GNSS Ocean Reflected Signals Per Heg DTU Space Technical - - PowerPoint PPT Presentation

Per Høeg DTU Space Technical University of Denmark

GNSS Ocean Reflected Signals

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Content

• Experimental setup
• Instrument
• Measurements and observations
• Spectral characteristics, analysis and retrieval method

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Experiment

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Altitude: > 3000 meters Year: 2004

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GNSS Ocean Reflected Signals

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• GNSS ocean reflected signals describe the height

and the roughness of the ocean

• The characteristics of the reflected signal depend
• n the scattering properties of the sea surface and

the footprint of the reflection zone

• The footprint size and shape in turn depends on

the signal incidence angle and the relative velocities of transmitter and receiver

• Scattering properties of the sea surface (the

roughness parameter) relates to the ocean wave characteristics

Motivation

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• Studies of Sea Surface Height Processes
• GEROS on the ISS Columbus Module

Ocean Sea Surface Height Processes

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Oceanic observations carry signals

• f a wide range of related processes.

The observed fingerprints of these processes have temporal time scales from 1 hour to thousands of years and spatial scales from ten to tens thousands of kilometres. The figure illustrates the spatial and temporal scales for these processes and indicates phenomena, which can be investigated with GEROS- ISS data complementary to and distinct from the planned NASA SWOT mission and ESA and NASA radar altimetry missions (Revised from Zuffada et al., 2005).

Power Spectrum of Sea Surface Heights (SSH)

7 The black SSH power spectrum is for reference based on Jason altimeter observations (pass 132). The red curve gives the error spectrum of the NASA SWOT mission. The solid black line is the expected spectral continuation. The intersection of the spectral signal with the noise floor at 10km determines the resolving capabilities for the SWOT instrument (JPL, NASA, 2009).

500 km

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Experiment

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• 10
• 5

5 10 15 20 25 30 Azimuth-Elevation (2004-10-4 19:34:0 p:\p-roft\m-functions\almanacs\yuma267.txt) 1 4 5 6 7 8 10 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 31 Azimuth relative North (deg) Elevation (deg)

Azimuth (deg) Time of day (hours)

5 10 15 20

• 10
• 5

5 10 15 20 25 30 Elevation (2004-10-5 0:0:0 p:\p-roft\m-functions\almanacs\yuma267.txt) 1 4 5 6 7 8 10 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 31 Time UTC (hours) Elevation (deg)

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Experiment

Antenna Front-End Receiver Command and Data Storage

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200 400 600 800 1000 1200 5 10 15 20 25 30 Tangent height (km) Atmospheric Doppler (Hz)

Closed Loop tracking: Carrier Phase is phase locked to the received signal. Open Loop tracking (raw mode): Carrier Phase is measured relative on-board Doppler model

Instrument

20 40 60 80 100 120 6.45 6.5 6.55 6.6 6.65 6.7 6.75 6.8 6.85 6.9

Time [s] Doppler [km/s]

CODE NCO / GEN CARRIER NCO ON-BOARD DOPPLER MODEL LOOP FILTER arctan Discrim. LOOP FILTER Dot Prod. Discrim.



ms 10 , 1

E/P/L E/P/L Punctual I/Q OL: 1 kHz Meas. Packaging Code Phase Carrier NCO Code Phase Carrier Phase CCSDS Data CL OL Front End

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Instrument

(Navigation Data De-modulation)

24.74 24.76 24.78 24.8 24.82 24.84 24.86 24.88 24.9 24.92 0.1 0.2 0.3 Time [s] Amplitude

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50 1 2 3 4 x 10

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Frequency [Hz] Amplitude

• 200

200

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• 100

100 200 I Q

20 ms 20 ms

24.76 24.78 24.8 24.82 24.84 24.86 24.88 24.9 24.92 0.1 0.2

Amplitude [-]

24.76 24.78 24.8 24.82 24.84 24.86 24.88 24.9 24.92

• 1
• 0.5

0.5 1

Time [s] Phase [ l ]

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Measurements

(De-trended Power Spectra)

Background signal frequency drift are removed using a least squares fit parabola to the main phase.

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Measurements

(Power Spectra at Different Elevation Angles)

Power spectra as function of frequency difference (f-f0) from the main signal peak f0. Clock related spectral slope of f-2. No clock correction has been applied.

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Measurements

(Trend Analysis)

Variation of the slope in the frequency region 1 - 5 Hz of the power spectrum, as function of elevation angle. The red straight line is the linear least squares fit to the curve in the elevation angle interval, 0-5 degrees.

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Spectral Analysis

Direct signal Ocean reflected signal h



h/sin h/sincos2  

Path length difference:

h / sincos2

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Spectral Analysis

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2 4 6 8 10 12 14 2 4 6 8 10 12 Day of October 2004 Wind speed (m/s) 2 4 6 8 10 12 14 24 25 26 27 28 29 Day of October 2004 Temperature (deg C) 2 4 6 8 10 12 14 1010 1012 1014 1016 Day of October 2004 Pressure (mbar)

Meteorological Conditions

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The State Model

Tracking the position of a reflection point can be viewed as estimation of the state of the dynamical system based on sets of measurements. We assume that the state (parameterized by its position, height and velocity) is a first-

• rder Markov process of the form (time-varying stochastic process):

is the reflection point state vector at the time k is the unknown system noise input Here, the state vector consists of the 3-dimensional position and velocity vectors The discrete time matrices:

1 1 k k k k k

F G W   



 

K



k

W

2

2

M M M k k M M M

t I t I I F and G O I t I                     

Particle Filtering Method

𝜄𝑙 =

𝑞𝑙 𝑤𝑙

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The Observation Model

The system has M received signals and a single GNSS transmitter. The time-variant mth received signal in the kth snapshot is given as: The signal component: is the complex zero-mean Gaussian noise process with spectral height denotes the complex amplitude of the wave propagation path carrier frequency, the transmitted signal the delay of the signal received from the mth received signal at time t in the kth

• bservation window

, , , ,

( ) ( ) ( ) ( )

m k m k m k m k

y t x t z t t    

,

( 2 ( )) , , ,

( ) ( ) ( ( ))

c m k

j f t m k m k m k

x t t u t t e

 

   

, ( ) m k t



2 



, ( ) m k t



c

f

, ( ) m k t

 ( ) u t

Particle Filtering Method

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The Particle Filtering Algorithm

A sequential Bayesian estimation method is used to estimate recursively the conditional probability density function and denote respectively, a sequence of observations and state vectors, from the 1st to the kth measurement cycle The proposed particle filter technique makes use of a fixed number of particles, where each particle is associated with a state vector Steps for each new observation: 1) Predict the states of particles and calculate the weights 2) Re-sampling 3) Estimate the power density function

1: 1: y k k

p y 

i k i i k k i k i k

p v                  

Particle Filtering Method

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Horizontal probability density functions at the reflection location (in meters)

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100

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100

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200 100

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100

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Sea Surface Reflection Zone

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Conclusions

• The spectral variances are driven by the atmospheric physical conditions, sea

surface roughness and wind dynamics.

• Spectral noise characteristics follows a power distribution related to the clock

noise and the receiver amplitude estimation.

• Estimated spectral variances link directly to the turbulence structure function

constant of the measured atmosphere region.

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Thank you !