KR100594969B1 - Method of correcting the orbit of sar image - Google Patents

Abstract

The present invention relates to a method for correcting satellite trajectory of a synthetic opening radar image, and more particularly, to extract an initial satellite trajectory using the synthetic opening radar image and information obtained from the header, and to accurately measure a ground reference point of the synthetic opening radar image. And after performing the first orbital correction so that the initial satellite orbit is close to the actual satellite orbit using the same, the second orbital correction is performed to make the orbit of the first calibrated satellite closer to the real orbit using the satellite rotation model. The present invention relates to a satellite orbital correction method for a synthetic aperture radar image.

Satellite orbit correction method of the composite aperture radar image of the present invention,

In the method for correcting the satellite trajectory of the synthetic opening radar image expressed as a function of time t as shown in Equation 1 below,

,

,

,

,

,

,

,

,

)를 추출하는 단계;(a) Using the synthetic aperture radar image and the header information, the initial orbital parameters of the satellite (

,

,

,

,

,

,

,

,

Extracting;

다수를 추출하는 단계;(b) a ground reference point corresponding to the image reference points (i, j) contained in the composite aperture radar image by a digital topographic map or GPS survey;

Extracting a plurality;

(c) The initial orbital information parameter obtained in step (a) is set as an initial value, and the orbital information parameter is repeatedly updated by substituting a plurality of image reference points and ground reference points obtained in step (b) into the following SAR geometric model. A first satellite orbital correction step of determining the value;

만큼 회전시켜 위성궤도를 보정하는 제2 위성궤도보정 단계;를 포함하여 이루어진다.(d) The satellite orbit corrected in step (c) is scaled by k, as shown in the following satellite rotation model, on a plane perpendicular to the direction of travel of the satellite.

And a second satellite orbital correction step of correcting the satellite orbit by rotating as much as possible.

Synthetic Opening Radar, Orbital Information Parameter, Digital Topographic Map, GPS Survey, SAR Geometry Model, Satellite Rotation Model

Description

Satellite Orbit Correction Method of Synthetic Opening Radar Image Using GPS Surveyed Ground Control Points {Method of correcting the orbit of SAR Image}

1 is a block diagram showing a satellite orbital correction method of a composite opening radar image according to the present invention.

2 is a view showing the geometry of the synthetic aperture radar.

3 is a view showing the geometry according to the satellite rotation model according to the present invention.

4 is a view comparing difference coherence produced using the satellite orbit obtained in each step of the present invention.

The present invention relates to a method for correcting satellite trajectory of a synthetic opening radar image, and more particularly, to extract an initial satellite trajectory using the synthetic opening radar image and information obtained from the header, and to accurately measure a ground reference point of the synthetic opening radar image. And after the first orbital correction is performed so that the initial satellite orbit is closer to the actual satellite orbit, the second orbital correction is performed to make the orbit of the first calibrated satellite closer to the real orbit using the satellite rotation model. The present invention relates to a satellite orbital correction method for a synthetic aperture radar image.

Synthetic aperture radar (SAR) imaging is currently being applied in many fields. The radargrammetry of the composite aperture radar image has produced numerical elevation data of many regions from the RADARSAT-1 SAR image, and has already produced the data for all regions in Korea, and the SAR interferometry of the composite aperture radar image. ) Has produced numerical elevation data for most of the world through a project called the Shuttle Radar Topography Mission (SRTM). In addition, the differential SAR interferometry, which can measure the ground subsidence from the synthetic aperture radar image by several millimeters, is recognized as the only way to observe the ground subsidence two-dimensionally. It is used in many fields, such as landslide measurement and landfill settlement.

However, in order to use these techniques, one must know the exact orbit of the satellite at the time the composite aperture radar image was taken. Satellites such as ERS-1 / 2 and ENVISAT provide very accurate orbits, but satellites such as RADARSAT-1 and JERS-1 do not provide accurate orbital information. The trajectory must be corrected.

Conventional methods used to extract accurate orbital information represent satellite orbits as polynomials over time, and SAR geometries represent the initial satellite position, velocity, image capture time, and ground reference point for images extracted from header information. In this paper, only the method of updating satellite orbit information parameters is used. However, since the satellite moves along a well-defined ellipsoid, the simple representation of the satellite's trajectory as a time polynomial and the use of SAR geometry models are limited to approaching the true orbit of the satellite. In particular, it is difficult to apply the corrected satellite orbit as it is in the differential inference method that calculates the ground settlement accurately.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned conventional problems, and an object of the present invention is to provide a method for correcting inaccurate satellite orbit information of a synthetic opening radar image with an accurate satellite orbit close to the actual satellite orbit. .

