  We propose a strategy for optimizing a sensor trajectory in order to estimate
the time dependence of a localized scalar source in turbulent channel flow. The
approach leverages the view of the adjoint scalar field as the sensitivity of
measurement to a possible source. A cost functional is constructed so that the
optimal sensor trajectory maintains a high sensitivity and low temporal
variation in the measured signal, for a given source location. This naturally
leads to the adjoint-of-adjoint equation based on which the sensor trajectory
is iteratively optimized. It is shown that the estimation performance based on
the measurement obtained by a sensor moving along the optimal trajectory is
drastically improved from that achieved with a stationary sensor. It is also
shown that the ratio of the fluctuation and the mean of the sensitivity for a
given sensor trajectory can be used as a diagnostic tool to evaluate the
resultant performance. Based on this finding, we propose a new cost functional
which only includes the ratio without any adjustable parameters, and
demonstrate its effectiveness in predicting the time dependence of scalar
release from the source.
