Scheduling nonlinear sensors for stochastic process estimation
Scheduling nonlinear sensors for stochastic process estimation
复制标题
调度非线性传感器进行随机过程估计
DOI：
10.23919/acc.2017.7963015
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
George Pappas
中科院分区：
文献类型：
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作者：
Vasileios Tzoumas;Nikolay A. Atanasov;A. Jadbabaie;George Pappas
在本文中，我们专注于激活只有几个传感器，在许多可用的，估计批处理状态的随机过程的利益。这个问题在诸如目标跟踪和同时定位和地图绘制（SLAM）的应用中是重要的，并且通常在我们需要对迄今为止所采取的轨迹进行良好估计的问题中是重要的，例如，用于线性化目的。它是具有挑战性的，因为它涉及随机系统的演变在很大程度上是未知的，传感器与非线性测量，和有限的操作资源，约束在每个测量步骤的主动传感器的数量。我们提供了一个算法适用于一般的随机过程和非线性测量的时间复杂性是线性的规划范围内，其性能是一个乘法因子1/2远离最佳性能。这是值得注意的，因为该算法提供了一个显着的计算优势，超过多项式时间算法，实现最佳近似因子1/e。此外，对于高斯过程和高斯噪声污染的非线性测量的重要类别，我们的算法享有相同的时间复杂度为线性系统和测量的最先进的算法。我们实现我们的结果证明两个属性的熵的批量状态向量的条件下的测量：a）它是supermodular的传感器的选择; B）它有一个稀疏模式（涉及块三对角矩阵），便于其评估在每个传感器集。
In this paper, we focus on activating only a few sensors, among many available, to estimate the batch state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and mapping (SLAM), and in general, in problems where we need to have a good estimate of the trajectory taken so far, e.g., for linearisation purposes. 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 up to 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 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.