Abstract
Ultra-rapid clock products provide the main parameters for real-time or near real-time precise point positioning services. However, it has been found that BeiDou ultra-rapid clock offsets do not meet the requirements for high-accuracy applications because of their low accuracy, especially regarding the prediction parts. This study proposes an improved model for BDS satellite ultra-rapid clock offset prediction based on BDS-2 and BDS-3 combined estimation. First, the preprocessing of the clock offset based on frequency data and a denoising method that employed a Tikhonov regularization algorithm was introduced to refine the observed series for predictive modeling. Second, given the coexistence of BDS-2 and BDS-3 satellites and the advantages of the BDS-3 onboard atomic clock, inter-satellite correlations between different satellites were used to adjust the stochastic function in estimating the coefficients for the prediction model. Third, to further improve the accuracy of the prediction model, the residuals of the clock offsets were analyzed by partial least squares regression, in which the main components related to the clock offsets were modeled by a back-propagation neural network. Six experimental schemes were introduced to verify the improved model. Experiments were divided into two groups to compare the preprocessing strategy and prediction model. The experimental results indicated: (1) both the BDS-2 and BDS-3 predicted clock offsets were mutually beneficial in the improved model; (2) because of the lower quality of the observed clock offset from BDS-3, preprocessing was used to improve the prediction accuracy by 1.0–15.2% for BDS-2, and reaching 23.2–31.9% for BDS-3; (3) the accuracy of the clock offsets were improved by 30.7–47.3% for BDS-2, and by 49.9–59.3% for BDS-3 within an 18-h period. The proposed improved model was found to have a significant effect on optimizing the ultra-rapid clock products of the International GNSS Monitoring and Assessment Service and GNSS analysis centers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chang G, Chen C, Yang Y et al (2018) Tikhonov regularization based modeling and sidereal filtering mitigation of GNSS multipath errors. Remote Sens 10(11):1801
Chen J, Hu X, Tang C et al (2016) Orbit determination and time synchronization for new-generation BeiDou satellites: Preliminary results. Sci Sinica 46(11):119502
CSNPC (2009) China Satellite Navigation Project Center. Compass/Beidou Navigation Satellite System Development. CSNPC, Beijing
Dai W, Huang D, Cai C (2014) Multipath mitigation via component analysis methods for gps dynamic deformation monitoring. GPS Solut 18(3):417–428
Davis J, Bhattarai S, Ziebart M (2012) Development of a Kalman filter based GPS satellite clock time-offset prediction algorithm. Eur Freq Time Forum, IEEE
Guo H, Yang Y (2009) Analyses of main error sources on time-domain frequency stability for atomic clocks of navigation satellites. Geo Inf Sci Wuhan Univ 34(2):218–221
Hauschild A, Montenbruck O, Steigenberger P (2013) Short-term analysis of GNSS clocks. GPS Solut 17(3):295–307
Hu C, Wang Q, Wang Z et al (2018) New-generation BeiDou (BDS-3) experimental satellite precise orbit determination with an improved cycle-slip detection and repair algorithm. Sensors 18(5):1402
Huang G, Zhang Q (2012) Real-time estimation of satellite clock offset using adaptively robust Kalman filter with classified adaptive factors. GPS Solut 16(4):531–539
Huang G, Zhang Q, Xu G (2014) Real-time clock offset prediction with an improved model. GPS Solut 18(1):95–104
Huang G, Cui B, Zhang Q et al (2018) An improved predicted model for BDS ultra-rapid satellite clock offsets. Remote Sens 10(1):60
Kosaka M (1987) Evaluation method of polynomial models’ prediction performance for random clock error. J Guid Control Dyn 10(6):523–527
Lau L (2017) Wavelet packets based denoising method for measurement domain repeat-time multipath filtering in GPS static high-precision positioning. GPS Solut 21(2):461–474
Mao Y, Wang Q, Hu C et al (2019) New clock offset prediction method for BeiDou satellites based on inter-satellite correlation. Acta Geod Geoph 54(1):35–54
Montenbruck O, Hugentobler U, Dach R et al (2012a) Apparent clock variations of the Block IIF-1 (SVN62) GPS satellite. GPS Solut 16(3):303–313
Montenbruck O, Steigenberger P, Schönemann E (2012b) Flight characterization of new generation GNSS satellite clocks. J Inst Navig 59(4):291–302
Qing Y, Lou Y, Dai X et al (2017) Benefits of satellite clock modeling in BDS and Galileo orbit determination. Adv Space Res 60(12):2550–2560
Senior K, Coleman M (2017) The next generation GPS time. J Inst Navig 64(4):411–426
Senior K, Ray J, Beard R (2008) Characterization of periodic variations in the GPS satellite clocks. GPS Solut 12(3):211–225
Si S, Su X (2011) Mathematical modeling. National Defence Industry Press, Changsha
Strandjord K, Axelrad P (2018) Improved prediction of GPS satellite clock sub-daily variations based on daily repeat. GPS Solut 22(3):58. https://doi.org/10.1007/s10291-018-0723-0
Su M, Zheng J, Yang Y et al (2018) A new multipath mitigation method based on adaptive thresholding wavelet denoising and double reference shift strategy. GPS Solut 22(2):40. https://doi.org/10.1007/s10291-018-0708-z
Tan S (2017) Innovative development and forecast of BeiDou system. Acta Geodaetica Cartogr Sin 46(10):1284–1289
Tian J, Huang G, Wang L et al (2017) A data quality control method for the Beidou-2 satellite clock bias. J Geodesy Geodyn 37(2):215–220
Tikhonov A, Arsenin V (1977) Solutions of ill-posed problems. Wiley, New York
Vannicola F, Beard R, White J (2010) GPS block IIF rubidium frequency standard life test. In: Proceedings of the 23rd international technical meeting of the satellite division of the ION GNSS + 2010, pp 812–819
Wang J, Wang J, Roberts C (2009) Reducing GPS carrier phase errors with EMD-wavelet for precise static positioning. Survey Review 41(312):152–161
Wang Y, Lv Z, Qu Y et al (2017) Improving prediction performance of GPS satellite clock bias based on wavelet neural network. GPS Solut 21(2):523–534
Wang Q, Hu C, Mao Y (2018) Correction method for the observed GNSS ultra-rapid orbit based on DOP values. Sensors 18(11):3900
Yang Y (2018) Performance analysis of BDS-3 demonstration system. ISGNSS, Hong Kong
Yang Y, Li J, Xu J et al (2011) Contribution of the Compass satellite navigation system to global PNT users. Chin Sci Bull 56(26):2813–2819
Yang Y, Li J, Wang A et al (2014) Preliminary assessment of the navigation and positioning performance of BeiDou regional navigation satellite system. Sci China Earth Sci 57(1):144–152
Zheng D, Zhong P, Ding X et al (2005) Filtering GPS time-series using a vondrak filter and cross-validation. J Geodesy 79(6–7):363–369
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No: 41874039), the Jiangsu Natural Science Foundation (Grant No. BK20181361) and the Jiangsu Dual Creative Teams Program Project Awarded in 2017 (2018ZZCX08). The author thanks the International GNSS Monitoring and Assessment Service (iGMAS) for the data and products.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hu, C., Wang, Q., Min, Y. et al. An improved model for BDS satellite ultra-rapid clock offset prediction based on BDS-2 and BDS-3 combined estimation. Acta Geod Geophys 54, 513–543 (2019). https://doi.org/10.1007/s40328-019-00270-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40328-019-00270-8