Global Gravitational Search Algorithm-Aided Kalman Filter Design for Volterra-Based Nonlinear System Identification
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Global Gravitational Search Algorithm-Aided Kalman Filter Design for Volterra-Based Nonlinear System Identification Lakshminarayana Janjanam1 Durbadal Mandal2
· Suman Kumar Saha1 · Rajib Kar2 ·
Received: 3 February 2020 / Revised: 24 October 2020 / Accepted: 4 November 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper proposes an efficient global gravitational search (GGS) algorithm-assisted Kalman filter (KF) design, called a GGS-KF technique, for accurate estimation of the Volterra-type nonlinear systems. KF is a well-known estimation technique for the dynamic states of the system. The best estimate is achieved if the system dynamics and noise statistical model parameters are available at the beginning. However, to estimate the real-time problems, these parameters are unstipulated or partly known. Due to this limitation, the performance of the KF degrades or sometimes diverges. In this work, two steps have been proposed for unknown system identification while overcoming the difficulty encountered in KF. The first step is to optimise the parameters of the KF using the GGS algorithm by considering a properly balanced fitness function. The second step is to estimate the unknown coefficients of the system by using the basic KF method with the optimally tuned KF parameters obtained from the first step. The proposed GGS-KF technique is tested on five different Volterra systems with various levels of noisy (10 dB, 15 dB and 20 dB) and noise-free input conditions. The simulation results confirm that the GGS-KF-based identification approach results in the most accurate estimations compared to the conventional KF and other reported techniques in terms of parameter estimation error, mean-squared error (MSE), fitness percentage (FIT%), mean-squared deviation (MSD), and cumulative density function (CDF). To validate the practical applicability of the proposed technique, two benchmark systems have also been identified based on the original data sets. Keywords Volterra model · System identification · Kalman filter · Global gravitational search algorithm · Benchmark system
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Lakshminarayana Janjanam [email protected]
Extended author information available on the last page of the article
Circuits, Systems, and Signal Processing
1 Introduction Adaptive filters are widely used in various applications, such as prediction, system identification, channel equalisation, and noise cancellation. One of the primary applications is in the system identification problem in various engineering domains [45]. In general, three types of systems can be found in nature, such as linear, nonlinear and combination of both, and accordingly, identification of system can be of three types. In linear system identification, finite impulse response (FIR) and infinite impulse response (IIR) filters are used for identification due to their simplicity in mathematical modelling. In recent days, meta-heuristic search techniques have been incorporated for parametric estimations. In [15, 16, 24, 37, 44], the
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