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

Download From Pressure to Depth - Pressure to Depth Estimation of underwater vertical position Havbunnskartlegging og Inspeksjon ... - Thereafter, table look-up with linear interpolation

Post on 10-Mar-2018

214 views

Category:

Documents

1 download

Embed Size (px)

TRANSCRIPT

  • 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

Recommended

View more >