A Novel Method for Satellite Clock Bias Prediction Based on Phase Space Reconstruction and Gaussian Process
LEI Yu1,2,3,CAI Hong-bing1,2,ZHAO Dan-ning1,3
1.National Time Service Center, Chinese Academy of Sciences, Xi’an, Shaanxi 710600, China
2.Key Laboratory of Time and Frequency Standards, Chinese Academy of Sciences, Xi’an, Shaanxi 710600, China
3.University of Chinese Academy of Sciences, Beijing 100049, China
Abstract:A novel method for satellite clock bias prediction incorporating phase space reconstruction and Gaussian process (GP) is proposed in this paper. Firstly a polynomial model is employed to fit the clock bias time series in terms of its characteristics, and then the noise of the polynomial fitting residual is reduced by the empirical mode decomposition (EMD) algorithm. Secondly, phase space reconstruction is performed for the de-noised residual series according to its chaotic characteristics. Finally, Gaussian process is established so as to forecast the residual on the basis of reconstructed phase space, and then the predicted clock bias can be yielded by adding the trend term to the forecasted residual. The IGS ultra-rapid observed (IGU-O) product is used to set up a clock model, and short-term prediction experiments are carried out. The results have indicated that the proposed method outperforms the IGS ultra-rapid predicted (IGU-P) solutions at least on a daily basis.
雷雨,蔡宏兵,赵丹宁. 基于相空间重构与高斯过程的卫星钟差预报[J]. 计量学报, 2016, 37(3): 318-322.
LEI Yu1,2,3,CAI Hong-bing 1,2,ZHAO Dan-ning 1,3. A Novel Method for Satellite Clock Bias Prediction Based on Phase Space Reconstruction and Gaussian Process. Acta Metrologica Sinica, 2016, 37(3): 318-322.
[1]王宇谱,吕志平,陈正生,等.卫星钟差预报的小波神经网络算法研究[J].测绘学报,2013,42(3):323-330.
[2]郭承军,滕云龙.基于小波分析和神经网络的卫星钟差预报性能分析[J].天文学报,2010,51(4):395-403.
[3]Xu B, Wang Y, Yang X H. A Hybrid Model for Navigation Satellite Clock Error Prediction[J]. Computational Intelligence Studies in Computational Intelligence,2013, 465: 307-316.
[4]Takens F. Detecting Strange Attractors in Turbulence[J]. Lecture Notes in Mathematics, 1981, 898: 366-381.
[5]Rasmussen C E, Williams C K I. Gaussian Processes for Machine Learning[M]. Cambridge: MIT Press, 2006.
[6]Huang N E, Shen Z, Long S R, et al. The Empirical Mode Decomposition and Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis[J]. The Royal Society, 1998, 454: 903-995.
[7]甘雨,隋立芬.基于经验模分解的陀螺信号消噪[J].测绘学报,2011,40(6):745-750.
[8]Kim H S, Eykholt R, Salas J D. Nonlinear Dynamics, Delay Times, and Embedding Windows[J]. Physics D: Nonlinear Phenomenon, 1999, 127(1): 48-60.
[9]Rosenstein M T, Collins J J, C J De Luca. A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets[J]. Physics D: Nonlinear Phenomenon, 1993, 121(5): 117-134.