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An Outlier Recognition Method Based on Improved CUSUM for GPS Time Series

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Geo-informatics in Sustainable Ecosystem and Society (GSES 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 980))

Abstract

In order to effectively identify the abnormal data in the GPS (Global Positioning System) monitoring data, the method of the CUSUM (Cumulative Sum) median control chart was introduced. Aiming at the problem that the traditional mean control graph cannot accurately identify the outliers in the actual sample data, a GPS anomaly data recognition algorithm based on the CUSUM median control chart was proposed, and the basic principles and calculation steps were given. On the basis, considering the influence of non-normal data in the calculation of the algorithm, a method of converting to normal data was given. Finally, the feasibility and effectiveness of the proposed method were verified by simulation data. The experimental results show that the proposed algorithm has a good effect. Compared with the traditional CUSUM control chart, the abnormal value recognition ability was improved, and the false alarm rate was also effectively controlled.

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References

  1. Jiang, W., Liu, J.: Analysis of long-term deformation of reservoir using continuous GPS observations. Acta Geodaetica Cartogr. Sin. 41, 682–689 (2012). (in Chinese)

    Google Scholar 

  2. Xu, S., Zhang, H., Yang, Z., Wang, Z.: GPS Measuring principle and application. Wuhan University Press, Wuhan (2001). (in Chinese)

    Google Scholar 

  3. Jiang, W., Liu, H., Liu, W., He, Y.: CORS development for Xilongchi dam deformation monitoring. Geomatics Inf. Sci. Wuhan Univ. 37, 949–952 (2012). (in Chinese)

    Google Scholar 

  4. Kuang, C., Dai, W.: Measurement of wind-induced vibration of tall buildings using GPS and wavelet application. Geomatics Inf. Sci. Wuhan Univ. 35, 1024–1028 (2010). (in Chinese)

    Google Scholar 

  5. Kuang, C., Yi, Z., Dai, W., Zeng, F.: Measuring wind-induced response characteristics of tall building based on GPS PPP method. J. Central S. Univ. 44, 4588–4596 (2013). (in Chinese)

    Google Scholar 

  6. Yi, T., Guo, Q., Li, H., Lin, Y.: Multi-step identification algorithm based on relational negative selection for GPS abnormal monitoring data. J. Vib. Eng. 28, 1–8 (2015). (in Chinese)

    Google Scholar 

  7. Miao, C., Wang, M., Tian, H., Feng, Z.: Damage alarming of long-span suspension bridge based on GPS-RTK monitoring. J. Central S. Univ. 22, 2800–2808 (2015). (in Chinese)

    Article  Google Scholar 

  8. Tie, J.: Statistical Methods of Quality Management. China Machine Press, Beijing (2006)

    Google Scholar 

  9. Yi, T., Guo, Q., Li, H.: The research on detection methods of GPS abnormal monitoring data based on control chart. Eng. Mech. 30, 133–141 (2013). (in Chinese)

    Google Scholar 

  10. Shapiro, S.S., Wilk, M.B.: An analysis of variance test for normality (complete samples). Biometrika 52, 591–611 (1965)

    Article  MathSciNet  Google Scholar 

  11. Silverman, B.W.: Using kernel density estimates to investigate multimodality. J. Roy. Stat. Soc. 43, 97–99 (1981)

    MathSciNet  Google Scholar 

  12. Emanuel, P.: On estimation of a probability density function and mode. Ann. Math. Stat. 33, 1065–1076 (1962)

    Article  MathSciNet  Google Scholar 

  13. Quesenberry, C.P.: On properties of binomial Q charts for attributes. J. Qual. Technol. 27, 204–213 (1993)

    Article  Google Scholar 

  14. Mertikas, S.P., Damianidis, K.I.: Monitoring the quality of GPS station coordinates in real time. GPS Solutions 11, 119–128 (2007)

    Article  Google Scholar 

  15. Tran, K.P., Castagliola, P., Celano, G.: Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts. Statistical Papers, pp. 1–27 (2018)

    Google Scholar 

  16. Hu, X., Zhou, X., Huang, W., Jiang, G.: Design of the CUSUM Median Chart. J. Appl. Stat. Manage 37, 469–477 (2018). (in Chinese)

    Google Scholar 

  17. Siegmund, D.: Error probabilities and average sample number of the sequential probability ratio test. J. Roy. Stat. Soc. 37, 394–401 (1975)

    MathSciNet  MATH  Google Scholar 

  18. Moustakides, G.V.: Optimal stopping times for detecting changes in distributions. Ann. Stat. 14, 1379–1387 (1986)

    Article  MathSciNet  Google Scholar 

  19. Xie, Z.: MATLAB statistical analysis and application: 40 case studies. Beihang University Press, Beijing (2010). (in Chinese)

    Google Scholar 

Download references

Acknowledgments

The project was financially supported by the National Natural Science Foundation of China (no. 41404004).

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Correspondence to Chao Liu .

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Wu, H., Li, M., Liu, C. (2019). An Outlier Recognition Method Based on Improved CUSUM for GPS Time Series. In: Xie, Y., Zhang, A., Liu, H., Feng, L. (eds) Geo-informatics in Sustainable Ecosystem and Society. GSES 2018. Communications in Computer and Information Science, vol 980. Springer, Singapore. https://doi.org/10.1007/978-981-13-7025-0_42

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  • DOI: https://doi.org/10.1007/978-981-13-7025-0_42

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-7024-3

  • Online ISBN: 978-981-13-7025-0

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