Volterra filter modelling of non-linear system using Artificial Electric Field algorithm assisted Kalman filter and its experimental evaluation

Abstract

The main objective of this paper is to improve the identification efficiency of non-linear systems using the Kalman filter (KF), which is optimised with the Artificial Electric Field (AEF) algorithm. The conventional KF suffers from the proper tuning of its parameters, which leads to a divergence problem. This issue has been solved to a great extent by the meta-heuristic AEF algorithm assisted Kalman filter (AEF-KF). This paper proposes three steps for the identification of the systems while solving the problem as mentioned above. Firstly, it converts the identification model to a measurement problem. Next, the AEF algorithm optimises the KF parameters by considering the fitness function with the KF equations. The third step is to identify the model using conventional KF algorithm with the optimised KF parameters. To evaluate the performance of the proposed method, parameter estimation error, mean squared error (MSE), fitness (FIT) percentage, statistical information and percentage improvement are considered as the performance metrics. To validate the performance of the proposed method, five distinct non-linear models are identified with the Volterra model using KF and the AEF-KF techniques under various noisy input conditions. Besides, the practical applicability of the proposed approach is also tested on two non-linear benchmark systems using experimental data sets. The obtained simulation results confirm the efficacy and robustness of the proposed identification method in terms of the convergence speed, computational time and various performance metrics as compared to KF, Kalman smoother (KS) which is optimised using different state-of-the-art evolutionary algorithms and also other existing recently reported similar types of stochastic algorithms based approaches.