An efficient identification approach for highly complex non-linear systems using the evolutionary computing method based Kalman filter

Abstract

This paper proposes a new and efficient approach where a nature-inspired optimisation technique has abetted the Kalman filter (KF) for accurately solving the parametric estimation problem of highly complex non-linear systems. The KF is the best optimal state estimator in terms of normalised mean squared error (NMSE) for linear Gaussian state-space models. However, the use of mismatched noise statistics in KF might result in performance degradation. To address this issue, three steps are proposed in this work for the accurate estimation of the unknown non-linear system parameters by using the Volterra model. The first step is to reformulate the Volterra model into a measurement form. Secondly, the KF parameters are optimised by using an evolutionary algorithm with an efficient objective function. The third step is to estimate the coefficients of the unknown system by using the KF technique with the help of optimally tuned KF parameters achieved in the second step. In simulations, three distinct higher memory size second-order Volterra models, two non-linear benchmark systems and the primary path of active-noise control (ANC) system based on real data sets are identified by using the basic KF, genetic algorithm (GA) assisted KF (GA-KF), particle swarm optimisation (PSO) assisted KF (PSO-KF), firefly algorithm (FA) assisted KF (FA-KF) and ant lion optimisation (ALO) assisted KF (ALO-KF) techniques. The experimental results illustrate that the ALO-KF approach leads to better coefficient estimation compared to FA-KF, PSO-KF, GA-KF, and basic KF methods.