US 9,316,716 B2 · Dynamic attitude measurement method of star sensor based on gyro's precise angular correlation

Abstract

The disclosure discloses a dynamic attitude measurement method of a star sensor based on gyro's precise angular correlation. On the basis that a dynamic compensation is performed on each of the measurement exposure frames of the star sensor and a fixed star matching vector matrix having dynamic error and noise influence is obtained in a prior art, a transform matrix between every two adjacent measurement frames of the star sensor is precisely measured by a unit including three gyros fixedly coupled with the star sensor. The transform matrix correlates the matched vector matrixes of the adjacent measurement frames of the star sensor. Finally, a correlated measurement equation is established with a series of correlated measurement frames, which is corresponding to processing a series of measurement frames as a single measurement frame.

A dynamic attitude measurement method of a star sensor based on gyro's precise angular correlation utilizing an attitude measurement device comprising a gyro unit comprising three single-axis gyros mounted orthogonally to each other and a star sensor rigidly and fixedly coupled with the gyro unit, wherein said method comprising:

1) establishing a synchronous sampling time sequence of the gyro unit and the star sensor so as to configure sampling frequency of the gyro unit to be integral multiple of exposure frequency of the sensor star;
2) sampling by the sensor star with the exposure frequency so as to measure a sequence of frames of star image comprising a 1st frame, . . . , a (i−1)th frame, and a ith frame, and performing dynamic motion compensation and denoising processing on each frame of the sequence of frames of star image so as to extract n effective star points from each frame of the sequence of frames of star image;
3) searching and matching the n effective star points extracted from each frame of the sequence of frames of star image with a standard star image, obtaining direction vectors p1, p2, . . . , and pn of the n effective star points from each frame of the sequence of frames of star image in an inertial coordinate system wherein the direction vectors p1, p2,and pn form a direction vector matrix P of the n effective star points from each frame in the inertial coordinate system, and obtaining direction vector s1, s2, . . . , and sn of the n effective star points from each frame of the sequence of frames of star image in a star sensor coordinate system, wherein the direction vector s1, s2, . . . , and sn form a direction vector matrix S of the n effective star points from each frame in the star sensor coordinate system;
4) during each period from a start point of sampling a current star image frame by the star sensor to a start point of sampling a star image frame immediately next to the current star image by the star sensor, simultaneously sampling angular velocity of the gyro unit by the gyro unit with the sampling frequency, and calculating an angular correlation matrix from the current star image frame to the next star image frame:
a) measuring three angular velocity components Ωx,Ωy, and Ωz along X-axis, Y-axis and Z-axis in a gyro unit coordinate system of the gyro unit by sampling the angular velocity of the gyro unit by the gyro unit with the sampling frequency, and calculating angular velocity Ωssof the star sensor with following equation:
Ωss=CgussΩgu
wherein Ωgu=[Ωx,Ωy, Ωz]T,symbol[·]Tdenotes a transposed matrix of ·, and the Cguss denotes transform matrix from the gyro unit coordinate system to the star sensor coordinate system;
b) setting an initial value q (0) of an attitude quaternion q as [1,0,0,0]T, and updating the attitude quaternion q with following equation:
q
⁡
(
λ
)
=
[
q
0
⁡
(
λ
-
1
)
,
-
q
1
⁡
(
λ
-
1
)
,
-
q
2
⁡
(
λ
-
1
)
,
-
q
3
⁡
(
λ
-
1
)
q
1
⁡
(
λ
-
1
)
,
q
0
⁡
(
λ
-
1
)
,
-
q
3
⁡
(
λ
-
1
)
,
q
2
⁡
(
λ
-
1
)
q
2
⁡
(
λ
-
1
)
,
q
3
⁡
(
λ
-
1
)
,
q
0
⁡
(
λ
-
1
)
,
-
q
1
⁡
(
λ
-
1
)
q
3
⁡
(
λ
-
1
)
,
-
q
2
⁡
(
λ
-
1
)
,
q
1
⁡
(
λ
-
1
)
,
q
0
⁡
(
λ
-
1
)
]
⁢
[
cos
⁡
(

