RKHS Based Dynamic State Estimator for Non-Gaussian Radar Measurements

In the case of a non-linear system, the dynamic state of the targets (position, velocity, and acceleration) is estimated by an extended Kalman filter (EKF). The theory of EKF is established on the assumption that measurements follow Gaussian distribution. However, in practice, this assumption falls short and limits the application of EKF. In literature, to deal with the non-Gaussianity, the maximum correntropy criterion (MCC)-based EKF (EKF-MCC) has been studied well. The MCC, an information-theoretic criterion, claims to effectively deal with the system's non-Gaussianity. Nevertheless, like EKF, EKF-MCC also approximates the known system non-linearity with a Jacobian. The Jacobian provides the first-order approximation of the non-linearity and hinders the estimation accuracy achieved by EKF-MCC, particularly for complex target motion models. Therefore, in this work, firstly, we propose to use EKF-MCC for estimating the dynamic state of the target from non-Gaussian measurement. After that, utilizing MCC, we propose reproducing kernel Hilbert space (RKHS) based non-linear estimation of system non-linearity and using it with EKF-MCC. Amid non-linear estimation utilizing MCC, the proposed filter is named EKF-MCC-RKHS. The simulation performed to estimate the dynamic states of the complex constant acceleration (CA) target motion model validates the superiority of EKF-MCC-RKHS over recently introduced EKF-MCC and traditional EKF.