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Distributed consensus-based Kalman filtering in sensor networks with quantised communications and random sensor failures

机译：具有量化通信和随机传感器故障的传感器网络中基于共识的分布式卡尔曼滤波

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摘要

This study investigates the signal estimation problem in noisy sensor networks with quantised communications. The sensors are subject to random sensor failures, and synchronously take noisy measurements to produce local estimates by using a Kalman filtering scheme at each sampling instant. A quantiser is considered to be embedded in each sensor, and the probabilistic quantisation strategy is adopted to reduce the energy consumption. In between two sampling instants, each sensor collects quantised local estimates from its neighbours and runs a consensus-based fusion algorithm to generate a fused estimate. The process noises and measurement noises are considered to be spatially uncorrelated, a recursive equation is presented to calculate the estimation error covariance matrix and an upper bound is derived for the estimation performance index. Moreover, a sufficient condition for the convergence of the upper bound of the estimation performance index is also presented. Two types of optimisation problems are constructed for cases of infinite and finite recursions, respectively, where the former one focuses on minimising the derived upper bound of the estimation performance index, and the latter one aims to minimise the energy consumption subject to a constraint on the estimation performance. Illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.
机译：这项研究调查了带有量化通信的噪声传感器网络中的信号估计问题。传感器会遭受随机传感器故障的影响，并且会在每个采样时刻使用卡尔曼滤波方案同步进行噪声测量以产生局部估计。量化器被认为是嵌入在每个传感器中的，并且采用概率量化策略来减少能耗。在两个采样时刻之间，每个传感器从其邻居收集量化的本地估计值，并运行基于共识的融合算法以生成融合估计值。过程噪声和测量噪声在空间上不相关，提出了一个递归方程来计算估计误差协方差矩阵，并为估计性能指标导出了上限。此外，还提出了使估计性能指标的上限收敛的充分条件。针对无限递归和有限递归情况分别构造了两种类型的优化问题，其中前一种专注于最小化推导的估计性能指标的上限，而后一种旨在最小化受约束的能耗。估算效果。提供了说明性的例子来证明所提出的理论结果的有效性。

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