传感器网络中的分布式共识算法：量化数据和随机链路故障
Distributed Consensus Algorithms in Sensor Networks: Quantized Data and Random Link Failures
摘要：
研究了具有量化数据和随机链路故障的传感器网络中的分布式平均一致性问题。为了实现一致性，在量化之前将抖动（小噪声）添加到传感器状态。当量化器的范围是无界的（可数数量的量化器水平），随机逼近表明，共识是渐近实现的概率为1，并在一个有限的随机变量的均方。我们表明，均方误差（m.s.e.）可以通过调整链路权重序列来使其任意小，代价是算法的收敛速度。为了研究量化器范围有界时随机链接的抖动一致性，我们建立了无界量化器样本路径的一致有界性。这需要表征量化器状态的采样路径上取的上确界的统计特性。这是通过将量化器的状态向量分成两个分量来实现的：一个分量沿着一致子空间，另一个分量沿着与一致子空间正交的子空间。证明使用极大不等式的下鞅和上鞅序列。从这些，我们得出的概率界限上的两个连续性的偏移，从量化器状态矢量的偏移的概率界限如下。本文展示了如何使用这些概率界来设计量化器参数，并探讨量化器级别的数量，量化步骤的大小，所需的饱和概率，以及所需的准确度$ε$远离共识之间的权衡。最后，本文说明了量化器的设计与数值研究。
英文摘要：
The paper studies the problem of distributed average consensus in sensor networks with quantized data and random link failures. To achieve consensus, dither (small noise) is added to the sensor states before quantization. When the quantizer range is unbounded (countable number of quantizer levels), stochastic approximation shows that consensus is asymptotically achieved with probability one and in mean square to a finite random variable. We show that the meansquared error (m.s.e.) can be made arbitrarily small by tuning the link weight sequence, at a cost of the convergence rate of the algorithm. To study dithered consensus with random links when the range of the quantizer is bounded, we establish uniform boundedness of the sample paths of the unbounded quantizer. This requires characterization of the statistical properties of the supremum taken over the sample paths of the state of the quantizer. This is accomplished by splitting the state vector of the quantizer in two components: one along the consensus subspace and the other along the subspace orthogonal to the consensus subspace. The proofs use maximal inequalities for submartingale and supermartingale sequences. From these, we derive probability bounds on the excursions of the two subsequences, from which probability bounds on the excursions of the quantizer state vector follow. The paper shows how to use these probability bounds to design the quantizer parameters and to explore tradeoffs among the number of quantizer levels, the size of the quantization steps, the desired probability of saturation, and the desired level of accuracy $ε$ away from consensus. Finally, the paper illustrates the quantizer design with a numerical study.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
