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The association or "fusion" of multiple-sensor reports allows the generation
of a highly accurate description of the environment by enabling efficient
compression and processing of otherwise unwieldy quantities of data. Assuming
that the observations from each sensor are aligned in feature space and in
time, this association procedure may be executed on the basis of how well each
sensor's vectors of observations match previously fused tracks. Unfortunately,
distance-based algorithms alone do not suffice in those situations where
match-assignments are not of an obvious nature (e.g., high target density or
high false alarm rate scenarios).
Our proposed approach is based on recognizing that, together, the sensors'
observations and the fused tracks span a vector subspace whose dimensionality
and singularity characteristics can be used to determine the total number of
targets appearing across sensors. A properly constrained transformation can
then be found which aligns the subspaces spanned individually by the observations
and by the fused tracks, yielding the relationship existing between both sets of
vectors ("Procrustes Problem"). The global nature of this approach thus enables
fusing closely-spaced targets by treating them--in a manner analogous to PDA/JPDA
algorithms - as clusters across sensors.
Since our particular version of the Procrustes Problem consists basically of a
minimization in the Total Least Squares sense, the resulting transformations
associate both observations-to-tracks and tracks-to--observations. This means
that the number of tracks being updated will increase or decrease depending on
the number of targets present, automatically initiating or deleting "fused"
tracks as required, without the need of ancillary procedures. In addition, it
is implicitly assumed that both the tracker filters' target trajectory models
and the sensors' observations are "noisy", yielding an algorithm robust even
against maneuvering targets. Finally, owing to the fact that Procrustes
Association yields the optimal linear associator, the combined sensor and fused
track information minimizes tracking Kalman Filter residuals, hence providing
very accurate track updates.
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