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160719 / /F
All errors given below may be assumed to be RMS errors provided
the sensor errors used are also RMS errors or RMS uncertainties.
With this simplification the total system error can be calculated by
the root mean squared addition of the individual contributions.
Note that because of this, no effort has been made with respect to
the signs of the individual error terms, and as given below the signs
may thus not always be correct.
The coordinate system used assumes the x-axis to point forwards
(alongtrack), the y-axis to point starboard (acrosstrack), and the
z-axis to point vertically downward. A normal installation is
assumed with all beam-steering in the y-z plane
Errors in range (
∆R
into vertical errors (
from the vertical considered:
∆z = ∆R cos Ô
∆z = ∆ÔR sin Ô = ∆ÔD tan Ô
The position error (∆x or ∆y) is also determined by range and
angular errors:
∆x or ∆y = ∆R sin Ô
∆x or ∆y = ∆ÔR cos Ô = ∆ÔD
Echo sounder errors
The error of a multibeam echo sounder is theoretically dependent
upon a signal-to-noise ratio. However, provided that the
signal-to-noise ratio is above 10 dB, the following equations have
been found to model the depth and acrosstrack position errors of
the Kongsberg Simrad multibeam echo sounders very well:
∆R
s
(
)
2
∆
=
Z A
2
∆R
s
(
)
2
∆
=
Z P
2
∆R
s
(
)
2
∆
=
Y A
2
∆R
s
(
)
2
∆
=
Y P
2
in m) and angle (
∆Ô
) by simple geometry with
∆z
D
Ψ
2
+ ( cτ
y
)
2
cos
2
Ô +
4
+ ( cτ
)
cos
Ô + 0.04∆R
2
2
4
D
Ψ
2
+ ( cτ
y
)
2
sin
2
Ô +
4
144
0.04∆R
+ ( cτ
)
2
sin
2
Ô +
4
Technical reference
in radians) will translate
as the angle
Ô
tan
Ô
2
2
144
D sin Ô
Ψ
s
y
2
D cos Ô
Ψ
s
y
tan Ô
359
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