In addition, by providing accurate satellite orbits, accurate numerical elevation data can be produced by stereogram (Radargrammetry) or interference (SAR interferometry). Another aim is to make accurate ortho-images using numerical elevation data present in.

In order to achieve the above object, the satellite orbit correction method of the synthetic aperture radar image of the present invention,

In the method for correcting the satellite trajectory of the synthetic opening radar image expressed as a function of time t as shown in Equation 1 below,

,

,

,

,

,

,

,

,

)를 추출하는 단계;(a) Using the synthetic aperture radar image and the header information, the initial orbital parameters of the satellite (

,

,

,

,

,

,

,

,

Extracting;

다수를 추출하는 단계;(b) a ground reference point corresponding to the image reference points (i, j) contained in the composite aperture radar image by a digital topographic map or GPS survey;

Extracting a plurality;

(c) The initial orbital information parameter obtained in step (a) is set as an initial value, and the orbital information parameter is repeatedly updated by substituting a plurality of image reference points and ground reference points obtained in step (b) into the following SAR geometric model. A first satellite orbital correction step of determining the value;

만큼 회전시켜 위성궤도를 보정하는 제2 위성궤도보정 단계;를 포함하여 이루어지고,(d) The satellite orbit corrected in step (c) is scaled by k, as shown in the following satellite rotation model, on a plane perpendicular to the direction of travel of the satellite.

And a second satellite orbital correction step of correcting the satellite orbit by rotating as much as possible.

는 하기의 수학식7에 의해 얻어지는 것을 특징으로 하고,K of step (d) and

Is obtained by the following Equation 7,

는 시간 t에 대한 1차까지 구한 것을 특징으로 한다.K and

Is obtained up to the first order of time t.

=

,

,

)는 하기의 수학식1과 같이 시간 t에 대한 2차 다항식으로 표현될 수 있다. The position of the satellite rotating around the earth (the position of the satellite in the global coordinate system)

=

,

,

) May be expressed as a second order polynomial for time t, as shown in Equation 1 below.

Equation 1

는 위성의 위치를 시간에 대한 미분으로 표현할 수 있으므로, 하기의 수학식2와 같이 시간 t에 대한 1차 다항식으로 표현할 수 있다. And the speed of the satellite

Since the position of the satellite can be expressed as a derivative with respect to time, it can be expressed as a first-order polynomial for time t as shown in Equation 2 below.

Equation 2

,

,

,

,

,

,

,

,

)를 알면 특정 시간에서의 위성의 위치(궤도)뿐만 아니 라 위성의 속도도 알 수 있다. 따라서 이들을 위성의 궤도정보 파라미터라 정의한다.As can be seen from the above equations (1) and (2), (

,

,

,

,

,

,

,

,

) Shows the satellite's speed as well as the satellite's position (orbit) at a particular time. Therefore, these are defined as satellite orbit information parameters.

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

1 is a block diagram schematically illustrating a method for correcting satellite trajectory of a synthetic opening radar image according to the present invention, as shown in (a) extracting an initial orbital information parameter, and (b) extracting a ground reference point. And (c) a first satellite orbital correction step, and (d) a second satellite orbital correction step. For reference, as shown in FIG. 1, the steps (a) and (b) do not have a mutual relationship.

The extracting of the initial orbital information parameter may include obtaining an initial value necessary for the first satellite orbital correction step.

,

,

)와, 위성의 속도(

,

,

)가 포함되어 있다. The synthesized aperture radar image and the header information for this image include the shooting time (t) at the satellite and the satellite position at the time of shooting (

,

,

) And the speed of the satellite (

,

,

) Is included.

However, such header information is provided intermittently rather than continuously. In general, when a satellite makes one round of the earth, it is provided at 8 points or more at regular intervals.

Therefore, in order to know the satellite position and velocity at a specific time which is not provided by the header information, fitting the position and velocity of the satellite as a function of time t as shown in Equations 1 and 2, Information should be substituted into these equations to determine the value of the trajectory information parameter.

,

,

,

,

,

,

,

,

)라 할 때 이들은 위성의 궤도가 보정되기 전의 위성의 위치를 특정하게 되므로 이들을 초기 궤도정보 파라미터라 정의한다. The track information parameter value determined by the header information is (

,

,

,

,

,

,

,

,

Since they specify the position of the satellite before the satellite's orbit is corrected, they are defined as initial orbit information parameters.

