The Effect of Colored Noise on Automatic Offset Detection ......IGS 2018, Wuhan, China, 29/10 –...
Transcript of The Effect of Colored Noise on Automatic Offset Detection ......IGS 2018, Wuhan, China, 29/10 –...
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IGS 2018, Wuhan, China, 29/10 – 2/11 2018 1
The Effect of Colored Noise on Automatic Offset Detection in GNSS Time Series
M. S. Bos (1)
R. M. S. Fernandes (1)
M. Karegar (2)
(1) SEGAL (UBI/IDL), Covilhã, Portugal
(2) School of Geosciences, University of South Florida, USA
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IGS 2018, Wuhan, China, 29/10 – 2/11 2018
Part 1:
The limitations of automatic offset detection
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Problem statement
• Nowadays there are thousands of GNSS stations and most ofthe derived coordinate time series contain offsets.
• Gazeaux et al. (2013) have shown that undetected offsetsare now the largest contributors to the estimated trend error(±0.2 mm/yr manual detection, ±0.4 mm/yr automateddetection).
• We need an improved automatic offset detection algorithm.
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Still a lot of unknown offsets in the time series
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Gazeaux et al. (2013)
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• Simply test for each point of the time series if adding an offsetimproves the fit with the observations.
• To quantify the improvement we use the log-likelihood functionL:
constant C=covariance matrix r=residuals
• The higher the value of L (less negative), the more likely theoffset has occurred in reality
• Our strategy is to evaluate which location gives themost likely epoch for an offset.
How can we detect an offset?
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What are the possible outcomes of the offset detection algorithm?
• True Positive (TP): Algorithm has detected a realoffset.
• False Positive (FP): Algorithm has detected a falseoffset.
• False Negative (FN): Algorithm has NOT detected areal offset.
• “True Negative (TN)” is missing but can be computed from the otherthree
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Detection of Offsets in GPS Experiment (DOGEx)
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manualautomatic
better
Automatic offset detection algorithm have high % FP
Gazeaux et al. (2013)
Hector + visual offset detection
SimonWilliams(visual)
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Automatic Detection using Synthetic Data
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L=-170
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Automatic Detection using Synthetic Data
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L=-170L=-149
Estimating 1 offset gives a larger log-likelihood value (less negative).
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Automatic Detection using Synthetic Data
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L=-170L=-149L=-115
Estimating 50 offsets gives a better fit and therefore an even larger log-likelihood value.
When do we stop adding more offsets?
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Statement: Offsets does not occur everyday
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• We have assumed we have no prior knowledge about thelikelihood of having any number of offsets.
• However, we know from experience that the probability of
an offset occurs is low (only in exceptional situations) andthis needs to be taken into account in the log-likelihoodfunction.
• So, we need to have a criterium to stop the search!
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Bayesian Information Criterion
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Popular stopping criteria is the Bayesian Information Criterion(BIC).
Assume L is the likelihood, k the number of parameters in thenoise model and n the number of observations:
The higher the likelihood L (better the noise model), the lowerthe AIC/BIC value.
More offsets, higher penalty. This avoids to have too manyoffsets.
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Limitations of BIC
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• The Bayesian Information Criterion has been derived bytaking the limit to infinite long time series.
• BIC is probably widely used because it is easy implemented
and it gives a first good rough idea of the amount of offsets.
• Good alternative empirical penalty functions have beendeveloped.
• However, empirical penalty functions depend on the type ofdata being analyzed and the Bayesian interpretation can belost.
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BICC – Corrected BIC
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• For finite time series, which is the case of GNSS dailysolutions, we are using a corrected BIC (Bos et al., inpreparation):
Depends on noise A priori info about
size of the offsetA priori info about number of offsets
• This is BIC with more a priori information = BICc
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Part 2:
Does this theoretical hogwash actually
work?
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HECTOR – Time-Series Analysis(http://segal.ubi.pt/hector/)
Simultaneously Computation of:
• Secular Trend• Seasonal Signals
• Automatic Offset Detection• Exponential / Logarithmic
Post-relaxation• Power-law errors
• Spectrum Index
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IGS 2018, Wuhan, China, 29/10 – 2/11 2018
Detection of Offsets in GPS Experiment (DOGEx)
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manualautomatic
better
Gazeaux et al. (2013)
Hector + automatic detection
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IGS 2018, Wuhan, China, 29/10 – 2/11 2018
Part 3:
Is it Least Squares dead to estimate velocities?
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Do we really need to estimate offsets?
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• MIDAS (Blewitt et al., 2016), based on the median ofvelocities computed using a temporal sliding window, is agood solution when you only want to estimate one (and onlyone) velocity from your time-series.
• However, other signals exist on the time-series that can beof interest.
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MIDAS vs. Hector + Offset Detection
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• We used all time series of NGL (~3000 stations = ~9000time-series) and analyzed them with MIDAS and Hector.
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MIDAS vs Hector 9000 NGL time series
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velocity difference > 10 mm/yr
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velocity difference > 10 mm/yr
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Summary• Automatic offset detection is becoming a practical necessity.
• To obtain this result, we had to improve the Bayesian InformationCriterion to incorporate information about the probability of the size
and spacing between offsets.
• Using DOGEx as the benchmark: our algorithm is the best automated
one (comparison with the others in 2013)!
• HECTOR (BICc) is slower but we have demonstrated it can handle
thousands of stations (the comparison using the 9000 NGL time-series
took 2 weeks time).
• Agreement of MIDAS with Hector is good. For problematic stations
Hector seems to have the edge but it is difficult to quantify.
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IGS 2018, Wuhan, China, 29/10 – 2/11 2018
MAP OF:- Seismic/GNSS stations- Laboratories-- etc….
Diversity in data type and formats
http://www.epos-eu.org/ride/
Research InfrastructureLIst
• 244ResearchInfrastructures
• 138Institutions• 22countries• 2272GNSSreceivers• 4939seismicstations• 464TBSeismicdata• 1.095PBStorage
capacity• 828instrumentsin118
Laboratories
25
EPOS: European Plate Observing System
HECTOR (trend estimation and offset detection) will be used inEPOS-GNSS Operational Services
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IGS 2018, Wuhan, China, 29/10 – 2/11 2018
Thanks / Obrigado / ����
[email protected]@[email protected]
Nice/ProductiveQuestions/Remarks/Suggestions:
Nasty Ones:[email protected]