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Novel generalization of Volterra LMS algorithm to fractional order with application to system identification

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Abstract

In the present study, a novel generalization of Volterra least mean square (V-LMS) algorithm to fractional order is presented by exploiting the renowned strength of fractional adaptive signal processing. The fractional derivative term is introduced in weight adaptation mechanism of standard V-LMS to derive the recursive relations for modified V-LMS (MV-LMS) algorithm. The design scheme of MV-LMS algorithm is applied to parameter identification of Box–Jenkins system by taking different values of fractional orders, step-size variations and small to high signal-to-noise ratios. The proposed adaptive variables of MV-LMS are compared from true parameters of Box–Jenkins systems as well as with the results of the V-LMS for each case. The correctness and reliability of the given scheme MV-LMS are also validated from the results of statistical performance measures calculated on large dataset based on multiple independent runs.

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Authors and Affiliations

  1. Department of Electronic Engineering, International Islamic University, Islamabad, Pakistan

    Naveed Ishtiaq Chaudhary

  2. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock Campus, Attock, Pakistan

    Muhammad Asif Zahoor Raja & Naseer Ahmed

  3. Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad, Pakistan

    Muhammad Saeed Aslam

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  1. Naveed Ishtiaq Chaudhary
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  2. Muhammad Asif Zahoor Raja
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  3. Muhammad Saeed Aslam
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Correspondence to Naveed Ishtiaq Chaudhary.

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Chaudhary, N.I., Raja, M.A.Z., Aslam, M.S. et al. Novel generalization of Volterra LMS algorithm to fractional order with application to system identification. Neural Comput & Applic 29, 41–58 (2018). https://doi.org/10.1007/s00521-016-2548-5

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