Vaisala IRIS - Figure 104 Vectors Used for Velocity Correction in Earth Coordinates

The interface either device is the RCP antenna control unit. The orientation and navigation
information is passed to IRIS through the serial line connection to the antenna controller.
Antenna
Location
Y
A
Y
AI
Y
A
Y
I
INU Location
Y
I
Y
AS
Y
A
Y
S
Y
S
Ship Center
of Rotation
Y
IS
Y
I
Y
S
Figure 104 Vectors used for Velocity Correction In Earth Coordinates
In general, the INU is not located at either the ship center of rotation or the antenna. The
location vectors are shown in the previous figure in earth coordinates. The position vector of
the antenna in earth coordinates can be expressed as:
INU Case: y
A
= y
1
+ y
A
− y
1
Gyro Case: y
A
= y
S
+ y
A
− y
S
so that,
INU Case:
y
A
= y
1
+ Δy
AI
Gyro Case: y
A
= y
1
+ Δy
AS
where,
Δy
AI
= y
A
+ y
I
and
Δy
AS
= y
A
+ y
S
Expressing the Δ vectors in terms of the ship relative coordinates yields:
INU Case: y
A
= y
1
+ A
−1
Δy′
AI
Gyro Case:
y
A
= y
S
+ A
−1
Δy′
AS
Dierentiating these two expressions yields the final expressions for the antenna velocity:
INU Case: y
A
= y
I
⋅
+ A
⋅
−1
Δy′
AI
Gyro Case: y
A
= y
S
⋅
+ A
⋅
−1
Δy′
AS
Note that since the INU, antenna and ship center coordinates are not changing relative to
the ship coordinates,
y
AS
⋅
= y
AI
⋅
= 0
The components of the matrix A
-1
are as follows:
IRIS Product and Display User Guide M211319EN-H
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