Limits of static processing in a dynamic environment

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• Limits of static processing in a dynamic
  environment

Matt King, Newcastle University, UK
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Static Processing

• Good for these examples

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Static Processing

• But what about this?

Detrended
5 min positions
Whillans Ice Stream
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Background

• Common GPS processing approaches in glaciology
• Kinematic approach
• Antenna assumed moving constantly
• Coordinates at each and every measurement epoch
• Kinematic solutions often difficult due to long
  between-site differences
• Quasi-static approach
• Antenna assumed stationary for certain periods
  (0.5-24h)
• 24h common for solid earth
• lt4h common for glaciology
• But is this always valid?

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GPS Data Processing Approaches

• Quasi-static
• Kinematic
• Quasi-static assumption is that site motion
  during each session is averaged out

0.5-24h
White noise or random walk model
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Motion and Least Squares

• Functional model
• Should fully describe the relationship between
  parameters X and observation l with normally
  distributed residuals v
• F(X)l v
• Stochastic model
• Can attempt to mitigate or account for functional
  model deficiencies
• Unmodelled (i.e., systematic) errors will
  propagate according to the geometry of the
  solution
• Station-satellite geometry
• Estimated parameters (e.g., undifferenced
  Precise Point Positioning solutions vs
  double-differenced ambiguity fixed vs ambiguity
  float)

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Systematic Error Propagation

• Estimated parameters
• Station coordinates (X,Y,Z)
• AND real-valued phase ambiguity (N) parameters
• Clock errors differenced out (in double
  difference solutions)
• Once ambiguities estimated, statistical tests
  applied to fix to integers
• Fixing not always possible
• Site motion could induce incorrect ambiguity
  fixing

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Real vs ImaginaryExample on the Amery Ice Shelf
GAMIT 1hr quasi-static solutions
Track Kinematic solution
King et al., J Geodesy, 2003
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Whats happening?

• Presence of motion during static sections
• Violates least-squares principle of normal
  residuals
• Leads to biased parameter estimates
• Simulation
• How does a 1m/day signal and 1m tidal signal in
  1 hr static solutions propagate into the
  parameters?
• Real broadcast GPS orbits
• Precise Point Positioning approach simulated
• Site 70S

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Whats happening?
Ambiguity estimates mapped
Latitude
North (m)
Ambiguities fixed
East (m)
Height (m)
Ambiguities not fixed
Satellites East of site
Ambiguity (m)
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Horizontal Motion Only

• GAMIT 1h solutions over modified zero baseline

Period related to satellite pass time?
0N
90S
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Horizontal Motion Only

• Simulation grounded case
• How does a 1m/day signal 1 hr static solutions
  propagate into the parameters?
• Various flow directions (N, NE, E)
• 1hr solutions
• Various latitudes
• Site 70S

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Whats Happening?
Ambiguity estimates mapped
North (m)
Ambiguities fixed
Ambiguities not fixed
East (m)
Height (m)
King et al., J Glac., 2004
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Whillans Ice Stream

• Based on simulation would expect
• Agreement during stick
• Biases during slip
• But not in kinematic solutions

4hr quasi-static solutions
5min kinematic solutions
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Response to tidal forcing how much is real?

• Rutford Ice Stream (W Antarctica) experiences
  tidal modulation of its flow
• How much of this signal is real?

Rutford Ice Stream
Window considered here
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Response to tidal forcing how much is real?

• Two processing approaches
• Precise point positioning (GIPSY)
• Relative to a base station (Track), 30km away
• Tidal decomposition of de-trended along-flow
  velocity
• PPP very large response at high frequencies
  from little downstream vertical forcing
• e.g., M2 vertical tide 1.5m 2SK5 probably
  lt0.05m

GIPSY (PPP)
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Response to tidal forcing how much is real?

• Relative vs PPP
• LF (fortnightly) terms in good agreement
• Relative processing HF terms not sig.

GIPSY (PPP) and Track (relative)
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Response to tidal forcing how much is real?

• Relative vs PPP
• In relative processing, smaller diurnal and
  semi-diurnal vertical tide terms not significant
• Same data
• Why the differences?

GIPSY (PPP) and Track (relative)
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Response to tidal forcing how much is real?

• Relative processing is rover minus base (TOLL)
• How much signal is being differenced by the base?
• Gives tidal error spectrum for SEI1
• HF signal evident at base station on rock
• Common GPS satellite position biases?
• Care needed in interpreting HF velocity signals
  in glaciological GPS time series
• LF velocity signals are reliable in all solutions

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Solid Earth Issues

• Propagation of mis/un-modelled periodic signals
  (e.g., ocean tide loading displacements) in 24h
  solutions
• Well described by Penna Stewart (GRL, 2003) and
  Penna et al., JGR, 2007.
• Admittances in float ambiguity PPP solutions up
  to 120 in worst case (S2 north component into
  local up)
• Depends on coordinate component of mismodelled
  signal frequency geometry
• Output frequencies depend on input frequency
• Annual, semi-annual and fortnightly, amongst many
  others

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Periodic Signals
mm
Penna et al., JGR, 2007
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Effect in real data

• King et al, GRL, 2008

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Conclusions

• Biases may exist in positions on moving ice from
  GPS
• Up to 40-50 of unmodelled vertical signal
• Up to 10 of unmodelled horizontal signal
• May be offsets, periodic signals or both in east,
  north and height components
• Height biases of concern when validating Lidar
  missions
• Periodic signals may result in wrong
  interpretation as tidal modulation (or
  contaminate real tidal modulation)
• To measure bias-free ice motion using GPS
• Fix ambiguities to correct integers (not always
  possible)
• Use kinematic solution (may require
  non-commercial software)
• For 24h solutions
• Periodic signals propagate
• Other sub-daily signals (e.g., multipath) need
  further study