Maximum correntropy sparse Gauss–Hermite quadrature filter and its application in tracking ballistic missile

Abstract

A novel robust filter referred as maximum correntropy sparse Gauss–Hermite quadrature filter (MCSGHQF) is proposed. The novel algorithm makes use of the sparse Gauss–Hermite quadrature (SGHQ) rule to numerically compute Gaussian-weighted integrals, which are propagated through non-linear state equation, and then a weighted means and covariance is taken. As the sensor measurements are always corrupted by non-Gaussian noise which is typically glint noise or mixed Gaussian-impulsive noise, the measurement update is redesigned based on the maximum correntropy criterion instead of minimum mean square error. Therefore, the MCSGHQF could exhibit robustness to the non-Gaussian measurement noise, especially impulsive noise. In addition, the study proposes the use of MCSGHQF for ballistic missile tracking during midcourse phase to deal with the non-Gaussian noise. The tracking performance is compared with that of SGHQ filter (SGHQF), Huber-based filter and extended Kalman filter by Monte-Carlo simulations. The simulation results demonstrate that the MCSGHQF is effective in glint noise case and exhibits superior to Huber-based filter in mixed Gaussian-impulsive noise case.