# US 2014/0191894 A1 · Three-dimensional positioning method

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- Number: US 2014/0191894 A1
- Document ID: US20140191894A1
- Status: Published application
- Kind: A1
- Application number: 13/869,451
- Filed: 2013-04-24
- Published: 2014-07-10
- Earliest claimed: 2013-01-04
- Assignees: National Central University
- Applicants: National Central University
- Inventors: Liang-Chien Chen; Chin-Jung Yang
- Web page: https://patentgrep.com/patent/US20140191894A1

## CPC

- G01S 13/9027: {Pattern recognition for feature extraction}
- G01C 21/005: {with correlation of navigation data from several sources, e.g. map or contour matching (G01C21/30 takes precedence)}
- G01S 13/86: Combinations of radar systems with non-radar systems, e.g. sonar, direction finder
- G01S 13/867: {Combination of radar systems with cameras}
- G06T 7/55: from multiple images
- B64G 1/1028: {using optical means for mapping, surveying or detection, e.g. of intelligence}
- B64G 1/1035: {using radar for mapping, surveying or detection, e.g. of intelligence}
- G06T 2207/10036: Multispectral image; Hyperspectral image
- G06T 2207/10044: Radar image
- G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01C: MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY (measuring liquid level G01F; radio navigation, determining distance or velocity by use of propagation effects, e.g. Doppler effects, propagation time, of radio waves, analogous arrangements using other waves G01S)
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- B64G: COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR

## Abstract

A three-dimensional positioning method includes establishing the geometric model of optical and radar sensors, obtaining rational function conversion coefficient, refining the rational function model and positioning the three-dimensional coordinates. Most of the radar satellite companies and part of the optical satellite only provide satellite ephemeris data, rather than the rational function model. Therefore, it is necessary to obtain the rational polynomial coefficients from the geometric model of optical and radar sensors; followed by refining the rational function model by the ground control points, so that object image space intersection is more serious; and then followed by measuring the conjugate point on the optical and radar images. Finally, the observation equation is established by the rational function model to solve the three-dimensional coordinates. It is obvious from the above results that the integration of optical and radar images does achieve the three-dimensional positioning.

## Claims

### Claim 1

A three-dimensional positioning method with the integration of radar and optical satellite images, comprising at least the following steps:
(A) establishing an optical image geometric model: direct georeferencing is used as a basis to establish the geometric model of the optical images;
(B) establishing a radar image geometric model: the geometric model of the radar images is established based on Range-Doppler equation;
(C) obtaining a rational polynomial coefficients: based on the rational function model, optical satellite images are subject to back projection according to virtual ground control points in a geometric model for optical images; an image coordinate corresponding to the virtual ground control points is obtained by using collinear conditions; from the geometric model for radar images, radar satellite images are subject to back projection according to the virtual ground control points; according to the distance and the Doppler equation to obtain an image coordinate corresponding to the virtual ground control points; and rational polynomial coefficients for the optical images and the radar images are generated to establish a rational function model;
(D) refining the rational function model: in the rational function model, the image coordinate is converted to a rational function space and calculated as a rational function space coordinate; the rational function space coordinate and the image coordinate according to the ground control points are used to obtain affine conversion coefficient; after the completion of the linear conversion, the system error correction is finished; and by means of least square collocation, the partial compensation is executed for amendments so as to eliminate systematic errors; and
(E) three-dimensional positioning: after the rational function model is established and refined, conjugate points are measured from the optical images and radar images; those conjugate points are put into the rational function model to establish an observing equation of three-dimensional positioning; and positioning a target at a three-dimensional spatial coordinate can be finished by least square method.

### Claim 2 (depends on 1)

The method of claim 1, wherein at the above step (A), optical image geometric model is established using a direct geographic counterpoint method with a mathematical formula is as follows:
{right arrow over (G)}={right arrow over (P)}+S{right arrow over (U)},
Xi=X(ti)+SiuiX
Yi=Y(ti)+SiuiY
Zi=z(ti)+SiuiZ,
wherein, {right arrow over (G)} is a vector from Earth centroid to the ground surface; {right arrow over (P)} is a vector from Earth centroid to a satellite; Xi, Yi, Zi are respectively ground three-dimensional coordinates; X(ti), Y(ti), Z(ti) are satellite orbital positions; uiX, uiY, uiZ are respectively image observation vectors; Si is the amount of scale; and ti is time.

### Claim 3 (depends on 1)

The method of claim 1, wherein the above step (B), the geometric model of the radar images based on the radar distance and Doppler equation has the mathematical formula as follows:
R
⇀
=
G
⇀
-
P
⇀
,


R
⇀

=

G
⇀
-
P
⇀

,

f
d
=
-
2
λ


R
⇀

t
,
wherein {right arrow over (R)} is a vector from the satellite to a ground point; {right arrow over (G)} is a vector from the Earth centroid to a ground point of the vector; and {right arrow over (P)} is a vector from the Earth centroid to a satellite.

### Claim 4 (depends on 1)

The method of claim 1, wherein the rational function model at the step (C) is obtained by getting rational polynomial coefficients according to a large number of virtual ground control points and the least square method, based on the rational function model with a mathematical formula as follows:
S
RFM
=
p
a

(
X
,
Y
,
Z
)
p
b

(
X
,
Y
,
Z
)
=
∑
i
=
0
i
=
3
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∑
j
=
0
j
=
3
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∑
k
=
0
k
=
3
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a
ijk
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X
i
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Y
j
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k
∑
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=
0
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=
3
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∑
j
=
0
j
=
3
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∑
k
=
0
k
=
3

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b
ijk

X
i
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Y
j
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Z
k
L
RFM
=
p
c
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(
X
,
Y
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)
p
d
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X
,
Y
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=
3
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j
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=
3
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∑
k
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0
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=
3

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c
ijk
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X
i
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Y
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k
∑
i
=
0
i
=
3
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=
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=
3
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∑
k
=
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k
=
3


d
ijk

X
i

Y
j

Z
k
,
wherein aijk, bijk, cijk and dijk are respectively rational function coefficients.

### Claim 5 (depends on 1)

The method of claim 1, wherein at the step (D), the rational function model is refined by correcting the rational function model via affine transformation with a mathematical formula as follows:
Ŝ=A0×SRFM+A1×LRFM+A2
{circumflex over (L)}=A3×SRFM+A4×LRFM+A5
wherein Ŝ and {circumflex over (L)} are respectively corrected image coordinates; and A0˜5 are affine conversion coefficients.

### Claim 6 (depends on 1)

The method of claim 1, wherein at the step (E), the observation equation of the three-dimensional positioning has a mathematical formula as follows:
[
υ
S
1
υ
L
1
υ
S
2
υ
L
2
]
=
[
∂
S
1
∂
X
∂
S
1
∂
Y
∂
S
1
∂
Z
∂
L
1
∂
X
∂
L
1
∂
Y
∂
L
1
∂
Z
∂
S
2
∂
X
∂
S
2
∂
Y
∂
S
2
∂
Z
∂
L
2
∂
X
∂
L
2
∂
Y
∂
L
2
∂
Z
]

[

X

Y

Z
]
+
[
S
^
1
-
S
1
L
^
1
-
L
1
S
^
2
-
S
2
L
^
2
-
L
2
]
.