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首页> 外文期刊>Signal Processing, IEEE Transactions on >Consensus-Based Distributed Total Least Squares Estimation in Ad Hoc Wireless Sensor Networks
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Consensus-Based Distributed Total Least Squares Estimation in Ad Hoc Wireless Sensor Networks

机译：Ad Hoc无线传感器网络中基于共识的分布式总最小二乘估计

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摘要

Total least squares (TLS) is a popular solution technique for overdetermined systems of linear equations, where both the right-hand side and the input data matrix are assumed to be noisy. We consider a TLS problem in an ad hoc wireless sensor network, where each node collects observations that yield a node-specific subset of linear equations. The goal is to compute the TLS solution of the full set of equations in a distributed fashion, without gathering all these equations in a fusion center. To facilitate the use of the dual-based subgradient algorithm (DBSA), we transform the TLS problem to an equivalent convex semidefinite program (SDP), based on semidefinite relaxation (SDR). This allows us to derive a distributed TLS (D-TLS) algorithm, that satisfies the conditions for convergence of the DBSA, and obtains the same solution as the original (unrelaxed) TLS problem. Even though we make a detour through SDR and SDP theory, the resulting D-TLS algorithm relies on solving local TLS-like problems at each node, rather than computationally expensive SDP optimization techniques. The algorithm is flexible and fully distributed, i.e., it does not make any assumptions on the network topology and nodes only share data with their neighbors through local broadcasts. Due to the flexibility and the uniformity of the network, there is no single point of failure, which makes the algorithm robust to sensor failures. Monte Carlo simulation results are provided to demonstrate the effectiveness of the method.
机译：总最小二乘法（TLS）是一种超定线性方程组的流行解决方案技术，其中右侧和输入数据矩阵都被认为是嘈杂的。我们考虑一个自组织无线传感器网络中的TLS问题，其中每个节点收集观​​察结果，这些观察结果产生特定于节点的线性方程组。目标是以分布式方式计算整个方程组的TLS解，而无需在融合中心中收集所有这些方程式。为了方便使用基于对偶的次梯度算法（DBSA），我们基于半定松弛（SDR）将TLS问题转换为等效的凸半定程序（SDP）。这使我们能够导出一种分布式TLS（D-TLS）算法，该算法满足DBSA收敛的条件，并获得与原始（无松弛）TLS问题相同的解决方案。即使我们绕过SDR和SDP理论，最终的D-TLS算法也依赖于在每个节点上解决类似TLS的局部问题，而不是计算上昂贵的SDP优化技术。该算法是灵活的并且完全分布式的，即，它不对网络拓扑进行任何假设，并且节点仅通过本地广播与其邻居共享数据。由于网络的灵活性和统一性，没有单点故障，这使得该算法对传感器故障具有鲁棒性。提供了蒙特卡罗仿真结果以证明该方法的有效性。

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