Novel hybrid robust fractional interpolatory cubature Kalman filters

In this paper, a novel class of fractional interpolatory cubature Kalman filters (FICKFs) based on interpolatory cubature rule (ICR) is presented, which can achieve a custom degree of accuracy under the Bayesian filtering framework. The fractional cubature Kalman filter (FCKF) and the fractional unscented Kalman filter (FUKF) can be considered as particular types of the proposed FICKFs algorithm. In addition, a robust FICKF and also a hybrid robust FICKF are developed to estimate the states of a fractional-order nonlinear system, in the presence of uncertainty. This robust FICKF is formulated by combining a traditional FICKF and an uncertainty estimator. The hybrid robust FICKF is constructed by using a switching mechanism between a FICKF and a robust FICKF, such that it can provide accurate estimation in the presence or absence of uncertainty. Moreover, the algorithm performance is analyzed and evaluated by the state estimation of Malaria fractional nonlinear model with temporary immunity. Simulation results demonstrate that the FICKFs with suitable free parameters is better than the existing filters with the same degree. In especial case for uncertain systems, hybrid robust FICKF improves the convergence and accuracy of estimation. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.