However, the problem is that the header information provided by many satellites is incorrect as described above. Thus, the satellite's orbit obtained by inaccurate header information is also inaccurate.

 Therefore, in order to correct an inaccurate satellite orbit close to the actual satellite orbit, (c) the first satellite orbit correction step is performed. For the first satellite orbital correction, a ground reference point corresponding to the initial orbital information parameter extracted in step (a) and the image reference point extracted in step (b) described below is required.

을 추출하는 단계이다.In the extracting of the ground reference point (b), the ground reference point corresponding to the image reference point (i, j) of the synthetic opening radar image may be used.

Extracting step.

로 표현한 것이다. 상기 지상좌표에 대응하는 위치를 합성개구레이더 영상에서 찾아 영상좌표

를 추출한다. 보다 정확한 위성궤도를 얻기 위해서 지상기준점은 한 영상에 고루 분포하도록 하여야 한다. 사용되는 지상기준점의 개수는 최소 5점 이상이어야 하며, 일반적으로 10개 이상을 사용한다.Using the digital topographic maps and topographic maps published by the National Institutes of Korea, or the location corresponding to the ground control point (GCP) obtained by GPS ground survey in the field, correspond to the synthetic opening radar image. The ground reference point is the ground coordinate where the position can be easily determined in the image such as a road, an intersection, a lake bank and an embankment.

It is expressed as. Image coordinates by finding the position corresponding to the ground coordinates in the synthetic aperture radar image

Extract In order to obtain more accurate satellite orbit, the ground control point should be distributed evenly in one image. The number of ground control points used should be at least 5 points, generally 10 or more.

In the step (c) of the first satellite orbital correction, the values of the orbital information parameters of Equations 1 and 2 representing the position and velocity of the satellite are more accurately represented. To this end, the initial orbital information parameter extracted from the steps (a) and (b), the image reference point and the ground reference point are substituted into the SAR geometric model represented by the following equations 3 and 4, and the orbital information parameter is obtained using the Newton-Rapson method. The value will be updated repeatedly.

From the geometry of the synthetic aperture radar (SAR) image shown in FIG. 2, the following SAR geometry models (Equations 3 and 4) are established.

Equation 3

Equation 4

과 지상기준점

사이의 거리를 나타낸다. 이 값은 빛의 속도(c)를 갖는 레이더파를 위성에서 쏘고 받는 시간(

)에 의해 얻 어진다.(R=c

/2)Where R is the satellite

And ground control points

Indicates the distance between. This value is the time to shoot and receive a radar wave from the satellite with the speed of light (c)

Is obtained by (R = c

/2)

Hereinafter, a process of obtaining the track information parameter will be described briefly.

다수를 이에 대입한다. 여기서 R은 영상좌표의 (j)에 비례하고, t는 영상좌표의 (i)에 비례한다. 그래서 (i), (j)를 알면 (t), (R)은 테이블에 의해 직접 구해진다. 따라서 수학식1,2가 대입된 수학식3,4에서 미지수는 궤도정보 파라미터 (

,

,

,

,

,

,

,

,

) 이다. Equations 1 and 2 are substituted into Equations 3 and 4. And the image reference point (i, j) extracted in step (b) and the ground reference point corresponding thereto.

Many are substituted into this. Where R is proportional to (j) of the image coordinate and t is proportional to (i) of the image coordinate. So, knowing (i), (j), (t) and (R) are directly obtained by the table. Therefore, in Equations 3 and 4, in which Equations 1 and 2 are substituted, the unknown is an orbital information parameter (

,

,

,

,

,

,

,

,

) to be.

In Equations 3 and 4, in which Equations 1 and 2 are substituted, since the solution of the orbital information is difficult to obtain by the general method, the nonlinear equations are linearized through the Taylor series expansion generally used in numerical photogrammetry. We then use the Newton-Rapson method to update the solution. For this purpose, an initial value of the trajectory information parameter is required, and the initial value uses the initial trajectory information parameter extracted in step (a).

The orbital information parameter repeatedly updated through the first satellite orbital correction step represents a more accurate position and velocity of the satellite. However, since the satellite is moving along the ellipsoid, updating the orbital information parameter only stays close to the orbit of the actual satellite. Therefore, a second satellite orbit correction step is required to make the satellite orbit more accurate.

