Vehicle state, including location and motion information, plays an essential role on the Internet of Vehicles (IoV). Accurately obtaining the system state information is the premise of realizing precise control. However, the statistics of system process noise are often unknown due to the complex physical process. It is challenging to estimate the system state when the process noise statistics are unknown. This paper proposes a new adaptive high-degree unscented Kalman filter based on the improved Sage–Husa algorithm. First, the traditional Sage–Husa algorithm is improved using a high-degree unscented transform. A noise estimator suitable for the high-degree unscented Kalman filter is obtained to estimate the statistics of the unknown process noise. Then, an adaptive high-degree unscented Kalman filter is designed to improve the accuracy and stability of the state estimation system. Finally, the target tracking simulation results verify the proposed algorithm’s effectiveness.

With the development of the industry, the physical model of controlled object tends to be complicated and unknown. It is particularly important to estimate the state variables of a nonlinear system when the model is unknown. This paper proposes a state estimation method based on adaptive fusion of multiple kernel functions to improve the accuracy of system state estimation. First, a dynamic neural network is used to build the system state model, where the kernel function node is constructed by a weighted linear combination of multiple local kernel functions and global kernel functions. Then, the state of the system and the weight of the kernel functions are put together to form an augmented state vector, which can be estimated in real time by using high‐degree cubature Kalman filter. The high‐degree cubature Kalman filter performs adaptive fusion of the kernel function weights according to specific samples, which makes the neural network function approximate the real system model, and the state estimate follows the real value. Finally, the simulation results verify the feasibility and effectiveness of the proposed algorithm.

According to the actual application system model which has bias, this paper analyzes the shortage of the conventional augmented algorithm, the two‐stage cubature Kalman filtering algorithm, which is presented on the basis of a two‐stage nonlinear transformation. The core ideas of the algorithm are to obtain the block diagonalization of the covariance matrix using the matrix transformation and avoid calculating the covariance of the state and bias to reduce the amount of calculation and ensure a smooth filtering process. Then, the equivalence of the two‐stage cubature Kalman filtering algorithm and the cubature Kalman filtering algorithm is proved by updating equivalent transformation. Through the experiment of trajectory tracking of a wheeled robot, it is verified that the two‐stage cubature Kalman filtering algorithm can obtain good tracking accuracy and stability with the presence of unknown random bias. Simultaneously, the equivalence of the two‐stage cubature Kalman filtering algorithm and cubature Kalman filtering algorithm is verified again using the contrast experiment.

This study presents the two-stage cubature Kalman filter (TSCKF), which is a sophisticated technique designed to address the issue of variations in system models in real-life scenarios, and utilises nonlinear twostage transformations to reorganise covariance matrices into a block-diagonal structure, effectively overcoming the limitations of conventional augmented methods. This technique effectively eliminates the need to calculate the cross-covariance between state variables and biases. This leads to a substantial reduction in computational load and facilitates seamless operation of the filter. The TSCKF design is underpinned by a robust theoretical framework, which ensures optimal computational efficiency while also ensuring precise estimations. This work demonstrates the mathematical equivalence between the TSCKF and the standard cubature Kalman filter (CKF) by utilising updated information equivalent transformations, and empirically verifies the equivalence through trajectory tracking experiments conducted on two-wheeled robotic systems subjected to random perturbations, thus affirming the greater accuracy and dependability of the TSCKF in tracking scenarios. Moreover, comparison evaluations offer further proof of the same performance between both methodologies. This study introduces a highly efficient approach in the domain of nonlinear systems and provides a dependable remedy for scenarios where traditional filtering procedures may be inadequate due to deficiencies in the system model.

As a bidirectional cognitive model for dealing with uncertainty, cloud model (CM) are commonly used in application scenarios such as fault diagnosis, system modeling, and evaluation. CM achieves bidirectional conversion between qualitative concepts and quantitative values through forward cloud transformation (FCT) and backward cloud transformation (BCT) algorithms. Among them, the BCT algorithm obtains key parameters that characterize the randomness and fuzziness of concepts through the analysis of quantitative sample data, namely the expectation ( Ex ), entropy ( En ), and hyper entropy ( He ) for CM. However, the existing BCT algorithms adopt an integrated modeling approach, ignoring the impact of data with different distribution characteristics on obtaining key parameters for CM. Therefore, this paper proposes a BCT algorithm based on Kullback Leibler (KL) divergence, aiming to refine the process for obtaining key parameters of CM by analyzing the distribution differences between sample data. Firstly, the corresponding atomization template dataset (ATD) is obtained by conducting a coarse-grained analysis of the sample data. Then, calculate the KL divergence between sample data and ATD to effectively evaluate the atomization state of CM after transforming the sample data. Based on the evaluation results, two differentiated BCT strategies are designed for both atomization and non-atomization states to obtain key parameters of CM. Finally, a comparative analysis is conducted between the proposed method and traditional BCT algorithms, using the University of California Irvine (UCI) benchmark dataset and real fault diagnosis data for error analysis. The experimental results indicate that the proposed method can obtain more accurate key parameters of CM than other BCT algorithms.