Gaussian–Versoria Mixed Kernel Correntropy-Based Robust Parameter and State Estimation for Bilinear State–Space Systems with Non-Gaussian Process and Measurement Noises

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.