(d) The second satellite orbital correction step is a satellite rotation that improves the rotation of the satellite approximately corrected through the first satellite orbital correction step from the earth's center to the satellite and the rotation of the satellite in the vertical direction. The model is used to calibrate to a more accurate trajectory.

의 크기를 k만큼 스케일링하고, 위성의 진행방향에 수직면(정확히 위성 센서의 관측방향 벡터 (

)와 위성의 위치벡터

가 이루는 면)상에서

만큼 회전시키는 것이다. 3 illustrates the geometry of the satellite rotation model for the second satellite orbit correction. Referring to this, the position vector of the satellite that has undergone the first satellite orbit correction step is illustrated.

Scale the magnitude of k by a plane perpendicular to the direction of travel of the satellite (exactly the direction of

) And the position of the satellite

On the plane of the

It is to rotate as much.

)는 아래의 수학식5로 표현되는 회전모델로 정의된다. In this way, the position vector of the satellite that has undergone the second

) Is defined as the rotation model represented by Equation 5 below.

Equation 5

는 3차원 공간상에서 한 선에 대한 회전에 관한 문제로 다음과 같은 행렬로 표현할 수 있다. here,

Is a problem about rotation about a line in three-dimensional space and can be expressed as the following matrix.

Equation 6

,

,

는

벡터의 방향코사인 성분을 나타낸다. here,

,

,

Is

The direction cosine component of a vector is shown.

만큼 회전시킴으로서 보다 정확한 위성궤도로 보정을 하게 되었다. 이제 우리는 회전각

와 스케일 요소 k를 결정하면 된다. As seen above, we scale the position vector of the satellite that has undergone the first satellite trajectory correction step by k as the satellite rotation model,

By rotating it as much as possible, a more accurate satellite orbit was calibrated. Now we have a rotation angle

This is done by determining and k.

)에 의해 정확한 값을 얻을 수 있다. 그리고 각 지상기준점(상기 (b)단계에서 추출한 지상기준점)과 위성의 거리

의 제곱과 제2 위성궤도보정을 거친 위성

과 지상기준점

과의 거리의 제곱의 차가 최소가 되도록(즉, 수학식7을 만족하도록)하는 회전각

와 스케일 요소 k를 결정함으로서, 위성궤도를 실제 궤도에 보다 근접하게 보정하게 된다. To this end, the following Equation 7 is proposed. In Equation 7, R denotes the distance between the satellite and the ground reference point, and the time at which the satellite shoots and receives the radar wave moving at the speed of light (c).

) To get the correct value. And the distance between each ground reference point (the ground reference point extracted in step (b)) and the satellite.

Satellite after the square of and the second satellite orbit correction

And ground control points

Rotation angle such that the difference in the square of the distance between

By determining and the scale factor k, the satellite orbits are corrected closer to the actual orbits.

Equation 7

와 스케일 요소 k를 시간 t에 대한 1차 까지 계산할 경우 4점 이상이 필요하다. 실험결과 GPS측량의 오차 또는 수치지형도의 오차를 보정하기 위해 10점 정도 를 이용하는 것이 바람직하다.Where n is the number of ground reference points and n = 1,2,3,4... Is any one of the number of rotation angle

At least four points are needed to calculate and scale elements k up to the first order of time t. As a result of experiment, it is desirable to use about 10 points to correct the error of GPS survey or the digital topographic map.

와 스케일 요소 k는 아래의 수학식8과 같이 시간에 대한 다항식으로 표현된다. And the rotation angle

And the scale factor k are expressed as polynomials over time as shown in Equation 8 below.

Equation 8

와 k는 시간 t에 대해 1차까지 계산하는 것이 바람직하다. 이는 2차, 3차 이상으로 계산하는 것은 계산과정이 복잡하여 시간이 많이 소요될 뿐만 아니라 과보정의 위험이 있기 때문이다.In Equation 8

And k are preferably calculated up to the first order for time t. This is because the calculation of the second and third orders is complicated and time consuming, and there is a risk of overcorrection.

,

,

,

)(시간의 1차까지 계산하는 경우)에 대한 편미분 값이 0이 되어야한다. 즉, 아래의 수학식9가 성립되어야 한다.In order to satisfy Equation 7, four parameters expressed in Equation 8

,

,

,

The partial differential value for) (if calculating up to the first order of time) should be zero. That is, Equation 9 below must be established.

