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A wavelet-based hybrid approach to remove the flicker noise and the white noise from GPS coordinate time series

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Abstract

Understanding the destructive interference of noise involved in GPS coordinate time series is crucial for improving the reliability of GPS applications. The majority of the noise consists of both flicker and white noise, both of which are well characterized by a stochastic process following a power-law noise model. To simplify the noise removal for GPS coordinate time series, the noise is usually regarded as pure white noise rather than a mixture of flicker noise and white noise. This work proposes a wavelet-based integrated solution that merges the strengths of Shannon entropy and wavelet thresholding to remove flicker and white noise at the same time. A GPS coordinate time series, spanning 128 days from the GPS monitoring station at the Jinduicheng Mine in Shanxi, China, was selected to test the proposed algorithm. The results demonstrate that both flicker noise and white noise are worthy of attention because they can lead to a seriously misunderstandings about error in a GPS coordinate time series. The utility of our proposed algorithm in removing flicker and white noise is shown to be more comprehensive than the use of wavelet thresholding alone. The findings further reveal that the advance elimination of flicker noise is beneficial for subsequently utilizing wavelet thresholding to delete the white noise in a GPS coordinate time series. This will greatly improve the reliability of GPS coordinate time series, allowing such data to be applied to a wide range of fields.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (40901214 and 41301588), the China Postdoctoral Science Foundation (2013M 531749, 2012T50691), the Hong Kong Scholars Program (XJ2012036), the Hong Kong Polytechnic University under Projects (G-YZ26), the Fundamental Research Funds for the Central Universities (2013-IV-040), and the self-determined and innovative research funds of WUT (20131049708009). Additionally, we are grateful to American Journal Experts for English editing of the manuscript. The helpful comments and suggestions from two anonymous reviewers are very gratefully acknowledged.

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Authors and Affiliations

  1. School of Resources and Environmental Engineering, Wuhan University of Technology, Wuhan, 430070, People’s Republic of China

    Hao Wu, Kui Li, Jianhua Zhang & Hua Li

  2. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hunghom, Kowloon, Hong Kong

    Hao Wu & Wenzhong Shi

  3. Department of Geography, University of California, Santa Barbara, Santa Barbara, CA, 93106-4060, USA

    Keith C. Clarke

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  1. Hao Wu
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  2. Kui Li
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  3. Wenzhong Shi
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  4. Keith C. Clarke
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  5. Jianhua Zhang
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  6. Hua Li
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Correspondence to Wenzhong Shi.

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Wu, H., Li, K., Shi, W. et al. A wavelet-based hybrid approach to remove the flicker noise and the white noise from GPS coordinate time series. GPS Solut 19, 511–523 (2015). https://doi.org/10.1007/s10291-014-0412-6

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  • DOI: https://doi.org/10.1007/s10291-014-0412-6

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