  The estimation of spatiotemporal data from limited sensor measurements is a
required task across many scientific disciplines. The sensor selection problem,
which aims to optimize the placement of sensors, leverages innovations in
greedy algorithms and low-rank subspace projection to provide model-free,
data-driven estimates. Alternatively, Kalman filter estimation balances
model-based information and sparsely observed measurements to collectively make
an estimation, with many related optimization algorithms developed for
selecting optimal sensors. The majority of methods have been developed for
stationary sensors, with relatively limited work estimating spatiotemporal data
using mobile sensors that leverage both Kalman filtering and low-rank features.
We show that mobile sensing along dynamic trajectories can achieve the
equivalent performance of a larger number of stationary sensors, with
performance gains related to three distinct timescales: (i) the timescale of
the spatio-temporal dynamics, (ii) the velocity of the sensors, and (iii) the
rate of sampling. Taken together, these timescales strongly influence how
well-conditioned the estimation task is. Mobile sensing is particularly
effective for spatio-temporal data that contain spatially localized structures,
whose features are captured along dynamic trajectories. We draw connections
between the Kalman filter performance and the observability of the state space
model, and propose a greedy path planning algorithm based on minimizing the
condition number of the observability matrix. Through a series of examples of
increasing complexity, we show that mobile sensing improves Kalman filter
performance in terms of better limiting estimation and faster convergence.
