From Pressure to Depth Estimation of underwater vertical position Havbunnskartlegging og Inspeksjon 6.-8. Februar 2008 Geilo Ove Kent Hagen Avd Maritime Systemer FFI
From Pressure to DepthEstimation of underwater vertical position
Havbunnskartlegging og Inspeksjon
6.-8. Februar 2008
Geilo
Ove Kent Hagen
Avd Maritime Systemer
FFI
Underwater pressure measurement
Sea surface
Pressure sensor
Vehicle reference point
Atmospheric
pressure
Pressure field = Hydrostatic pressure field + Dynamic pressure field
Water level
MSL
Dynamic near field:
• Current-Hull effects
• Wave-Body interactions
Hydrostatic pressure
• The pressure p equals the weight per unit area of the water and atmosphere column above the vehicle
• There exists a 1-1 relationship between pressure and depth z
• Rule of thumb: 10 m water depth = 1 atmosphere
• Challenges:
– The density ρ depends on pressure and hence on depth
– Gravitational acceleration g depends on the vehicle’s
position
pg
zρ
∂=
∂
JordenJordenEarthVehicle
Atmosphere
Ocean
z
Density of sea water
• Depends on pressure
• Depends on temperature
• Depends on salinity
0
Density
ρ
0ρ ρ>
0ρ ρ<
0ρ ρ>
Salt
”Measuring” the density of sea water
• CTD (Conductivity, Temperature, Density)
– Pressure, p
– Temperature, T
– Conductivity, C
• Salinity is estimated by UNESCO formula
”Practical Salinity Scale (1978)”
(PSS-78)
• Density is estimated by UNESCO formula”International Equation of Sate of sea water (1980)”
(IES-80)
PSS-78
0
S , ,C
S T pC
=
IES-80 ( , , )S T pρ ρ=10
02
10
04
10
06
10
08
10
10
10
12
10
14
10
16 10
18
10
20
10
22
10
24
10
26
10
28 10
30
10
32
Salinity [psu]
Tem
pera
ture
[degC
]
IES-80 density at atmospheric pressure
5 10 15 20 25 30 35 40
0
5
10
15
20
25
30
1000
1005
1010
1015
1020
1025
1030
Hydrostatic pressure to depth from a CTD profile
• Measure the conductivity C(p) and temperature profile T(p) in the water column
• Estimate the salinity profile
• Integrate the hydrostatic equation from vehicle depth to the water level
0 0
1g( , , )
( )
pz
z dz dpp
φρ
Λ =∫ ∫
0
IES0
1 11 g ( )
2 ( ( ), ( ), )
p
zz z dp
S p T p pγ φ
ρ
+ =
∫
Latitude and longitude
A crude model of gravitationCTD profile
PSS-78( ) S ( ( ), ( ), )S p C p T p p=
UNESCO Pressure to Depth
Standard ocean: S=35 psu and T=0 °C
– Specific volume
– Specific volume anomaly
IES-80
IES-80
IES-80 IES-80 IES-80
1V ( , , )
( , , )
( , , ) V ( , , ) V (35,0, )
V S T pS T p
S T p S T p p
ρ
δ δ
= =
= = −
IES-80 IES-80
0 0
1 1V (35,0, ) ( ( ), ( ), )
g( , ) 9.8
p p
z p dp S p T p p dpp
δφ
= +∫ ∫
Standard ocean UNESCO equation:
- Integral: 4’th order polynomial fit in p
- Gravitation:
0g( , ) g ( )(1 )p
p pφ φ γ= +
International equation of gravity at surface Increasing linearly with pressure (depth)
Geopotential height anomaly
- Cumulative numerical integration of the profile
- Thereafter, table look-up with linear interpolation
Hydrostatic pressure to depth below MSL
1. Subtract atmospheric pressure at sea surface
2. Use the standard oceanUNESCO equation for pressure to depth below the sea surface
3. Estimate geopotential height anomaly from the CTD profile, and add to depth
4. Subtract estimated water level above MSL
CTD profile & Geopotential height anomaly
Slowly varying error
Breiangen, December 2001
Surface wave induced pressure field
• Waves attenuate with depth
– High attenuation: wind waves
– Low attenuation: swells
• The field becomes more regular with depth
0 0.05 0.1 0.15 0.2 0.25 0.30
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Frequency [Hz]
S( ω
) [m
2s]
Significant wave height: 5 m, Peak time period: 8 s, Water depth: 80 m
JONSWAP surface wave spectrum
JONSWAP at 5 m depth
JONSWAP at 10 m depth
JONSWAP at 15 m depth
• Swell and wind waves:
– Period: 0.2 – 15 s
– Frequency: 5 – 0.06 Hz
• No longer 1-1 between pressure and depth