Equation 9

,

,

,

,

,

,

,

)는 제1 위성궤도보정 단계와 같이 사진측량학에서 사용하는 Newton- Rapson방법을 사용하여 구할 수 있다. 참고로, 여기서 초기치는

=1,

=

=

=0 이다.Since four equations are given as in Equation 9, four unknowns (

,

,

,

) Can be obtained using the Newton-Rapson method used in photogrammetry as in the first satellite orbital correction step. For reference, the initial value here

= 1,

=

=

= 0

FIG. 4 is a diagram comparing differential interferograms produced using satellite trajectories obtained in each step of the present invention. (A) shows a satellite trajectory obtained by using only header information. Satellite orbits that have undergone satellite orbital correction are used, and (C) uses heterogeneous orbits that have undergone the second satellite orbital correction. The longitudinal stripes represented here represent residual fringes. This makes sense as the waves meet, cancel and reinforce each other. The distance between the two satellites determines the offset and reinforcement of this fringe. Fig. 4A shows an uncorrected track, with reinforcement and cancellation at too short intervals than in the actual track. Fig. 4B shows the first orbital correction, but the gap between the reinforcement and the offset is correct, but because the satellite orbit is approximately corrected, it appears bent due to the difference. 4 (c) shows after the second trajectory correction, and corrects the fringes appearing because they are corrected with the correct trajectory.

The brief description of the satellite orbital correction method of the composite aperture radar image of the present invention described above is as follows.

를 구한다.(a) Initial satellite orbit using radar image and header information

Obtain

를 구한다. (b) (c) First calibrated satellite trajectory by extracting ground control points by numerical topographic maps or GPS surveys and substituting them into SAR geometric models

Obtain

를 위성회전모델을 이용하여 k만큼 스케일링하고

만큼 회전시켜 제2 보정된 위성궤도

를 구한다. (d) first calibrated satellite orbit

Is scaled by k using satellite rotation model

Rotated by

Obtain

The present invention can be variously modified and can take various forms and only the specific embodiments thereof are described in the detailed description of the invention. It should be understood, however, that the present invention is not limited to the particular methods mentioned in the detailed description of the invention, but rather all modifications, equivalents and alternatives falling within the spirit and scope of the invention as defined by the appended claims. It should be understood to include.

As described above, in the orbital correction method of the composite aperture radar image according to the present invention, the inaccurate satellite orbit information of the synthetic aperture radar image is represented by a polynomial of time, and then improved using the ground reference point and the SAR geometric model method. In addition, by correcting the trajectory once more using the satellite rotation model, it is possible to extract accurate orbits close to the actual orbits and to produce accurate numerical elevation data using stereo or interference techniques. It can be observed, and it is effective to make an ortho image by using existing digital elevation data.

Claims (2)

In the method for correcting the satellite trajectory of the synthetic opening radar image expressed as a function of time t as shown in Equation 1 below, (a) Using the synthetic aperture radar image and the header information, the initial orbital parameters of the satellite (

,

,

,

,

,

,

,

,

Extracting; (b) a ground reference point corresponding to the image reference points (i, j) contained in the composite aperture radar image by a digital topographic map or GPS survey;

Extracting a plurality; (c) The initial orbital information parameter obtained in step (a) is set as an initial value, and the orbital information parameter is repeatedly updated by substituting a plurality of image reference points and ground reference points obtained in step (b) into the following SAR geometric model. A first satellite orbital correction step of determining the value; (d) The satellite orbit corrected in step (c) is scaled by k, as shown in the following satellite rotation model, on a plane perpendicular to the direction of travel of the satellite.

And a second satellite orbital correction step of correcting the satellite orbits by rotating as much as the satellite orbital correction method. here, Equation 1 is

This, This is the position vector of the satellite

Is expressed by dividing into x, y, and z components,

,

,

,

,

,

,

,

,

Is the orbital information parameter of the satellite, The SAR geometric models are the following Equations 3 and 4, Equation 3 is

ego, Equation 4 is

This, R satellite

And ground control points

Is the distance of,

Denotes the satellite's position as the velocity of the satellite and differentiates Equation 1 into time t, The satellite rotation model is the following equation 5, Equation 5 is

This,

Is the position vector of the first orbitally corrected satellite,

Is the position vector of the second orbitally corrected satellite, k and

Is calculated by the following Equation 7, Equation 7 is

This, n is the number of ground reference points, n = 1,2,3,4... Is any one of

ego,

to be. The method of claim 1, K and

Is a value calculated by the first order with respect to time t.

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