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


There is no abstract available for this article.


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


Appendixes A–D.


[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       京公网安备11010102003388号