Fast varying error
x [m]
z [
m]
Predicted depth error due to dynamic wave pressure field
-200 -150 -100 -50 0 50 100 150 200
0
5
10
15
20
25
30
35
40
45
50
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Near field effects
• The pressure measurement depends on the vehicle’s water referenced velocity and the sensor’s location on the hull:
• Counteract through design
• Compensate through model
• Wave-body interaction:
– Long wave approximation:
• Wave length >> vehicle dimension
• Vehicle (neutrally buoyant) follows the particle path in the waves
– Otherwise:
• Scattering potential caused by the vehicle’s presence in the incoming waves
• Radiation potential caused by the vehicle’s response to the incoming waves
– The motion may be counteracted by the vehicle’s control system
Uncertain fast and slowly varying errors Robustness needed
Precise depth estimation using NavLab
Pressure
IMU
GPS
DVL
Cmp
Optional
UnescoOptional
Unesco
E
S
TI
M
A
TO
R
E
S
TI
M
A
TO
R
S
M
OO
T
H
IN
G
S
M
OO
T
H
IN
G
P
RE
P
R
OC
P
RE
P
R
OC
CTD Tide Atm
Robust
noise parameters
Robust
noise parameters
E
XP
O
R
T
E
XP
O
R
T
Smoothed
Position
Attitude
Depth
Pressure
NavLab OneClick
Automatic processing controller
• Combine UNESCO pressure to depth with inertial
navigation
• Inertial navigation estimates the vehicle’s short term
motion with high precision – filters wave induced “pressure sensor noise”
Test with HUGIN 1000
Inertial Measurement Unit: iXSea IMU 120
Doppler Velocity Log: RDI WHN 600 kHz
Pressure sensor: FSI Mirco CTD
Multi beam echo sounder: EM 3000
La Spezia, Italy:
• Low amplitude swell
• Shallow water • Flat seafloor
HUGIN 1000 was operated from R/V Leonardo of the
NATO Undersea Research Centre
NavLab post-processing: smoothed depth
• Bias oscillation period ~ 7.5 s
• Sea floor depth ~ 17 m
• HUGIN’s depth ~ 6 m
• Wave length of the swells causing the oscillations ~ 100 m
• The long wave approximation is
valid – HUGIN follows the wave motion
5110 5120 5130 5140 5150 5160 5170 5180
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Time [s]
[m]
depthm error (bias and total) and KF-model (1 and 3 sigma)
std =0.10262
5110 5120 5130 5140 5150 5160 5170 5180
-6.4-6.2
-6-5.8-5.6
Time [s]
-Depth
[m
]
Altitude control in long waves
• Waves change the vehicle’s altitude while the pressure stays the same
• The control system counteracts this by going deeper/shallower
• The pressure increases/decreases – altitude decreases/increases
5110 5120 5130 5140 5150 5160 5170 5180
-6.4-6.2
-6-5.8-5.6
Time [s]
-Depth
[m
]
Altitude increase
Same pressure
Altitude decrease
Pressure increase
EM 3000
bathymetry
Only hydrostatic pressure to depth conversions
Uses the output of Preproc in NavLab
EM 3000
bathymetry
Kalman filtered
depth
This is achievable in real-time
Uses the
output of the Estimator in
NavLab
EM 3000
bathymetry
Filtered by optimal smoothing
This is achievable in post-processing
Uses the output of
Smoothing in NavLab
Conclusion
• By combining inertial navigation with the UNESCO pressure to depth conversions, precise depth estimates can be made for underwater vehicles, even when operating in the surface wave pressure field
• Applications for improved depth estimates:
– Improve post-processing of digital terrain models, and seabed imaging
– Improve real-time depth control of underwater vehicles
– Improve bathymetric measurement inputs to terrain navigation
• References:– Fofonoff & Millard: ”Algorithms for computation of fundamental properties of seawater”,
UNESCO Technical Papers in marine science 44, 1983
– Hagen & Jalving: ”Converting Pressure to Depth for Underwater Vehicles”, FFI-Rapport, (TBP)
– Willumsen, Hagen, and Boge: ”Filtering depth measurements in underwater vehicles for improved seabed imaging”, Oceans Europe 2007, Aberdeen
– www.navlab.net
– www.ffi.no/hugin