From Pressure to Depth Estimation of underwater vertical position

Transcription

1 From Pressure to Depth Estimation of underwater vertical position Havbunnskartlegging og Inspeksjon Februar 2008 Geilo ve Kent Hagen Avd Maritime Systemer FFI

2 Underwater pressure measurement Atmospheric pressure Sea surface Water level MSL Pressure field = Hydrostatic pressure field + Dynamic pressure field Pressure sensor Dynamic near field: Vehicle reference point Current-Hull effects Wave-Body interactions

3 Hydrostatic pressure Atmosphere cean p =ρ g Jorden Earth z Vehicle z 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

4 Density of sea water Density ρ 0 Depends on pressure ρ > ρ 0 Depends on temperature ρ < ρ 0 Salt Depends on salinity ρ > ρ 0

5 Measuring the density of sea water CTD (Conductivity, Temperature, Density) Pressure, p Temperature, T Conductivity, C Salinity is estimated by UNESC formula Practical Salinity Scale (1978) (PSS-78) 30 S C = S PSS-78, T, p C0 IES-80 density at atmospheric pressure Density is estimated by UNESC formula International Equation of Sate of sea water (1980) (IES-80) ρ = ρ ( S, T, p) IES-80 Temperature [degc] Salinity [psu]

6 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 S( p) = S ( C( p), T ( p), p) PSS-78 Integrate the hydrostatic equation from vehicle depth to the water level z g( φ, Λ, z) dz= 0 0 Latitude and longitude p 1 ρ( p) dp p 1+ γ g ( φ) z = z z dp 2 ρ ( S( p), T ( p), p) IES A crude model of gravitation CTD profile

7 UNESC Pressure to Depth Standard ocean: S=35 psu and T=0 C Specific volume Specific volume anomaly V = V ( S, T, p) = IES-80 ρ IES-80 1 ( S, T, p) δ = δ ( S, T, p) = V ( S, T, p) V (35,0, p) IES-80 IES-80 IES-80 p 1 1 z= V (35,0, p) dp+ δies-80 ( S( p), T ( p), p) dp g( φ, p) 9.8 IES p Standard ocean UNESC equation: - Integral: 4 th order polynomial fit in p - Gravitation: g( φ, p) = g ( φ)(1 + γ p) 0 p Geopotential height anomaly - Cumulative numerical integration of the profile - Thereafter, table look-up with linear interpolation International equation of gravity at surface Increasing linearly with pressure (depth)

8 Hydrostatic pressure to depth below MSL 1. Subtract atmospheric pressure at sea surface CTD profile & Geopotential height anomaly 2. Use the standard ocean UNESC 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 Slowly varying error Breiangen, December 2001

9 Surface wave induced pressure field Predicted depth error due to dynamic wave pressure field Waves attenuate with depth High attenuation: wind waves Low attenuation: swells z [m] The field becomes more regular with depth Significant wave height: 5 m, Peak time period: 8 s, Water depth: 80 m JNSWAP surface wave spectrum JNSWAP at 5 m depth JNSWAP at 10 m depth JNSWAP at 15 m depth x [m] Swell and wind waves: Period: s Frequency: Hz -0.6 S(ω) [m 2 s] No longer 1-1 between pressure and depth Fast varying error Frequency [Hz]

10 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 therwise: 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

11 Precise depth estimation using NavLab CTD Tide Atm Combine UNESC pressure to depth with inertial navigation Inertial navigation estimates the vehicle s short term motion with high precision filters wave induced pressure sensor noise Pressure ptional ptional Unesco Unesco Robust Robust noise noise parameters parameters IMU GPS DVL P P R R E E P P R R C C E E S S T T I I M M A A T T R R S S M M T T H H I I N N G G E E X X P P R R T T Smoothed Position Attitude Depth Pressure Cmp NavLab neclick Automatic processing controller

12 Test with HUGIN 1000 La Spezia, Italy: Low amplitude swell Shallow water Flat seafloor Inertial Measurement Unit: ixsea IMU 120 Doppler Velocity Log: RDI WHN 600 khz Pressure sensor: FSI Mirco CTD Multi beam echo sounder: EM 3000 HUGIN 1000 was operated from R/V Leonardo of the NAT Undersea Research Centre

13 NavLab post-processing: smoothed depth depthm error (bias and total) and KF-model (1 and 3 sigma) std = Bias oscillation period ~ 7.5 s Sea floor depth ~ 17 m [m] HUGIN s depth ~ 6 m Wave length of the swells causing the oscillations ~ 100 m -Depth [m] Time [s] Time [s] The long wave approximation is valid HUGIN follows the wave motion

14 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 Same pressure Pressure increase Altitude increase Altitude decrease -Depth [m] Time [s]

15 EM 3000 bathymetry nly hydrostatic pressure to depth conversions Uses the output of Preproc in NavLab

16 EM 3000 bathymetry Kalman filtered depth This is achievable in real-time Uses the output of the Estimator in NavLab

17 EM 3000 bathymetry Filtered by optimal smoothing This is achievable in post-processing Uses the output of Smoothing in NavLab

18 Conclusion By combining inertial navigation with the UNESC 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, UNESC 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, ceans Europe 2007, Aberdeen