In this paper, we present an optimization-based formulation for privacy-utility tradeoff in the Ensemble and Unscented Kalman filtering framework, with a focus on space situational awareness. Privacy and utility are defined in terms of a lower and an upper bound on the state estimation error covariance, respectively. Synthetic sensor noise is used to satisfy these bounds and is determined by solving an optimization problem. Given privacy and utility bounds, we present optimization problem formulations to determine a) the maximum noise for which utility is satisfied or the estimation errors are upper-bounded, b) the minimum noise for which privacy is satisfied or the estimation errors are lower-bounded, c) the optimal noise that satisfies utility constraints and maximizes privacy, and d) the optimal noise that satisfies privacy constraints and maximizes utility. We demonstrate application of these formulations to the tracking of the International Space Station, and highlight the optimal privacy vs utility tradeoff for this dynamical system.

中文翻译：

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从集成和无迹卡尔曼滤波角度实现空间态势感知的隐私和效用感知数据共享

在本文中，我们在 Ensemble 和 Unscented Kalman 过滤框架中提出了一种基于优化的隐私-效用权衡公式，重点是空间态势感知。隐私和效用分别根据状态估计误差协方差的下限和上限进行定义。合成传感器噪声用于满足这些界限，并通过求解优化问题来确定。给定隐私和效用界限，我们提出优化问题公式来确定 a) 满足效用或估计误差上限的最大噪声，b) 满足隐私或估计误差下限的最小噪声, c) 满足效用约束并最大化隐私的最优噪声，d) 满足隐私约束和最大化效用的最优噪声。我们展示了这些公式在国际空间站跟踪中的应用，并强调了这个动态系统的最佳隐私与效用权衡。