## 1 Introduction  
Due to the extensive variety of significant uses in technology, including target tracking, navigation, posture determination, automation, and telecommunications, the filtering approaches for estimating states in dynamical models with state space have gained a lot of interest in the past few decades [1; 2; 3; 4]. It is well known that the best estimations for a linear Gaussian system are Kalman filters (KFs). On the other hand, the optimum or analytical solutions of the posterior probability density functions (PDFs) are typically not accessible for a nonlinear Gaussian system. Thus, the extended Kalman filter (EKF) [5] is a common nonlinear Kalman-type filter that uses first-order linearization to give an estimate of the nonlinear equation before completing the operation of filtering using the traditional KF approach. Additionally, the unscented Kalman filter (UKF) [6], the cubature Kalman filter (CKF) [7], and the Gaussian-Hermite Kalman filter [8] are a few examples of nonlinear filters with less optimality that have been paid more attention for several years. Furthermore, the above-mentioned nonlinear filters result inappropriately when they are implemented in a situation coupled with non-Gaussian noise. There is the possibility that estimation accuracy will be affected, which may be due to third-party interference or inaccurate sensors from the state and the measurement outliers [9]. Later, several kinds of robust nonlinear filters were designed by integrating the design principles of the Gaussian approximation KF with the robustness cost function developed from [PERSON]'s M-estimation [10]. Another commonly used approach for describing non-Gaussian noise is by employing Student's t distribution along with the polynomial decay property [11]. This method takes into account the heavy-tailed nature of non-Gaussian noise. On the basis of these ideas, several researchers have introduced the variational Bayes nonlinear filter (VBNF) and the Student's t-based robust nonlinear filter (RSTNF) [12]. The PDF with the posterior state vector is still a Student's t PDF having the fixed-point iterations in the RSTNF, where the non-Gaussian processing and the measured noises are considered as Student's t PDFs having the same degree of freedom (DoF) criteria [13]. VBNFs consider the process noise which has a Gaussian distribution that incurs the danger of worse estimation performance when it is used with non-Gaussian process noise [14]. To overcome the problems associated with the non-Gaussian noises, correntropy has been used for the process [15]. For the linear non-Gaussian frameworks, the maximum correntropy-based Kalman filters were initially suggested in [16]. Beside this, researchers have also focused on the optimization criteria in information theoretic learning (ITL) [17] in recent years. By incorporating the ITL values, the estimation can be calculated straight from the source. Correntropy is one of the information-theoretic quantities; it has been used recently as a reliable cost to deliver notable performance improvements in various sectors for different applications [17, 18]. It is capable of capturing higher-order statistics of losses. The novel maximum correntropy extended Kalman filter (MCEKF) has been provided as a solution to this issue [19]. More precisely, the maximal correntropy criterion (MCC) in ITL refers to the optimization criterion for correntropy [20, 21]. Many investigations have been carried out on filters against heavy-tailed non-Gaussian noises with robustness adaptivity for GPS navigations with effective performance [22, 23]. Further, EKF, multiple-model filters, and modelling noise followed by a Gaussian distribution are used to increase resilience against the outliers, but computational complexity and effort will always be a limiting factor. On the other hand, iterative techniques are frequently utilized to reach an MCC solution. The straightforward and simple-to-understand gradient-based algorithms are the most widely utilized approaches [24, 25].