Generalized Correntropy Sparse Gauss–Hermite Quadrature Filter for Epidemic Tracking on Complex Networks

The dynamic estimation of epidemic spreading on networks is essential for controlling morbidity. Nonlinear Kalman filters, which are capable of estimating the hidden state of a nonlinear system, can be utilized for dynamic state estimation of epidemic spreading. Traditional nonlinear Kalman filters perform optimization using the minimum mean square error (MMSE) criterion. Since observable measurements are generally corrupted by non-Gaussian noise, maximum correntropy criterion (MCC)-based nonlinear Kalman filters have been used for improving robustness against non-Gaussian noise. In comparison with the MCC, generalized correntropy is more robust and flexible in the presence of non-Gaussian noise. In this article, epidemic spreading is described by a compartmental model, i.e., susceptible-infected-recovered-susceptible model. Based on the compartmental model, the generalized correntropy-based sparse Gauss–Hermite quadrature filter (GCSGHQF) is proposed for epidemic tracking on homogeneous networks. The GCSGHQF approximates the Gaussian-weighted integrals by utilizing the sparse Gauss–Hermite quadrature rule. In addition, the generalized correntropy is applied to enhancing robustness in the presence of non-Gaussian noise. Simulation results show that the GCSGHQF exhibits a higher filtering accuracy and improves robustness compared to traditional nonlinear Kalman filters.