a scaled unscented transformation process and deterministic sampling technique to approximate the posteriori probability density with higher precision [8,9]. However, the artificial selection of parameters may impact the filtering performance. Recently, the most numerically stable and accurate cubature Kalman filter (CKF) has been introduced [10]. The CKF approximates multi-dimensional integrals in Bayesian filtering under a Gaussian assumption, offering advantages such as rigorous theoretical derivation, third-order filtering accuracy, and reliable stability [11,12]. The CKF is extensively employed in applications like spacecraft attitude estimation and trajectory tracking due to its higher estimation precision and convergence rate for high-dimension systems [13,14]. Nevertheless, computational inaccuracies and the limited word length of the computers may result in the state error covariance of CKF losing the property of being symmetric positive definite, which can ultimately lead to divergence. To prevent divergence while maintaining positive specificity, the square-root cubature Kalman (SR-CKF) has been developed, transmitting both the predicted and the posteriori square roots of error covariance to avoid negativity in the covariance matrix in iterations [15,16]. In practical situations, system parameters may be drastically impacted by faults or external disturbances, leading to uncertainties and potential degradation and instability in common filters. Moreover, it is difficult to determine information on these modeling uncertainties. Thus, to deal with modeling errors and system uncertainties, robust estimation methods and adaptive state estimations have been proposed. The \(H\mathfrak{so}\) filter is designed by reducing the extreme scenario estimation discrepancies, while it is sensitive to the quantity of weighting functions and performance boundaries defined by users [17,18]. On the other hand, an innovative and robust estimation strategy termed as a smooth variable structure filter (SVSF) has been introduced [19, 20, 21]. It is a robust iterative estimation refinement method based on the smooth variable structure principles that enhances the robustness and stability by effectively managing modeling uncertainties. Combining the SVSF with the EKF or UKF has been suggested to improve robustness of the system uncertainties [22]. Additionally, an algorithm named CSVSF, which combines CKF and SVSF, is proposed [23]. However, these prior works assume a Gaussian measurement noise, neglecting heavy-tailed non-Gaussian noises existing in the system. To address heavy-tailed non-Gaussian noises and impulsive noises in engineering applications, various methods have been explored. The Huber robust function and information theoretic learning (ITL) are commonly used techniques for filtering non-Gaussian noises. The ITL captures high-order statistics, leading to a direct improvement in filter performance [24,25]. Specifically, the maximum correntropy criterion (MCC) has shown effectiveness in non-Gaussian conditions by maximizing the correntropy between the system output and desired performance [26,27]. Kalman filtering methods based on the MCC have exhibited exceptional performance in impulsive noise scenarios [28, 29, 30, 31]. However, challenges related to MCC implementation have been addressed using an efficient fixed-point iterative method [32]. Notably, parameter uncertainties inherent in real-world applications are often overlooked. As the kernel bandwidth significantly influences the presentation of the MCC, the selection of the kernel bandwidth mentioned previously is typically conducted through trial and error by users, which is complex and impacts the accuracy of the filter. This paper proposes an MKMC-CSVSF which combined the SR-CKF and SVSF under the multi-kernel maximum correntropy criterion (MKMC)to enhance the robustness against lumped uncertainties and heavy-tailed non-Gaussian noises commonly encountered in practical implementations such as a FSHC.