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Acta Geodaetica et Geophysica

, Volume 54, Issue 4, pp 483–497 | Cite as

A heuristic singular spectrum analysis method for suspended sediment concentration time series contaminated with multiplicative noise

  • Fengwei Wang
  • Yunzhong ShenEmail author
  • Qiujie Chen
  • Weiwei Li
Original Study
  • 39 Downloads

Abstract

This paper proposes a heuristic singular spectrum analysis (SSA) approach to extract signals from suspended sediment concentration (SSC) time series contaminated by multiplicative noise, in which multiplicative noise is converted to approximate additive noise by multiplying with the signal estimate of the time series. Therefore both the signal and noise components need to be recursively estimated. Since the converted additive noise is heterogeneous, a weight factor is introduced according to the variance of additive noise. The proposed heuristic SSA approach is employed to process the SSC series in San Francisco Bay compared to the traditional SSA and homomorphic log-transformation SSA approach. By using our heuristic SSA approach, the first 10 principal components derived can capture 96.49% of the total variance with the fitting error of 6.17 mg/L, better than those derived by traditional SSA approach and homomorphic log-transformation SSA approach that catch 88.97% and 87.35% of the total variance with the fitting errors of 14.47 mg/L and 15.03 mg/L, respectively. Therefore, our heuristic SSA approach can extract more signals than traditional SSA and homomorphic log-transformation SSA approach. Furthermore, the results from the simulation cases show that all the mean root mean squared errors and mean absolute errors derived by our heuristic SSA are smaller than the traditional and homomorphic log-transformation SSA, which indicate that the extracted signals by heuristic SSA approach are much closer to the real signals than those by the other two approaches. Therefore it can be conclude that our heuristic SSA approach performs better in extracting signals from SSC time series contaminated with multiplicative noise.

Keywords

Singular spectrum analysis Suspended sediment concentration Time series Multiplicative noise Missing data 

Notes

Acknowledgements

This work is mainly sponsored by the National Key R&D Program of China (2017YFA0603103) and the Natural Science Foundation of China (Projects: 41731069 and 41274035). We are grateful to the anonymous reviewers for their constructive comments.

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Copyright information

© Akadémiai Kiadó 2019

Authors and Affiliations

  • Fengwei Wang
    • 1
  • Yunzhong Shen
    • 1
    Email author
  • Qiujie Chen
    • 1
  • Weiwei Li
    • 2
  1. 1.College of Surveying and Geo-informaticsTongji UniversityShanghaiPeople’s Republic of China
  2. 2.College of GeomaticsShandong University of Science and TechnologyQingdaoPeople’s Republic of China

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