## 1 Introduction
incorporated the SCKF into the interactive multi-model theory (IMM) to achieve adaptation to noise by selecting sub-models with different noise through the Markov state transfer matrix. However, the number of switchable submodels is limited and the selection needs to be made empirically, so the interaction results are limited, which improves accuracy in the model noise to some extent but does not achieve a real-time accurate update of the noise [11]. [PERSON] et al. replaced the sub-filter in the federated Kalman filter (FKF) with a CKF and designed a triple federated Kalman filter to construct a closed-loop system by using fuzzy logic to correct the added adaptive adjustment factor. This algorithm is highly fault-tolerant and stable while improving the accuracy of the algorithm estimation, but its structure is complex and requires the construction of sub-filters and main filters, so repeated information distribution, fusion, and calculation will affect the accuracy and computation rate, which is not suitable for practical industrial production [12]. There are attempts to use deep learning to estimate the vehicle's state. [PERSON] et al. observed tire longitudinal forces and lateral vehicle speed through a proposed neural network (NN) estimator, using radial basis functions to approximate the unknown noise in the vehicle dynamics model. Eventually, the designed estimator was proven to be stable by the Lyapunov equation [13]. The process noise and measurement noise in most current studies on state estimation are assumed to satisfy the Gaussian distribution, while in practice, measurement data may be disturbed by various environmental factors, resulting in significant deviations between individual measurement data and other data, i.e., outliers, whose nearby noise has a heavy-tailed characteristic, which is a general non-Gaussian phenomenon [14; 15]. In a nonlinear non-Gaussian environment, the minimum mean square error (MMSE) on the KF shows high sensitivity, which degrades the performance of the KF significantly [16; 17; 18]. Therefore, it is of significant research interest and value to design estimation algorithms to cope with non-Gaussian, thick-tailed noise. [PERSON] et al. use the Gaussian-student's t mixture distribution, which uses a variational Bayesian approach to provide a Gaussian approximation. A Student's t distribution shows a larger variance than the Gaussian distribution and therefore better describes the non-Gaussian nature of the noise [19]. Researchers have found that particle filters (PF) can handle nonlinear and non-Gaussian distribution problems. A large number of samples are required, however, and the problem of sample sparsity occurs in high-dimensional state spaces. To estimate the state under non-Gaussian noise and bad data, [PERSON] et al. integrated a time-varying multidimensional scaling factor with a cubic particle filter (CPF) using [PERSON]'s M-estimation theory. However, PF and CPF have difficulties with integration calculations in high-dimensional spaces and require more computational resources [20]. Error entropy is a learning criterion that is widely used in various fields of information theoretic learning. However, since the error entropy possesses a Gaussian kernel function that does not arbitrarily change its form [21]. This also leads to the fact that algorithms based on error entropy can only handle certain specific types of noise, and thus algorithms based on error entropy are only applicable to specific types of noise. Replacing the MMSE in the traditional Kalman filter with the minimum error entropy (MEE) criterion can obtain the minimum error entropy Kalman filter (MEEKF). The error entropy describes the uncertainty of the estimated value [22]. The extended Kalman filter based on MEE can freely adjust its shape characteristics using the generalized Gaussian kernel function, thus improving the robustness of the filter [23]. However, in highly nonlinear systems, the calculation of higher-order moments complicates the algorithm.