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Singular Value Decomposition applied on altimeter waveforms Page P. Thibaut, J.C.Poisson, A.Ollivier : CLS – Toulouse - France F.Boy, N.Picot : CNES – Toulouse - France
Context of the study ,[object Object],[object Object],[object Object],[object Object],[object Object],Igarss 2011 – Vancouver – Pierre THIBAUT
[object Object],[object Object],[object Object],Truncated Singular Value Decomposition for Noise Reduction Igarss 2011 – Vancouver – Pierre THIBAUT Taking the S matrix representing the noisy signal (Wfs matrix) J1 Ku band raw waveforms gate index Waveform index S= S + B Discarding small singular values of S (which mainly represent the additive noise) J1 Ku band filtered waveforms gate index Waveform index The rank-k matrix Ak represents a filtered signal noise signal + noise S=  1 VS 1 +….+  k VS k +…..  r VS r S= U  V* Computing the Singular Value Decomposition SVD filtering S (m,n) : WF matrix (m= 104; n=300) U (m,m), V*(n,n): unit matrices  (m,n) : diagonal matrix
[object Object],[object Object],[object Object],[object Object],Truncated Singular Value Decomposition for Noise Reduction Waveforms classification Estimation Process (retracking) SVD Igarss 2011 – Vancouver – Pierre THIBAUT Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 12 Class 23 Class 13 Class 24 Class 15 Class 0 Class 21 Class 35 Class 16 Class 99 Brown echos Peak echos Very noisy echos Linear echos Peak at the end of the echos Very large peak echos Brown + Peaky echos CS 32 Brown + strong decreasing plateau ?? Doubt Brown + leading edge perturbation Peaky + Noise Brown + Peak echos Leading at the end + noise Brown + Peaky + linear variation Brown + increasing leading edge
[object Object],Page Class 1 Class 2 Class 12 Class 15 Class 16 Class 3 Parameters used for the SVD noise reduction Igarss 2011 – Vancouver – Pierre THIBAUT
Parameters used for the SVD filtering ,[object Object],[object Object],Page 96 % threshold ,[object Object],[object Object],[object Object],Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
Parameters used for the SVD filtering Page 92 % threshold ,[object Object],[object Object],[object Object],[object Object],[object Object],Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
[object Object],[object Object],Parameters used for the SVD filtering Page 90 % threshold ,[object Object],[object Object],[object Object],Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
[object Object],[object Object],Parameters used for the SVD filtering Page 88 % threshold ,[object Object],[object Object],[object Object],Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
[object Object],[object Object],Parameters used for the SVD filtering Page 84 % threshold ,[object Object],[object Object],[object Object],Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
[object Object],[object Object],Parameters used for the SVD filtering Page 80 % threshold ,[object Object],[object Object],[object Object],Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
J1 Ku band raw waveforms J1 Ku band filtered waveforms gate index gate index Waveform index Waveform index Truncated Singular Value Decomposition Noise Reduction
Truncated Singular Value Decomposition for Noise Reduction Raw waveforms Filtered waveforms Igarss 2011 – Vancouver – Pierre THIBAUT
Impact on range (threshold of 84 %) SLA variation latitude MLE4 SVD+MLE4 SLA spectrum – Ku band 8 cm at 20 Hz 5 cm at 20 Hz MLE4 SVD+MLE4 Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
Impact on range (threshold of 90 %) Page - SLA Prod - SLA SVD SLA variation SLA spectrum – Ku band 8 cm at 20 Hz 7 cm at 20 Hz Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
[object Object],Impact on range (threshold of 90 %) Page Bias : SLA SVD = SLA Prod – 4 mm (except for small waves) Igarss 2011 – Vancouver – Pierre THIBAUT
Impact on SWH (threshold of 84%) SWH variation latitude SWH spectrum – Ku band MLE4 SVD+MLE4 MLE4 SVD+MLE4 54 cm at 20 Hz 12 cm at 20 Hz Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
[object Object],Page Bias : SWH SVD = SWH Prod - 3 cm (Ku) Two SWH populations appear in the SWH distribution SWH SVD SWH Prod Impact on SWH (threshold of 90 %) SWH spectrum – Ku band 54 cm at 20 Hz 40 cm at 20 Hz Igarss 2011 – Vancouver – Pierre THIBAUT
Page Small impact on residuals (smaller on the leading adge; higher on the trailing edge) SVD Impact on residuals (threshold of 90 %) Igarss 2011 – Vancouver – Pierre THIBAUT
Performances on noise level ,[object Object],Page ,[object Object],[object Object],Igarss 2011 – Vancouver – Pierre THIBAUT 20 Hz 1 Hz Ku C Ku C Range 7.07 cm (products = 8.02) 16.6 cm (products = 20.14) 2.64 cm (products = 2.81) 4.6 cm (products = 5.34) SWH 38.27 cm (products = 50.7) 100 cm (products = 120) 11 cm (products = 14) 25.35 cm (products = 32.73) Sigma0 0.307 dB (products = 0.376) 0.13 dB (products = 0.13) 0.14 dB (products = 0.16) 0.11 dB (products = 0.11)
Applications on a track that corsses the Alghulas current (South Africa) ,[object Object],Page SLA SWH Igarss 2011 – Vancouver – Pierre THIBAUT
Applications on a track that corsses the Alghulas current (South Africa) ,[object Object],Page SLA 20 Hz SLA SVD20 Hz (84 %) SLA 1 Hz Igarss 2011 – Vancouver – Pierre THIBAUT
Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],Igarss 2011 – Vancouver – Pierre THIBAUT
Thank you !
No impact of the SVD on mispointing angle

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SVD_PThibaut_VancouverIgarss2011.ppt

  • 1. Singular Value Decomposition applied on altimeter waveforms Page P. Thibaut, J.C.Poisson, A.Ollivier : CLS – Toulouse - France F.Boy, N.Picot : CNES – Toulouse - France
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12. J1 Ku band raw waveforms J1 Ku band filtered waveforms gate index gate index Waveform index Waveform index Truncated Singular Value Decomposition Noise Reduction
  • 13. Truncated Singular Value Decomposition for Noise Reduction Raw waveforms Filtered waveforms Igarss 2011 – Vancouver – Pierre THIBAUT
  • 14. Impact on range (threshold of 84 %) SLA variation latitude MLE4 SVD+MLE4 SLA spectrum – Ku band 8 cm at 20 Hz 5 cm at 20 Hz MLE4 SVD+MLE4 Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
  • 15. Impact on range (threshold of 90 %) Page - SLA Prod - SLA SVD SLA variation SLA spectrum – Ku band 8 cm at 20 Hz 7 cm at 20 Hz Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
  • 16.
  • 17. Impact on SWH (threshold of 84%) SWH variation latitude SWH spectrum – Ku band MLE4 SVD+MLE4 MLE4 SVD+MLE4 54 cm at 20 Hz 12 cm at 20 Hz Igarss 2011 – Vancouver – Pierre THIBAUT 700m 10km
  • 18.
  • 19. Page Small impact on residuals (smaller on the leading adge; higher on the trailing edge) SVD Impact on residuals (threshold of 90 %) Igarss 2011 – Vancouver – Pierre THIBAUT
  • 20.
  • 21.
  • 22.
  • 23.
  • 25. No impact of the SVD on mispointing angle