A Collaborative Sensing and Model-Based Real-Time Recovery of Fast Data Flows From Sparse Measurements

This article considers the real-time recovery of a fast time series by using sparsely sampled measurements from sensors whose sampling speeds are prohibitively slow originally. Specifically, when the fast signal is an autoregressive process, we propose an online information recovery algorithm that reconstructs the dense underlying temporal dynamics fully by systematically modulating two slow sensors, and by exploiting a model-based fusion of the sparsely collected data. We provide the design of collaborative sensing and model-based information recovery algorithm, impacts of parameter choosing and model singularity, and methods to reduce computational complexity and increase prediction robustness. The proposed method is experimentally verified in an optical beam steering platform for additive manufacturing. Application to a closed-loop disturbance rejection problem reveals the feasibility to eliminate fast disturbance signals with the slow and not fully aligned sensor pair in real time, and in particular, the rejection of narrow-band disturbances whose frequencies are much higher than that of the Nyquist frequencies of the sensors.