from pressure to depth - pressure to depth estimation of underwater vertical position...

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 depends on pressure and hence on depth

Gravitational acceleration g depends on the vehicles

position

pg

z

=

JordenJordenEarthVehicle

Atmosp

here

Ocea

n

z

Density of sea water

Depends on pressure

Depends on temperature

Depends on salinity

0

Density

0 >

0

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 formulaInternational Equation of Sate of sea water (1980)

(IES-80)

PSS-78

0

S , ,C

S T pC

=

IES-80 ( , , )S T p =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

=

0

IES0

1 11 g ( )

2 ( ( ), ( ), )

p

zz z dp

S p T p p

+ =

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

= =

= =

IES-80 IES-80

0 0

1 1V (35,0, ) ( ( ), ( ), )

g( , ) 9.8

p p

z p dp S p T p p dpp

= +

Standard ocean UNESCO equation:

- Integral: 4th order polynomial fit in p

- Gravitation:

0g( , ) g ( )(1 )pp p = +

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(

) [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 vehicles water referenced velocity and the sensors 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 vehicles presence in the incoming waves

Radiation potential caused by the vehicles response to the incoming waves

The motion may be counteracted by the vehicles 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 vehicles 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

HUGINs 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 vehicles 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

From Pressure to DepthEstimatio...Underwater pressure measurementHydrostatic pressureDensity of sea waterMeasuring the density of sea w...Hydrostatic pr