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arXiv 1609.08536eess.SYcs.ROcs.SYmath.OC
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为随机过程估计调度非线性传感器

Scheduling Nonlinear Sensors for Stochastic Process Estimation

University of Pennsylvania(宾夕法尼亚大学);Massachusetts Institute of Technology(麻省理工学院)

Vasileios Tzoumas, Nikolay A. Atanasov, Ali Jadbabaie, George J. Pappas

AI总结:

本文研究在众多可用传感器中仅激活少数传感器以估计随机过程状态的问题,提出了一种时间复杂度与规划周期线性相关的算法,性能优于多项式时间算法,且在高斯过程等场景下具有与最优算法相当的效率。

摘要:

本文聚焦于在众多可用传感器中仅激活少量传感器以估计感兴趣随机过程状态的问题。该问题在目标跟踪和同时定位与建图(SLAM)等应用中具有重要性。由于涉及演化未知的随机系统、非线性测量传感器以及限制的操作资源,该问题具有挑战性。我们提供了一种适用于一般随机过程和非线性测量的算法,其时间复杂度与规划周期线性相关,性能与最优性能相差一个乘法因子1/2。这值得注意,因为该算法在计算优势上显著优于达到最佳近似因子1/e的多项式时间算法。此外,对于重要的高斯过程和受高斯噪声污染的非线性测量,我们的算法具有与最先进线性系统和测量算法相同的时间复杂度。我们通过证明批量状态向量在测量条件下的熵的两个性质来实现我们的结果:a)在传感器选择上是超模的;b)具有稀疏模式(涉及块三对角矩阵)使其在每个传感器集合上易于评估。

英文摘要:

In this paper, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and mapping (SLAM). It is challenging since it involves stochastic systems whose evolution is largely unknown, sensors with nonlinear measurements, and limited operational resources that constrain the number of active sensors at each measurement step. We provide an algorithm applicable to general stochastic processes and nonlinear measurements whose time complexity is linear in the planning horizon and whose performance is a multiplicative factor 1/2 away from the optimal performance. This is notable because the algorithm offers a significant computational advantage over the polynomial-time algorithm that achieves the best approximation factor 1/e. In addition, for important classes of Gaussian processes and nonlinear measurements corrupted with Gaussian noise, our algorithm enjoys the same time complexity as even the state-of-the-art algorithms for linear systems and measurements. We achieve our results by proving two properties for the entropy of the batch state vector conditioned on the measurements: a) it is supermodular in the choice of the sensors; b) it has a sparsity pattern (involves block tri-diagonal matrices) that facilitates its evaluation at each sensor set.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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