Lithium-ion batteries have become an important power source in low-carbon transportation energy, and the safe operation and remaining useful life prediction are of great significance. Aiming at the shortcomings of existing methods, such as low prediction accuracy and a short prediction period, this paper proposes a real-time update high-order extended Kalman filter method based on fixed-step life prediction for vehicle lithium batteries based on the principle of combining models and data. First, the state model describing the parameters in the dynamic energy attenuation model is established, and the energy attenuation model is regarded as the observation model of the system to meet the requirements of establishing the Kalman filter. Secondly, the multi-step prediction equation of the state model is established by iterative recursion. At the same time, the multi-step prediction equation between the existing energy output value and the future output value is established based on the multi-dimensional Taylor network (MTN). The multiplicative noise term introduced in the dynamic modeling process is regarded as the hidden variable of the system to meet the requirements of establishing the multi-step linear predictive Kalman filter. Finally, the effectiveness of the new method is verified by digital simulation examples.

As an emerging artificial intelligence technology, federated learning plays a significant role in privacy preservation in machine learning, although its main objective is to prevent peers from peeping data. However, attackers from the outside can steal metadata in transit and through data reconstruction or other techniques to obtain the original data, which poses a great threat to the security of the federated learning system. In this paper, we propose a differential privacy strategy including encryption and decryption methods based on local features of non-Gaussian noise, which aggregates the noisy metadata through a sequential Kalman filter in federated learning scenarios to increase the reliability of the federated learning method. We name the local features of non-Gaussian noise as the non-Gaussian noise fragments. Compared with the traditional methods, the proposed method shows stronger security performance for two reasons. Firstly, non-Gaussian noise fragments contain more complex statistics, making them more difficult for attackers to identify. Secondly, in order to obtain accurate statistical features, attackers must aggregate all of the noise fragments, which is very difficult due to the increasing number of clients. We conduct experiments that demonstrate that the proposed method can greatly enhanced the system’s security.