Prediction of time series empowered with a novel SREKRLS algorithm

Bilal Shoaib, Yasir Javed, Muhammad Adnan Khan, Fahad Ahmad, M. Majeed, Muhammad Saqib Nawaz, Muhammad Adeel Ashraf, Abid Iqbal, Muhammad Idrees

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For the unforced dynamical non-linear statespace model, a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article. The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems. With the help of an ortho-normal triangularization method, which relies on numerically stable givens rotation, matrix inversion causes a computational burden, is reduced. Matrix computation possesses many excellent numerical properties such as singularity, symmetry, skew symmetry, and triangularity is achieved by using this algorithm. The proposed method is validated for the prediction of stationary and non-stationary MackeyGlass Time Series, along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness. By the learning curves regarding mean square error (MSE) are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS. This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays, which is efficient in developing very-large-scale integration (VLSI) applications with non-linear input data. Multiple experiments are carried out to validate the reliability, effectiveness, and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares (EKRLS) algorithm.
Original languageEnglish
Pages (from-to)1413-1427
Number of pages15
JournalComputers, Materials and Continua
Issue number2
Publication statusPublished - 5 Feb 2021


  • kernel methods
  • square root adaptive filtering
  • givens rotation
  • Mackey glass time series prediction
  • recursive least squares
  • kernel recursive least squares
  • extended kernel recursive least squares
  • square root extended kernel recursive least squares algorithm

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