# Kalman Filter-Based Differential Privacy Federated Learning Method
## 1 Introduction  
With the development of industry and the improvement in computing power, the application of artificial intelligence in various fields of people's lives has been becoming more popular, affecting many aspects, including medical care, logistics, face and voice recognition, etc. There is a wide application of machine learning and profound learning benefits from computing power and massive data. The traditional machine learning and deep learning model rely on data centers and require large amounts of high-quality data. With the increasing requirements of machine learning and deep learning in our lives, the requirements for data quantity and quality are also higher. In addition, in production and life, other companies and organizations need to pay to collect massive amounts of data. Aside from the cost, protecting users' privacy is also an important factor limiting the data obtained. To address these issues, Google proposed federated learning [1; 2; 3], which has attracted attention from scholars and organizations. Federated learning can train models using decentralized data, which significantly increases the amount and quality of data. On the other hand, the participating nodes are not required to provide their own local data in federated learning. They only need to deliver the training results to protect the user's data privacy. However, federated learning does not make the user's privacy completely invulnerable, and the user's privacy may be obtained through the shared model parameters [4; 5].  
Two schemes have been proposed to improve privacy protection in federated learning, one based on homomorphic encryption [6; 7; 8; 9] and the other based on differential privacy [10; 11; 12; 13]. However, these methods have difficulties in practical application due to their limitations. Differential privacy relies on adding noise to the original data or training results to protect privacy, and it may reduce the model's accuracy. Too much noise can make the model less accurate than expected. At the same time, too little noise will not achieve the protection of user privacy, making it challenging to balance privacy protection and accuracy [8]. Homomorphic encryption techniques rely on complex encryption and decryption computations, which may cost a large amount of time. At the same time, the different computing power of devices and the different time used in complex calculations situations can make the aggregation unsynchronized [14].  
To solve the above problems of federated learning, Kalman filter-based differential privacy federated learning (KDP-FL) is proposed. The proposed scheme consists of two parts, using differential privacy to protect the gradient privacy in federated learning and using the Kalman filter to reduce the noise added to preserve privacy in order to improve the accuracy of the global model. The main contributions of this paper are as follows.  
1. A multiparty cooperative model training scheme that protects data privacy is proposed.
2. A differential privacy federated learning algorithm is proposed to protect user data privacy by a differential privacy mechanism.
3. The noise introduced by the differential privacy mechanism is reduced by Kalman filtering to improve the model's accuracy.