δΦ

/
2
)
(
δΦ
x
/

δΦ

)
⁢
sin
⁡
(

δΦ

/
2
)
(
δΦ
y
/

δΦ

)
⁢
sin
⁡
(

δΦ

/
2
)
(
δΦ
z
/

δΦ

)
⁢
sin
⁡
(

δΦ

/
2
)
]
wherein q(λ−1) denotes the attitude quaternion before the λth sampling by the gyro unit, q(λ) denotes the attitude quaternion after the λth sampling by the gyro unit, δφ denotes an angular increment of the gyro unit in the star sensor coordinate system during a time interval δτ,wherein the time interval δτ is a time interval of the λth sampling by the gyro unit, and δφ=[δφx,δφy,δφz]T=Ωss(λ)δτ, δφx, δφz denotes components of δφ along X-axis, Y-axis, and Z-axis in the star sensor coordinate system, Ωss (λ) denotes the angular velocity of the star sensor at the λth sampling in the star sensor coordinate system, |δφ| denotes module of δφ, and sin( )denotes sine function;
c) repeating the measuring three angular velocity components Ωx, Ωy, and Ωz along X axis, Y-axis and Z-axis in the gyro unit coordinate system of the gyro unit, the calculating angular velocity Ωss of the star sensor and the updating the attitude quaternion q based on the calculated angular velocity Ωss of the star sensor, until start point of sampling the next star image frame by the star sensor;
d) calculating, based on the updated attitude quaternion q at the start point of the sampling the next star image frame by the star sensor, the angular correlation matrix from the current star image frame to the next star image frame with following equation:
C
m
m
-
1
=
(
q
0
2
+
q
1
2
-
q
2
2
-
q
3
2
2
⁢
(
q
1
⁢
q
2
-
q
0
⁢
q
3
)
2
⁢
(
q
1
⁢
q
3
+
q
0
⁢
q
2
)
2
⁢
(
q
1
⁢
q
2
+
q
0
⁢
q
3
)
q
0
2
-
q
1
2
+
q
2
2
-
q
3
2
2
⁢
(
q
2
⁢
q
3
-
q
0
⁢
q
1
)
2
⁢
(
q
1
⁢
q
3
-
q
0
⁢
q
2
)
2
⁢
(
q
2
⁢
q
3
+
q
0
⁢
q
1
)
q
0
2
-
q
1
2
-
q
2
2
+
q
3
2
)
wherein m denotes the number of the next star image frame in the sequence of frames of star image, m−1 denotes the number of the current star image frame in the sequence of frames of star image, Cmm−1 denotes the angular correlation matrix from the current star image frame to the next star image frame, and q0, q1, q2, q3 denotes four elements of said updated attitude quaternion;
5) based on the sequence of frames of star image comprising the 1st frame, . . . , the (i−1)th frame, and the ith frame measured by the star sensor and the calculated angular correlation matrixes of each pair of star image frames comprising two adjacent star image frames, according to following correlation equation, calculating an optimal attitude matrix {tilde over ({tilde over (C)}ssini(1) of the 1th frame relative to the inertial coordinate system by using a least square method;
and obtaining an optimal attitude matrix {tilde over ({tilde over (C)}ssini(l0)of the l0th frame relative to the inertial coordinate system by multiplying the optimal attitude matrix {tilde over ({tilde over (C)}ssini(1) of the 1th frame by the angular correlation matrix Cl01 from the l0th frame directly to the 1th frame, i.e., {tilde over ({tilde over (C)}ssini(l0)={tilde over ({tilde over (C)}ssini(1)Cl01, wherein l0ε[2,i], and Cl01=C21C32. . . Cl0l0−1,
wherein the correlation equation is:
{
[
P
1
,
P
2
,
…
⁢
,
P
i
]
=
C
ss
ini
⁡
(
1
)
[
(
S
1
+
E
1
)
,
(
S
2
1
+
E
