logo

SCIENCE CHINA Information Sciences, Volume 61, Issue 12: 129206(2018) https://doi.org/10.1007/s11432-018-9634-7

Bayesian random Fourier filters for Gaussian noises

More info
  • ReceivedJul 6, 2018
  • AcceptedSep 30, 2018
  • PublishedNov 22, 2018

Abstract

There is no abstract available for this article.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61671389, 61672436).


Supplement

Appendixes A–D.


References

[1] Kivinen J, Smola A J, Williamson R C. Online Learning with Kernels. IEEE Trans Signal Process, 2004, 52: 2165-2176 CrossRef Google Scholar

[2] Ma W, Duan J, Man W. Robust kernel adaptive filters based on mean p-power error for noisy chaotic time series prediction. Eng Appl Artificial Intelligence, 2017, 58: 101-110 CrossRef Google Scholar

[3] Deng C W, Huang G B, Xu J. Extreme learning machines: new trends and applications. Sci China Inf Sci, 2015, 58: 1-16 CrossRef Google Scholar

[4] Rasmussen C E, Williams C K I. Gaussian Processes for Machine Learning. Cambridge, MA: MIT Press, 2006. Google Scholar

[5] Bouboulis P, Pougkakiotis S, Theodoridis S. Efficient KLMS and KRLS algorithms: a random Fourier feature perspective. In: Proceedings of IEEE Workshop on Statistical Signal Processing, 2016. Google Scholar

[6] Särkkä S. Bayesian Filtering and Smoothing. Cambridge: Cambridge University Press, 2013. Google Scholar

[7] Zeng N, Wang Z, Zhang H. Inferring nonlinear lateral flow immunoassay state-space models via an unscented Kalman filter. Sci China Inf Sci, 2016, 59: 112204 CrossRef Google Scholar

[8] Zhang Y, Huang Y. Gaussian approximate filter for stochastic dynamic systems with randomly delayed measurements and colored measurement noises. Sci China Inf Sci, 2016, 59: 92207 CrossRef Google Scholar

[9] Zhao C, Guo L. PID controller design for second order nonlinear uncertain systems. Sci China Inf Sci, 2017, 60: 022201 CrossRef Google Scholar

  •   

    Algorithm 1 Online Bayesian random Fourier filter

    Initiation: $\delta^2_n$, $\delta^2_D$, $D$, ${\boldsymbol~P}_1$, and ${\hat{\boldsymbol\theta}}_1.$

    while $\{{\boldsymbol~x}_k,~y_k\}$ $(k>1)$ available do

    (1) Transform the input data by (2);

    (2) Calculate ${{\boldsymbol~P}_{k|k-1}}$ and ${\boldsymbol~G}_k$ by (7) and (14);

    (3) Update ${\boldsymbol~P}_k$ and ${\hat~{~\boldsymbol\theta}}_k$ and by (12) and (13);

    end whlile

Copyright 2020 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1