Multi-fidelity sensor selection: Greedy algorithms to place cheap and expensive sensors with cost constraints

We develop greedy algorithms to approximate the optimal solution to the multi-fidelity sensor selection problem, which is a cost constrained optimization problem prescribing the placement and number of cheap (low signal-to-noise) and expensive (high signal-to-noise) sensors in an environment or state space. Specifically, we evaluate the composition of cheap and expensive sensors, along with their placement, required to achieve accurate reconstruction of a high-dimensional state. We use the column-pivoted QR decomposition to obtain preliminary sensor positions. How many of each type of sensor to use is highly dependent upon the sensor noise levels, sensor costs, overall cost budget, and the singular value spectrum of the data measured. Such nuances allow us to provide sensor selection recommendations based on computational results for asymptotic regions of parameter space. We also present a systematic exploration of the effects of the number of modes and sensors on reconstruction error when using one type of sensor. Our extensive exploration of multi-fidelity sensor composition as a function of data characteristics is the first of its kind to provide guidelines towards optimal multi-fidelity sensor selection.