Model-Based Sparse Information Recovery by a Collaborative Sensor Management

This paper considers the real-time recovery of a fast time series (e.g., updated every T seconds) by using sparsely sampled measurements from two sensors whose sampling intervals are much larger than T (e.g., MT and NT, where M and N are integers). 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 the sensor speeds MT and NT, and by exploiting a model-based fusion of the sparsely collected data. We provide the collaborative sensing design, parametric analysis and optimization of the algorithm. Application to a closed-loop disturbance rejection problem reveals the feasibility to annihilate 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 the Nyquist frequencies of the sensors.