Error Bounds and Guidelines for Privacy Calibration in Differentially Private Kalman Filtering
Error Bounds and Guidelines for Privacy Calibration in Differentially Private Kalman Filtering
复制标题
差分隐私卡尔曼滤波中隐私校准的误差界限和指南
DOI：
10.23919/acc45564.2020.9147779
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
M. Hale
中科院分区：
文献类型：
--
作者：
Kasra Yazdani;M. Hale
差分隐私已经成为一个正式的框架，用于保护控制系统中的敏感信息。一个关键的特性是它不受后处理的影响，这意味着可以在私有化数据上执行任意的事后计算，而不会削弱差分隐私。因此，过滤私有数据流是常见的。为了描述这种设置的特征，本文提出了卡尔曼滤波差分私人状态轨迹的误差和熵界。我们考虑系统中的输出轨迹被私有化，以保护产生它的状态轨迹，我们提供的先验和后验误差和微分熵的卡尔曼滤波器，这是处理私有化的输出轨迹的界限。使用我们开发的误差范围，然后，我们提供的准则来校准隐私级别，以保持过滤器的错误在预先指定的范围内。仿真结果证明了这些发展。
Differential privacy has emerged as a formal framework for protecting sensitive information in control systems. One key feature is that it is immune to post-processing, which means that arbitrary post-hoc computations can be performed on privatized data without weakening differential privacy. It is therefore common to filter private data streams. To characterize this setup, in this paper we present error and entropy bounds for Kalman filtering differentially private state trajectories. We consider systems in which an output trajectory is privatized in order to protect the state trajectory that produced it. We provide bounds on a priori and a posteriori error and differential entropy of a Kalman filter which is processing the privatized output trajectories. Using the error bounds we develop, we then provide guidelines to calibrate privacy levels in order to keep filter error within pre-specified bounds. Simulation results are presented to demonstrate these developments.