Privacy and Performance Trade-Offs in Both Estimation and Detection for Large-Scale Systems

This paper investigates the trade-offs between privacy and performance in both estimation and detection for large-scale systems. Each subsystem estimates its local state using local information and data received from its neighbours. Considering the unreliability of the communication networks, we assume that the privacy data is vulnerable to eavesdropping and bias injection attacks. To maintain privacy, we propose a stochastic quantization-based privacy scheme to preserve the measurement outputs, where the privacy level is measured by differential privacy. However, quantization may lead to degradation in both estimation and detection performance. Therefore, we firstly investigate the trade-off between privacy level and estimation performance and establish an optimization problem to obtain the optimal quantization interval. Then, we analyze the trade-off between privacy level and detection performance and formulate an optimization problem to obtain the optimal quantization interval. Finally, a numerical example is provided to verify the effectiveness of theoretical results.