  We are concerned with a novel sensor-based gesture input/instruction
technology which enables human beings to interact with computers conveniently.
The human being wears an emitter on the finger or holds a digital pen that
generates a time harmonic point charge. The inputs/instructions are performed
through moving the finger or the digital pen. The computer recognizes the
instruction by determining the motion trajectory of the dynamic point charge
from the collected electromagnetic field measurement data. The identification
process is mathematically modelled as a dynamic inverse source problem for
time-dependent Maxwell's equations. From a practical point of view, the point
source should be assumed to move in an unknown inhomogeneous background medium,
which models the human body and the surroundings. Moreover, a salient feature
is that the electromagnetic radiated data are only collected in a limited
aperture. For the inverse problem, we develop, from the respectively
deterministic and stochastic viewpoints, a dynamic direct sampling method and a
modified particle filter method. Both approaches can effectively recover the
motion trajectory. Rigorous theoretical justifications are presented for the
mathematical modelling and the proposed recovery methods. Extensive numerical
experiments are conducted to illustrate the promising features of the two
proposed recognition approaches.
