Distributed estimation in the context of sensor networks is considered, where distributed agents are given a set of sensor measurements, and are tasked with estimating a target variable. A subset of sensors are assumed to be faulty. The objective is to minimize i) the mean square estimation error at each node (accuracy objective), and ii) the mean square distance between the estimates at each pair of nodes (consensus objective). It is shown that there is an inherent tradeoff between the former and latter objectives. Assuming a general stochastic model, the sensor fusion algorithm optimizing this tradeoff is characterized through a computable optimization problem, and a Cramer-Rao type lower bound for the achievable accuracy-consensus loss is obtained. Finding the optimal sensor fusion algorithm is computationally complex. To address this, a general class of low-complexity Brooks-Iyengar Algorithms are introduced, and their performance, in terms of accuracy and consensus objectives, is compared to that of optimal linear estimators through case study simulations of various scenarios.
翻译:在对传感器网络进行分布式估计时,考虑对传感器网络进行分布式估计,给分布式物剂进行一套传感器测量,并责成其估计目标变量。一组传感器被认为有缺陷。目标是尽量减少每个节点的平均平方估计错误(准确性目标),以及每对节点的估计数之间的平均平方距离(协商一致目标)。显示前者与后两个目标之间有着内在的权衡。假设一个一般的随机模型,优化这一权衡的传感器聚合算法通过一个可计算优化的问题来定性,并获得一个可实现的准确性-一致损失的较低约束的Cramer-Rao类型。找到最佳的传感器聚合算法是计算上复杂的。要解决这个问题,引入了一个低兼容度的普通类别,在准确性和共识目标方面,其表现与通过对各种情景进行案例研究模拟的最佳线性估测值相比较。