Randomized Sensor Selection for Nonlinear Systems With Application to Target Localization
Randomized Sensor Selection for Nonlinear Systems With Application to Target Localization
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DOI：
10.1109/lra.2019.2928208
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发表时间：
2019-07
影响因子：
5.2
通讯作者：
S. Bopardikar;Osama Ennasr;Xiaobo Tan
中科院分区：
文献类型：
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作者：
S. Bopardikar;Osama Ennasr;Xiaobo Tan
给定一个非线性动力系统，这封信考虑的问题，选择一个子集的传感器，具有可证明的保证标准度量相关的非线性可观测性Gramian的总集合。的关键贡献是一个简单的随机算法，采样的传感器均匀不更换，并产生概率保证的最小特征值或逆的条件数的非线性可观测性Gramian相对于完整的传感器集。数值研究表明，实用的理论结果在于在政权的传感器的总数量大，其中的组合性质的问题提出了一个重大的计算挑战。数值结果表明，在两种情况下，使用扩展卡尔曼滤波器的移动目标定位的问题：一个使用范围传感器和另一个与时间差的到达测量。当与使用所有的传感器进行定位相比时，观察到随着传感器数量的减少而性能的优雅退化。还观察到，对于某些指标，所提出的方法提供了一个改进的启发式，选择传感器在一个贪婪的方式的基础上的贡献，一个额外的传感器对可观测性Gramian度量。
Given a nonlinear dynamical system, this letter considers the problem of selecting a subset of the total set of sensors that has provable guarantees on standard metrics related to the nonlinear observability Gramian. The key contribution is a simple randomized algorithm that samples the sensors uniformly without replacement, and yields probabilistic guarantees on the minimum eigenvalue or the inverse of the condition number of the nonlinear observability Gramian relative to that of the complete set of sensors. Numerical studies reveal that the utility of the theoretical results lies in the regime of large total number of sensors wherein the combinatorial nature of the problem presents a significant computational challenge. The results are demonstrated numerically on a problem of moving target localization using an extended Kalman filter in two scenarios: one using range sensors and another with time-difference-of-arrival measurements. A graceful degradation of performance with a decreased number of sensors is observed when compared to the use of all of the sensors for localization. It is also observed that for certain metrics, the proposed approach provides an improvement over a heuristic that selects the sensors in a greedy manner based on the contribution of an additional sensor toward the observability Gramian metric.