  A LiDAR Statistical Barnes Objective Analysis (LiSBOA) for optimal design of
LiDAR scans and retrieval of the velocity statistical moments is proposed. The
LiSBOA represents an adaptation of the classical Barnes scheme for the
statistical analysis of unstructured experimental data in N-dimensional spaces
and it is a suitable technique for the evaluation over a structured Cartesian
grid of the statistics of scalar fields sampled through scanning LiDARs. The
LiSBOA is validated and characterized via a Monte Carlo approach applied to a
synthetic velocity field. This revisited theoretical framework for the Barnes
objective analysis enables the formulation of guidelines for optimal design of
LiDAR experiments and efficient application of the LiSBOA for the
post-processing of LiDAR measurements. The optimal design of LiDAR scans is
formulated as a two cost-function optimization problem including the
minimization of the percentage of the measurement volume not sampled with
adequate spatial resolution and the minimization of the error on the mean of
the velocity field. The optimal design of the LiDAR scans also guides the
selection of the smoothing parameter and the total number of iterations to use
for the Barnes scheme.
