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