  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.