2
1
)
,
…
⁢
,
(
S
i
1
+
E
i
1
)
]
S
l
0
1
=
(
∏
r
=
2
r
=
l
0
⁢
⁢
C
r
r
-
1
)
⁢
S
l
0
=
C
l
0
1
⁢
S
l
0
E
l
0
1
=
(
∏
r
=
2
r
=
l
0
⁢
⁢
C
r
r
-
1
)
⁢
E
l
0
=
C
l
0
1
⁢
E
l
0
,
l
0
∈
[
2
,
i
]
wherein P1, P2, . . . Pi are direction vector matrixes of the effective star points, which are obtained by search-matching for each of the 1th frame, the 2nd frame, . . . , the ith frame of the sequence of frames of star image measured by the star sensor, in the inertial coordinate system and S1, S2, . . . , Siare direction vector matrixes of the effective star points, which are obtained by search-matching for each of the 1th frame, the 2nd frame, . . . , the ith frame of the sequence of frames of star image measured by the star sensor, in the star sensor coordinate system;
E1, E2, . . . , Ei are error vector matrixes of the effective star points for each of the 1th frame, the 2nd frame, . . . , the ith frame of the sequence of frames of star image, which are caused by extraction error of star points;
Cssini(1) is a transform matrix from a coordinate system of the star sensor for the 1th frame to the inertial coordinate system and Crr−1 , is the angular correlation matrix from the rth frame of the sequence of frames of star image to the (r−1)th frame of the sequence of frames of star image;
6) calculating attitude angles φx, φy and φz of the 0Ath frame of the sequence of frames of star image by using the optimal attitude matrix {tilde over ({tilde over (C)}ssini(l0A)of the l0Ath frame of the sequence of frames of star image obtained in step 5) with following equation and outputting the calculated sequence of frames of star image as dynamic attitude of the star sensor, wherein l0Aε[1,i]:
{
ϕ
x
=
arcsin
⁡
[
C
~
~
ss
ini
⁡
(
3
,
2
)
]
ϕ
y
=
-
arctan
⁡
[
C
~
~
ss
ini
⁡
(
3
,
1
)
⁢
/
⁢
C
~
~
ss
ini
⁡
(
3
,
3
)
]
ϕ
z
=
-
arctan
⁡
[
C
~
~
ss
ini
⁡
(
1
,
2
)
⁢
/
⁢
C
~
~
ss
ini
⁡
(
2
,
2
)
]
;
wherein, {tilde over ({tilde over (C)}ssini(3,2), {tilde over ({tilde over (C)}ssini(3,1), {tilde over ({tilde over (C)}ssini(3,3), {tilde over ({tilde over (C)}ssini(1,2) and {tilde over ({tilde over (C)}ssini(2,2)are matrix elements in the optimal attitude matrix {tilde over ({tilde over (C)}ssini(l0A) of the l0Ath frame of the sequence of frames of star image, and a first digit in parentheses denotes row number in the optimal attitude matrix {tilde over ({tilde over (C)}ssini(l0A) and a second digit in parentheses denotes column number in the optimal attitude matrix {tilde over ({tilde over (C)}ssini(l0A), arcsin denotes anti-sine function and arctan denotes anti-tangent function,
wherein the dynamic attitude of the star sensor reflects the dynamic attitude of a motion carrier, on which the star sensor is fixed, and
wherein the dynamic attitude of the motion carrier is used for the navigation-positioning of the motion carrier.

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Dynamic attitude measurement method of star sensor based on gyro's precise angular correlation

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Dynamic attitude measurement method of star sensor based on gyro's precise angular correlation

Life of this patent

Abstract

Claims5