Post on 02-Jan-2016
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SVY 207: Lecture 13Ambiguity Resolution
• Aim of this lecture:– To introduce methods of ambiguity resolution in detail
and to look at applications of these for RTK GPS.
• Overview– Relative positioning review
– Ambiguity resolution review
– Ambiguity resolution - Motivation
– Ambiguity resolution techniques
– Implications for GPS surveying
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Relative positioning - Review• Requirements - Precise engineering surveying
– 2 stations (baseline), or multiple stations (network)
– Carrier phases from 4 satellites, then double-difference
– Use broadcast orbits and clocks
– Assume values for one station and its clock time
– Estimate, using weighted least squares, station coordinates, and carrier phase ambiguities
» fix ambiguities to integer values and iterate.
– Achievable precision: < 1 cm
» over few 10 km using broadcast orbits
– Can be post-processed or real-time
• Process depends upon AMBIGUITY RESOLUTION
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Relative positioning - Review• Review
– Recall ‘one-way’ carrier phase model (in metres)
LAj A
j Aj c tA c t j Baj
– Use differencing techniques to solve for carrier phase bias
BABjk BAB
j BABk
(BAj BB
j BAk BB
k
BAj BB
j BAk BB
k
– Remember: BAj (N
j jA)
– Each bias BABjk has an integer ambiguity
– Double difference carrier phase model becomes:
LABjk AB
jk ABjk NAB
jk
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Relative positioning - Review
• Review cont’d
• Step 1: Least squares “float” solutionLAB
jk ABjk AB
jk NABjk
– estimate station coordinates, atmospheric delay, and carrier phase ambiguity NAB
jk
• Step 2: Ambiguity resolution– example: fix NAB
jk to nearest integer:
• Step 3: Least squares “fixed” solutionLAB
jk NABjk AB
jk ABjk
– left side is known: ambiguity-resolved carrier phase
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Ambiguity Resolution
• Motivation - – Resolution of initial phase ambiguity is key to sub-
centimetre position accuracy in GPS surveying
– Fewer parameters to estimate greater precision
– Time period to resolve ambiguities
– Prior to 1995 majority of GPS employed static techniques
– (Remondi 1985) ‘rapid-static’ approach
» Ambiguities could be resolved in minutes as opposed to hours
» Greater efficiency
» New applications - RTK, Machine guidance etc...
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Ambiguity ResolutionMotivation cont’d
100 experiments2.2 km baselinedual frequency phase data3D coordinate system: local North, East, Up7 satellites2 epochs of data with 5 seconds in between
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Ambiguity Resolution
• More detail– Specifically, ambiguity resolution OR “Initialisation” is
the problem of finding N, where :
N = The full cycles of double differenced N’s
– If can initialise then difference between two epochs, collected by same receiver to same satellite = change in topocentric range i.e.,
L’ (L N) – Initialisation not easy, requires
» Good station-satellite relative geometry
» Low level of observation errors
» Reliable algorithm
– Need to be able to validate if have initialised correctly
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Ambiguity Resolution
• Classical ‘static’ Techniques – Majority use TWO step approach
» First step to estimate station coordinates and real-valued ambiguities
» Second step to resolve initial ambiguities to integer values -methods include:
• Round real values to nearest integers
• Use estimated errors to evaluate if resolution to integer is feasible. Ambiguity only fixed if integer value is within an appropriate confidence interval e.g. +/- 3
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Ambiguity Resolution
• More modern techniques– Developed since the early 1990’s
» Ambiguity searching • Form all feasible combinations of integer ambiguity values
around the real-valued estimates. Test each set of ambiguities to find the most probabilistic values. This technique also known as ambiguity searching. This method also suitable for On-the-Fly (OTF) initialisation.
» Suitable for both static and kinematic applications
» For short baselines precision is comparable to traditional techniques
» All follow similar approach - c.f. lecture 12
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Ambiguity Resolution– An example - Ambiguity Function method (After Mader
[1992]) - (1)
» Determine approximate coordinates• Use pseudo-ranges to compute approximate coordinates for
unknown point
• Determine a search volume typically a cube around approximate postition
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Ambiguity Resolution– An example - Ambiguity Function method (2)
» Construct an ambiguity mapping function such that when the observed minus computed phase single difference is an integer for all observations, the function will be a maximum
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Ambiguity Resolution
– An example - Ambiguity Function method (3)
» For each integer point contained within cube ‘test points’ compute ambiguity function
» Correct ‘test position’ should emerge as a recognisable peak, with largest ambiguity function value
» Test if the position with the highest ambiguity function is correct. - Statistical testing
» If pass statistical testing then fix ambiguities if fail then re-try with next epoch of data
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Ambiguity Resolution
• Computational Aspects– Construction of optimal search space - e.g. 1m cube with
integer spacing at 1cm results in 1million test ambiguity combinations
– Fast robust algorithm
– Effective validation and rejection criteria
• Geometrical Aspects– Dependant on geometry of observation e.g. geometry of
satellite constellation w.r.t. base and rover station
– Quality of actual signals being observed
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Ambiguity Resolution
• Implications for GPS surveying– Increased efficiency resulting from reduced requirement
for long data observation sessions
» with no loss of precision over short baselines
– Kinematic surveying now true alternative to Total Station
– Addition of Radio to base and rover stations allows Real Time Kinemtic Surveying, but…
» Never with poor DOP values
» Always ensure ambiguities resolved
» Take checks during survey e.g. re-survey known points
» Follow sound survey practise at all times.
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Ambiguity Resolution
• References» GPS world ‘innovations’
• April 1993
• April 1994
• May 1995
• September 1998
• May 2000
» Teunissen P.J.G., Kleusberg A., ‘GPS for Geodesy’, 2nd ed, Springer
» Leick A., ‘Satellite Surveying’ 2nd ed, Wiley