This paper investigates the joint state and parameter estimation issue of the bilinear state–space system with non-Gaussian process noise and non-Gaussian measurement noise. Tackling such an issue is challenging because either of these noises may seriously degrade the estimation performance. To significantly counteract the negative effect of these non-Gaussian noises, a Gaussian–Versoria mixed kernel correntropy (GVMKC)-based cost function is introduced by integrating two different types of kernel functions into a mixed kernel. Subsequently, a GVMKC-based Kalman filtering and a GVMKC-based robust recursive least squares method are derived for estimating the system states and parameters, respectively. Thus, a robust joint parameter and state estimation method is developed by implementing the interactive computation. The effectiveness of the proposed method is confirmed by simulation examples.
Wang et al. (Tue,) studied this question.