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Optimal Volterra-based nonlinear system identification using arithmetic optimization algorithm assisted with Kalman filter

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Abstract

This paper presents the handling of nonlinear system identification problem based on Volterra-type nonlinear systems. An efficient arithmetic optimization algorithm (AOA) along with the Kalman filter (KF) is being used for the estimation/identification purpose. The KF is proved to be a good state estimator in estimation theory. It is used to estimate the unknown variables with some given measurements observed over time. However, the performance of KF technique degrades while dealing with real-time state estimation problems. To overcome the problem encountered in KF technique, two steps are followed for nonlinear system identification. The first one involves evaluation of the KF parameters using the AOA algorithm by taking a considerable fitness function. The second step is to estimate the parameters of Volterra model using the KF method utilizing the optimal KF parameters attained in first step. In order to prove the efficiency of the proposed KF assisted AOA algorithm is further tested on various benchmark unknown Volterra models. Simulated results are reported in terms of mean square error (MSE), mean square deviation (MSD), Volterra coefficients estimation error, and fitness percentage. The results are compared with other similar algorithms such as sine cosine algorithm (SCA) assisted KF (SCA-KF), cuckoo search algorithm (CSA) assisted KF (CSA-KF), particle swarm optimization (PSO) assisted KF (PSO-KF) and genetic algorithm (GA) assisted KF (GA-KF). The reported results reveal that AOA-KF algorithm is the right choice for nonlinear system identification problem compared to the SCA-KF, CSA-KF, PSO-KF and GA-KF.

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    Authors and Affiliations

    1. Uttarakhand Technical University, Dehradun, Uttrakhand, India

      Sandeep Singh

    2. Maharaja Surajmal Institute of Technology, New Delhi, India

      Sandeep Singh

    3. G.B Pant University of Agriculture and Technology, Pantnagar, Uttrakhand, India

      Alaknanda Ashok

    4. Netaji Subhas University of Technology, New Delhi, India

      Tarun Kumar Rawat

    Author notes

    1. Alaknanda Ashok and Tarun Kumar Rawat have contributed equally to this work.

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      Singh, S., Ashok, A. & Rawat, T.K. Optimal Volterra-based nonlinear system identification using arithmetic optimization algorithm assisted with Kalman filter. Evolving Systems 14, 117–139 (2023). https://doi.org/10.1007/s12530-022-09439-z

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