Differential Privacy Kalman Filtering for Graphical Dynamic Systems: Performance Improvement and Privacy Calibration

This paper investigates differential privacy Kalman filtering for graphical dynamic systems. An enhanced differential privacy Kalman filter is initially developed by leveraging the topology, a unique characteristic of graphical dynamic systems, to improve the filtering performance. And then upper and lower error bounds of the enhanced filter are established to evaluate the recipient's ability to infer sensitive data. Based on these error bounds, a privacy calibration guideline is provided to balance privacy and usability of sensitive data. A notable feature of the enhanced filter is that its Kalman gain matrix is a diagonal matrix, which facilitates the independent update of information at each node by reducing the coupling between nodes. This feature diminishes the accumulation of filtering errors, thereby improving the data availability for the recipient. Finally, the effectiveness of the proposed approach is verified through a simulation of epidemiological data analysis, and the results show that the enhanced filter performs well in systems with high privacy levels.