Optimal state estimation with measurements corrupted by Laplace noise
Optimal state estimation with measurements corrupted by Laplace noise
复制标题
拉普拉斯噪声破坏的测量的最佳状态估计
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
H. Sandberg
中科院分区：
文献类型：
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作者：
Farhad Farokhi;Jezdimir Milošević;H. Sandberg
研究了线性离散时间系统的最优状态估计问题。受差分隐私文献的启发，假设测量被拉普拉斯噪声破坏。使用随机化方法近似状态的最优最小均方误差估计。该方法的原理是将拉普拉斯噪声改写为瑞利随机变量的高斯噪声。近似值和最佳估计值之间的距离小于常数的事件的概率被确定为在随机化方法中使用的并行卡尔曼滤波器的数量的函数。该估计器，然后与最佳线性估计，最大后验概率（MAP）估计的状态，和粒子滤波器进行比较。
Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the state is approximated using a randomized method. The method relies on that the Laplace noise can be rewritten as Gaussian noise scaled by Rayleigh random variable. The probability of the event that the distance between the approximation and the best estimate is smaller than a constant is determined as function of the number of parallel Kalman filters that is used in the randomized method. This estimator is then compared with the optimal linear estimator, the maximum a posteriori (MAP) estimate of the state, and the particle filter.