Consensus on state and time: Decentralized regression with asynchronous sampling

An implicit assumption made in several studies on sensor systems is that the time and frequency at which sensor measurements are taken is consistent across all the distributed sensing sites. In reality, the times of measurement often lack consistency and integrity, and this is an intrinsic vulnerability of wide area sensor system. Data logs coming from different analog to digital converters (ADCs) are not in phase and may differ also in the sampling rate, in some cases because heterogeneity in the sensors and in others because the data are simply not refreshed in the data historians with the same frequency. Lack of good synchronization in sensing may be the result of a malfunction or also due to intentional delay attacks. This premise motivates our work, where we advance the area of decentralized signal processing and consider explicitly timing errors and nonhomogenous sampling rates in least square estimation problems with distributed sensing. For linear observations models, we provide a necessary and sufficient condition for identifiability of the time offsets. We propose an algorithm for the joint regression on the state vector and time offsets. The algorithm also exploits the asynchrony and redundancy in the spatial sampling to attain sub-Nyquist sampling resolution of the slow sensor feeds. Importantly, this also leads to the development of a novel decentralized algorithm. The efficacies of the proposed decentralized algorithm are shown by both convergence analysis and numerical simulations.