Prediction of Time Series Empowered with a Novel SREKRLS Algorithm

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 ort...

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Vydané v:	Computers, materials & continua Ročník 67; číslo 2; s. 1413 - 1427
Hlavní autori:	Shoaib, Bilal, Javed, Yasir, Adnan Khan, Muhammad, Ahmad, Fahad, Majeed, Rizwan, Saqib Nawaz, Muhammad, Adeel Ashraf, Muhammad, Iqbal, Abid, Idrees, Muhammad
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Henderson Tech Science Press 2021
Predmet:	Algorithms Integrated circuits Kernels Learning curves Least squares Mathematical analysis Matrices (mathematics) Noise levels Symmetry Systolic arrays Time series Very large scale integration
ISSN:	1546-2226, 1546-2218, 1546-2226
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Abstract	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.
AbstractList	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.
Author	Javed, Yasir Majeed, Rizwan Adnan Khan, Muhammad Ahmad, Fahad Saqib Nawaz, Muhammad Shoaib, Bilal Iqbal, Abid Adeel Ashraf, Muhammad Idrees, Muhammad
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SubjectTerms	Algorithms Integrated circuits Kernels Learning curves Least squares Mathematical analysis Matrices (mathematics) Noise levels Symmetry Systolic arrays Time series Very large scale integration
Title	Prediction of Time Series Empowered with a Novel SREKRLS Algorithm
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