Iterative UKF under generalized maximum correntropy criterion for intermittent observation systems with complex non-Gaussian noise

Abstract

The traditional unscented Kalman filters (UKFs) under the maximum correntropy criterion provide a powerful tool for nonlinear state estimation with heavy-tailed non-Gaussian noise. Nevertheless, the above-mentioned filters may yield biased estimates because the Gaussian kernel function can only handle certain types of non-Gaussian noise. Additionally, the use of statistical linearization methods can result in approximation errors when solving linear observation equations, while the system may also experience observation data loss. Therefore, a new iterative UKF with intermittent observations under the generalized maximum correntropy criterion is proposed for systems with complex non-Gaussian noise, called GMCC-IO-IUKF. Firstly, the connection between the UKF with and without intermittent observations is established by designing a coefficient matrix including intermittent observation variables, so as to derive the UKF with intermittent observations under the maximum correntropy criterion. Secondly, for the measurement update of GMCC-IO-IUKF, a nonlinear regression augmented model that can deal with both prediction and observation errors is established using the coefficient matrix and the nonlinear function. To better adapt to different types of non-Gaussian noise, the generalized Gaussian kernel function is substituted for the traditional Gaussian kernel function. Theoretically, GMCC-IO-IUKF can achieve better estimation performance by directly employing the nonlinear function and the latest iteration value. Finally, a classical target tracking model is used to evaluate the estimation performance and feasibility of our proposed GMCC-IO-IUKF algorithm. It appears from the experiment results that our proposed GMCC-IO-IUKF can not only promote estimation precision but also handle complex non-Gaussian noise flexibly.