Estimating missing data for sparsely sensed time series with exogenous variables using bidirectional-feedback echo state networks

Missing data estimation (MDE) for time series is a crucial issue concerned with various applications based on the Internet of Things (e.g. sparse mobile crowdsensing). Although many approaches have been proposed to address this issue, they are either insufficiently considered or computationally expensive for data correlations. Motivated by this, an echo state network (ESN) with bidirectional-feedback connections is first proposed to skillfully encode temporal, cross-domain, and lagging correlations into the high-dimensional state of the reservoir. Meanwhile, the output weight (the only unknown parameter of the network) can be trained quickly by reservoir computing to reduce computation overhead. On this basis, an improved version with multiple reservoirs is designed to further integrate data correlations from information flows in different directions. Finally, a general process for MDE based on ESN architecture is developed for popularization and application. Experimental results of various missing rates under different missing mechanisms show that the proposed models perform better than the current methods in estimation accuracy.