  Previous studies have demonstrated that gravitational radiation reliably
encodes information about the natural emission direction of the source (e.g.,
the orbital plane). In this paper, we demonstrate that these orientations can
be efficiently estimated by the principal axes of <L_a L_b>, an average of the
action of rotation group generators on the Weyl tensor at asymptotic infinity.
Evaluating this average at each time provides the instantaneous emission
direction. Further averaging across the entire signal yields an average
orientation, closely connected to the angular components of the Fisher matrix.
The latter direction is well-suited to data analysis and parameter estimation
when the instantaneous emission direction evolves significantly. Finally, in
the time domain, the average <L_a L_b> provides fast, invariant diagnostics of
waveform quality.
