly reduced compared to the conventional method. The combination of the MEPA method and the proposed eigenvector entropy shows more robust performance against noise without increasing the computation time. Based on the experimental results, it can be seen that the proposed method outperforms the conventional method in terms of computation time and noise degradation of radar image.

The proposed autofocus method can be applied to ISAR images or SAR images, which are two-dimensional radar images, and can be applied to the production of three-dimensional radar images according to circumstances. In addition, the proposed autofocus method has advantages over existing methods in terms of real-time acquisition and quality improvement of radar images, and non-cooperative target recognition (NCTR) or automatic target recognition, which is a target identification method using radar images. It is expected to greatly improve the target identification performance and the real-time processing performance when applied to the field.

Although the present invention has been described with reference to the embodiments shown in the drawings, these are merely exemplary and will be understood by those skilled in the art that various modifications and equivalent other embodiments are possible. Therefore, the true technical protection scope of the present invention will be defined by the technical spirit of the appended claims.

1 is a conceptual diagram of obtaining a radar image by mounting a SAR system on an aircraft,

2 is a conceptual diagram of an ISAR system;

3 is a change in range profile before and after performing distance alignment;

4 is a flowchart of a radar image autofocus method based on eigenvector entropy according to an embodiment of the present invention;

5 is a three-dimensional CAD model and three-dimensional scatter scattering model of B737,

6 is a scenario of movement of a target;

값 결정을 위한

의 분포도,7 is

For value determination

Distribution of,

8 is a comparison of radar images using the SSA technique,

9 is a comparison of radar images using the MEPA technique.

Claims (8)

(a) receiving a radar signal comprising a plurality of pulses reflected from the target after being transmitted to a moving target side; (b) compressing the received plurality of pulses in a distance direction to generate a plurality of range profiles, which are one-dimensional radar images, and distance-aligning the range profiles, respectively; (c) calculating a covariance matrix from an initial matrix obtained from the radar signal on which the distance alignment is performed; (d) calculating eigenvalue decomposition of the covariance matrix, and computing eigenvector matrices including eigenvectors and eigenvalue matrices including eigenvalues, respectively; (e) the larger of the eigenvalues

Corresponding to eigenvalues

Calculating a new eigenvector matrix using the four eigenvectors and then performing Fourier or inverse Fourier transform to generate an image matrix including Eigen Profiles; (f) estimating a phase error that minimizes entropy of the image matrix; And and (g) generating the radar image from which the phase error is removed by applying the estimated phase error to the initial matrix and performing Fourier or inverse Fourier transform. The method according to claim 1, wherein the initial matrix (

)silver, Is defined by Equation 1, The initial matrix (

Down-Range is a distance direction, and Cross-Range corresponds to a time axis and each pulse is received according to the movement of the target. .

(

: Number of range bins for the distance direction,

= Number of received pulses,

: Phase error actually generated by the movement of the target,

= Phase error (

The radar signal,

= Phase error (

The radar signal, assuming that is not included,

,

) The method according to claim 2, wherein step (c), The initial matrix (

Covariance matrix defined by Equation 2 using the column vector of

),

(

Conjugate Transpose Operation on a Matrix The step (d) A method of auto radar image focusing based on eigenvector entropy, which is performed by solving eigenvalue decomposition of Equation (2).

,

,

(

Is the eigenvector matrix,

)of

Eigenvectors

Square matrix with,

= Covariance matrix as the eigenvalue matrix

Eigenvalues

Is a diagonal matrix whose elements are all zeros and the remaining elements are all zeros,

,

Conjugate Transpose Operation on a Matrix The method of claim 3, wherein the eigenvalues (

)silver, As shown in Equation 4, the sizes are arranged in ascending order, The eigenvectors (

Is the eigenvalues (

Radar image autofocus method based on the eigenvector entropy, aligned to correspond to the size of.

The method of claim 3, wherein step (e) The eigenvalues (

) Large in size

Corresponding to eigenvalues

New eigenvector matrices using

) Is calculated as Equation 5,

The new eigenvector matrix (

) Is the initial matrix (

Phase error in

Equation 5 is redefined as Equation 6 as

(At this time,

,

= Phase error (

Eigenvectors of the covariance matrix obtained from the radar signal containing

= Phase error (

Eigenvectors of the covariance matrix from the radar signal, assuming no) New Eigenvector Matrix of Equation 6

) Is Fourier or inverse Fourier transformed so that the eigen profiles

New including)

The image matrix of

) Is generated as in Equation 7, radar image autofocus method based on eigenvector entropy.

,

The method according to claim 5, wherein step (e), The eigenvectors (

Is the number of eigenvectors required for optimization

A radar image autofocus method based on eigenvector entropy, which is performed by estimating a dog using Equation (8).

,

(

Denominator of: the covariance matrix (

Obtained from

Eigenvalues (

As the sum of

Total information contained in pulse signals,

Molecular: The covariance matrix (

Obtained from

Eigenvalues (

As the sum of

Total information contained in pulse signals,

: Any value between 0 and 1) The method according to claim 5, wherein in step (f), Entropy of the image matrix

) Is defined by Equation 9, and the entropy (

To estimate the estimated phase error (

) Is a radar image autofocus method based on eigenvector entropy defined by Equation (10).

(

= Estimated phase error (

), Including image matrix

),

: remind

Is normalized to the power of the image)

The method according to claim 7, wherein (g) step, The estimated phase error (

Using)

Overridden and redefined

Is the initial matrix (

) And then Fourier or inverse Fourier transform in the row direction,

Produces a focused two-dimensional radar image with) Overridden

A method for auto focusing radar images based on eigenvector entropy represented by Equation (11).

Images